## Question about travelling faster than light.

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

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 Quote by PAllen then purely by Lorentz transform, you arrive back before you left.
Amazing! +
 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.

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 Quote by 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);
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.
 Quote by rjbeery and that beyond the EH time runs backwards from +inf from A's perspective.
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This is nonsense. Do you have reference?
 Quote by rjbeery 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).

 Quote by PAllen 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.
 Recognitions: Gold Member 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. [url]http://phys.org/news/2012-10-physicists-special-relativity.html looks like I got the link working http://rspa.royalsocietypublishing.org/content/early/2012/09/25/rspa.2012.0340.full.pdf+html

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 Quote by rjbeery ...... traveling at c at the EH. No G-P coordinates required.
What coordinates ARE you using at the event horizon? Not Schwarzchild - they don't work there.

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 Quote by rjbeery 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.]

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 Quote by PAllen 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 travelling 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 existance of the tachyon nor likely to do so lol. Just curious on how to interpret the above. Not to hijack the thread lol

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 Quote by Mordred looks like I got the link working http://rspa.royalsocietypublishing.o....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.

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 Quote by Mordred Brings up an interesting thought. As tachyons are often descibed as travelling 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 existance 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.

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 Quote by Nugatory 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.

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 Quote by PAllen 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.

 Quote by PAllen 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.
 Quote by PAllen 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 here you go.

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 travelled 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)

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 Quote by rjbeery 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.

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 Quote by rjbeery 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.