Question about travelling faster than light.

PAllen

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

Ah, ok, that makes sense.

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

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

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

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

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

PeterDonis

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

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 travelling 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

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

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.