Question about travelling faster than light.

[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.

 

[rjbeery]

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

You are right, I've never studied tachyons, thanks for the link. What I meant by "ambiguously interpreted" is that the causal order of their measurements is ambiguous as would be true with any two spacelike separated events. I was pointing out that an object moving into a past light cone does not have to have a spacelike world line.

 

[PAllen]

You are right, I've never studied tachyons, thanks for the link. What I meant by "ambiguously interpreted" is that the causal order of their measurements is ambiguous as would be true with any two spacelike separated events. I was pointing out that an object moving into a past light cone does not have to have a spacelike world line.

It either needs to move back in time or follow a spacelike path. Specifically, given two events A and B, with B not in A's past light cone, the only paths from B to the past of A are via a backwards time like path (its past and future are reversed compared to A), or a spacelike path. This follows from the the fundamental features of Minkowski geometry.

 

[PeterDonis]

What I meant by "ambiguously interpreted" is that the causal order of their measurements is ambiguous as would be true with any two spacelike separated events.

Ah, ok, that makes sense.

I was pointing out that an object moving into a past light cone does not have to have a spacelike world line.

An object can't move into a past light cone; to do that it would have to travel backwards in time, and it would have to do so in *every* reference frame.

[Edit: I see PAllen's response interprets "moving into a past light cone" more generally. My response is a sub-case of his, which is more general, and correct.]

 

[rjbeery]

An object can't move into a past light cone; to do that it would have to travel backwards in time, and it would have to do so in *every* reference frame.

Agreed! But this all stemmed from the concept of traveling faster than c, which was granted as an impossibility we were making an exception for. In the c=infinity graph, a negative slope (implying v > c) would have a world line traveling into its past light-cone. We cannot move faster than finite c any more than we can move faster than infinite c, but the point remains: claiming that "traveling faster than c is equivalent to traveling backwards in time" is a reasonable interpretation IMHO.

 

[PeterDonis]

But this all stemmed from the concept of traveling faster than c, which was granted as an impossibility we were making an exception for.

We only made the exception for the case of a finite c. The case of an infinite c is fundamentally different. See below.

claiming that "traveling faster than c is equivalent to traveling backwards in time" is a reasonable interpretation IMHO.

You're missing a key difference between the case of finite c and the case of infinite c. In the case of finite c, moving faster than c only appears as moving backwards in time in certain frames; there are other frames in which the faster than c movement still appears to go forward in time. "Faster than c" just means "emission and reception are spacelike separated", and spacelike separated events can still be dealt with theoretically even if we don't think tachyons are possible in reality.

In the case of infinite c, "faster than c" means moving backwards in time in *every* frame. Transforming between frames doesn't change the time coordinate at all. So there is no such thing as "spacelike separated" if c is infinite; there is only "forwards in time" (normal motion slower than c) and "backwards in time", which can't be allowed at all, not even as an "exception" to study theoretically.

 

[rjbeery]

We only made the exception for the case of a finite c. The case of an infinite c is fundamentally different. See below...

Wait a minute, you're allowing us to discuss unicorns but not leprechauns?

 

[PeterDonis]

Wait a minute, you're allowing us to discuss unicorns but not leprechauns?

Well, this thread was about unicorns; if you want to start a separate thread about leprechauns, go ahead. I'm just trying to make sure everyone understands which are the unicorns and which are the leprechauns.

 

[PeterDonis]

Wait a minute, you're allowing us to discuss unicorns but not leprechauns?

I'll put my more serious response here in a separate post. The OP of the thread said he didn't intend to have an unphysical discussion; he wanted to discuss what the implications were of assuming that tachyons were possible in a relativistic theory. That means a theory where c is finite; in such a theory you can indeed make the assumption and explore its implications. You can't even make the assumption to start with if c is infinite.

[Edit: This means I should have phrased my response a few posts ago differently; the words "making an exception" aren't a good description of what we're actually doing when we assume tachyons are possible in a relativistic theory with finite c. In my post #41 I summarized the implications; as I said there, the implications are considered by many to be physically unreasonable, but they're not impossible.]

 

[SJBauer]

Alright, working with your assumptions –
1. (I know this is impossible because we cannot create an infinite amount of energy but assume it is achievable)
2. 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)

Per your question, “once the object exceeds the speed of light time becomes negative so does that mean the object travels backwards in time?”

The answer is no because you are assuming Time has direction. Rather only our perception of Time has ennobled Time with a direction. Within the effects of SpaceTime, Time is just cause and effect. Ergo you cannot have the effect before the cause. What does go negative is the mass’ density – Which is assuming that the object can actually exceed the speed of light.

 

[PeterDonis]

What does go negative is the mass’ density – Which is assuming that the object can actually exceed the speed of light.

It's actually the *square* of the invariant mass (not "mass density") that is negative for a tachyon, *if* the normal energy-momentum relation is used (the one which gives a positive mass squared for ordinary timelike objects). The invariant mass itself is the square root of a negative number, i.e., imaginary.