Question about travelling faster than light.

[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.

 

[SJBauer]

Tachyons are theoretical particles or waves that travel faster than the speed of light. Tachyons exist in a theoretical world where objects have negative mass. Negative mass is most easily define as a volume of negative density; i.e. -mass = volume * -density. Ergo negative mass density. This is preferable to calculations using invariant mass that involve the square root of a negative number, i.e., imaginary.

 

[PAllen]

Tachyons are theoretical particles or waves that travel faster than the speed of light. Tachyons exist in a theoretical world where objects have negative mass. Negative mass is most easily define as a volume of negative density; i.e. -mass = volume * -density. Ergo negative mass density. This is preferable to calculations using invariant mass that involve the square root of a negative number, i.e., imaginary.

Repeating a wrong doesn't make it right. There is no accepted definition of mass or energy for tachyons that comes out negative. Total energy and KE for a tachyon are positive. Mass (rest, invariant) is imaginary. Please do not repeat again a false statement.