special relativity - Why can't matter pass the speed of the light?

I have the following questions.

1. 
   

   Why can't matter pass the speed of the light?

   
   



2. 
   

   What happens to an object when it comes close to the speed of the light?

   
   


3. 
   

   What makes the object unable to surpass this speed limit?

   
   

   And finally, I need to know whether this speed limit has been experimentally proven?

   
   

Answer

For one explanation see "Simple derivation of the special theory of relativity without the speed of light axiom".

What is a transformation?

We'll denote an event by a point in space and time, with coordinates $(t,x,y,z)$. A transformation tells us how the coordinates of this event change from one observer to another, when the observer is moving with a constant velocity in your frame.

Why is there a speed limit?

From the linked article:

The best argument on this issue is given in [11]: either particles can be accelerated to arbitrary speeds, or they cannot. If they can, we get the Galileo transformation, if they cannot, then there must exist, mathematically speaking, a least upper bound c to particle speeds in any one inertial frame. By the relativity principle, this bound must be the same in all inertial frames, moreover, the speed c – whether attained or not by any physical effect – must transform into itself (otherwise we could get higher speed than c of some particle when transformed from S to S ′ ). But when c transforms into itself, we are lead uniquely to the Lorentz transformation by the usual procedure employed in most of the texts. Thus the relativity principle by itself necessarily implies that all inertial frames are related either by Galilean transformations, or by Lorentz transformations with some universal c. The only role of the speed of light axiom is the determination of c.

The basic principles which the Newtonian theory (and also the special theory of relativity) is built on are homogeneity, isotropy and the principle of relativity. This allows two and only two possible transformations: Galilean and Lorentzian. Experimentally the Galilean is not satisfactory for many reasons (the apparent speed of light limit and other problems), so we need to take the Lorentz one. There is no other option left, unless we want to sacrifice the principle of relativity or homogeneity or isotropy.

The linked article asserts that Galilean and Lorentzian geometries are the only possible geometries, given some reasonable physical assumptions. Galilean transformations are the ones that people are the most familiar with. Odds are you think in terms of Galilean transformations. If we live in a Galilean world, this means that you and I agree on what a moment of time is. One moment for me is the same as one moment for you; particles can be accelerated to arbitrarily high speeds; and the ideas of the old "luminiferous aether" are acceptable. (that is to say, if a photon is travelling at $c$, and you're traveling alongside the photon at speed $c/2$, you see the photon moving away from you at speed $c/2$)

But that isn't the only geometry allowed. Lorentzian geometry asserts something different: You and I can not agree upon moments of time and particles can't be accelerated to arbitrarily high speeds.

So, with the basic assumptions ("homogeneity, isotropy and the principle of relativity") we have two possible geometries, and if we start experimenting, we find that Galilean geometry does not hold.

I hope that gives a more satisfactory answer to $1$ and $3$. We observe that Galilean transformations don't hold and so our previous assumptions lead us to relativity. In Lorentzian geometry (relativity), it doesn't really make sense for a reference frame to move faster than light. (If one wants to interpret the equations literally, you have to know that everything has a factor of $1/\sqrt{1-v^2/c^2}$. As $v$ crosses the speed of light, this quantity jumps from real, to infinite, to imaginary! You'd wind up with complex coordinates.)

One thing you have to understand is that if a particle moves and communicates with an average speed faster than that of light, Lorentzian geometry (relativity) dictates that this would be equivalent to time travel.