Will The Theory of Relativity allow me to travel Backwards in Time?

  • #51
PeterDonis
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So Lorentz invariance, as you understand it, means that the two views should be ok, but in fact only one is and the other is not.
I think that's an acceptable way of putting it.

That is a non sequitur. At leat there is another possibility: Lorentz invariance, as you understand it, is wrong.
Which would not refute what I said; I said "Lorentz invariance says this scenario is not possible". Obviously if Lorentz invariance is wrong then one can no longer use it to say the scenario is not possible. I have already said that several times. But Lorentz invariance has been verified by countless experiments, so it is certainly not just wrong. It is possible that Lorentz invariance is violated in ways we can't (yet) measure; we won't know for sure until we can make more accurate measurements, over a wider domain.

You are assuming that relativity, when stressed under the tension of FTL, brings about two contradictory situations; hence you kill the messenger, you rule out FTL travel. Instead I assume that relativity, in face of FTL travel, only seems to offer contradictory explanations; hence I infer that those explanations are not really contradictory, so I reinterpret them.
This only works if you exclude "Lorentz invariance" from "relativity". But how do you justify that, when Lorentz invariance is a fundamental feature of the theory? Both SR and GR include Lorentz invariance (local Lorentz invariance, in the case of GR, but that's enough for what we're discussing here). You can't "reinterpret" SR or GR to change that; the Lorentz invariance of SR and GR makes definite physical predictions, which for the scenario we've been discussing are the ones I've described. There's no way to alter those predictions without altering the theory.

So if you are admitting the possibility that Lorentz invariance is wrong, you are basically saying we can't use SR or GR to analyze this situation. If that's the case, all bets are off: we can't say anything about it at all unless you can offer some alternative theory that matches all the experimental predictions of SR and GR in the domains where they've been verified, but also allows violation of Lorentz invariance and consequent FTL travel in a situation like we've been discussing.

For this purpose, my epistemological approach is quite a down-to-earth one, apparently not clashing with scientific method. I am saying that the meaning of our concepts (in our discussions, the spacetime coordinates associated to events) is determined by why and how they are in practice set up, that is to say, for which practical purpose and on the basis of which empirical measurement activities.
I don't think I disagree with this as a general statement, in so far as I can parse a meaning from it at all. But for any specific case, how you actually make the connections between concepts and empirical measurements is theory-dependent. If you fix the theory, you fix the connection; conversely, if you want to change the connection, to change, for example, how an observer would "interpret" the light signals he receives that seem to indicate physically unreasonable consequences under standard SR, you have to change the theory.

Why period? You mean, “for no reason and hence without any domain of applicability”?
Of course not. The reason is that it is required by the logical structure of the theory; you can't change it without changing that logical structure, and hence changing the theory. The domain of applicability is at least as large as the domain of all the experiments that have been done that have confirmed the theory's predictions. It may be larger than that; we won't know for sure, as I said, until we've done more experiments over a wider domain. Obviously nobody has yet done direct experiments with rockets traveling at relativistic velocities, nor has anyone actually observed spacelike separated events that are causally connected. So the domain we're discussing here is definitely not part of the domain in which SR and GR have been experimentally confirmed. I've never suggested otherwise.

In my thought experiment, I did not include any unreasonable result, did I?
I didn't say you did. I said only that what you did specify in that thought experiment, combined with the logical structure of SR, leads to physically unreasonable consequences. If you want to reject the conclusion, you have only two alternatives:

(1) Change the specifications of the thought experiment so that, combined with the logical structure of SR, they do not lead to physically unreasonable consequences. The only way to do that is to eliminate the FTL travel--i.e., to ensure that no pair of spacelike separated events are ever causally connected.

(2) Change the theory: stop using standard SR and start using some other theory, with a different logical structure, that leads to different consequences, physically reasonable ones, when combined with the specifications you gave. I have no objection to taking this option in principle, but it doesn't mean much unless you have such an alternative theory. It doesn't seem like you do; and without it, we can't have a useful discussion because we don't have a set of common premises to start from.

You appear to think that there is a third option: keep the specs as they are, keep SR as it is, but somehow "reinterpret" things so the physically unreasonable consequences don't happen. That's not a possible option: the predictions of physically unreasonable consequences, which I have spent quite a bit of time now elucidating, don't depend on "interpretation". They are straightforward logical consequences of SR plus the assumption that any pair of spacelike separated events can be causally connected. Here "SR" does include the physical meaning we assign to coordinates in particular inertial frames in which particular observers are at rest. But as I said above, that's part of the theory; you can't change it without changing the theory's predictions, which means changing the theory.
 
  • #52
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Hi, PeterDonis and Saw. I think your discussion would be more definitive if you first specify a special relativity model to establish a context for the comments. For example, you could specify either a Lorentz Ether model or a Block Universe model--the discussion follows quite different lines, depending on which model you select, because those two models lead to different meanings of causality. I suppose there may be other models as well.

If you opt for the concept that we cannot specify a model, then you might not be able to draw any conclusions (perhaps that's where you've arrived).
 
  • #53
PeterDonis
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Hi, PeterDonis and Saw. I think your discussion would be more definitive if you first specify a special relativity model to establish a context for the comments. For example, you could specify either a Lorentz Ether model or a Block Universe model--the discussion follows quite different lines, depending on which model you select, because those two models lead to different meanings of causality.
Hi bobc2! Can you elaborate on the above? How would you deal with the given scenario under either or both of the models you mention? (I take it that you agree with my description of how "standard SR" deals with the scenario.)
 
  • #54
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Hi bobc2! Can you elaborate on the above?
I hate to get very far into this, because it soon leads into the kinds of speculations that are not appropriate for this forum. But, in the case of the block universe concept alluded to by a number of reputable physicists, we just have a 4-dimensional universe populated by 4-dimensional objects. The objects (4-D elementary particles and collections of particles) are represtented by their worldlines extending for vast distances along the 4th dimension--perhaps 10^13 miles, etc.). One fundamental issue to grapple with before applying this model to questions of faster-than-light travel is, "What is the meaning of causality?" Then there are other questions having to do with allowable geometric patterns and consciousness and the fundamental nature of time.

The 4-D objects are "just there". "Things don't happen, they just are" (to represent sentiments expressed by Weyl and Eddington). This means that you would not examine the plausibility of time travel from the standpoint of the usual causality considerations. One approach to a problem would be to draw a GR space-time diagram of a contemplated time travel scenario, then ask yourself whether the resulting worldlines are plausible.

You might decide that any such worldlines must be a possible solution to Einstein's equations. Of course Kurt Godel found such an example. But this is as far as the discussion has been carried in the literature (so far as I know). To understand what you are really describing in terms of a time traveler, you must carry the analysis further, and this then begins the speculations upon which I fear to tread. If the 4-D object is there, who or what is doing the traveling? The objects are all static, i.e., no motion--no traveling. Is consciousness some king of unidentifyable 3-D entity that travels at the speed of light along a worldline (representing a bundle of 4-D neurons)?

If one decides that consciousness travels along the worldline at the speed of light, this is a concept that might be consistent with timelike worldlines, but we have no basis for knowing whether there would even be a consciousness associated with a worldline looping back along a negative 4th dimension direction.

Once accepting a model of 4-D static objects embedded in the 4-D static unverse (the manifold?), you are free to question the laws of physics. Manifestly, the pattens of worldlines are not determined by F = ma, etc. The pattern is just there. You could weave a blanket using a set of rules that results in a very beautiful static object with interesting patterns. The rules you used had to do with geometric relationships--there was no F = ma involved.

Although there may be a "big bang" location on the 4-dimensional static unverse, it's just another geometric feature--not an event from which dynamic interactive processes evolve through causal interactions (that is, assuming the block universe model). But, how was the blanket of the 4-D universe created? What geometric rules were followed? Could there be exceptions to the rules?

I wanted to avoid the speculations, so I'll just leave it at that.

How would you deal with the given scenario under either or both of the models you mention? (I take it that you agree with my description of how "standard SR" deals with the scenario.)
 
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  • #55
PeterDonis
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The objects (4-D elementary particles and collections of particles) are represtented by their worldlines extending for vast distances along the 4th dimension
But that's part of the point--in the case of FTL travel, a portion of the worldline of some object is spacelike, not timelike. That means there is some frame in which that portion of the worldline has *no* extension in the "4th dimension". More generally, it means that segment of the wordline has a fundamentally different character than the others--it has a spacelike tangent vector instead of a timelike one.

The fundamental issue to grapple with before applying this model to questions of faster-than-light travel is, "What is the meaning of causality?"

The 4-D objects are "just there". "Things don't happen, they just are" (to represent sentiments expressed by Weyl and Eddington). This means that you would not examine the plausibility of time travel from the standpoint of the usual causality considerations. One approach to a problem would be to draw a GR space-time diagram of a contemplated time travel scenario, then ask yourself whether the resulting worldlines are plausible.
That is basically the point I have been making: if you accept Lorentz invariance and the rest of standard SR (regardless of which "interpretation" you use), a causal curve with a spacelike portion is not plausible. If you are willing to violate Lorentz invariance, then it may or may not be plausible; it depends on what alternate theoretical principle you put in place of Lorentz invariance and how it affects the rest of the theory.

Of course Kurt Godel found such an example.
Godel's solution contained closed *timelike* curves (CTCs). It did not contain causal curves that were spacelike. However, one consequence of the CTCs, AFAIK, is that there are pairs of spacelike separated *events* in a Godel universe that are causally connected (by means of a timelike curve that goes around a "loop", so to speak, from one to the other, rather than taking the "direct" spacelike route between them). So it is possible that the question of whether a solution like Godel's with CTCs is "plausible" is at least related to the question of whether spacelike causal curves are plausible.

Once accepting a model of 4-D static objects embedded in the 4-D static unverse (the manifold?), you are free to question the laws of physics.
Only to the extent that questioning the laws does not imply changing the manifold. If we are talking about flat Minkowski spacetime, then you at least have to restrict yourself to laws of physics that are consistent with flat Minkowski spacetime. If you are talking about manifolds that are solutions to the EFE, then you at least have to restrict yourself to laws of physics that are consistent with the EFE.
 
  • #56
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But that's part of the point--in the case of FTL travel, a portion of the worldline of some object is spacelike, not timelike. That means there is some frame in which that portion of the worldline has *no* extension in the "4th dimension". More generally, it means that segment of the wordline has a fundamentally different character than the others--it has a spacelike tangent vector instead of a timelike one.

That is basically the point I have been making: if you accept Lorentz invariance and the rest of standard SR (regardless of which "interpretation" you use), a causal curve with a spacelike portion is not plausible. If you are willing to violate Lorentz invariance, then it may or may not be plausible; it depends on what alternate theoretical principle you put in place of Lorentz invariance and how it affects the rest of the theory.

Godel's solution contained closed *timelike* curves (CTCs). It did not contain causal curves that were spacelike. However, one consequence of the CTCs, AFAIK, is that there are pairs of spacelike separated *events* in a Godel universe that are causally connected (by means of a timelike curve that goes around a "loop", so to speak, from one to the other, rather than taking the "direct" spacelike route between them). So it is possible that the question of whether a solution like Godel's with CTCs is "plausible" is at least related to the question of whether spacelike causal curves are plausible.

Only to the extent that questioning the laws does not imply changing the manifold. If we are talking about flat Minkowski spacetime, then you at least have to restrict yourself to laws of physics that are consistent with flat Minkowski spacetime. If you are talking about manifolds that are solutions to the EFE, then you at least have to restrict yourself to laws of physics that are consistent with the EFE.
Excellent points, PeterDonis. And I agree with everything you are saying here within the context you've adapted. However, I'm not sure we can apply your laws of physics criteria--not really knowing the rules for weaving the 4-D universe blanket, not knowing the rules used for coupling consciousness to the worldlines, and not knowing the rules involving the fundamental nature of time, and not knowing whether exceptions (and what kinds of exceptions) to the basic rules are possible.
 
  • #57
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Richard Feynman: "Why nature is mathematical is a mystery...The fact that there are rules at all is a kind of miracle."
 
  • #58
PeterDonis
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I'm not sure we can apply your laws of physics criteria
In general I agree; we have laws that seem to accurately predict experimental results within their domains, but that in no way guarantees that (a) those laws' predictions will continue to be confirmed as the domain of our experiments widens, or (b) that there is not some other set of laws that also can match experimental results in the known domains, while also predicting different results than our current laws in a wider domain.

My comments were more specifically directed at the case where we have already accepted at least some minimal set of laws: "Once accepting a model of 4-D static objects embedded in the 4-D static unverse (the manifold?)". That model itself restricts the laws you can consider. There may be other sets of laws that do not even use the concept of 4-D objects embedded in a 4-D manifold, but you can't consider them if you have already adopted the 4-D model.
 
  • #59
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In general I agree; we have laws that seem to accurately predict experimental results within their domains, but that in no way guarantees that (a) those laws' predictions will continue to be confirmed as the domain of our experiments widens, or (b) that there is not some other set of laws that also can match experimental results in the known domains, while also predicting different results than our current laws in a wider domain.

My comments were more specifically directed at the case where we have already accepted at least some minimal set of laws: "Once accepting a model of 4-D static objects embedded in the 4-D static unverse (the manifold?)". That model itself restricts the laws you can consider. There may be other sets of laws that do not even use the concept of 4-D objects embedded in a 4-D manifold, but you can't consider them if you have already adopted the 4-D model.
Good points, as always. It would still be interesting to know (assuming the block model) how the blanket appeared. Did it organize itself as a result of some unknown natural influences that are intrinsic to nature (thus, forcing upon us a set of physical laws), or was it created out of some mysterious process that is perhaps unknowable to the occupants of the fabric (thus, having a set of rules that are not necesarily followed in every detail of the fabric).

But, I yield to the expert on these matters.
 

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