Hypothetical Velocity Faster Than C: Exploring Relativity

[frost_zero]

I know it isn't possible for any mass/massless body to have velocity more than the speed of light in vacuum but what if it was done hypothetically?
As far as I know length and time of an object undergo a transformation so that the laws of physics remain same between observers at rest and observers in uniform motion
with the length parallel to direction of motion changing to LII = L√1-(v^2/c^2)
And the time of the body relative to others changing to t = t0/√1-(v^2/c^2)
here if the velocity was 2c then it would give us L|| = L√-3
I don't have much idea about complex numbers but if it hypothetically happened then what would happen to the length?
Similarly what would happen to the time? Could there be a transformation such that the laws remain same under uniform motion and rest and also allow velocities more than c? I am new to relativity and its concepts so it may not be 100% correct.

 

[PeroK]

Hypothetical particles that travel faster than ##c## are called tachyons:

https://en.wikipedia.org/wiki/Tachyon

You can certainly study these and deduce some properties, such as a tachyons having negative energy in some inertial frame.

I'm not sure it makes much sense to try to apply the Lorenz transformation to get the frame of reference of a tachyon in terms of imaginary times and lengths.

 

[Drakkith]

Look at your transformation equation. When the velocity is greater than c you get a negative number inside the square root, which requires an imaginary number to solve. What does an apparent length of, say, 2i even mean? Did the object appear to turn inside out? Backwards? Rotated?

It doesn't make any sense. So either the equation doesn't apply to objects exceeding the speed of light, there's a useful and accurate way to make sense of a length with an imaginary number, or nothing can exceed the speed of light.

 

[Orodruin]

I know it isn't possible for any mass/massless body to have velocity more than the speed of light in vacuum but what if it was done hypothetically

Tachyons have been mentioned, but note that they are not ordinary particles in any shape or form (if they even exist). Apart from that, your question applied to regular matter is a non-starter. You are asking for a prediction of what would happen according to a theory if something that cannot happen in that theory happens.

 

[fresh_42]

I trust the math and the Lorentz transformations show that there is no way from slower to faster than light, because of the singularity. However, the complex numbers are so deeply interwoven in our reality as we describe it, i.e. they show up in physics and mathematics all the time, that they are the truly real and natural numbers. So I wouldn't rule out the existence of tachyons in our current state of knowledge.

The last statement is only an opinion and pure speculation, so I breached our rules with that sentence. All I have is the evidence complex numbers provide in all the rest of physics.

I close this thread as this seems to be the only possible direction such a discussion can have. All other factual issues have been addressed, so the question can be considered as answered.

 

[Nugatory]

As far as I know length and time of an object undergo a transformation so that the laws of physics remain same between observers at rest and observers in uniform motion
with the length parallel to direction of motion changing to LII = L√1-(v^2/c^2)
And the time of the body relative to others changing to t = t0/√1-(v^2/c^2)

The derivation of these formulas starts from assumptions that also require that ##v \lt c##. Thus, they cannot be used when ##v \ge c##; the infinities and negative square roots that appear when we try are just the math telling us that it is being misapplied.