Calculating length contraction at speed $c$ (not near it) Is the Lorentz transform applicable to speeds that are lower than light only?Because I'm trying to calculate length contraction of objects moving at speed $c$ (not near it) and it turns always 0. Is my calculation correct?Please help I'm just a beginner
Suppose a 5 m object is traveling at $c$,so
$$        x'=x/γ$$
\begin{align}
x&=x'\sqrt{(1- (v^2)⁄(c^2)}\\
x&=5\sqrt{1-1}\\
x&=5\sqrt0\\
x&=0
\end{align}
Not infinite right?
If so then the rule will have no length?
 A: This is a case of applying a result outside of the context in which it was validly derived.
The Lorentz transformation does not exist for relative speed $v = c$.
Recall that the Lorentz transformation relates the coordinates in one inertial coordinate system to another uniformly (relatively) moving inertial coordinate system.
In the transformation, there is a Lorentz factor
$$\gamma_v = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}$$
but $\gamma_c$ does not exist since the denominator vanishes for $v = c$ and division by zero is undefined.
Intuitively, we 'know' that one is at rest with respect to one's self (a ruler is not moving with respect to itself).
However, according to the Lorentz transformations, an object with speed $c$ in one inertial reference frame has speed $c$ in all inertial reference frames.
Thus, a ruler with speed $c$ in one inertial reference frame has speed $c$ in all inertial reference frames.
In other words, there is no inertial reference frame in which such a ruler is at rest.
So, it isn't meaningful to think about length contraction in this way.  The formula for length contraction in your question assumes that the ruler has length $L$ in the inertial reference frame in which it is at rest but there is no $L$ to speak of since there is no inertial reference frame in which the ruler is at rest. 
A: 
"1. Is the Lorentz transform applicable to speeds that are lower than light only? -- 2. Because I'm trying to calculate length contraction of objects moving at speed c (not near it) and it turns always 0.".



*

*Yes.

*Moving any object with mass would require infinite energy (not available) to move it at the speed of light. Even moving a proton (very light weight) would require infinite energy to move at light speed (and an enormous amount of energy to move almost that fast).
Light (a photon) has no weight and moves only at the speed of light. 
Light moving, or an observer moving relative to the source, does not alter the mass (or weight) of light but does alter the frequency.
Source: https://en.wikipedia.org/wiki/Length_contraction#Geometrical_considerations
A: You're right. 
If you could move at the speed of light, you would not see any length: every object would have zero length; this is called the "length contraction" and it is one of the two phenomena caused by traveling at the speed of light. The other is the time dilatation.
