Length contraction and field theory

[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?

 

[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...

 

[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.

 

[marlon]

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.

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)²)-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...

 

[kurious]

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

 

[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

 

[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.

 

[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...

 

[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.