# Length contraction and field theory

1. Jul 25, 2004

### kurious

If length contraction was quantized, then a particle of a given radius could have a constant radius for many observers moving at different speeds.
Could such a particle be used to formulate a quantum field theory?

2. Jul 25, 2004

### marlon

No , the contraction would still occur, only in different scales depending on the speed of the observer. The effect of length-contraction cannot be excluded because it is due to the universal property of a constant lightspeed. This counts for every observer, regardless of the speed or even the quantization-procedure you wish to execute...

3. Jul 25, 2004

### kurious

Provided mass is quantized too, the quantity mass x radius would be a constant for all observers regardless of velocity.
This is a kind of invariance.

4. Jul 25, 2004

### marlon

hmmm, quantized mass???
I think not, mass has to evolve conform the special relativity. Even if the restmass was to be quantized, then still you cannot exclude the effects coming from de 1/sqrt(1-(v/c)Â²)-term for the mass. this term ,as a pointed out before, comes from the fact that c is an universal constant.

If you want to achieve your goals, you would have to give up the constant lightspeed value

Einstein would be turning himself in his grave...

5. Jul 25, 2004

### kurious

By quantized mass I meant 1 / (1 -nv^2/c^2)^1/2
where n is an integer and similar for the radius

6. Jul 25, 2004

### marlon

Well ok, but as i see it you still cannot say "independent of velocity" because of the v. So why would this be constant for each and every observer

7. Jul 25, 2004

### kurious

Because Velocity = nv or V^2 = (nv)^2
v is constant and n is an integer that only increases
for a given observer if they are moving faster than a certain threshold speed.

Last edited: Jul 25, 2004
8. Jul 25, 2004

### marlon

I think this is getting a little bit to vague.

this integer that only increases for ...., I don't buy that.

Still, your situation remains unchanged. There will still be contraction because there is a speed v. if v were to be 0 (not constant) than there is no contraction...

9. Jul 25, 2004

### kurious

Let's use the idea of (mass x length) = constant.
No quantization.

Is the contraction to zero radius at c a problem?
If so then we can guess how to stop it.
One way would be just to write:

LENGTH = Rest Length x ( 1-v^2/c^2 + small constant)^1/2

if mass = m0 / ( 1-v^2/c^2 + small constant)^1/2

then:
(mass x length) = m0 / ( 1-v^2/c^2 + small constant) x

Rest Length x ( 1-v^2/c^2 + small constant)^1/2

= constant = m0 x Rest length

Perhaps we can use this as a basis for a field theory with
an electron that has a radius and that is not point-like.

The small constant would mean that mass does not become infinite
but that it reaches a finite value and so rest masses can,in principle be accelerated to the speed of light.

Last edited: Jul 26, 2004