Re: Limit As v Approaches c is Indeterminate Unless m0(v) is Defined

On 22 mai, 14:30, Darwin123 <drosen0...@xxxxxxxxx> wrote:
On May 22, 11:37 am, srp2...@xxxxxxxxx wrote:> On 22 mai, 08:49, richards....@xxxxxxxxxxxxx wrote:

According to the theory of Special Relativity;
m = m0/√(1 - v^2/c^2)

If v=c and m0=0, then m is undefined. However, this does not mean
that the limit of m is undefined, as m0 approaches 0 and v approaches
c.

I see what you mean, but let's see how this pans out in physical
reality.

Can an electron ever have a mass lower than 9.10938188E-31 kg ?

If the answer is no, then how could m0 of anything be less than
this value except mathematically on a *** of paper ?

In physical reality, the only way I see m0 becoming negligible
(instead of approaching zero) is if the kinetic energy provided
is so huge that it becomes so huge that it practically equals
the electromagnetic field of the moving system. And even
then, the magnetic field of the rest mass energy as infinitesimal
as it then becomes, still overburdens the electromagnetic
part.

I understand that the following equation is thrown in
without proper setting up or background, but it is easy
to use since only the electron Compton wavelength
and the wavelength of the added energy are required
for the calculation, but if you play with it, you will
see what I mean.

The only way to really get to c is to remove the
massive particle.

http://pages.videotron.com/ceber/moving_electron.jpg

If there is a relationship, also called a constraint, between m0
and v, in addition to the relativistic equation, then there can be a
well defined value for m. However, the value for m will be determined
by that constraint.

I am curious as to what constraint you would consider as
causing m0 to vary for the electron for example (I always tend
to try and confirm the validity of mathematical and philosophical
conclusions by matching them with physical reality).

Obviously, E=hf is an equation defined only in quantum mechanics or
its semiclassical approximations. One way to handle the limit is to
define a constraint between m0 and v such that mc^2=hf. This is a
semiclassical approximation of an exact theory of quantum
electrodynamics.

But then, don't you make the rest mass of the electron dependent
on its velocity ? I agree for its relativistic mass as it moves, but
how can this make sense when the only energy present is
the rest mass energy of the electron. Again, I refer here to
a real physical case.

However, lets take this approximate model seriously. The
relationship between m0 and v is an integral part of the particle. The
constraint is what basically defines the type of particle it is.
I think your error is assuming that m0 is not a function of v.

That's effectively what I assume. But is it really an error ?

For the equation I show you above for the moving electron,
the table reveals that the velocity depends on only half
the kinetic energy provided, the other half coming out as
an electromagnetic oscillation that contributes the added mass.

If this approach was not consistent, how could it possibly
provide the verified relativistic velocity curve, and the correct
relativistic mass at any possible velocity ?

The value of m0 is not well defined because there are no point
particles.

Meaning that there are no particles behaving "point-like". It seems
to me that experimental reality shows otherwise, don't you think ?

But you talked yourself of "localized electromagnetic field".
Shouldn't such a field behave point-like as it moves ?

This is impossible for a particle that is the source of a
field of finite size.

I wonder why you think this. Why should it be impossible ?
Can you elaborate ?

The reason is that one can not accelerate the
field that surrounds the particle in a uniform manner.

Again, what if the particle was the field itself. Like a local
standing oscillating electromagnetic field ? Localized and
behaving point-like by definition.

The limit of
propagation velocity (c) really makes the whole idea of "point
particle" inconsistent at velocities close to c. The interaction of
the particle with its own field makes m0 poorly defined.

I wonder if our fundamental views can be reconciled. We obviously
have conflicting basic assumptions.

In relativistic quantum mechanics, one can define an m0 because
the position of a particle is uncertain.

On paper certainly. But does the fact that the wave function is unable
to localize a moving physical particle mean that it may not in fact
be localized ? The latter was de Broglie's view in fact. He was
convinced (and so was Einstein and Planck) that particles were
always localized and followed precise least action trajectories even
though the QM math was not precise anough to account for the fact.

However, photons don't exist in the classical relativity.

But they seem to exist in physical reality.

Perhaps this is what you meant by saying that hf=mc^2 is not valid.

I think it is valid only for one value of f. The value that matches
the rest mass energy of the electron making up m0.

Here is the logic

http://pages.videotron.com/ceber/decoupling_orbit.jpg

I think it cannot be valid for a moving electron since it fails
as soon as f falls below the frequency of the rest mass
energy of the particle.

However, the reason isn't that the inertial
mass is unreal. The inertial mass is very real. A box full of photons
bouncing back and forth will have a very real inertial mass.

Absolute agreement.

It is m0 which is unreal in classical relativity. m0 is the result of the
interaction between a source particle and the source fields. Read my
other post for a bigger explanation.

In my understanding, m0 when photons are considered is made
up of its oscillating electromagnetic field and always amounts
to half its total complement of energy whatever that amount of
energy is. This m0 can vary across the whole scale.

But if a massive particle is involved, then the buck can only
stop downwards when the physical m0 of the massive particle
is reached. No velocity lower than 0 is possible and no mass
lower than m0 is possible for the less massive known particle,
the electron.

I believe this is why general relativity is considered a field
theory. Point particles don't exist in general relativity because m0
doesn't exist in general relativity. All fields have a finite extent
in general relativity.

Well, even if GR or QM (man made theories) stated that localized
electrons behaving point-like and with invariant rest mass of
9.10938188E-31 kg don't exist, it seems to me that we have
ample proof that they do exist and are used without restraint
in high energy accelerators, being guided on precise very
well defined trajectories on which the experimentalist know
at every moment where they are at.

I must say though that my primary reference is not GR or QM,
which are of course self consistent theories, but experimentally
observed physical reality. If observation differs, I tend to
stick with observation. My view is that since physical reality
cannot be changed, then QM and GR have to adapt if at
some point they can't account for observation.

André Michaud
.

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