Question about travelling faster than light.

[Synchronised]

So when a moving object reaches the speed of light time dilates so I assume if an object that has mass somehow achieves the speed of light time stops moving (since it is traveling slower and slower) and once the object exceeds the speed of light time becomes negative so does that mean the object travels backwards in time? (I know this is impossible because we cannot create an infinite amount of energy but assume it is achievable)

 

[nitsuj]

So when a moving object reaches the speed of light time dilates so I assume if an object that has mass somehow achieves the speed of light time stops moving (since it is traveling slower and slower) and once the object exceeds the speed of light time becomes negative so does that mean the object travels backwards in time? (I know this is impossible because we cannot create an infinite amount of energy but assume it is achievable)

It's impossible for more than the energy issue.

Would need to read about SR and specifically about metrics. Going "back in time" is just going back in coordinate time. Not same as travel back in time to 1905, like time travel sci-fi. In other words the clock on board your spaceship wouldn't start ticking backwards...just think of the paradox there you would just keep being forced back in time to the point you started to travel ...back in time. lol oh imagination

 

[Nugatory]

So when a moving object reaches the speed of light time dilates so I assume if an object that has mass somehow achieves the speed of light time stops moving (since it is traveling slower and slower) and once the object exceeds the speed of light time becomes negative so does that mean the object travels backwards in time? (I know this is impossible because we cannot create an infinite amount of energy but assume it is achievable)

The question you have asked cannot be answered. It's like asking "If a pig could fly, would it be able to catch a bumblebee? I know this is impossible because pigs don't have wings, but assume that they do."

You might, however, try searching the web, wikipedia, and this forum for "tachyons", which are hypothetical faster-than-light particles with many interesting properties. Just be skeptical about the sources; there's a lot of over-simplified junk out there.

 

[Synchronised]

The question you have asked cannot be answered. It's like asking "If a pig could fly, would it be able to catch a bumblebee? I know this is impossible because pigs don't have wings, but assume that they do."

You might, however, try searching the web, wikipedia, and this forum for "tachyons", which are hypothetical faster-than-light particles with many interesting properties. Just be skeptical about the sources; there's a lot of over-simplified junk out there.

So it is simply impossible to 'travel back in time'.

 

[Nugatory]

So it is simply impossible to 'travel back in time'.

As far as we know so far, yes, it is impossible. If it ever turns out to be possible (and I would bet very very long odds against this) it won't be by somehow accelerating an object to the speed of light.

 

[WannabeNewton]

It depends on if you want to talk about observed reality as we know it now or possible pathological examples and also what you mean by "time travel". In a non time - orientable space - time you have point(s) where one cannot differentiate between future and past for example.

 

[rjbeery]

So when a moving object reaches the speed of light time dilates so I assume if an object that has mass somehow achieves the speed of light time stops moving (since it is traveling slower and slower) and once the object exceeds the speed of light time becomes negative so does that mean the object travels backwards in time? (I know this is impossible because we cannot create an infinite amount of energy but assume it is achievable)

You're getting answers that are being technical and not very "fun". The simplistic answer is that your speculation is correct, traveling faster than light could be considered to be the same thing as traveling backwards in time.

 

[nitsuj]

You're getting answers that are being technical and not very "fun". The simplistic answer is that your speculation is correct, traveling faster than light could be considered to be the same thing as traveling backwards in time.

The "fun" traveling back in time is the most remote, as in not even remotely possible.

 

[rjbeery]

The "fun" traveling back in time is the most remote, as in not even remotely possible.

Agreed, but the OP admitted that he understood the answer would lie outside of reality. Ya Grinch. :P

 

[nitsuj]

Agreed, but the OP admitted that he understood the answer would lie outside of reality. Ya Grinch. :P

Agreed

 

[ModusPwnd]

The simplistic answer is that your speculation is correct, traveling faster than light could be considered to be the same thing as traveling backwards in time.

How so? What simplifications are you making to conclude this? As far as I know its not a simplification, rather its flat out wrong. Its a conclusion that comes from misunderstanding the time dilation formula rather than a simplification. Is this not the case?

 

[Synchronised]

How so? What simplifications are you making to conclude this? As far as I know its not a simplification, rather its flat out wrong. Its a conclusion that comes from misunderstanding the time dilation formula rather than a simplification. Is this not the case?

Yes, time would become imaginary which is impossible.

 

[ModusPwnd]

Yes, time would become imaginary which is impossible.

Nor is imaginary time negative time, not under any simplification. The only reason I can see that people think going faster than light equates to going back in time is that they think its a simplification or 'close enough' to move the negative sign out of the square root and turn your imaginary number into a negative number. Other than this fallacy, where would anybody get this notion that traveling faster than light equates to going back in time?

 

[PAllen]

Nor is imaginary time negative time, not under any simplification. The only reason I can see that people think going faster than light equates to going back in time is that they think its a simplification or 'close enough' to move the negative sign out of the square root and turn your imaginary number into a negative number. Other than this fallacy, where would anybody get this notion that traveling faster than light equates to going back in time?

How about because FTL in one inertial frame is a back in time path in another? How about that if FTL exists, and the principle of relativity applies to it, then communication with the past is trivially possible. It's got nothing to do with imaginary anything.

 

[ModusPwnd]

Perhaps... I have never heard either of those as claims for why FTL in SR allows for time travel. Neither really is time travel. Not in the sense of the original post.

The notion I get from people and non-physics students is that they take the fact that time dilates as you approach "c" and conculde that time stops at "c" and then goes backwards when you are over "c". This is an error of course and is usually how I see the time travel idea in SR justified. Look at the original post, "once the object exceeds the speed of light time becomes negative ". Confusing imaginary time with negative time is the source of his error.

 

[PAllen]

Perhaps... I have never heard either of those as claims for why FTL in SR allows for time travel. Neither really is time travel. Not in the sense of the original post.

The notion I get from people and non-physics students is that they take the fact that time dilates as you approach "c", stops at "c" and then goes backwards when you are over "c". This is an error of course and is usually how I see the time travel idea in SR justified. Look at the original post, "once the object exceeds the speed of light time becomes negative ". Confusing imaginary time with negative time is the source of his error.

If you travel FTL in one frame, accelerate quickly to speed near c, and travel FTL back, then purely by Lorentz transform, you arrive back before you left. Just look up tachyon anti-telephone. Basically, if the Lorentz transform applies to FTL paths, and if FTL travel is possible in any frame, then travel to the past is possible. Since both of these assumptions are core to relativity, it is correct to say that relativity + FTL travel implies travel back in time.

FYI: I've never heard any other explanation than the above. Reputable books would never mention the nonsense argument you refer to. The above argument goes back a 100 years.

 

[rjbeery]

Perhaps... I have never heard either of those as claims for why FTL in SR allows for time travel. Neither really is time travel. Not in the sense of the original post.

The notion I get from people and non-physics students is that they take the fact that time dilates as you approach "c" and conculde that time stops at "c" and then goes backwards when you are over "c". This is an error of course and is usually how I see the time travel idea in SR justified. Look at the original post, "once the object exceeds the speed of light time becomes negative ". Confusing imaginary time with negative time is the source of his error.

Think in terms of tipping over light cones. We all agree that it's impossible, but the notion is not 100% without merit.

 

[ModusPwnd]

I'm not talking about reputable books. I'm talking about non-reputable people (no offense to the original poster :P)

 

[nitsuj]

then purely by Lorentz transform, you arrive back before you left.

Amazing! +

 

[rjbeery]

Under the Schwarzschild coordinate system and a classical analysis, the distant observer A could make the case that the infalling object B has a coordinate velocity of c at the EH; that this occurs at t=+inf; that beyond the EH B has a coordinate velocity > c (because B is still being accelerated); and that beyond the EH time runs backwards from +inf from A's perspective.

In other words, there is an interpretation of BH's which suggests that an infalling body reaches the singularity "before" it crosses the EH. Please discount all of the above with the caveat that we're being highly speculative with no "reality restrictions" here, but I have in fact seen an analysis of BH's done in this manner.

 

[PAllen]

Under the Schwarzschild coordinate system and a classical analysis, the distant observer A could make the case that the infalling object B has a coordinate velocity of c at the EH; that this occurs at t=+inf; that beyond the EH B has a coordinate velocity > c (because B is still being accelerated);

This much is true, but is mixed up. The coordinates in which you can say object falls through horizon at c and continues inside at > c are one set of coordinates (Gullestrand-Panlieve, for example). The coordinates that say t->+infinity on approach to horizon are different coordinates (Schwarzschild coordinates). So this mixes coordinates, and fails to note that coordinates only get meaning through computation of observables via the metric. In which case all these coordinate statement lose their exotic appearance. They are coordinate artifacts.

and that beyond the EH time runs backwards from +inf from A's perspective.

.
This is nonsense. Do you have reference?

In other words, there is an interpretation of BH's which suggests that an infalling body reaches the singularity "before" it crosses the EH. Please discount all of the above with the caveat that we're being highly speculative with no "reality restrictions" here, but I have in fact seen an analysis of BH's done in this manner.

Again, I've read many BH treatments, both popular and mathematical, both by scientists, science writers, and cranks, and I've not seen such claims. Would be interested in seeing a reference to a writer who is that loony.

The truth (per GR - who knows in the real world), is that clock falling through the horizon ticks forward normally through the horizon and up to the singularity. Light always appears to move at normal speed relative to this observer, locally. As for 'from the point of view of a distant observer', the only thing you can say physically is that the distant observer can never see or get any information about the history of the infaller crossing and beyond the horizon. So it is hard to know what 'point of view' [about these events they can't detect] to ascribe to them. Note, however, that the distant observer can send signals to the infaller that are received by the infaller (until the infaller reaches the singularity).

 

[rjbeery]

This much is true, but is mixed up. The coordinates in which you can say object falls through horizon at c and continues inside at > c are one set of coordinates (Gullestrand-Panlieve, for example). The coordinates that say t->+infinity on approach to horizon are different coordinates (Schwarzschild coordinates). So this mixes coordinates, and fails to note that coordinates only get meaning through computation of observables via the metric. In which case all these coordinate statement lose their exotic appearance. They are coordinate artifacts.

One thing at a time here. I'm still at work, technically! :)
If we consider the B's "coordinate velocity" to be A's calculation of the required escape velocity at that point then A would consider B to be traveling at c at the EH. No G-P coordinates required.

 

[Mordred]

This article is related to this post, it describes extending Einsteins theory to faster than speed of light using Lorenz transforms.

Thought some ppl may be interested in it I've been unable to get the original paper however.
http://phys.org/news/2012-10-physic...early/2012/09/25/rspa.2012.0340.full.pdf+html

 

[Nugatory]

... traveling at c at the EH. No G-P coordinates required.

What coordinates ARE you using at the event horizon? Not Schwarzschild - they don't work there.

 

[PAllen]

One thing at a time here. I'm still at work, technically! :)
If we consider the B's "coordinate velocity" to be A's calculation of the required escape velocity at that point then A would consider B to be traveling at c at the EH. No G-P coordinates required.

First coordinate velocity, now escape velocity. Escape velocity is the speed relative to a local static observer required to reach spatial infinity; or equivalently, the speed a free faller from infinity would have locally, relative to said static observer. There are no static observers at or inside the horizon, so the concept is undefinable, not c, or > c.

[edit: For the fanciful purposes of this thread, you can note that tachyons (any particle presumed to follow spacelike paths = > c) could escape from inside to outside and event horizon. However, that doesn't define any concept of escape velocity. Specific to escape velocity is the feature that a radial, timelike geodesic with escape velocity relative to some static observer has zero speed relative to a static observer in the limit at infinite distance. A spacelike geodesic that crossed the horizon would remain spacelike everyhwhere - i.e. it would still be moving FTL at infinity. Thus there is no possible concept of an object starting < c relative to static observer and getting to be > c relative to static observer. A timelike geodesic is timelike up to the singularity; a spacelike geodesic is spacelike everywhere. This is related to the notion that tachyons are as strongly prohibited from slowing down to c as normal particles are prohibited from reaching c.]

 

[Mordred]

This is related to the notion that tachyons are as strongly prohibited from slowing down to c as normal particles are prohibited from reaching c.]

Brings up an interesting thought. As tachyons are often descibed as traveling back in time. which brought up the law of causality. If by the above statement above. The tachyon would never be able to change its timeline vector either. So it could never violate its own spacetime causality Would it still violate causality in our spacetime?

I know they have never proven the existence of the tachyon nor likely to do so lol. Just curious on how to interpret the above. Not to hijack the thread lol

 

[Nugatory]

looks like I got the link working
http://rspa.royalsocietypublishing.org/content/early/2012/09/25/rspa.2012.0340.full.pdf+html

Wasn't this discussed here a few months back? I have a vivid memory of reading a thread about it somewhere, but can't find it right now.

 

[PAllen]

Brings up an interesting thought. As tachyons are often descibed as traveling back in time. which brought up the law of causality. If by the above statement above. The tachyon would never be able to change its timeline vector either. So it could never violate its own spacetime causality Would it still violate causality in our spacetime?

I know they have never proven the existence of the tachyon nor likely to do so lol. Just curious on how to interpret the above. Not to hijack the thread lol

This is an interesting point. The causality violated by a process using tachyons is causality along some timelike (normal) world line that sends tachyons to someone else and gets a reply back before they sent. Or, in the case of tachyon rocket, the rocket returns before it left - from the point of view of the world line it left. Causality along the tachyon path itself is undefined.

 

[PAllen]

Wasn't this discussed here a few months back? I have a vivid memory of reading a thread about it somewhere, but can't find it right now.

Here's the thread. It appears to be bunk.

https://www.physicsforums.com/showthread.php?t=642823

 

[Mordred]

Ah didn't know there was a thread already on that article

 

[nitsuj]

How about because FTL in one inertial frame is a back in time path in another? How about that if FTL exists, and the principle of relativity applies to it, then communication with the past is trivially possible. It's got nothing to do with imaginary anything.

Everything you said before "It's got nothing to do with imaginary anything" had everything to do with imagination.

 

[rjbeery]

Again, I've read many BH treatments, both popular and mathematical, both by scientists, science writers, and cranks, and I've not seen such claims. Would be interested in seeing a reference to a writer who is that loony.

First coordinate velocity, now escape velocity. Escape velocity is the speed relative to a local static observer required to reach spatial infinity; or equivalently, the speed a free faller from infinity would have locally, relative to said static observer. There are no static observers at or inside the horizon, so the concept is undefinable, not c, or > c.

If you're going to claim that Newtonian escape velocity has no meaning at the event horizon then you're either intellectually sandbagging or simply not being fanciful enough on an admittedly fanciful subject.

Considering time to move backwards within the event horizon is not difficult; pick a radius and keep it constant. I'm not here to convince you of this, I don't really care one way or the other, but you asked for other references so http://curious.astro.cornell.edu/question.php?number=652.

EDIT: That link seems to be flaky, sometimes it works and sometimes it does not. Below is the article...

What kind of time reversal takes place inside the event horizon of black holes?

Many people are fascinated by the famous "event horizon" of a black hole, the boundary of the region out of which nothing can escape. The mechanism that gives it this property is strange and amazing--it has to do with the idea of causality.

Merlin from the King Arthur legends was supposed to have lived his life backwards--the first thing he experienced was his death and the last was his birth, hence his ability to foretell the future. To us, however, time feels as though it flows only forward. This feeling actually comes from the more general property of causality. In a region like the one here on Earth, you can only remember events that meet 2 criteria: (1) it has to have been in the past, and (2) it has to have happened at a distance no more than what light could have traveled since it happened. The second rule is just the familiar light speed limit. The first is called causality, and it's why you won't meet anyone like Merlin here at home.

Here comes the strange part. General relativity (that same theory supported by so many experiments and needed to make the GPS system work) predicts that, simply by compressing any piece of matter down enough to make a black hole, you create a region where this just isn't true. Inside the event horizon, time and space change places. Therefore the new restrictions go like this: in order for you to remember something, (1) it has to have happened farther from the center of the black hole than where you are now, and (2) if T is the time that it would take light to travel to you from the location of the event, then it happened either no more than T hours ago or T hours into the future.

I recommend thinking about this at least until your head starts to hurt. First of all, note that restriction #1 prevents you from moving away from the center of the black hole, and therefore from going back across the event horizon. Also note that it says "farther", not "at least as far". This means that not only can't you move away from the center, you can't even stand still. Also we see that everyone inside the event horizon is a psychic. This happens because light can travel to you from events in the future, so you can quite literally see them. You can't see anything closer to the center than you are because light can't travel away from the center. If you look away from the center, though, you see two images of everything--one from T hours in the past and one from T hours in the future. For nearby objects, these two images will look just the same, since T will be very small due to the large speed of light. For faraway objects, though, they could be completely different. For instance, if both you and Tolstoy were in a black hole and were separated by 3 light years, you could be watching him start and finish War and Peace at once. At that point in time, he would only be done with half of the book. Of course, you'd want to try sending him a message with the text of the book, to save him some work writing it, but you couldn't--he can't see you at all, since you're closer to the center of the black hole than he is. Pity.

If you think about it for a while, you'll be able to come up with loads of strange situations that can happen inside a black hole--but none of them will be logically inconsistent (such as would be the case if you had been able to send Tolstoy the last chapter of his book before he had written it). There are even more when you consider that realistic astronomical black holes should actually have 2 event horizons--the causality flip discussed above happens at the outer event horizon, and then flips back at the inner event horizon.

January 2005, Sara Slater (more by Sara Slater) (Like this Answer)​

 

[PeterDonis]

Think in terms of tipping over light cones.

"Tipping over light cones" only happens in curved spacetime (in fact it's one way of describing what spacetime curvature *is*). It's a completely separate concept from "traveling faster than light", which can be analyzed purely in flat spacetime.

 

[PeterDonis]

Considering time to move backwards within the event horizon is not difficult; pick a radius and keep it constant.

No, this doesn't work, because inside the EH, a curve of constant radius is spacelike, not timelike. So there's no such thing as "time" along such a curve.

 

[PeterDonis]

Inside the event horizon, time and space change places.

This is only true in a particular coordinate chart, the interior Schwarzschild chart. It is not true in other charts. Also, it is not necessary to ground the further statements made; see below.

Therefore the new restrictions go like this: in order for you to remember something, (1) it has to have happened farther from the center of the black hole than where you are now, and (2) if T is the time that it would take light to travel to you from the location of the event, then it happened either no more than T hours ago

All of this is correct, *and* it is independent of any coordinate chart; and it does *not* require that "time and space change places".

or T hours into the future.

This is *not* correct, and I don't understand where the author is getting it from. Light signals have to move inward inside the horizon, just like everything else. There's no way for light "from the future", meaning at a smaller radius, to get to you at a larger radius. It *is* possible for you to see light that was emitted "below" you, if it was emitted radially outward; but that's because you "catch up" to the light, i.e., you decrease in radius faster than the light does. That doesn't mean the light was emitted "in the future" relative to you; that's impossible.

You can't see anything closer to the center than you are because light can't travel away from the center.

No, but you *can* "catch up" to light emitted radially outward from someplace "below" you. See above.

If you look away from the center, though, you see two images of everything--one from T hours in the past and one from T hours in the future.

Again, I don't know where the author is getting this from. It is true that there are light paths which go "around" the hole, so you can in fact see multiple images from the same source, which have gone around the hole different numbers of times. But none of those images come from "the future". (Also, such light paths are not purely radial, obviously, since they go around the hole. That makes them more complicated to analyze, and I don't think the author fully appreciates those complications.)

For instance, if both you and Tolstoy were in a black hole and were separated by 3 light years, you could be watching him start and finish War and Peace at once.

Possible, yes, but only if both events were in your *past* light cone. This should be obvious, since you're watching them both.

At that point in time, he would only be done with half of the book.

Nope--both events ("start the book" and "finish the book") are in your past light cone, so "at that point in time", *every* event on Tolstoy's worldline between the two events must also be in your past light cone, including the one where he is halfway done.

Also, since all of those events are on Tolstoy's worldline, they are all timelike separated, so there is *no* "point in time" by *anyone*'s clock which contains more than one of them.

Of course, you'd want to try sending him a message with the text of the book, to save him some work writing it, but you couldn't--he can't see you at all, since you're closer to the center of the black hole than he is.

Which also means that *none* of the events on his worldline are in your future--events in your future are all closer to the center of the hole than you, and Tolstoy is not. I think this person is failing to completely analyze their own scenario.

There are even more when you consider that realistic astronomical black holes should actually have 2 event horizons--the causality flip discussed above happens at the outer event horizon, and then flips back at the inner event horizon.

It is true that rotating holes and charged holes have two horizons, not one, but "causality flip" is an erroneous way to describe what happens at those horizons. See above.

 

[rjbeery]

Good God, you guys are putting a lot of effort into proving that unicorns don't exist. How about this: make a standard graph with Length as the horizontal and Time as the vertical axes. Velocity would be represented as the slope of a world line, with a horizontal world line representing light. Now, extend the slope to be negative, and you can clearly see a quick-and-dirty analogy as to why traveling faster than c would be equivalent to traveling backwards in time.

 

[Nugatory]

Good God, you guys are putting a lot of effort into proving that unicorns don't exist. How about this: make a standard graph with Length as the horizontal and Time as the vertical axes. Velocity would be represented as the slope of a world line, with a horizontal world line representing light. Now, extend the slope to be negative, and you can clearly see a quick-and-dirty analogy as to why traveling faster than c would be equivalent to traveling backwards in time.

If time is horizontal and length is vertical, then a 45-degree diagonal line x=t (x=ct, and we'll make life easier by agreeing to measure time in seconds and distance in light seconds so that c=1) corresponds to a light signal traveling at the speed of light.

The faster than light travel paths are the ones that leave the origin with positive slope between 0 and 1; and negative slope between -1 and 0 (for travel to the left, in the -x direction).

The horizontal line corresponds to a completely meaningless infinite coordinate velocity.

 

[rjbeery]

If time is horizontal and length is vertical, then a 45-degree diagonal line x=t (x=ct, and we'll make life easier by agreeing to measure time in seconds and distance in light seconds so that c=1) corresponds to a light signal traveling at the speed of light.

The faster than light travel paths are the ones that leave the origin with positive slope between 0 and 1; and negative slope between -1 and 0 (for travel to the left, in the -x direction).

The horizontal line corresponds to a completely meaningless infinite coordinate velocity.

No. This is my graph with my axes, and I declare that c=infinity for this exercise, just as you arbitrarily declared c=1. The point is that if slope represents velocity on this graph then traveling backwards in time would have a negative slope...which is faster than c. If one more person tries to explain why this isn't possible I'm going to have an aneurysm, I'm done trying to hold peoples' hands on this. This is exactly why I originally said you guys were giving the OP technical answers that were lacking in "fun"...sheesh!

 

[PeterDonis]

This is exactly why I originally said you guys were giving the OP technical answers that were lacking in "fun"...sheesh!

If you don't want to play by the rules of actual physics, then you should stop bringing in references that are trying to play by the rules of actual physics. You're the one that brought in the discussion about event horizons and black holes, for example, which makes no sense if you're just trying to give "fun" but obviously unphysical answers to the OP.

(In any case, I'm not sure the OP intended to have a "fun, but unphysical" discussion. I think he was trying to ask a question about actual physics; he simply misunderstood the actual physics he was asking about.)

 

[Synchronised]

(In any case, I'm not sure the OP intended to have a "fun, but unphysical" discussion. I think he was trying to ask a question about actual physics; he simply misunderstood the actual physics he was asking about.)

I did not intend to have an unphysical discussion. Since Cern and Gran Sasso claimed neutrinos travel FTL someone on YouTube tried to explain the impact of this discovery if it was true and he said if we can travel faster than light we can travel backwards in time so I was just wondering whether this statement is correct of not.

 

[PeterDonis]

I did not intend to have an unphysical discussion.

I didn't think you did, but I appreciate the confirmation.

Since Cern and Gran Sasso claimed neutrinos travel FTL someone on YouTube tried to explain the impact of this discovery if it was true and he said if we can travel faster than light we can travel backwards in time so I was just wondering whether this statement is correct of not.

I may be repeating things that have already been said in this thread, but just to summarize briefly:

(1) If a particle can travel faster than light, then there will be some inertial frames in which the time of emission of the particle will be *later* than the time of reception, rather than earlier. This can be interpreted as the particle "traveling backwards in time". But this will always be frame-dependent; there will always be other frames in which the time of emission is earlier than the time of reception.

(2) If the particle's FTL speed is determined relative to the emitter--i.e., if the particle's speed is always the same v > c in the emitter's rest frame--and if the FTL particles can be used to send information signals, then it is possible to have a closed loop of information signals: that is, a piece of information can arrive at the sender before it is sent (if the receiver/emitter that reflects back the FTL signal is moving fast enough relative to the original sender who receives the return signal). This is widely considered to be physically unreasonable, but it is possible to construct logically consistent scenarios where this happens (at the cost of constraining the "free will" of persons in the scenario).

(3) If the particle's FTL speed is determined relative to some fixed inertial frame--i.e., if the particle's speed is always the same v > c relative to, say, the rest frame of the Sun, regardless of how the emitter is moving relative to the Sun--then it is not possible to have closed information loops as in #2. However, such a law for determining the particle's FTL speed involves a "preferred frame"--one particular inertial frame is "special" compared to all the others--and this is also widely considered to be physically unreasonable. But again, it is possible to construct logically consistent scenarios where this happens; though in these scenarios, things will still look highly counterintuitive in some inertial frames (since, by #1 above, there will always be *some* frames in which the FTL particles appear to go backwards in time, even if closed information loops are not present).

The upshot is that, because FTL particles imply either #2 or #3, and both #2 and #3 are widely considered to be physically unreasonable, FTL particles are widely considered to be physically unreasonable. But "physically unreasonable" is not the same as "logically impossible".

 

[rjbeery]

I didn't think you did, but I appreciate the confirmation.



I may be repeating things that have already been said in this thread, but just to summarize briefly:

(1) If a particle can travel faster than light, then there will be some inertial frames in which the time of emission of the particle will be *later* than the time of reception, rather than earlier. This can be interpreted as the particle "traveling backwards in time". But this will always be frame-dependent; there will always be other frames in which the time of emission is earlier than the time of reception.

(2) If the particle's FTL speed is determined relative to the emitter--i.e., if the particle's speed is always the same v > c in the emitter's rest frame--and if the FTL particles can be used to send information signals, then it is possible to have a closed loop of information signals: that is, a piece of information can arrive at the sender before it is sent (if the receiver/emitter that reflects back the FTL signal is moving fast enough relative to the original sender who receives the return signal). This is widely considered to be physically unreasonable, but it is possible to construct logically consistent scenarios where this happens (at the cost of constraining the "free will" of persons in the scenario).

(3) If the particle's FTL speed is determined relative to some fixed inertial frame--i.e., if the particle's speed is always the same v > c relative to, say, the rest frame of the Sun, regardless of how the emitter is moving relative to the Sun--then it is not possible to have closed information loops as in #2. However, such a law for determining the particle's FTL speed involves a "preferred frame"--one particular inertial frame is "special" compared to all the others--and this is also widely considered to be physically unreasonable. But again, it is possible to construct logically consistent scenarios where this happens; though in these scenarios, things will still look highly counterintuitive in some inertial frames (since, by #1 above, there will always be *some* frames in which the FTL particles appear to go backwards in time, even if closed information loops are not present).

The upshot is that, because FTL particles imply either #2 or #3, and both #2 and #3 are widely considered to be physically unreasonable, FTL particles are widely considered to be physically unreasonable. But "physically unreasonable" is not the same as "logically impossible".

#1 seems suspect to me. Is there a theoretical frame in which tachyons (if they were to exist) are not moving backward in time?

 

[Nugatory]

#1 seems suspect to me. Is there a theoretical frame in which tachyons (if they were to exist) are not moving backward in time?

Yes. The endpoints of any faster-than-light journey are space-like separated.

Example: Tachyon travels from here to Alpha Centauri at a speed of 2c in a frame in which Earth and Alpha Centauri are at rest. In that frame, Earth and AC are separated by about four light years, so the journey takes about two years, and the tachyon arrives two years after it left. If the tachyon were carrying a newspaper, the news would be two years old when it arrived.

Now there is something special about the tachyon's behavior as observed in some frames. For example, an observer in a spaceship passing by at a sufficiently high velocity relative to Earth and AC might conclude that the arrival event happened before the departure event. This is only possible with space-like separations such as those between the endpoints of a tachyonic journey. But it is a real stretch to call that traveling backwards in time.

[Edit: I really strongly recommend that you try playing with the Lorentz transforms to see if you can find the speed of the passing spaceship, relative to the Earth and AC, such that in a frame in which the spaceship is at rest, the departure and arrival events of the tachyon are simultaneous. Until you can do that exercise (very basic algebra once you've set the problem up correctly, the challenge is learning how to set the problem up) you will be totally at the mercy of the pop-sci writers who spew out cool-sounding but deeply misleading hand-wavy explanations]

 

[Nugatory]

No. This is my graph with my axes, and I declare that c=infinity for this exercise, just as you arbitrarily declared c=1.

I don't understand how you can declare c=infinity - we've measured the speed of light, we know what it is, and we know that it's not infinity. I can choose to use units of miles and seconds, so c=186,000, or light-seconds and seconds so c=1, or meters and seconds, so c=3x10⁸ or furlongs per fortnight so c=1.8x10¹²; but there is no choice of units that will allow c=infinity.

[Edit: Someone with too much time on their hands might consider checking my calculation using the FF units ]

 

[Mordred]

I'd like to know how he would graph c=infinity on a graph paper lol.

 

[Nugatory]

I'd like to know how he would graph c=infinity on a graph paper lol.

Actually, it is possible on the x-t graph that he's describing; on those graphs velocities are represented by the reciprocal slope of the tangent to a curve. So an infinite velocity can be drawn as a horizontal line. The problem is something else: c isn't infinite, so that horizontal line doesn't tell us anything about hypothetical superluminal but finite velocities.

 

[Mordred]

ah KK makes sense its something I've never done lol but then again i study physics for enjoyment lol

 

[PeterDonis]

#1 seems suspect to me. Is there a theoretical frame in which tachyons (if they were to exist) are not moving backward in time?

Yes, of course. Naty1 gave a good example.

 

[rjbeery]

Yes. The endpoints of any faster-than-light journey are space-like separated.

This is not necessarily true. In my c=infinity graph moving faster than c would put the tachyon's endpoint in our past light cone which is not space-like separated. I've never heard that tachyons could be ambiguously interpreted to have space-like separated emission/absorption points.

 

[PeterDonis]

This is not necessarily true.

Yes, it is; it's part of the *definition* of a tachyon.

In my c=infinity graph moving faster than c would put the tachyon's endpoint in our past light cone which is not space-like separated.

Your c = infinity graph is irrelevant to any discussion of tachyons, because if c = infinity then it's impossible for anything to travel faster than c, so there is no useful concept of "tachyons". There are also no useful concepts of "light cones" or "spacelike separation" at all. All of those concepts only make sense if c is finite.

I've never heard that tachyons could be ambiguously interpreted to have space-like separated emission/absorption points.

Then you haven't read much about tachyons. See, for example, here:

http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/tachyons.html

Btw, I don't understand why you use the phrase "ambiguously interpreted". There's no ambiguity at all about whether two events are spacelike separated.