What happens to time when a body reaches the speed of light?

[Nirav Chavda]

beyond "c" what happens?!

it is said that beyond speed of light the body is not defined hence there is no question of this body to exceed c.
Yet for the purpose of argument let's assume that we have acheived a way by which a body can be propelled to c.(lets say by zero point energy or by some negative energy creation or something smart)

then what will happen to the time passage to that body. will it become imaginary (this is concluded from einstein's equation) or will it become negative ??

 

[selfAdjoint]

Formally, if v > c, then the relativistic frame conversion factor
$$\gamma = \frac{1}{\sqrt{1- \frac{v^2}{c^2}}}$$
becomes complex, since the quantitiy subtracted under the square root is greater than the quantity subtracted from, and you therefore have the square root of a negative quantity. Physicists invented a hypothetical class of particles called tachyons; their mass is a pure imaginary, a multiple of $$\sqrt{-1}$$, they always traveled at speeds greater than c, and the energy for them to slow down to c increased toward infinity just as it does for us to accelerate to c. In the 1980s there were papers about these hypothetical particles and it was worked out that they would see time backwards from us. Gregory Benford, a physicist and sf writer, devised a hypothetical device for talking to the past he called the tachyonic telephone, and he used it in his classic sf novel Timescape.

Then the string theorists found tachyons in their bosonic strings. Considering them unphysical they were jubilant when perturbative superstring theory came along and was able to cancel the tachyons out. But, when non-perturbative M-theory was discovered, tachyons reappeared, and by this time physicists were able to deal with them. So tachyons, particles that travel faster than light, are a part of modern string theory, though I believe they don't show up in its bottom line.

 

[HallsofIvy]

"t" becomes negative. Exactly what negative t means is up you. Some people assert that that means moving back in time but I have never seen a good argument for that interpretation!

 

[JesseM]

"t" becomes negative. Exactly what negative t means is up you. Some people assert that that means moving back in time but I have never seen a good argument for that interpretation!

"t" in what equation becomes negative? Certainly FTL signals would lead to the possibility of sending information backwards in time, although maybe this isn't what you're talking about. But for the benefit of anyone who doesn't know the reasoning behind this, it has to do with the fact that different reference frames define simultaneity differently--if you have a signal that moves faster-than-light but forward in time (ie the event of the signal being received happens after the event of it being sent) in one frame, it will always be possible to find another inertial frame where the signal moved back in time (the event of the signal being received happened before the event of it being sent). Assuming the laws of physics work the same way in every reference frame, then if it's possible to send a signal back in time in some frame, it must be possible to do so in any frame, and this leads to the possibility of sending information backwards in time. If you and I are moving apart slower than light, then I can send a signal which moves FTL in my frame and back in time in your frame, and you can send a reply that moves FTL in your frame and back in time in my own, and by arranging the speeds correctly it will be possible for me to receive your reply before I send the original signal.

 

[quantumdude]

Yes, it's not "t", but "Δt" (the time interval between two events) that becomes negative. That's where the idea of going backwards in time comes from.