What would happen if some signal could move faster than light?

The two postulates of STR doesn't say that any signal cannot move faster than light. It also doesn't assert that any signal except light cannot have velocity equals to that of light. So at the very beginning of analysis of STR we cannot say anything about the argument of "light having the ultimate(fastest) speed". Infact STR shows that we cannot accelerate a material particle to achieve and exceed the speed of light but we cannot just deny the existence of particles which could be generated similar to photons which at their creation can have speed equals to or greater than $c$ because they have achieved this speed at their birth they are not been accelerated to achieve this speed.

So Suppose there exists a hypothetical signal named schite having velocity=infinity but the speed of light is still same for all the inertial observers "would the events A and B be dissimultaneous in train's frame to validate constancy of speed of light in the Einstein's rail thought experiment"?

Moreover could we use this schite signal to synchronize clocks?

In other words would time dilation and length contraction exist?

I have heard little bit about tachyons. It is said using tachyons we can transmit signals at higher speed than $c$ if (assuming hypothetically) such particles exists can we use them to synchronize clocks?

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Showing that trans-luminal signalling is equivalent to sending messaged backward in time (and putting causality in question) in a standard exercise. And sure you could "synchronize" clocks but it wouldn't mean anything reliable because time dilation still means that the proper time of various paths between two time-like separated events still varies. –  dmckee Feb 23 '14 at 15:11
@dmckee If we synchronize two clocks seperated in space using schite(infinite speed signal) signal would they remain synchronized in all inertial frames moving at a certain speed? –  user31782 Feb 23 '14 at 15:16
–  John Rennie Feb 23 '14 at 16:09
I have learnt somewhere from the Lorentz transformation of the tachyons, that when tachyon interacts with a normal particle and it creates another tachyon and a particle without disturbing the momentum of the particle (by virtue of itself, tachyon can never be detected). If we look at this way, I think tachyons can't transfer information to normal particles. This is just my idea, could be wrong. I suggest you look for how tachyons (as particles not field) interact with normal particles. –  user35952 Feb 26 '14 at 5:37
@user35952 techyons are explain at the last of my book but i am struck at the beginning. I haven't reached even at Lorentz transformation. What to say there are enumerable questions in my head. –  user31782 Feb 26 '14 at 11:57

The two postulates of STR doesn't say that any signal cannot move faster than light.

This superficial appearance is deceiving. After all, the postulates involve notions such as inertial frame and speed; therefore they require and presume definitions of

Correspondingly, here c is of course understood as (magnitude of) signal front velocity (instead of "phase velocity", or "group velocity").

In summary: the detailed definitions of the notions and quantities appearing in the famous formulation of the postulates of STR imply that any "speed" is determined in reference to unambiguous "signal speed".

And applied to the question title asked above:
it is of course an absurd proposition that some signal should "move faster" (from some particular sender, to some particular receiver) than any signal exchanged between this particular pair of participants.

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we cant track a signal moving with a velocity more than C.we can say that it will not interfere with the material matter.it can pass through any matter with out making a interaction with it as it will pass through the matter as of its momentum hf/c2*infinity in this instance which is very high. even though it passes through it the body will be perfectly elastic and will retain its orginal shape with no deformation.

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Frankly you are not answering my question. It appears you are new here. Please use latex and be to the point to the question. You are going to have downvotes so this is my advice. –  user31782 Feb 23 '14 at 16:03