# Zero lenght contraction in SR

1. Dec 24, 2003

### deda

In Einstein's SR the velocity of the light (c) is same in every referent frame. Let us for instance assume we don't know its exact value and try to estimate it. The relative distance suffers contractions depending on the velocity of the frame like this:
$$L=L_0\sqrt{1-\frac{V^2}{c^2}}$$
where L0 is the rest frame distance; L is the relativ contracted distance; V is the velocity of the frame.
But what if V=c or we have the photon's point of view?
Then every distance contracts to zero meaning that from the very instance of its creation the photon is already every where. This is only possible if c=infinity or the light transmition is instant. The c=infinity can only be result of direct change of charge(the wave nature) or direct change of the mass (the particle nature). If it happens then the changes affect the rest of the universe instantly.

2. Dec 24, 2003

### Janus

Staff Emeritus
The universe contracts to zero length from the frame of the photon meaning that the photon takes zero time to cross the universe at c. Zero distance divided by any velocity equals zero time, so c need not be infinite.

On the other hand, from the universe's frame, its distance doesn't contract and the photon takes just the amount of time to cross any distance as it would need traveling at 300,000 km/s, so again, c is not infinite.

So from neither frame do you have to consider c as infinite.

3. Dec 25, 2003

### deda

I think we should not forget that if length contracts the way it does, the time sequence necessary to pass that length delates this way:
$$T=\frac{T_0}{\sqrt{1-\frac{V^2}{c^2}}}$$
So the if V -> c then T=infinity.
Now if we would try to calculate c as L/T=dx/dt then c=0/infinity.
This is the worst case of undefined number cause it's neither 0 neither 3E8km/s nor infinity. A totaly undefined number.

If it is so in photon's frame then it's so in every frame.

4. Dec 25, 2003

### MathematicalPhysicist

correct me if im wrong but i thought the equations that describe length contraction and time dilation are only for use for matter not for the light itself which already is with c speed.

5. Dec 25, 2003

### deda

It applies to every object in motion.I don't see why a photon would be special.