FTL Part II: Just Plain Cheating
In our last exciting episode we considered the possibility that the dictum Causality, Relativity, FTL travel: chose any two may not be strictly true. Consult the comment thread for discussion, particularly some thought experiments offered by commenter Luke.
I cannot vouch for the validity of these arguments, only that they are either a) valid, or b) extremely high quality bullshit, and I choose a as my working hypothesis.
Einsteinian street-legal FTL is, as the discussion takes note, subject to certain constraints. Its use in a story is, in turn, subject to some meta-level contraints. So far as I can tell, it is consistent only with the 'jump' style of FTL, in which you pre-select your destination before hitting the big red button. FTL in which you navigate freely seems ruled out. And you are taking your chances with drawing (or narratively describing) a 'subway map' of FTL jump routes, unless you can ensure that your map meets the requirements for a directed acyclic graph.
You have been warned.
Having said that, the whole subject is pretty much moot unless you are a physicist, or can credibly impersonate one. Nearly all your readers will ignore your validation, and assume either that you are jiving them as part of the story, or else that you are simply a crank. (Which will not help them buy into the story.) Within the SF world, FTL is more or less universally understood to be a pure dodge, dumping physics for the sake of story. And it is just as universally accepted on that basis.
A point made in comments to last post was that there are also STL workarounds, even for such tropes as interstellar empires. Said commenter Horselover Fat: "For FTL, you need to dump Einstein. For STL empires, you need to dump your cultural assumptions. And you choose to dump Einstein?"
Very good question. My answer would be that cultural assumptions tie in closely to characterization, right at the heart of fiction. Change them greatly and your story pretty much has to be about those changes. Dumping Einstein, not so much. (Note: I am not saying that you need to ignore the laws of physics, only that - in space opera - you can.)
You do still have to fake it convincingly. As I suggested last post, the less you say about your specific handwaves the better off you will probably be. You also have to adhere to some internal consistency. If FTL jumps require generating Stupendous Energy on demand, you need to deal with the implications of a technology that can do this. Similarly, if you need to travel 100 AU in normal space to reach jump points, you need a normal-space drive capable of doing so in convenient time. (And if you stick with relativistic STL, you need a beaucoup powerful drive.)
All of which produces, or can produce, its own awkward complications. If your interstellar tramp freighter has a drive engine capable of slagging a continent, the movement of such ships anywhere near an inhabited planet will be very strictly regulated. This may spoil some otherwise charming tropes. (Think Firefly.)
There are a host of other possible complications to bear in mind. If FTL jumps can be made by small spacecraft just above planetary atmospheres, you've opened the door to bomber-mission nuclear strikes, or even interstellar ICBM strikes. But if it takes too long to reach jump points in normal space you could end up at least partly defeating the purpose of FTL.
Another criticism I have seen is mildly meta: settings in which there is FTL for convenient star travel, while the rest of the technology pretty much resembles the Plausible Midfuture [TM]. The problem here is that you have supposedly had a fundamental revolution in physics, yet with no technological consequence other than FTL itself. How remarkably convenient ....
A reasonable counter-argument might be that relativity itself gave us the atomic bomb and nuclear subs to deliver it, but no atomic motorcycles or force-field steak knives. Nuclear power plants put out the same kind of juice as coal-fired plants, and for most story purposes are pretty much invisible. I imagine that modern physics is implicated in a host of everyday gadgets, but not in dramatic ways.
So, the presumed future physics that gives us FTL might also give us antigravity drive and other Cool Stuff, or - for different desired values of coolness - might have few other obvious effects besides fast interstellar travel.
For that matter, a Pretty Strong argument could be made that all of this is tech geek navel gazing, irrelevant to the practical problems of SF world building. Heinlein's Starman Jones remains a favorite of mine in spite of an FTL that requires you to violate relativity in normal space, before you even get to make the FTL jump.
And to take a more modern example, I thoroughly enjoyed Elizabeth Moon's Heris Serrano books, though the stuff that reads like hard SF is really almost pure bluff. The fact of the matter is that if onboard instruments indicate the approach of an enemy ship, and the characters respond to this situation in a persuasive way, we as readers do not insist that they stop to calibrate their instruments for us.
On the other hand, this blog is more or less dedicated to the art of faking details convincingly.
Discuss. (As if you needed an invitation.)
The subway-esque hyperspace image comes, via Google Images, from a screensaver website.
329 comments:
«Oldest ‹Older 201 – 329 of 329I've read that gills can't provide enought oxygen. But if it was them and lungs, then I wouldn't mind it either. And no, I haven't been scuba diving.
Luke:
When I say "...the acceleration phase deforms your coordinates sufficiently to have all points originally in your local past remain there in the new frame...", that only applies within my light cone, doesn't it?
Raymond:
When you change velocities the Lorentz transform describes your new coordinate system as measured from that velocity. Acceleration may take time (so that you do your things at a later time) but the acceleration doesn't deform coordinates when measured from the frame with the final velocity.
Luke:
Yeah, at first I was thinking that if it worked like Milo said, there would be events you could observe twice (once before acceleration, then once after), then I realized that for points outside the light cone, you wouldn't have observed them yet anyways, and their timelike coordinate can change without problem. So nevermind, I'm an idiot.
I've been limiting my effects to subluminal but relativistic time dilations. i.e. not actual faster than light but close to light speed. The formulae would imply that you do indeed start traveling back in time if you exceed light speed, but there are all kinds of reasons why that can't happen.
So are you saying that relativistic speeds are time travel or just the hypothetical exceeding light speed?
Most of my models for FTL travel don't actually involve moving faster than light, but rather manipulate space in some way to make things closer. In those cases, relativistic effects don't come into play because nobody is moving at significant velocities. My primary issue with FTL speed is that as you accelerate to light speed, time dilation essentially freezes you at light speed. If you exceed it, you'll start going back in time to the point where you weren't going FTL, at which point you accelerate again and then reverse time, etc.
There is no real possibility of time travel. You certainly can't go faster than light in normal space. That would upend all of GR.
If you move close to the speed of light, you simply change your rate of progress through time. Or, to use the phrase of a friend of mine, velocity can be considered as a normalized fourth-dimensional vector. (You're always moving at c. If you happen to be moving at v=0 through space, you're moving at c through time. If you go faster in space, you go slower in time.)
Citizen Joe:
So are you saying that relativistic speeds are time travel or just the hypothetical exceeding light speed?
Sub-luminal relativistic speeds do not allow time travel so long as you can never get from one point to another faster than light could by any means (including manipulating space to make things closer). Methods which do allow you to get from place to place faster than light could by other means (such as manipulating space to make things closer) have generally been referred to here as "FTL" even though at no point is a physical object traveling faster than light locally (since it can get from one place to another faster than light could when that light is traveling across flat space). If you allow FTL methods using this general definitions, you need to worry about possible time travel. For example, Milo's recent post about going back in time to prevent a war still has the same results if you are manipulating space to make things closer. Even relatively small changes in velocity can allow time travel with rapid FTL. To avoid this, you need to invoke the various methods that have been discussed previously - special frames or chronology protection. Either that or deal with the can of worms opened by time travel.
Raymond:
"There's something intuitively unphysical in that solution,"
Well duh. Everything we've been discussing here is unintuitive.
"I suspect that your assumption of instant acceleration may be the problem, but I'm honestly not sure."
I figured that since we weren't assuming any limits on the amount of energy or reaction mass a ship can carry, there's no reason it shouldn't be able to accelerate arbitrarily quickly. (The tendency of crew to get smushed by high accelerations is remedied using an array of oscillating hands.)
"My initial guess would be that the acceleration phase deforms your coordinates sufficiently to have all points originally in your local past remain there in the new frame - but I could be wrong on that."
But remember, it wasn't in your local past. It was in your subjective past, as recorded by the captain's log, but due to FTL, it wasn't in your past light cone. At (1000 ly, 0 ly, 0 ly, 10 y), your past light cone only covers (990 ly, 0 ly, 0 ly, 0 y) to (1010 ly, 0 ly, 0 ly, 0 y), not (0 ly, 0 ly, 0 ly, 0 y).
Sabersonic:
"Though personally, I figured that if "hyperspace" is real, then it would be more like an alturnate but parallel space-time like our own normal space-time and numerous others like it."
I'm dubious about the idea of a single, three-dimensional space that is parallel to ours. Parallel according to what?
Without a fourth dimension to move in, you could only be in either one space or the other. That kind of "jump" feels unphysical, somehow.
Raymond:
"(I want my gills and tail, dammit.)"
So are we talking about a mermaid tail or what?
Byron:
"Water adaptation is a very poor one for spaceflight."
Aquatic organisms already experience something similar to zero-gravity conditions, due to buoyancy. (Hence why they don't have to worry about supporting their own weight and can grow much larger, even without an internal skeleton.) Thus any aquatic adaptation would also help us with staying fit in zero gravity, by default.
However, actually bringing water with you on a spaceship in amounts large enough to fill your habitation space is a bad idea, due to its high mass. Even though it would make movement easier. What would be a good idea, however, is stubby "zero-gravity wings" that (due to the lack of gravity) don't need to worry about aerodynamics or being powerful enough to keep you aflight, but merely need to be enough to push against air when there are no other forces acting on you. These might look somewhat like fins.
Raymond:
"In terms of traversability, yes. In terms of timelike separation and expansion vectors, it's directed."
The important thing, however, is that you need an undirected acyclic graph, which is more strict than a directed acyclic graph. If you have wormholes A->B, B->C, and C->A, then this is a directed cycle. If you have wormholes A->B, B->C, and A->C, then this is an undirected cycle, but not a directed cycle, and so is permissible in a directed acyclic graph. However the latter can still break causality, unless you're very careful with your time displacement.
Oh, and speaking of time travel: it's the latest in a series of weird things that supposedly respectable scientists have been predicting might occur at the Large Hadron Collider.
Byron:
"(You're always moving at c. If you happen to be moving at v=0 through space, you're moving at c through time. If you go faster in space, you go slower in time.)"
This doesn't seem right. If this were the case, then going faster would cause less universal time to pass per unit of subjective time, when in fact the opposite is the case.
What is this universal time you speak of? What I meant was that the time vector is your subjective time.
Milo:
"But remember, it wasn't in your local past. It was in your subjective
past, as recorded by the captain's log, but due to FTL, it wasn't in
your past light cone."
That was my worldline intersecting the event (Raymond, *headdesk*). Anyone want to lend me an FTL drive? I promise I'll have it back before I left...
Ok, so if you have a method of "reaching out" (through hyperspace or extra dimensions) and swapping two areas of spacetime (and the mass imbedded in them) then as long as you balance the mass/velocity/energy on both sides of the warp/jump then you should be ok, and my scenario of jumpgates and jumps-from-star-to-star should work; or at least be plausible for story purposes.
Ferrell
Byron: "I've read that gills can't provide enought oxygen. But if it was them and lungs, then I wouldn't mind it either. And no, I haven't been scuba diving."
1. The main thing is the low oxygen content vs surface area. Well, unless you want to go for really radical genetic engineering & improve everything from mitochondrial respiration up... but you may want a Culture Mind for that...
2. Go somewhere tropical & try SCUBA diving. I've been to the Caribbean, Mauritius & the Red Sea - all absolutely beautiful places underwater.
Milo:
"So are we talking about a mermaid tail or what?"
Prehensile. Going for the Standard Amphibian Package.
"The important thing, however, is that you need an undirected acyclic graph, which is more strict than a directed acyclic graph...."
True. I'd forgotten that particular distinction. Point taken.
Ferrell:
Still need a special frame - which I think you meant to include, but you didn't mention.
Byron: I get it now. However, that is not a model of spacetime. Your coordinates are combining position coordinates "outside" the ship with time coordinates "inside" the ship. You cannot use this model to, for example, calculate "There will be a party over at Vega two weeks from now, what do I need to do to be there?".
True, but it is an interesting model of how relativity appears to work. I need to thank that friend.
Milo:
I think what Byron is getting at is that an object's four velocity - the change in its coordinates with respect to its proper time - transforms as a four vector with an invariant magnitude of c. In coordinates, the four velocity is gamma(c,v) = c*gamma(1,beta) where gamma has the usual meaning of the time dilation factor, v is the velocity, beta = v/c, and c is the speed of light in vacuum.
Yes, that's exactly what I meant.
Can you run that by me again?
Alright, let me see if I got this straight.
I start at point A with a wormhole with mouth a and b. I accelerate point b at subluminal relativistic speeds towards destination B, 1000 ly away. I won't do the math but let's say it gets there 1010 years later and time dilation means that mouth b is only 10 years older while mouth a is 1010 years older.
Now I step through the wormhole. When do I come out at location B?
The sidebars are getting more interesting than the main event.
If you were adapted to an aquatic existence, the extra mass of water would substitute for the mass of shielding you would need for a normal, air filled hab. Water would also address thermal management issues as well, for both the machinery and the biosphere you are carrying around for life support.
OTOH, it will suck to be you when you arrive at the new star system, since most of the observed planets to date are orbiting very close to the primary and are probably hot enough to melt metal. Hollowing out asteroids or filling plastic bags with air is the cheap and simple means for unadapted humans to create colony spaces; giant aquariums are still doable but somewhat harder and more resource intensive. (Luckily, if our solar system is an example there will be lots of water, just contained in comets, asteroids and ice moons in the far reaches of the system.
Citizen Joe:
Assuming year 0 is the launch date of the wormhole, then stepping through to B would put you at 1010 After Launch (AL). Stepping back to A would put you at 10 AL. This is all, of course, relative to the wormhole's origin.
Citizen Joe:
I start at point A with a wormhole with mouth a and b. I accelerate point b at subluminal relativistic speeds towards destination B, 1000 ly away. I won't do the math but let's say it gets there 1010 years later and time dilation means that mouth b is only 10 years older while mouth a is 1010 years older.
Actually, let's say that time dilation means mouth B is 141.77 years older (that's the only way you can get mouth B arriving at a time coordinate of 1010 years).
Now I step through the wormhole. When do I come out at location B?
Here is the sequence of events, using flat, non-wormhole space-time coordinates (a.k.a. Minkowski space-time):
event 0: x=0, t=0 - wormhole launched
event 1: x=0, t=141.77 y - people at home can step through wormhole mouth A to arrive through wormhole mouth B at event 2
event 2: x=1000 ly, t=1010 y - mouth B arrives, people stepping through mouth A at event 1 arrive.
So if you are measuring by Minkowski space-time coordinates, you step out at a time coordinate of 1010 years after launch.
Citizen Joe:
"I start at point A with a wormhole with mouth a and b. I accelerate point b at subluminal relativistic speeds towards destination B, 1000 ly away. I won't do the math but let's say it gets there 1010 years later and time dilation means that mouth b is only 10 years older while mouth a is 1010 years older.
Now I step through the wormhole. When do I come out at location B?"
You need to wait with stepping into mouth a until 10 years after the wormhole launch. Step into it earlier, and you get dumped somewhere in deep space.
After waiting for 10 years, you can step into a at A, and you will then exit b at B immediately upon its arrival, 1010 years after the launch from A's frame of reference. You can then step back into b and exit at a, and now you're back to A 10 years after the launch.
Incidentally, this means you have a temporal displacement of 1000 years over 1000 lightyears, which isn't right - the former number should be smaller than the latter. But I used your numbers. (According to the proper numbers, if mouth b arrives after 1010 years, mouth a can be entered after 141.77 years instead of 10 years. If you want a wormhole that can be entered after 10 years, then you need the delivery to take only 1000.05 years. The formula is: a^2 + (d/c)^2 = b^2, where a is the opening time at A, b is the opening time at B, d is the distance, and c is the speed of light, so in this case d/c = 1000 years.)
Thucydides:
"Hollowing out asteroids or filling plastic bags with air is the cheap and simple means for unadapted humans to create colony spaces; giant aquariums are still doable but somewhat harder and more resource intensive."
Is it now? Water is everywhere in comets and asteroids, and you just need to melt it. Oxygen can be split from water or silica (rock). Nitrogen is comparatively harder to come by in large quantities, and we need it for a healthy atmosphere that doesn't cause everything to burst into flame.
Milo: I'm dubious about the idea of a single, three-dimensional space that is parallel to ours. Parallel according to what?
Without a fourth dimension to move in, you could only be in either one space or the other. That kind of "jump" feels unphysical, somehow.
For first point: Considering that the entire human species lives in the "Normal Space" (or a vast majority of said species in certain settings that might feature settlement and colonization of "hyperspace" in the assumption that it IS hospitable enough for such a venture) then it would be parrellel to us and the space-time we occupy.
For second point: Which is why I call it a space-time rather then just space. General Relativity and Special Relativity states that the universe as we know it is a weave of three-dimensional space with the one dimension that is time. What would realistically or even plausibly be the reason that another space-time plane would lack the dimension of time?
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Raymond said: "Still need a special frame - which I think you meant to include, but you didn't mention."
Yes, I did forget it; tired and in a hurry and you leave out importaint stuff! So for a special or privelaged frame, how about using as your 'master clock' echos of the big bang reverberating through "jump space" that are the same anywhere in the universe and aren't dependent on 'local' time distortions caused by differences in local velocities? Does that sound plausible?
Ferrell
Delurking!
This blog seems as good a place as any to raise a couple of cosmological questions in hope of getting a layman-readable response:
a) When a photon is redshifted due to the expansion of the universe, what happens to the energy it loses?
b) Does the observed number of photons received from distant objects fall off faster than 1/r^2 (since that same universal expansion spreads the emitted photons over a wider area)?
c) Presuming b) is true, does gravity follow the same pattern?
Andrew
Welcome to a new commenter! (I hope someone can answer those questions, because God knows I can't.)
I'm beginning to wonder if the spam filter is actually protecting causality ...
Andrew:
When a photon is redshifted due to the expansion of the universe, what happens to the energy it loses?
It goes away. In general relativity, energy is only conserved when the curvature is weak and gravity is approximately Newtonian (or if you can surround a highly curved region of spacetime with a closed surface far enough away that everywhere on the surface has weak curvature). Over the length of the observable universe, the curvature is significant and energy is no longer guaranteed to be conserved.
Another way of looking at it is that conservation of energy is a mathematical (not physical) result of time invariance symmetry. If the laws of physics are the same today as they were yesterday and as they will be tomorrow, energy is conserved
http://en.wikipedia.org/wiki/Noether%27s_theorem
If you have an otherwise isolated system subject to a constant potential energy will be conserved within that system but if it is subject to a time varying potential energy within that system is not conserved (if you look at the larger picture, including what is making that potential, you find that energy is being exchanged with the environment - except for certain cases in general relativity). In the case of the universe, it is an isolated system subject to time varying conditions (it's expansion) so mathematically you wouldn't expect energy to be globally conserved in this system.
Does the observed number of photons received from distant objects fall off faster than 1/r^2 (since that same universal expansion spreads the emitted photons over a wider area)?
I'm not really sure - I think in this case you would have trouble defining r since the space in which you are measuring r keeps expanding.
Presuming b) is true, does gravity follow the same pattern?
No. Gravity over the scale of the universe is quite different from the Newtonian approximation where point sources can be described as a field falling off as 1/r^2. In these circumstances gravity cannot be described as a field or a force but rather you need to go to the Einsteinian view of gravity as curvature of space-time. Gravity, over the expanse of the universe taken in entirety, and ignoring minor local variations in density, follows the pattern of a dynamic expanding (or for some models at some times, contracting) space-time.
I'm beginning to wonder if the spam filter is actually protecting causality ...
Nah, it's just achieved sentience and is bored!
Thanks Luke. I had no idea that GR trumped conservation of mass/energy - that seems a big thing to trump. Would it be theoretically possible to take advantage of this to generate arbitrary quantities of energy (to build wormholes, perhaps)?
Andrew
Andrew:
Thanks Luke. I had no idea that GR trumped conservation of mass/energy - that seems a big thing to trump. Would it be theoretically possible to take advantage of this to generate arbitrary quantities of energy (to build wormholes, perhaps)?
The problem is that, as mentioned, energy is conserved if space-time is locally mostly flat, or if you can surround non-flat spacetime by a closed surface where the space-time is mostly flat. At the earth and sun and solar system, space-time is mostly flat. Even around extreme objects like black holes, if you go far enough away space-time is mostly flat. Even over the scale of galactic superclusters space-time is mostly flat. This all makes it hard to go far enough away to be able to violate energy conservation.
One way to sort of get around this is to start a new universe. If you imagine our universe as a flat infinitetly stretchable rubber sheet, this would be if you glued a straw to the sheet and started blowing to blow out an expanding bubble like a balloon - the bubble is the new universe. It is connected to our universe by a wormhole - the neck where our flat sheet meets the bubble. This doesn't create any more energy in this universe, but you can go into the other universe and use energy there if you want (you just can't take it back to this universe without paying as much energy into the new universe as you take out).
Luke:
"One way to sort of get around this is to start a new universe."
Ah, should be a piece of cake ;)
"This doesn't create any more energy in this universe, but you can go into the other universe and use energy there if you want"
So could we use this to defeat information entropy? I.e., perform an extremely expensive computation in the other universe, then bring back the results (which are just cheaply storable data) without bringing back the energy used to produce them?
Luke:
How would one determine how much energy is present in the new universe? Whatever you bring in?
Raymond:
How would one determine how much energy is present in the new universe? Whatever you bring in?
From who's point of view? From this universe, there's just the mass-energy of this end of the wormhole connecting the two universes, so yes, whatever you bring in. From within the other universe the total amount of energy cannot be defined, although once you zoom in on small enough regions that they appear mostly flat, energy starts to become a useful descriptor again.
Luke:
I'm just wondering what you'd have to play around with in your new pocket universe...
Raymond:
I'm just wondering what you'd have to play around with in your new pocket universe...
If the symmetries of the vacuum break the same way as ours - galaxies, stars, planets. If you can't get to stars in other universes, build your own universe and send the wormhole mouth in that universe to a likely habitable planet. And when this universe becomes old and threadbare and dangerously high on entropy, filled with dead and dying stars - make a new, fresh and vibrant universe to go live in.
Unless you can't get the vacuum symmetries to break the same way. In which case, who knows. A slew of particles which can't exist in our universe, and whether they can form stars and life or leave you with nothing other than sparse gas or the occasional black hole is difficult to say.
"And when this universe becomes old and threadbare and dangerously high on entropy, filled with dead and dying stars - make a new, fresh and vibrant universe to go live in."
["Let there be light." -Ed.]
Milo:
So could we use this to defeat information entropy? I.e., perform an extremely expensive computation in the other universe, then bring back the results (which are just cheaply storable data) without bringing back the energy used to produce them?
Apologies for the delay - blogger seems to be having difficulties showing posts in a timely manner.
In any event, yes. A new universe starts out with the entropy in the patch of space that you use to create it, and during inflation that entropy gets distributed across an immense volume (quite likely many cosmological horizons). More entropy is created in the process, of course, but the new universe, much like our universe, starts out in a low entropy state and evolves toward a high entropy state.
Ok, I see we have a difference of opinion on the time travel. And the specific numbers I gave were not meant to be accurate but rather to point in the general direction of the time shifting.
As I was figuring, the wormhole takes off at Universal Standard Time (UST) 0y. It arrives at the destination at UST 1010y. The Clock on the Mouth A flight recorder says UST 1010y. The clock on the mouth B flight recorder says (whatever that obscure number was that Luke calculated). The clock at the destination says UST 1010y. Thus, stepping through doesn't do any time travel, but one end of the wormhole is significantly older than the other end. But if I fly in a 30 year old DC10 or a new 777, that doesn't affect my arrival time.
Citizen Joe:
The key thing to understand is that the flight recorders on both ends of the wormhole will read the same elapsed time. When the wormhole gets to its destination, both flight recorders will read 141.77 years. From the point of view of someone at mouth A, they travel to the future when they step through. If your "universal standard time" is from the frame of reference of someone at rest wrt mouth A, then arrival of mouth B at its destination happens when mouth A is at UST 141.77y, and mouth B is at UST 1010y. (Note: there is no "universal time", so your UST has to be with respect to something particular).
Citizen Joe:
"The Clock on the Mouth A flight recorder says UST 1010y."
Why does mouth a even have a flight recorder? It's not going anywhere.
Anyway, when does the clock at mouth a say UST 1010y? Obviously it will say that value at some point. You could ask what value a's clock is showing at the same time that b's clock is showing some value, but that requires some definition of "at the same time as".
What could happen is that:
- At UST 141.77y, you step into the wormhole from A to B. At B, you then send a radio message outside the wormhole to A, then take the wormhole back to A (outrunning the light beam) and wait for the message to arrive. You will detect the message arriving at UST 2010y, 1868.23 years after it was sent (from the wormhole's point of view).
- At UST 141.77y, you send a radio message outside the wormhole to B. You then step into the wormhole to B and wait until it arrives. It will arrive in UST 1141.77y, 131.77 years after it was sent (from the wormhole's point of view).
This has obvious corollaries. Say the wormhole is knocked out. If A immediately sends a replacement wormhole, even one with newer tech that gets there faster, then travel will be cut for at least 131.77 years from B's point of view (but potentially arbitrarily little time from A's point of view). But if B sends the replacement wormhole, then that earliest it can arrive is 1868.23 years after the accident from A's point of view (but potentially arbitrarily little time from B's point of view). This means that it's obviously far better for wormholes to be reopened in the same direction they were originally sent. Which could pose a problem if the civilization that originally set up the wormhole networks has collapsed, and the center of the civilized world is now somewhere else...
Hmm. Now I'm wondering if you could get these numbers to line up. *math math* Nope, except by sending the wormhole infinitely slowly so there's no time dilation. However, there is the neat reminder that the two reopening times will always add up to 2000 years (i.e., the distance between the two points, times two divided by c). Remember, this is assuming that the newer wormhole is higher-tech than the original one.
With sufficiently good tech for both the original and the new wormhole, you could get A's reopening time down to nearly zero, but B's reopening time will always be at least 1000 years, no matter what.
Raymond:
"(Note: there is no "universal time", so your UST has to be with respect to something particular)."
I'm guessing he was talking about coordinated universal time, which is not really all that universal since it's defined in Earth's reference frame (but is still used by space probes launched from Earth).
Also note that we've generally been assuming that the source and destination of the wormhole were both at rest or nearly at rest with each other before the wormhole was launched, meaning that their common frame can be taken as something reasonably close to a universal rest frame, as far as mathematical convenience is concerned. (This is an accurate assumption since most stars in a given galaxy are going to be moving less than 100 km/s relative to each other. That's gamma 1.0000001.)
And remember, there's always comoving time if you want something truly universal. (Comoving time is, to within the degee of accuracy we care about here, practically identical to the above shared rest frame of convenience.)
But clock A doesn't travel at relativistic speeds. Why would it have a time dilation? And then, once established and neither end is moving at relativistic speeds, why would the traveler have any time distortion?
UST, for the purpose of this thought exercise is some agreed upon baseline date that both locations know perhaps even magically. If you absolutely need some non-magical rational, then a star exactly in the middle between point A and B goes supernova exactly 500 years prior to launch, thus being recorded at the same time by both locations 500 years later or UST 0y.
Citizen Joe:
"But clock A doesn't travel at relativistic speeds. Why would it have a time dilation?"
It doesn't.
Again, before asking what a clock will show, you have to ask when that you're checking that clock. To test two clocks at the "same time", you need to define what you consider the same time. The most useful definition of "same time", as far as a wormhole-using civilization is concerned, is that both ends of any given wormhole are per definition synchronized, even though this differs from "same time" as viewed in either planet's normal frame of reference (and cannot be uniquely defined for the space between the solar systems - which you aren't planning on travelling through anyway).
What will happen is that you launch a wormhole. After it arrives and opens, you can then step through. If you step into the wormhole at 141.77 years according to that end's flight clock, then you will arrive at the other end at 141.77 years according to that end's flight clock (although according to the solar systems' rest frames, you will appear to have travelled to UST 1010y). Note that the source wormhole doesn't have any time dilation. Its clock reads 141.77 exactly 141.77 years after launch, according to the rest frame.
This means that you can step into a wormhole mouth while, from your own frame of reference, the other end hasn't arrived yet. You will then be transported into the "future" (according to your frame of reference, but not actually in your future light cone) where the wormhole has already arrived. Step back, and you will be transported back to the "past" (but, again, not in your past light cone).
By the way, note that if you couldn't step into the wormhole before the other end arrives, then it would be impossible to make use of the wormhole less than 1000 years after launch, regardless of how fast you hurl it. This makes it of limited usefulness for faster-than-light travel. (The tramlines are still FTL once built, but you don't get FTL expansion.)
Citizen Joe:
But clock A doesn't travel at relativistic speeds. Why would it have a time dilation?
Clock A does travel at relativistic speeds. From the point of view of someone observing along a path that goes through the wormhole clock A is moving just as fast as clock B. Similarly, clock B is just as stationary as clock A, when viewed through the wormhole. Thus, both clock A and clock B suffer the same time dilation, and no time dilation at all.
For example, instead of clock A and clock B, just have a clock, with gears and a battery and a quartz oscillator (or a cesium atomic oscillator if you prefer, and maybe a nuclear reactor to recharge the battery every so often). It turns a shaft that goes two ways. Each end of the shaft turns the hands on the face of clock-display. The shaft goes through the wormhole (or perhaps the clock itself is located in the wormhole and the shafts come out both ways, it makes no difference) and so a clock-display is on both sides of the wormhole. Since they are both driven by the same clock (and the space-time through a Visser wormhole is flat, so it can have no funny effects such as time dilation within that coordinate patch), they must remain in sync. However, the dynamics of time dilation apply nonetheless - Lorentz transformations don't care how your time ticks are driven. Again, you end up with clocks that remain in sync through the wormhole but where one is time dilated when viewed around the wormhole.
It feels like you guys are trying to play three card Monty.
Baseline Relativistic Experiment (no wormholes).
Assumption 1: Two distant points (1000 ly) have an event that is an agreed upon starting date.
Assumption 2: Both of the distant points are experiencing time at the same rate, i.e. not experiencing time dilation relative to one another.
Assumption 3: An object leaves the first point, traveling at relativistic speeds on a journey that should take 1010 years. (about 0.99c).
Question 1: What year is it at the destination when the object arrives?
Question 2: What year is it at the source when the object arrives at the destination?
Question 3: What does the flight recorder say the flight time was?
Milo:
"The tramlines are still FTL once built, but you don't get FTL expansion."
You don't get FTL expansion over the long run, even with FTL, because it takes time to consolidate new gains. It's like the railroads -- you can only build one, on the average, at about a mile a day (counting surveying, grading and ballasting, not just track laying). But once built you can travel that mile in a minute or two. That has been found to be economically useful. I don't see workhole networks (if possible) as being any different.
Citizen Joe:
It feels like you guys are trying to play three card Monty.
I am not familiar with this game.
Baseline Relativistic Experiment (no wormholes).
Assumption 1: Two distant points (1000 ly) have an event that is an agreed upon starting date.
For definiteness, we will label the events at these two points at the starting time as (0,0) and (0,1000 ly) using (t,x) to refer to a coordinate time t and a coordinate position x.
Assumption 2: Both of the distant points are experiencing time at the same rate, i.e. not experiencing time dilation relative to one another.
Thus their relative velocity is zero.
Assumption 3: An object leaves the first point, traveling at relativistic speeds on a journey that should take 1010 years. (about 0.99c).
This makes the analysis rather straightforward. Since space-time is globally Minkowski (that is, flat and simply connected) we can use basic special relativity.
Now, I am once again going to have to make the distinction between coordinate time, which can be useful as part of a complete coordinate (t,x) but does not represent anything real, and proper time (experienced elapsed time) which represents something real and physical.
Question 1: What year is it at the destination when the object arrives?
The arrival occurs at an event with coordinates in the original frame of (1010 y, 1000 ly).
Question 2: What year is it at the source when the object arrives at the destination?
Relativity forbids simultaneity, so you cannot meaningfully say that that the arrival event occurred at a specific time at the source. The source will calculate (after making observations) that the arrival event occurs at a coordinate time of 1010 y in their reference frame but they cannot conclude from that that arrival occurred a time of 1010 y at the source.
Question 3: What does the flight recorder say the flight time was?
This is the proper time of the launched object. This is unambiguously 141.77 years, with no weirdness about reference frame dependence.
Tony:
"You don't get FTL expansion over the long run, even with FTL, because it takes time to consolidate new gains."
Over the long run, perhaps not. However, FTL (or apparent-FTL, in the case of relativistic wormholes) expansion time for any given segment will have an effect on the frequency of new links. If a new link is a thirty-year project, that implies an additional level of long-term planning, and gains will be consolidated locally to a greater extent before a new link is created. If the same new link is only three years (apparent time), it becomes a more manageable project and more likely to occur before the current system has been exploited to the fullest.
Raymond:
"If a new link is a thirty-year project, that implies an additional level of long-term planning, and gains will be consolidated locally to a greater extent before a new link is created. If the same new link is only three years (apparent time), it becomes a more manageable project and more likely to occur before the current system has been exploited to the fullest."
The same applies to any FTL technology. If FTL travel is relatively expensive, it may in fact be decades before a frontier system gets regular service. If it's relatively inexpensive, there may be regular service within a few years.
In any case, as long as sublight travel is not generation ship slow, there's no reason to believe that actual expansion will travel much faster FTL as opposed to STL. It still takes several decades for a frontier to become deveolped enough to support further expansion. The differences between FTL and STL travel times will be eaten up by that dynamic.
Tony:
In any case, as long as sublight travel is not generation ship slow, there's no reason to believe that actual expansion will travel much faster FTL as opposed to STL. It still takes several decades for a frontier to become deveolped enough to support further expansion.
For the specific case of wormholes, there may be regions in the parameter space where you could have the speed of exploration far outpace the speed of colonization. If Dr. Bob the astrophysicist can send a wormhole to the Andromeda galaxy in less than a year for the cost of a reasonable government grant, he might decide to do so just to look back and see the Milky Way galaxy from the outside (allowing better mapping of our galaxy's structure and etcetera).
Three Card Monty is basically the Shell Game but played with cards. The dealer mixes around three cards in 'plain view' of the mark, using some fancy handwork. The mark then places a bet where he thinks the queen is (or the pea in the Shell Game). The first couple times, the dealer plays slow to make it easy for the mark so he wins. Then when the Mark thinks he is unstoppable, the dealer pulls a switch and the mark loses his money. One variant cheat is done by secretly replacing all the cards with queens. When you want the mark to win, you flip the card that he guessed. When you want him to lose, flip one of the others. Every card would appear to be THE queen. Another variant involves simply palming the queen while distracting the mark with witty reparte. At that point there are no queens on the table to pick, thus the mark is automatically wrong. Every time I try to pose what seems to be a simple question, you throw in some witicism and dodge it with some technospeak and then magically come up with your own conclusion. So, I'm just trying to figure out where you're palming the queen. It looks to be somewhere around question 2... i.e. what time is it at the origin when a relativistic object reaches its destination. So, while my initial bets are proving correct, i.e. same time at origin and destination, I'm guessing that when I make that a wormhole instead of a simple object, then the time at the origin will miraculously change, i.e. the queen gets palmed.
So, rather than place my bet, let me change the assumptions and test that.
Assumption 1: Source and destination are the same location.
Assumption 2: An object is launched at 0.99c in a circular orbit with a circumference of 1000 ly.
Question 1: When the object reaches its destination, what year is it at the destination?
Question 2: When the object reaches its destination, what year is it at the source (the same location as the destination)?
Question 3: What does the flight recorder say the travel time was?
Tony:
A) You can probably look at it as in/expensive in time, rather than just cash. So yes, some of the same ideas would apply. I think there would be some difference, though, if a new link can be completed within a single business cycle compared to a generation.
B) While overall expansion rate will indeed be eaten up by development time, exporation rate is a different beast. This would also lead to possible side effects such as half-abandoned colony sites (when another, better-suited planet was found, and the older colony never got big enough to represent enough of a sunk cost), further colonies being developed faster because of better conditions (think California) and dispossessed groups more able to move past the normal frontier (think the Mormons).
Re: Luke and Raymond
I think the speed of exploration might be faster with FTL in the very short term, but not so much over centuries.
Citizen Joe:
Nobody's trying to pull a fast one on you. This is just how the theory (general relativity) works.
So, for your new test:
- Let's change assumption 2 so the ship goes 500ly away, turns around, and comes back (assuming arbitrarily small acceleration time). This is so we don't have to construct a rotating frame, which is harder.
1: 1010y
2: Meaningless question. From the point of view of someone at rest with respect to the source, they'll sit and wait, toes tapping, until the destination point is reached.
3: 141.77y
Tony:
"I think the speed of exploration might be faster with FTL in the very short term, but not so much over centuries."
Over centuries, yes. But that initial distribution can be pretty important (and generally considered full of potential for storytelling).
Citizen Joe:
Every time I try to pose what seems to be a simple question, you throw in some witicism and dodge it with some technospeak and then magically come up with your own conclusion. So, I'm just trying to figure out where you're palming the queen.
I am trying to be precise in my terminology, because relativity can be confusing and using "everyday" terminology leads to erroneous conclusions. I am sorry if this makes it difficult to understand - initially relativity can seem very counter-intuitive as the models we use that seem to work well in everyday life break down.
If I were to guess where your difficulty lies, it would be with assuming that events separated in space can agree upon what time something happens - this comes from both assuming simultaneity of events is possible and failure to understand the difference between coordinate time and proper time, as evidenced by quotes such as "So, while my initial bets are proving correct, i.e. same time at origin and destination" which is physically meaningless. However, I am not you so I do not know if this is where you are having problems.
So, to continue ...
Assumption 1: Source and destination are the same location.
Perfectly doable.
Assumption 2: An object is launched at 0.99c in a circular orbit with a circumference of 1000 ly.
Let's use speed = 0.9900990099..., to keep a time of 1010 years so we can be consistent with previous discussions.
We need to specify a circumference of 1000 ly in which reference frame. I suspect you mean the reference frame of the people waiting back home, so let's use that.
Question 1: When the object reaches its destination, what year is it at the destination?
it is 1010 years after launch.
Question 2: When the object reaches its destination, what year is it at the source (the same location as the destination)?
Again, it is 1010 years after launch.
Question 3: What does the flight recorder say the travel time was?
141.77 years.
For these questions, the answers are unambiguous since all can be phrased in terms of proper time rather than coordinate time - how much time do the people waiting back home experience? How much time does the probe experience? None of this is coordinate frame dependent.
Raymond:
"Over centuries, yes. But that initial distribution can be pretty important (and generally considered full of potential for storytelling)."
Perhaps. But then one gets into flatlined tropes that are better off left unrevived, like the Discovery of the Lost People, or the Return of the Prometheans, or the Clash of Splinter Cultures.
Tony:
"Perhaps. But then one gets into flatlined tropes that are better off left unrevived, like the Discovery of the Lost People, or the Return of the Prometheans, or the Clash of Splinter Cultures."
Perhaps. Something like a relativistic wormhole network can give a new spin on it, though. That timelike displacement (and asymmetric wormhole replacement time) can mean that the Lost People aren't descendants turned to barbarism after the fall of empire - they're original members, with all that entails.
OK, so same experiments but with wormholes...
Case 1: 'exit' end of the wormhole goes 1000 ly away... result: time travel?
Case 2: 'exit' end of the wormhole goes in a circle... result: no time travel?
Does this have anything to do with the speed the wormhole moved to get to the destination?
Raymond:
"Perhaps. Something like a relativistic wormhole network can give a new spin on it, though. That timelike displacement (and asymmetric wormhole replacement time) can mean that the Lost People aren't descendants turned to barbarism after the fall of empire - they're original members, with all that entails."
Since I don't accept chronology-breaking technologies as realistic, i'm afraid you just lost a book sale.
Tony:
If it's a concern that I'd allow closed timelike curves, I was of course assuming the Chronology Protection Conjecture is in force, and no causality-breaking time machines are formed. There will be timelike separation in addition to spacelike, but frankly that's the interesting part.
If you don't accept that relativity screws around with intuitive notions of "over there" and "right now", may I direct you to Reality Is Unrealistic on the Evil Website.
Citizen Joe:
I know this was already answered, but I'm going to calculate the answers too in order to double-check and in order to make sure my relativity skills stay fresh.
"Baseline Relativistic Experiment (no wormholes).
Assumption 1: Two distant points (1000 ly) have an event that is an agreed upon starting date.
Assumption 2: Both of the distant points are experiencing time at the same rate, i.e. not experiencing time dilation relative to one another.
Assumption 3: An object leaves the first point, traveling at relativistic speeds on a journey that should take 1010 years. (about 0.99c).
Question 1: What year is it at the destination when the object arrives?"
1010 years after launch. (But due to the limited speed of light, 10 years after you detect the launch.)
However, if you had been carrying a wormhole, then this value is completely irrelevant to when your end of the wormhole will open. Stepping through the wormhole will not take you the other end at the same time, because relativity doesn't care about your definition of "at the same time".
"Question 2: What year is it at the source when the object arrives at the destination?"
1010 years after launch. (But due to the limited speed of light, you only detect the arrival 2010 years after launch.)
"Question 3: What does the flight recorder say the flight time was?"
141.77 years after launch.
Citizen Joe:
"So, rather than place my bet, let me change the assumptions and test that.
Assumption 1: Source and destination are the same location.
Assumption 2: An object is launched at 0.99c in a circular orbit with a circumference of 1000 ly."
I'm guessing you don't actually mean a literal orbit in the sense of circling a large gravity source, since I'm not sure what object might have a gravity strong enough for that kind of orbit, and since that would entail having to bring in general relativity.
Instead I will assume you meant a circular trajectory maintained by the continuous constant-strength firing of the spacecraft's engines.
"Question 1: When the object reaches its destination, what year is it at the destination?"
1010 years after launch.
"Question 2: When the object reaches its destination, what year is it at the source (the same location as the destination)?"
1010 years after launch, duh. Like you said, they're the same place.
"Question 3: What does the flight recorder say the travel time was?
142.48 years after launch. (This differs from the 141.77 year value due to rounding differences. 0.99 is not exactly 1000/1010.)
Tony:
"You don't get FTL expansion over the long run, even with FTL, because it takes time to consolidate new gains."
Good point. Although it depends on how common habitable/terraformable planets are. If they're only to be found every couple hundred lightyears or so (which still leaves millions of habitable stars in our galaxy), then we might not want to wait generations between colonizing each new world. If habitable systems are thousands of lightyears apart (which still leaves thousands of them in our galaxy), then we'll definitely not be happy waiting that long.
If nearly every star system is habitable/terraformable, then yeah, we're going to have our hands full just with places close to us.
Scientists and explorers will also want to poke around beyond the edge of firmly colonized space, if they can. Even if habitable worlds are common, there are other cosmic curiosities that aren't found anywhere near here. (Although some of the really "far" ones are only such because they only existed in earlier eras of the universe, and so all the ones we "see" now are long-dead objects billions of lightyears away whose light is just reaching us.)
Raymond:
"If the same new link is only three years (apparent time), it becomes a more manageable project and more likely to occur before the current system has been exploited to the fullest."
Good point. Not every settlement has to be a full-scale colonization project - there is a place for small outposts, which may be placed far before a serious colonization is undertaken. However, outposts do not usually build their own outposts ad infinum.
Tony:
"If FTL travel is relatively expensive, it may in fact be decades before a frontier system gets regular service. If it's relatively inexpensive, there may be regular service within a few years."
For wormholes, this brings up a question we've been ignoring, which is how hard it is to traverse a wormhole once it's been created. For our thought experiments, I've mostly been assuming planetary-surface tramlines, which mean that the only cost is in creating the wormholes and once they're in place you can effortlessly walk across (or maybe ride a donkey if you want something a little more high-tech).
Regardless of price, wormholes aren't likely to have a huge time component to traverse.
Luke:
"If Dr. Bob the astrophysicist can send a wormhole to the Andromeda galaxy in less than a year for the cost of a reasonable government grant, he might decide to do so just to look back and see the Milky Way galaxy from the outside (allowing better mapping of our galaxy's structure and etcetera)."
I thought about this for a moment, and realized that it works surprisingly well. The Andromeda end of the wormhole will be far into the future - but, at the same time, due to the great distance, it will be detecting light that was send in its distant past. These balance out and, if the wormhole was sent at sufficiently close to the speed of light, the Andromeda observatory will be able to observe how the Milky Way looked at the time the wormhole was launched.
Of course, if your civilization is a wormhole network crisscrossing numerous different time periods, it's anyone's guess what time period you'll even want to map the Milky Way in...
Tony:
"I think the speed of exploration might be faster with FTL in the very short term, but not so much over centuries."
Guess what, I care more about the short term than about centuries from now. Science fiction needs to be set in the future to give us fancy tech, but the earlier we get to play with that tech, the easier it is to write and relate to.
Tony:
"But then one gets into flatlined tropes that are better off left unrevived, like the Discovery of the Lost People, or the Return of the Prometheans, or the Clash of Splinter Cultures."
The Discovery of the Lost People or Clash of Splinter Cultures can very sensibly happen anytime that the size of colonized space outstrips the possible travel between colonized worlds. Note that this can happen regardless of how fast your travel is (barring nigh-infinite travel like wormholes) as long as colonized space is large enough. The only way to permanently prevent it is to have infinite travel speeds, or to have FTL travel speeds which increase at least as quickly as your colonized sphere does. (Humans populate a volume 100 lightyears in diameter, a travel speed of 1 lightyear/day will suffice. Humans expand to the edges of the galaxy, now you need travel speeds of 1000 lightyears/day to avoid fracturing.) So it's a matter of speed of research vs speed of colonization.
When you do meed your lost people, though, they aren't likely to be some isolationist utopia guarding long-secret wisdom. Instead, what you're going to get is one culture which is far higher-tech than the others, which then goes around "discovering" and conquering all the less-advanced ones (or, if you want to be a little more idealistic, peacefully assimilating their cultures through economical dominance).
Citizen Joe:
"OK, so same experiments but with wormholes...
Case 1: 'exit' end of the wormhole goes 1000 ly away... result: time travel?
Case 2: 'exit' end of the wormhole goes in a circle... result: no time travel?"
Wrong. In both cases, there is a time displacement of 868.23 years (plus or minus rounding errors) between the two ends of the wormhole, as viewed from the planets' rest frame(s).
In case 1, this time displacement does not lead to a breach of causality because the wormhole leads 1000 lightyears away and only 868.23 years into the future, making a spacelike separation. Thus you do not have a time machine as such, even though it appears to be such from some frames of reference.
In case 2, this time displacement does lead to a breach of causality because the wormhole leads 0 lightyears away and 868.23 years into the future, making a timelike separation. Thus you do have a time machine. There are two ways to resolve this. Either you can postulate some mechanism of wormhole physics which causes a wormhole to fall apart if you attempt to carry it in this manner. Or you can just accept the existance of time machines, and then figure out how to work with closed timelike loops.
Raymond:
"If you don't accept that relativity screws around with intuitive notions of "over there" and "right now", may I direct you to Reality Is Unrealistic on the Evil Website."
Of course I accept that relativity works as advertised. I just also happen to think that the arrow of time points in only one direction. So anything in relativity that leads to apparent time travel or anything other than clock slowing at divergent velocities has to be some species of mistaken interpretation.
Citizen Joe:
Case 1: 'exit' end of the wormhole goes 1000 ly away... result: time travel?
No time travel.
The wormhole connects events (t,x)=(141.77 y,0) with (t,x)=(1010 y, 1000 ly) *. Although the time coordinates are different, remember that the time coordinate by itself has no physical meaning. To someone moving at 87% the speed of light relative to home, the wormhole would connect equal time coordinates and in that reference frame even looking at coordinate time would not get you time travel.
What is relevant is that the events the wormhole connects are far enough apart that light cannot get between them. This means that there is no way that you can get from home at x=0 out to the wormhole destination and back to arrive before you left. Thus, there is no time travel in any meaningful physical sense.
Case 2: 'exit' end of the wormhole goes in a circle... result: no time travel?
Time travel.
The wormhole now connects events (t,x)=(141.77 y, 0) with (t,x)=(1010 y, 0) *. Going through the wormhole takes you from home back to home at a time 868.23 years in the past (or, if you go the other way through the wormhole, 868.23 years in the future). Since you can now affect events that happened in your own past you have time travel in a physically meaningful sense (leading to issues of paradoxes and such).
Does this have anything to do with the speed the wormhole moved to get to the destination?
This will affect the difference in the time coordinates connected by the wormhole - going slower makes the time coordinate differences smaller. It does not, however, change the qualitative result - taking a single wormhole in a straight line does not result in time travel while taking a wormhole in a circle back to its original location does result in time travel (although the slower you go, the closer you can get before you have a time machine).
* More generally, going in a straight line connects an event (t,0) with (t+868.23 y, 1000 ly) for any t > 141.77 y. similarly, a circular journey connects an event (t,0) with (t+868.23 y, 0) for any t > 141.77 y.
AHAH! I found the queen palming.
The wormhole now connects events (t,x)=(141.77 y, 0) with (t,x)=(1010 y, 0)
I don't subscribe to the belief that the dilated time in the first part is the reference point. I believe that the dilated time is just an illusion to those moving at relativistic speeds. So, while 141.77 years might pass for the wormhole mouth, that still maps to 1010 years to the rest of the universe. The end result is that time coordinate (1010y,0ly) is connected to (1010y, 0ly) which means no time travel. Now, since nobody has come back from the future to correct me, I stand by my interpretation.
Observation: If you have time machines created by wormholes in circular STL paths, then they will be of the "cannot travel back to earlier than when the time machine was built" kind. This is unlike time travel by FTL travel in arbitrary frames of reference, which would allow you to go as far back as you want.
Citizen Joe:
"So, while 141.77 years might pass for the wormhole mouth, that still maps to 1010 years to the rest of the universe."
But you're not travelling through the rest of the universe. You're travelling through the wormhole mouth.
Citizen Joe: "I don't subscribe to the belief that the dilated time in the first part is the reference point. I believe that the dilated time is just an illusion to those moving at relativistic speeds."
Tony: "I just also happen to think that the arrow of time points in only one direction. So anything in relativity that leads to apparent time travel or anything other than clock slowing at divergent velocities has to be some species of mistaken interpretation."
Those sound like statements of faith, more than anything. You are, of course, welcome to your opinion. I'm curious as to why you are so...insistent on the stranger effects of relativity being merely "interpretations".
Those sound like statements of faith, more than anything. You are, of course, welcome to your opinion. I'm curious as to why you are so...insistent on the stranger effects of relativity being merely "interpretations".
Not to mention that they are inconsistent with what is known about relativity (including parts of relativity that have been validated - specifically, non-simultaneity and frame dependent time ordering for space-like separations of events).
Raymond:
"Those sound like statements of faith, more than anything. You are, of course, welcome to your opinion. I'm curious as to why you are so...insistent on the stranger effects of relativity being merely "interpretations"."
Because they are. Nobody's sure how a valid theory of quantum gravity will affect the validity of classical analysis, so each analyst picks what he believes to be a correct interpretation. Some say traversible wormholes can be constructec and then subsequently manipulated in such a way to create CTCs. Other's say, no, the fabric of the universe seems to require chronological consistency, so analyses that seem to lead to CTCs must be missing something. I'm with the latter faction.
WRT why, well, that's simple enough -- we see chronology everywhere, so it must be fundamental at some level, like inertia. For the same general reasons that we have conservation of momentum, we should have conservation of chronology. Certainly it's an argument from analogy and expectation, but barring absolute disproof in practice, I think it's the most reasonable one, given what we know about the general properties of the universe.
Tony raises an interesting point about the long term speed of expansion of the human sphere being probably being STL even if individual trips can be made FTL.
Not that this probably also applies to comprehensive exploration, though not (given FTL) to single exploratory missions.
It is one thing to explore one star system 1000 ly away - quite another to explore every star within 1000 ly, or even a significant fraction of them, given that that a sphere of that radius contains on order of a million stars.
Possible grist for a future post ... let's not get into what exactly 'future' means, in whatever frame of reference.
Tony:
The wormholes we've been talking about aren't necessarily CTCs. They have timelike separations, which can be weird, but as long as there's sufficient spacelike separation to more than offset the timelike, causality isn't broken. And based on what we know of quantum mechanics, at the point where a wormhole would become a CTC (one with a lightlike separation, where the spacelike and timelike separations are equal), it's been shown that you'd see something similar to the infinite-blueshift effect (although not exactly the same, AIUI) which collapses the inner horizons of charged black holes and Kerr ring singularities. Basically, a photon going back in time and retracing its path would infintely multiply its amplitude, overwhelming any negative pressure keeping the wormhole open. This is what we're referring to when speaking of the Chronology Protection Conjecture.
All of this is, of course, conjectural unless and until we have wormholes to test. And yes, we're not sure about quantum gravity. It could easily disallow wormholes entirely, in which case all of this is moot. But if it doesn't (and some theories actually make it easier for wormholes to exist), there is still a mechanism within current science to prevent CTCs even with the existence of wormholes, however counterintuitive some of their properties may be.
Also, I think we'd more likely find FTL travel to be disallowed in its entirety than find quantum gravity to have the effects you propose.
Repost - first time was from phone, and got stuck in the Warp. Also and addition to the last paragraph, so consider this version canonical.
Tony:
The wormholes we've been talking about aren't necessarily CTCs. They have timelike separations, which can be weird, but as long as there's sufficient spacelike separation to more than offset the timelike, causality isn't broken. And based on what we know of quantum mechanics, at the point where a wormhole would become a CTC (one with a lightlike separation, where the spacelike and timelike separations are equal), it's been shown that you'd see something similar to the infinite-blueshift effect which collapses the inner horizons of charged black holes and Kerr ring singularities (although not exactly the same, AIUI). Basically, a photon going back in time and retracing its path would infintely multiply its amplitude, overwhelming any negative pressure keeping the wormhole open. This is what we're referring to when speaking of the Chronology Protection Conjecture.
All of this is, of course, conjectural unless and until we have wormholes to test. And yes, we're not sure about quantum gravity. It could easily disallow wormholes entirely, in which case all of this is moot. But if it doesn't (and some theories actually make it easier for wormholes to exist), there is still a mechanism within current science to prevent CTCs even with the existence of wormholes, however counterintuitive some of their properties may be.
Also, I think we'd more likely find FTL travel to be disallowed in its entirety than find quantum gravity to have the effects you propose (which sound essentially like a privileged frame of reference for the universe).
Rick:
I think you made the point that FTL and STL colonization might have similar speeds in your essay on Atomic Rockets. Your remark about comprehensive exploration versus single missions reminds me of Hamilton's Commonwealth Saga, where exploration and settlement by wormhole has taken place in steady 'expansion phases', giving rise to 'phase one space', etc., with the exception of one more distant planet aptly called Far Away, which was first explored because its star had given off an unexpectedly large flare, and was then settled when a derelict alien starship was found on its surface.
R.C.
Raymond:
Also, I think we'd more likely find FTL travel to be disallowed in its entirety than find quantum gravity to have the effects you propose (which sound essentially like a privileged frame of reference for the universe).
Not quite. It's just a simple conecture that when all frames of reference are reconciled, taking all physical effects into consideration, chronology will be preserved. I can't prove it -- nobody can. And if it is a valid conjecture, I'm perfectly agnostic as to the precise mechanism(s), with this caveat: I would prefer that the universe allows FTL communications of some kind, whatever other constraints have to be imposed to protect chronolgy.
Tony:
Well, if traversable wormholes of the sort we've been discussing are possible, and the chronology protection conjecture holds, then causality is safe. Chronology may bend a bit, in the manner we've described - then again, chronology is already a little bent according to GR.
Or are you specifically conjecturing something more restrictive?
RC - I think you made the point that FTL and STL colonization might have similar speeds in your essay on Atomic Rockets.
Among the many general virtues and pleasures of Atomic Rockets is a specific one for me - it preserves comments I made years ago at SFConsim-l, some of which I've entirely forgotten until re-encountering them.
Tony - by 'chronology will be preserved,' do you mean something more than causality being preserved? What I gather from the discussion by Luke and other commenters who actually understand this stuff, is that there might be cases of 'travel into the past' that permit none of the familiar time travel paradoxes. If my wormhole trip to Andromeda takes me to the year 2,002,011, and the return trip takes me 'back' to mere 2011, no harm, no foul.
(I'm not saying that you have no right to further convictions about the nature of temporality - just checking on whether such is intended.)
Tony:
"It's just a simple conjecture that when all frames of reference are reconciled, taking all physical effects into consideration, chronology will be preserved. I can't prove it -- nobody can."
The only evidence that I feel seriously supports the impossibility of time travel is a variation on the Fermi paradox. Specifically, if time travel will be invented at any point in the future, then we should already be seeing time travellers.
Ways around this are:
1. Time travellers have unanimously agreed to be discreet while in our era and are very, very good at blending in without being noticed. Or, humans have simply decided not to risk using time travel except for matters of extreme importance. (I feel this is unlikely as it clashes with my perception of human nature.)
2. The only possible time travel is of the "you can only go back to an existing reception device, so you can't go back before time travel was invented" variety. (Time travel based on spinning wormholes would indeed work this way.)
3. Time travel is physically possible, but won't be invented by humans (perhaps because we end up destroying ourselves first), and the aliens that do invent it don't care to visit our insignificant little blue planet.
There is also the factor that time travel, if possible, would so completely revolutionize any civilization that has access to and makes full use of it, that it would likely be impossible to preserve many of the things we have come to expect of our society. You may not believe that life may alter on such a fundamental level, but there is, of course, no evidence for this.
On the other hands, if you actually want a technological singularity, then time travel is a pretty good invention to justify it.
I'll also note that the ability to merely observe events in the past (for example, filming the dinosaurs in their natural habitat) without travelling there would not in fact violate causality, although it might have other ohysical issues (by quantum mechanics, you cannot observe something without interacting with it).
Re: conservation of chronology
What I'm conjecturing is taking the universe as a whole as a single coordinate system, and reconciling all inertial reference frames from t = 0 to the present, there would be an objective order of events. A would happen before B, which would happen before C, etc. So I guess I am conjecturing causality preservation, insomuch as causality is a consequence of time moving in a definable direction.
Time is always moving forward, but the EFFECTS of time can be modified by your speed. Since we don't have an objective way of measuring time directly, all we can do is measure its effects on an accepted frame of reference, counting heartbeats for example.
Citizen Joe:
"Time is always moving forward, but the EFFECTS of time can be modified by your speed. Since we don't have an objective way of measuring time directly, all we can do is measure its effects on an accepted frame of reference, counting heartbeats for example."
Not so much the effects of time as the perception of duration. But I did put in the caveat "reconciling all inertial reference frames" for this reason.
Perception implies a perceiver. I stand by my effects statement. Run a radioactive isotope through our specified 1000 ly loop experiment and it will only show 141 years of decay rather than the 1010 years elapsed time at home base.
The only other way to get around this (although not a very satisfying solution) would be that wormholes do not connect portions of the visible universe at all but are gateways to "otherwhen". The light cones would be so scrambled that there would be no interaction possible at all, or you are physically in a different universe (which might cause issues if that universe is based on different metrics and physical constants...)
Citizen Joe:
"Perception implies a perceiver. I stand by my effects statement. Run a radioactive isotope through our specified 1000 ly loop experiment and it will only show 141 years of decay rather than the 1010 years elapsed time at home base."
Perception in this case is the same kind of thing as the observer in discussion of the collapse of wave functions. The "observer" is not a literal, sentient spectator, but whatever physical phenomenon causes the function to collapse. Likewise, the perception of time is whatever physical event causes a physical "clock" to be "read". It could take the form of a measurement of radioactive decay at the end of the experiment, or it could be the ongoing interaction of physical processes that proceed at a slowed rate (from the perspective of an outside observer) due to relativistic time dilation.
Tony:
What you seem to be conjecturing is essentially a privileged reference frame. Which may or may not be true, but:
- At present, we have no idea how one would observe such a thing.
- Such a thing is unnecessary to preserve causality. As weird and counterintuitive some effects of relativity are, the speed of light keeps everything consistent. Not necessarily in the same order for all observers, but causally consistent (which should be differentiated from chronologically consistent). Total ordering is not strictly necessary. A partial ordering suffices quite nicely.
- If such a thing were a more accurate description of the universe, the theory would have to explain why relativistic effects exist at all. This is more difficult than you may think. General relativity can be derived from only two predicates: a constant speed of light, and Lorentz invariance. (In fact, I've heard it can be done with only Lorentz invariance.) All the strange (to us) effects follow a priori when placed in that context, but wouldn't really make sense by themselves otherwise. If there were a canonical reference frame, there would have to be additional justification for the lightspeed consequences we've observed. (Not that it couldn't be done, just that you'd have to have that extra explanation.)
What you seem to be conjecturing is essentially a privileged reference frame. Which may or may not be true, but:
- At present, we have no idea how one would observe such a thing.
So as was stated, the act of observation doesn't imply an intelligence taking notice, it's more a matter of physical interaction. With the Heisenberg Uncertainty Principle, the idea is that to observe a particle a photon would have to bounce off of it and back to a detector and that very act would alter trajectory and, possibly, the speed.
Now, here's the question: could there be anything special about intelligent perception of an event? Something where the observation of a conscious mind would be different than, say, a video camera making a recording?
jollyreaper:
"Now, here's the question: could there be anything special about intelligent perception of an event? Something where the observation of a conscious mind would be different than, say, a video camera making a recording?"
No, because an intelligent being's perceptions are all mediated by the usual physical mechanisms. A person seeing an event simply collects photons from the event and interprets them as having a pattern. If the pattern is new to the intelligence, then it can only describe the pattern by analogy to other patterns it knows. (Or, in the case of children learning to see, be told the significance of the pattern by a more experienced intelligence.)
Re: Raymond
I think the problem we're having here is that we were repsectively educated in different epochs, and visualize these things in different ways. I doubt we could achieve a consensus with a conference or class room and a few hours for a serious whiteboard session.
No, because an intelligent being's perceptions are all mediated by the usual physical mechanisms. A person seeing an event simply collects photons from the event and interprets them as having a pattern. If the pattern is
That's what I would tend to think but I've heard talk to the contrary and I'm not sure if that's just metaphysical wank or if there's anything to it.
jollyreaper:
"That's what I would tend to think but I've heard talk to the contrary and I'm not sure if that's just metaphysical wank or if there's anything to it."
It's ignorance -- willfull in my opinion, but what do I know... -- of what "observation" means in physics terms.
Tony:
"You don't get FTL expansion over the long run, even with FTL, because it takes time to consolidate new gains."
Another thing occured to me: you're assuming that only edge worlds are participating in colonization. However, if travel is sufficiently fast, then it becomes feasible (and even preferable, due to better industrial infrastructure, and due to higher population pressures) for core worlds to send their own colonization missions, bypassing the fringes entirely.
If all worlds that can do so participate in the colonization, then your empire's size is going to expand exponentially. From the outside, this would appear as a continuously accelerating speed of expansion. This would continue until you reach the limits of your travel technology (if ever, since technology may have improved by this time) where core worlds can no longer effectively participate in colonization, at which point expansion "slows" down to polynomial speed.
Even if worlds slightly inside from the edges can perform colonization, then that can still multiply the speed of expansion. If the ten outermost "layers" are allowed to participate in colonization at once, then you'll expand ten times as fast as if only one layer can colonize and then has to wait for the colony to advance to a state to launch its own missions.
Re: Milo
Presumably the core worlds are where the capital comes from to settle and consolidate the edge worlds. So the economic ability of the core to support expansion determines where the edge is to begin with.
I’d like to thank Luke and Raymond, especially, for tutoring us about FTL and relatively and causality, even though I still don’t have a very good grasp of these things.
Before this thread disappears to the next page, I’d like to posit a SFnal situation for review and see if it poses any causality hazards. It’s in an interstellar setting with post-plausible-midfuture-technology, including FTL travel.
Some assumptions:
1) Without giving away a lot of details, in the world I’m playing with, many stars are connected by “corridors” in which it is easier than usual to manipulate spacetime. Get in the corridor, and you can temporarily cause space to move or “inflate” in the direction of your destination. You then leave the inflated area before it collapses and drags you back to your starting point. Then you do it again.
You can’t jump instantaneously from one solar system to another, but by making a series of “jumps” (“surfs”?) within the corridor you can get from Sol to Alpha Centauri in about two weeks, ship time. Which is apparently also the same amount of time that passes in the Sol and AC systems. (Aside: Maybe I can make the galaxywide network of interconnected corridors be a galaxywide special frame of reference?)
2) There is no FTL communication between the stars, except for using the starships as couriers.
3) The spaceships have a magitech drive that lets them accelerate at about 1 gee. Normally they don’t exceed more than a few percent of the speed of light, as they travel from settled planets to the outer reaches of the local star system (circa Neptune’s orbit) where space is flat enough to enter the corridors.
4) It is possible to build and operate telescopes that use the local sun as a gravitational lens. (I hesitate to include links for fear of triggering the spam trap, but you can go to the Centauri Dreams website and search for the articles “Updating the Gravitational Focus Mission” and “The FOCAL Mission: To the Sun’s Gravity Lens” if you want more info.) If we had such a gravitational lensing telescope in Sol System, “the magnification would be so extreme that we could see vehicles moving on the streets of a habitable planet around one of the Centauri stars…”
However, to use our Sun as a gravitational lens, our telescope would have to be in a focal region at least 550 AU from the Sun. That’s hella far out. Among other things, it makes moving the telescope around the Sun to see different parts of the sky problematic.
However, a white dwarf star such as Van Maanen’s star could be useful as a gravitational lens from closer distances, starting as close as 0.13 AU. Assuming we could travel to the Van Maanen system (14 light years from Sol), and build or transport our telescope there, this is easier to work with.
Those are some of the starting assumptions. Now the situation…
1 of 2:
I’d like to thank Luke and Raymond, especially, for tutoring us about FTL and relatively and causality, even though I still don’t have a very good grasp of these things.
Before this thread disappears to the next page, I’d like to posit a SFnal situation for review and see if it poses any causality hazards. It’s in an interstellar setting with post-plausible-midfuture-technology, including FTL travel.
Some assumptions:
1) Without giving away a lot of details, in the world I’m playing with, many stars are connected by “corridors” in which it is easier than usual to manipulate spacetime. Get in the corridor, and you can temporarily cause space to move or “inflate” in the direction of your destination. You then leave the inflated area before it collapses and drags you back to your starting point. Then you do it again.
You can’t jump instantaneously from one solar system to another, but by making a series of “jumps” (“surfs”?) within the corridor you can get from Sol to Alpha Centauri in about two weeks, ship time. Which is apparently also the same amount of time that passes in the Sol and AC systems. (Aside: Maybe I can make the galaxywide network of interconnected corridors be a galaxywide special frame of reference?)
2) There is no FTL communication between the stars, except for using the starships as couriers.
3) The spaceships have a magitech drive that lets them accelerate at about 1 gee. Normally they don’t exceed more than a few percent of the speed of light, as they travel from settled planets to the outer reaches of the local star system (circa Neptune’s orbit) where space is flat enough to enter the corridors.
4) It is possible to build and operate telescopes that use the local sun as a gravitational lens. (I hesitate to include links for fear of triggering the spam trap, but you can go to the Centauri Dreams website and search for the articles “Updating the Gravitational Focus Mission” and “The FOCAL Mission: To the Sun’s Gravity Lens” if you want more info.) If we had such a gravitational lensing telescope in Sol System, “the magnification would be so extreme that we could see vehicles moving on the streets of a habitable planet around one of the Centauri stars…”
However, to use our Sun as a gravitational lens, our telescope would have to be in a focal region at least 550 AU from the Sun. That’s hella far out. Among other things, it makes moving the telescope around the Sun to see different parts of the sky problematic.
However, a white dwarf star such as Van Maanen’s star could be useful as a gravitational lens from closer distances, starting as close as 0.13 AU. Assuming we could travel to the Van Maanen system (14 light years from Sol), and build or transport our telescope there, this is easier to work with.
Those are some of the starting assumptions. Now the situation…
2 of 2:
Orbiting a red dwarf star HD-[string of numbers] is the planet Podunk. Local life has evolved there, but only a few small regions are habitable to human beings. There is one small outpost, Darwin Station, with about 300 residents. A primary activity of the outpost is investigating the local biota and cataloguing biochemicals that may be potentially useful for [Lord knows what]. This information is uploaded to the data clipper that visits the system two or three times a year (and delivers news and certain supplies from home).
Then one day Sirius Dick the space pirate comes barreling into the Podunk system and attacks the defenseless outpost. He steals Darwin’s precious database and kills most of the inhabitants; the few survivors are brought aboard the ship to be sold in the slave markets of Sigma Draconis IV.
A couple months later, a frigate of the Interstellar Patrol, HMS Intrepid (Captain Horatio Tiberius, commanding) visits the Podunk system and finds the settlement ruined and deserted. Some clues indicate very approximately when the attack occurred, but there are no witnesses or records to identify who did it.
But Captain Tiberius has an idea. He travels to Van Maanen’s star, which we will assume is four light years away, and talks to the monks who operate the Vatican’s GALILEO Mobile Gravitational Lensing Telescope there. Would they be willing to turn their telescope in the direction of the Podunk system approximately four years from now, when the light from the attack arrives, to observe the crime and perhaps record clues as to who did it?
One problem I can see is knowing exactly when to watch the Podunk system. I can see how it would be difficult to synchronize calendars, let alone clocks, between stars.
But the monks propose to use the entire Podunk system as a clock. Using known astronomical data, they can model the relative positions held by all seven planets in the Podunk system as they were at the approximate time of the attack. The monks will periodically observe the Podunk system through their super-telescope, watching for when its various planets approach the positions they held at the estimated time of the attack. When this time draws near, then the monks start watching the Podunk system constantly until they see the attack occur and record it. This might yield clues as to who the attacker was.
Is this likely to result in any causality problems? I don’t see how. For example, I can’t see any way that Captain Tiberius could use this information to travel back to the Podunk system and stop the attack before it happened. However, for some reason, this scenario is setting off causality alarms in the back of my head.
Any comments? About the relativity/causality situation, I mean.
... and it appears that both of my 2 posts have disappeared into the spam trap. Help, Rick!
’d like to thank Luke and Raymond, especially, for tutoring us about FTL and relatively and causality, even though I still don’t have a very good grasp of these things.
Before this thread disappears to the next page, I’d like to posit a SFnal situation for review and see if it poses any causality hazards. It’s in an interstellar setting with post-plausible-midfuture-technology, including FTL travel.
Some assumptions:
1) Without giving away a lot of details, in the world I’m playing with, many stars are connected by “corridors” in which it is easier than usual to manipulate spacetime. Get in the corridor, and you can temporarily cause space to move or “inflate” in the direction of your destination. You then leave the inflated area before it collapses and drags you back to your starting point. Then you do it again.
You can’t jump instantaneously from one solar system to another, but by making a series of “jumps” (“surfs”?) within the corridor you can get from Sol to Alpha Centauri in about two weeks, ship time. Which is apparently also the same amount of time that passes in the Sol and AC systems. (Aside: Maybe I can make the galaxywide network of interconnected corridors be a galaxywide special frame of reference?)
2) There is no FTL communication between the stars, except for using the starships as couriers.
3) The spaceships have a magitech drive that lets them accelerate at about 1 gee. Normally they don’t exceed more than a few percent of the speed of light, as they travel from settled planets to the outer reaches of the local star system (circa Neptune’s orbit) where space is flat enough to enter the corridors.
4) It is possible to build and operate telescopes that use the local sun as a gravitational lens. (I hesitate to include links for fear of triggering the spam trap, but you can go to the Centauri Dreams website and search for the articles “Updating the Gravitational Focus Mission” and “The FOCAL Mission: To the Sun’s Gravity Lens” if you want more info.) If we had such a gravitational lensing telescope in Sol System, “the magnification would be so extreme that we could see vehicles moving on the streets of a habitable planet around one of the Centauri stars…”
However, to use our Sun as a gravitational lens, our telescope would have to be in a focal region at least 550 AU from the Sun. That’s hella far out. Among other things, it makes moving the telescope around the Sun to see different parts of the sky problematic.
However, a white dwarf star such as Van Maanen’s star could be useful as a gravitational lens from closer distances, starting as close as 0.13 AU. Assuming we could travel to the Van Maanen system (14 light years from Sol), and build or transport our telescope there, this is easier to work with.
Those are some of the starting assumptions. Now th
Orbiting a red dwarf star HD-[string of numbers] is the planet Podunk. Local life has evolved there, but only a few small regions are habitable to human beings. There is one small outpost, Darwin Station, with about 300 residents. A primary activity of the outpost is investigating the local biota and cataloguing biochemicals that may be potentially useful for [Lord knows what]. This information is uploaded to the data clipper that visits the system two or three times a year (and delivers news and certain supplies from home).
Then one day Sirius Dick the space pirate comes barreling into the Podunk system and attacks the defenseless outpost. He steals Darwin’s precious database and kills most of the inhabitants; the few survivors are brought aboard the ship to be sold in the slave markets of Sigma Draconis IV.
A couple months later, a frigate of the Interstellar Patrol, HMS Intrepid (Captain Horatio Tiberius, commanding) visits the Podunk system and finds the settlement ruined and deserted. Some clues indicate very approximately when the attack occurred, but there are no witnesses or records to identify who did it.
But Captain Tiberius has an idea. He travels to Van Maanen’s star, which we will assume is four light years away, and talks to the monks who operate the Vatican’s GALILEO Mobile Gravitational Lensing Telescope there. Would they be willing to turn their telescope in the direction of the Podunk system approximately four years from now, when the light from the attack arrives, to observe the crime and perhaps record clues as to who did it?
One problem I can see is knowing exactly when to watch the Podunk system. I can see how it would be difficult to synchronize calendars, let alone clocks, between stars.
But the monks propose to use the entire Podunk system as a clock. Using known astronomical data, they can model the relative positions held by all seven planets in the Podunk system as they were at the approximate time of the attack. The monks will periodically observe the Podunk system through their super-telescope, watching for when its various planets approach the positions they held at the estimated time of the attack. When this time draws near, then the monks start watching the Podunk system constantly until they see the attack occur and record it. This might yield clues as to who the attacker was.
Is this likely to result in any causality problems? I don’t see how. For example, I can’t see any way that Captain Tiberius could use this information to travel back to the Podunk system and stop the attack before it happened. However, for some reason, this scenario is setting off causality alarms in the back of my head.
Any comments? About the relativity/causality situation, I mean.
That's it?
Thanks, KraKon! That's all of it -- dupes and all.(How do you do that?)
Stevo Darkly: I don't see anything in your scenario that violates causalty; no information from the future, nothing happening before the cause, so no violations.
Ferrell
I belatedly let the original posts out of spam jail!
I agree with Ferrell - so far as I can tell, there are no causality issues here. 'Seeing into the past' is odd in terms of our experience, but no violation of causality is implied, because no one is going back to change what happened; they are only recording it.
Thanks, Rick! And Ferrell!
(Would still love it if, say, Luke could pronounce on this as well, in case there are any non-obvious ramifications.)
Stevo Darkly:
"The spaceships have a magitech drive that lets them accelerate at about 1 gee."
Indefinitely?
Obligatory Rick Robinson's First Law of Space Combat test:
That would reach 1 Rick in 5 minutes (do damage equal to your mass in TNT), and 86 kiloRicks in 1 day (a 1 kiloton ship leaves a crater just over the size of the Tsar Bomba), but even a 10 kiloton ship after 1 year of acceleration you would "only" have around the energy of a dino-killer.
It takes 600 days (coordinate time) to gain kinetic energy equal to your mass energy, and 1000 days (coordinate time) to gain kinetic energy equal to twice you mass energy, which means that you cause antimatter levels of damage.
This isn't extremely unreasonable, though it warrants caution. Even if your ships are fuel-efficient enough to accelerate continuously for this duration, someone will probably notice what you're doing and interfere by the time you're able to build up super-destructive speeds. Also, you could cap propellant supplies at one month or so.
Formulas... (Note: Accuracy not guaranteed.)
E = m*c^2 * (cosh(tau*g/c)-1) = m*c^2 * 2*sinh(tau*g/c/2)^2
E = m*c^2 * (sqrt(c^2+(g*t)^2) / c - 1)
(E = kinetic energy. g = Earth gravity, or whatever you're accelerating at. c = speed of light. m = mass. tau = proper time. t = coordinate time. Coordinate time is measured from Earth, proper time is measured in the spacecraft's frame of reference.)
"travel from settled planets to the outer reaches of the local star system (circa Neptune’s orbit) where space is flat enough to enter the corridors"
At 1 gee brachistochrone (pretending we're in flat space), reaching Neptune's orbit takes some 11 days, assuming you don't care about coming to a stop when you get there. By this point you would have built up 10 megaRicks (compare to maybe 1 megaRick from a really efficient atomic bomb), meaning that a kiloton ship would deal several times the impact of Krakatoa (likely to cause major inconvenience but not the immediate termination of civilization). This means speeds of some 10000 km/s or 3% c.
"However, to use our Sun as a gravitational lens, our telescope would have to be in a focal region at least 550 AU from the Sun. That’s hella far out."
Just to be clear, the radius of the solar system can be interpreted as 110 AU (if you measure to the heliopause) or 230 AU (if you measure to the size of the bow shock). So 550 AU is well outside the solar system. It's also over 3 lightdays, but still very little compared to the distance to Proxima Centauri (270000 AU).
At 1 gee brachistochrone (again, flat space approximation, but this time taking into account the need to stop on the other end), 550 AU takes 67 days to reach.
"Among other things, it makes moving the telescope around the Sun to see different parts of the sky problematic."
I'll say!
And you can't wait for natural orbit - an observatory orbiting at 550 AU would take 12900 Earth years to complete one revolution. If it's even still strongly enough affected by the sun's gravity to not be perturbed out of its orbit by other effects.
(Note, 12900 = 550^1.5, rounded. Simple.)
"However, a white dwarf star such as Van Maanen’s star could be useful as a gravitational lens from closer distances, starting as close as 0.13 AU. Assuming we could travel to the Van Maanen system (14 light years from Sol), and build or transport our telescope there, this is easier to work with."
That depends on whether Van Maanen's star has a planet capable of being used as a base of operations for supplying the telescope.
(Oh, and white dwarfs aren't exactly "stars" since they're no longer undergoing fusion. Rather, they're stellar remnants, like neutron "stars" and black holes. Granted, astronomers are pretty fuzzy on their terminology too...)
"Orbiting a red dwarf star HD-[string of numbers] is the planet Podunk. Local life has evolved there, but only a few small regions are habitable to human beings."
I take it that is because these regions have been built of with pressurized dome infrastructure, rather than because a few spots on the planet naturally have an entirely different atmosphere or something?
"A primary activity of the outpost is investigating the local biota and cataloguing biochemicals that may be potentially useful for [Lord knows what]."
I expect that applications of some biochemical will only be discovered after the fact, after someone looked at it and went "Hey wait, I can use this for something...", rather than specifically setting out to find a biochemical with a certain application (this can more sensibly be done in a chemistry lab rather than by examining wildlife).
I mean, I doubt that when Alexander Fleming first discovered Penicillium mould growing in his petri dishes, he immediately knew that its uses would be combating disease and making really tasty cheese.
(Okay, so it seems the cheeses actually existed before the antibiotics. Whatever.)
"Some clues indicate very approximately when the attack occurred, but there are no witnesses or records to identify who did it."
Oh come on. There's plenty of technology. Just boot up anything too cheap for the pirates to bother ransacking and check logs to see when errors started mounting.
Besides, someone is bound to have left records, though probably not in an obvious location.
"One problem I can see is knowing exactly when to watch the Podunk system. I can see how it would be difficult to synchronize calendars, let alone clocks, between stars."
Anyone capable of performing interstellar travel should be capable of doing the math to compensate for temporal anomalies.
Anyway, since you're watching over a wide span of time (the entire period that the attack conceivably could have taken place in), it doesn't matter that much if you're off by a day or two.
"Is this likely to result in any causality problems? I don’t see how. For example, I can’t see any way that Captain Tiberius could use this information to travel back to the Podunk system and stop the attack before it happened."
Nope. As long as your FTL travel is constrained by a special frame of reference, there's no causality problems. Looking into the past like this might be unintuitive, but we can already see the Andromeda of 2.5 million years ago today! The farther you're trying to look into a past, the better a telescope you need to have - resolving a picture with such a small angular size has got to be difficult, even with gravitational lensing unobtainium.
It also means, though, that you'll have to wait at least 4 years before bringing the pirates to justice. But then again, if your detectives manage to find them by some other means before that time, then you can send a courier to Van Maanen's star and tell them to call off the plan.
Thanks, Milo! And Anonymous! (Although I sorta presume the unsigned "Anonymous" immediately preceding Milo's comment is from Milo also.)
I put together that scenario mostly just to test whether the combination of "looking into the past" (which, as you pointed out, astronomers already do, just not in such fine resolution) + "spaceships capable of traveling from one star system to another FTL" might somehow screw with the causality of the scenario. I couldn't see how it could -- but I wasn't sure whether I might have overlooked something subtle. I really don't have a good intuitive grasp of relativity at all. That's why I wanted to bounce the scenario off youse guys.
The economical, technological and planetary details of the scenario are peripheral to that, but I appreciate your feedback about that stuff anyway. I'll respond via a few other comments to follow.
Thanks for the reminder that any spaceship with torch-drive-like performance would make a helluva missile. Actually, it's even worse than that -- the magi-tech drive that my ships use is propellentless too. (Look up "induction sail" for info.) Basically, I decided that having to deal with rapid propellent consumption and attendant mass ratios was too constraining for the kinds of stories I'd like to tell.
However, I'm working out some economic and political background that generally makes large ships too valuable to throw away as super-missiles, and weapons of mass-destruction too much overkill to be militarily effective. Unlike most of you guys, I'm not envisioning large political organizations capable of fielding large military space fleets.
The world I'm building is a post-Westphalian, post-nation-state world where geographic location is less important. Instead of large contiguous nation-states, people of different political/cultural affiliations are more geographically mingled than they are today. It would be hard to lob a WMD against a concentrated population of your political enemies without killing a lot of friends and neutrals as well. (Imagine a war between geographically dispersed and intermingled groups such as, say, the Coca-Cola Company and the Mormons. They won't be throwing nukes at each other.)
This is inspired in part by medieval Iceland. Any free man of Iceland could choose to be a follower of any of the island's various "chieftains" (not a good translation, but it will do for now) regardless of where that freeman lived. That meant any chieftain could have followers anywhere on Iceland, and the farms of the followers of different chieftains were all intermingled among each other. And there was no one political authority over all the chieftains, either -- the island was "anarchic" in the technical sense of lacking a single overall head.
Arguably, this highly decentralized society was only "metastable." It eventually collapsed due to machinations by the king of Norway, some unwitting undermining by the Christian church, and some internal political weaknesses. But it did last for 350 years, which ain't bad. (How long do democratic republics last?)
I'm also assuming that tax-evasion technologies such as encrypted anonymous e-cash are both effective and in wide use. So government spending, including military spending, is highly constrained (arguably, perhaps, to a short-sighted degree). The private sector is correspondingly more powerful. There are lots of private security forces but no massive national space fleets with super-weapons. Violence is organized differently: there is very little war between massed state militaries but lots of fighting on the scale of gang warfare, plus some opportunistic piracy. The density of military force is low, and predatory types are more interested in stealing than destroying.
"Orbiting a red dwarf star HD-[string of numbers] is the planet Podunk. Local life has evolved there, but only a few small regions are habitable to human beings."
I take it that is because these regions have been built of with pressurized dome infrastructure, rather than because a few spots on the planet naturally have an entirely different atmosphere or something?
Actually, on such a planet, even if otherwise Earthlike, there may only be a few limited areas habitable to human beings due to temperatures and weather patterns.
An Earth-sized planet of a red dwarf star, if it were close enough and warm enough to have liquid water, would be tidally locked so that only one side of the planet faced the star.
For a long time many doubted that such a tidally locked world could harbor life at all, but more recent studies and simulations of water and air current circulation are painting a more optimistic view. Even so, the "back" of the planet would likely be entirely frozen over, and the center of the sunward side would be a blazing hot desert.
There might be a habitable belt on the sunward side, but there would also likely be severe winds and strange things like permanent shadows of mountains and stuff resulting in some weird and unpleasant weather. And who knows how much liquid water would be available on the sunward side, with so much frozen on the back. So that's why I'm assuming that even in the "habitable belt," there might just be a few "oases" where humans would be reasonably comfortable.
Gotta run -- more later.
"A primary activity of the outpost is investigating the local biota and cataloguing biochemicals that may be potentially useful for [Lord knows what]."
I expect that applications of some biochemical will only be discovered after the fact, after someone looked at it and went "Hey wait, I can use this for something...", rather than specifically setting out to find a biochemical with a certain application (this can more sensibly be done in a chemistry lab rather than by examining wildlife).
Yep, that's actually what I'm thinking. If there is life on other worlds, this might be one of the few things that could justify interstellar trade (if FTL travel is relatively cheap). Evolution can produce some odd things that human designers would never deliberately dream up, and some of these may be seredipitiously useful. A major "industry" of a colony world might be for the settlers to catalogue and describe the local biochemistry, and maybe send samples, for chemical and pharmaceutical labs back on Earth. "Hey, this plant sap has an unusual make-up and some weird properties -- maybe it would be useful as a solvent or a cancer cure or an improved glue for Post-It Notes or something. Why don't you use your sophisticated research facilities back home to investigate further?"
"Some clues indicate very approximately when the attack occurred, but there are no witnesses or records to identify who did it."
Oh come on. There's plenty of technology. Just boot up anything too cheap for the pirates to bother ransacking and check logs to see when errors started mounting.
Besides, someone is bound to have left records, though probably not in an obvious location.
Yeah, even as I wrote it I knew this was the weakest thing in the whole scenario. Even today we have near-ubiquitious video recording devices in our little phones. Somewhere in the colony would be a camera or phone or personal computing device with a record of the attack, and the pirates would be unable to find and grab/smash them all.
Stevo Darkly:
"(Although I sorta presume the unsigned "Anonymous" immediately preceding Milo's comment is from Milo also.)"
Yeah. Forgot to enter my name, sorry.
"However, I'm working out some economic and political background that generally makes large ships too valuable to throw away as super-missiles, and weapons of mass-destruction too much overkill to be militarily effective."
Using passenger jets as missiles is not militarily cost-effective either. This can be neatly circumvented if you stole your jets rather than building them yourself. There's also simple accidents to worry about.
Anyway, it's okay - I found (to my surprise) that numbers were less extreme than I was expecting.
"Arguably, this highly decentralized society was only "metastable"."
The problem is that if you're in a position of sufficient strength, you're going to try getting rid of any enemies that it is within your power to, and particularly ones which pose a threat due to their proximity to your own home.
You will end up with something like a Go board - as one chieftain's forces start dominating a part of the island, they will envelope and eliminate other chieftains' retainers.
To prevent this, you need strong incentives for different factions to live peacefully with each other even when they're within easy reach of each others' weapons. If the only combat is highly ritualized (probably favoring one-on-one duels between chosen champions, for example - to move away from the Iceland example - ones called "lawyers"), with the rules enforced by a higher authority or by mutual agreement (break the treaty and every other chieftain will gang up on you), then that would permit people to live next-door to their enemies without fearing assassination.
"Actually, on such a planet, even if otherwise Earthlike, there may only be a few limited areas habitable to human beings due to temperatures and weather patterns."
Temperature I'll buy. Although humans (like Eskimos) can live even in subzero temperatures, which are an obvious lower bound for any water-based life, if a planet has a much higher temperature than Earth (perfectly feasible, since Earth is at the lower end of the scale where water remains liquid), then only the poles and very high altitude peaks will be cool enough for humans.
I don't think weather is a good excuse. What weather patterns, short of giant years-long hurricanes or relentless Atacama-level drought, would prevent humans from entering? And both of those would hurt native life as well.
"For a long time many doubted that such a tidally locked world could harbor life at all, but more recent studies and simulations of water and air current circulation are painting a more optimistic view. Even so, the "back" of the planet would likely be entirely frozen over, and the center of the sunward side would be a blazing hot desert."
Would not. Simulations show that wind patterns will blow towards the hot pole, meaning that it will be a tropical rainforest, not a desert.
Anyway, if it were a blazing hot desert, than I'll classify that back under the "will hurt humans no more than it hurts native life" category.
A tidally locked planet would indeed have large areas uninhabitable to humans (the entire dark side, as you said) - but so does Earth (most of the planet is ocean). I don't think this justifies a description of "only a few small regions".
Well, since we're somewhat on the subject, might as well throw in a question of my own.
It isn't the Conservation of Causality (paygrade isn't nearly high enough to even think up the correctly worded question), but rather the Conservation of Angular Momentum as mentioned by Luke.
Basically, how do I plausibly keep that particular law intact with the FTL Drive I described in my responces in the Good Sheperd blog entry?
As for Stevo Darkly's scenario, well I don't see a violation of causality as far as I know it. It's one thing to see the past as if it happened before you, it's another to change past events either passively or actively.
Then again, I'm not even sure if the scenario that was described would even work in practice.
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Sabersonic: I'd go with the 'reducing time of transit' type of warp drive; have different 'grades' of drive (reduction of time in transit by 5, by 10, by 100, etc). That should help, I hope.
Ferrell
Ferrel - I'm not really sure what you meant by "Reducing Time of Transit", but I do get the idea of different Dive System grades for various "operational ranges" though I wasn't sure if that was really neccesssary since I envisioned star-to-star travel. Though then again, transit time ratio between Hyper spacetime and "normal" spacetime could also be a grade factor. Was that what you meant?
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Sabersonic; yes, (I should refrain from posting before coffee or when nodding off), I meant an FTL system that reduced the amount of time needed to go from point A to point B, instead of somehow increasing your delta-V without increasing your remass. You already said that you wanted sub-stellar range warp drive, so different 'grades' of your drive seemed the way to go; a small ship that can deploy from Earth orbit to Jupiter orbit and back again in a matter of hours would be very useful, even if it couldn't get from Sol to Alpha Centuri in a lifetime.
Ferrell
Ferrel - Oh, it's my IP Warp drive that you mentioned. Well considering that I initially envisioned it as a compliment to reaction drives both conventional and magi-tech torch types, though I'm not sure if the IP Warp Drive would improve either deltaV budget or transit time. Didn't really envisioned the IP Warp Drive to have the transit time measured in hours, more like days at best to half of what VASIMIR promised.
I'm more concerned with how I solve the Conservation of Angular Momentum on my Hyperspace Warp Dive System. Sure, I've tinkered with the idea so that the seemingly near instanantious transit time through Hyperspace via the drive is measured in days at the very least in "real" space-time, having said starcraft accelerate to the orbital velocity of the superior stellar-massed object before the jump, and even surrendered to the idea that Lagrange Points up to Gas Giants could be used as subsituted for stellar-mass gravity points if enough energy is pumped into the drive at the expense of an exponentially greater time dialation that is measured in decades rather than days via stellar-mass dives, but the way Luke explained the problem with such a drive system has me rather worried on my idea.
Not sure if decreased transit time would help solve my little magi-tech issue, but whatever would help make it not beat up physics as we know them to a pulp.
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Sabersonic: so long as your IP warp just compresses or 'attenuates' time, so that time flow for your starships never goes negative, then it should be fine. As for Conservation of Angular Motion, do what Luke suggessted and have an amount of matter equal to the ship's mass swap positions and speed/tragectory. Because you already use stellar poles for interstellar jump-off points, there should be lots of solar wind for the mass/energy/momentum swap.
Ferrell
So long as I keep the attenuated transit time of the IP Warp Drive away from anything near the minute range, I should be able to not suffer the "FTL is Time Travel" conundrum. Though to be honest, I think I feel safer if said transit is measured in days rather then hours. Not exactly fast enough to deal with emergencies, but certainly fast enough to keep the equilibrium of realistic plausability and onboard passenger boredome limits.
Still, there's just something strangely romantic about Cycler Stations being akin to a Cruise Ship. I know, I know, space is NOT an ocean, but I can't help it.
As for the Mass/Energy/Momentum Swap for the Dive System, I had originally envisioned the destination point to be a strange swirling "vortex" for lack of a better word of strange energies that indicates an incomming Hyperspace Dive equipped starcraft. Granted, it'll probably now look like a mini-black hole that's drawing in stellar matter into it but it's a big enough indicator that something's comming. Not sure how to work it out with my Stargate Off-Ramp idea or just hand wave it as usual.
Though I gotta wonder, considering the minimum size of the Starcrafts I envisioned (big MFs), wouldn't the Dive resemble a more explosive version of a Coronal Mass Ejection?
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Sabersonic:
It's not so much the duration of travel as the frame of reference you take when you jump. If you make it so that, say, you have to be stationary with reference to the star you're using as your jump point, that'll get rid of most of the problem. Then you just have to deal with the (relatively slight) difference in reference frames between stars - if the destination is moving away from the origin, theoretically you could jump, take on the new frame, then jump back, and end up earlier than you started. Just make sure the travel time is long enough that jumping there and back takes longer than the difference in coordinates.
Raymond - I am (unfortunately) familiar enough with the "FTL Travel equals Time Travel" problem to the point that the best idea's I've come up with to avoid such causality violating dives is probably just as full of holes as the "Jump Anywhere" Drive commonly seen nowadays.
All I could think of without resorting to Special Frames is, beyond making the transit time through the reference of "normal" space-time measured in days at the very least as opposed to the seemingly instant attenuated time of Hyper Space-Time such as a thousand parsec dive takes over a century to complete in "real" space-time as oppose to the hour long duration as experienced by the starcraft through Hyper space-time, that any possible time travel through the Dive System could only conclude with said starcraft converted into a flash of gamma rays. The only form of Time Travel that should have occured is the time dialation towards the future with no hope of traveling back into the past.
Now that I think of it, I'm not really sure if that flash of gamma rays is such a good idea to indicate an accidental passage through time. Though it's not anywhere near stellar-mass, I have a feeling that converting all of that matter into gamma rays would be some fraction of a Gamma Ray Burst.
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Sabersonic:
"All I could think of without resorting to Special Frames is [...] that any possible time travel through the Dive System could only conclude with said starcraft converted into a flash of gamma rays."
Ouch. Run on sentence.
But it doesn't work, because there is no exact moment at which time travel takes place. While most observers will agree that time travel took place at some point during the voyage (except for the observers on the ship itself), they will disagree on exactly when the first instance of time travel took place. And even in non-causality-violating FTL, you will still appear to travel back in time from some frames of reference. To be able to say which time travel is acceptable and which isn't, you need some sort of universal frame of reference - so you will only explode if you try to travel back in time according to the universal frame. But once you have a universal frame, it's easier to just not have any means of even getting close to time travel, rather than merely blowing up people who try.
"Though it's not anywhere near stellar-mass, I have a feeling that converting all of that matter into gamma rays would be some fraction of a Gamma Ray Burst."
A gamma ray burst produces about the same amount of energy as a supernova, 10^44 joules or 1 foe, only beamed in a more narrow direction so it appears to be more intense if you happen to be in the path of the beam. This equates 11 yottatons of matter-energy, which is in the range of a brown dwarf - 6 Jupiter masses, but only 0.0056 (1/179) of a Solar mass.
A WWII-in-SPACE! spaceship-sized mass-energy explosion would be 0.1 to 10 yottajoules (20 to 2000 teratons of TNT), which is in the range of a dino-killer (0.5 yottajoules) - big trouble if it happens on the surface of an inhabited planet, not really a concern in deep space.
Sabersonic said:"Now that I think of it, I'm not really sure if that flash of gamma rays is such a good idea to indicate an accidental passage through time. Though it's not anywhere near stellar-mass, I have a feeling that converting all of that matter into gamma rays would be some fraction of a Gamma Ray Burst."
Personally, I wouldn't want to be in the same star system as one of your ships that had an 'oopie!' :0
Ferrell
Milo - "Ouch. Run on sentence."
It was late and I wasn't sure how to word it otherwise.
As for Universal Frame, well I'm not even sure that's even possible with Special Relativity in the picture, let alone numerous extra-solar nations. Closest I could think of as a "Universal Time Frame" without resorting to an earth-centric view is by the lifetime of the Milky Way Galaxy and even then that's debatable.
"While most observers will agree that time travel took place at some point during the voyage (except for the observers on the ship itself), they will disagree on exactly when the first instance of time travel took place. And even in non-causality-violating FTL, you will still appear to travel back in time from some frames of reference."
I was thinking that something like that would have happened if I choose the "FTL Time Travel equals death" that those on the destination end would know that someone accidentally went backwards through time, but they don't know when or by whom. Which would be useful in preserving some sense of Causality since if one knows not only when the "accident" would occur but by what ship then it would cause a kind of paradox.
Of course, the whole "Time Travel is Relative" and all that is one reason why I didn't ask for a way to make my FTL idea Causality-safe. It's bad enough to know that, by Special Relativity, all FTL equates to time travel. Probably be (slightly) easier to just decree that one can't time travel via the Hyperspace Dive System, even though supporters of Special Realtivity and their mothers say that it can in theory.
"big trouble if it happens on the surface of an inhabited planet, not really a concern in deep space"
Probably a good reason why to have such destination points be Stellar-massed objects rather than stars.
Ferrel - "Personally, I wouldn't want to be in the same star system as one of your ships that had an 'oopie!'"
Unfortunately, the accident culminates in a Gamma Burst (not sure if "ray" would really be manifested) at the star system destination. That star's equatorial plane to be exact. Though then again, considering the mass swapping proposal to keep true the Conservation of Angular Momentum, the Gamma Explosion could occur at either end of the Dive. Though chances are I'm probably wrong on that one.
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All FTL is Just Plain Cheating. As someone who writes both Fantasy and SF, the usual rule is to just make your magic systems consistent and "relatable". Relatable meaning, your audience won't need a PhD in physics to understand what's happening in the story.
FTL and Hard SF are a Venn diagram with no overlap.
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