The existence of point particles and an infinite universe

[BruceW]

I think there is something in Relativistic quantum electrodynamics that specifically requires the electron to literally be a point particle (unlike the proton which has structure). Unfortunately, I don't know the details, it is an area I would really like to learn more about. I guess it's true that it is only point particle in current theory, but I mean, it is fairly well established theory. Not like Supersymmetric theory for example, which is less well-established.

 

[fet2105]

Only in current theory. We do not know whether the electron is point or not - some future theory might give the electron some size. I recall reading that Schwinger also did not think that the electron should be considered as a point, but most probably any theory with non-point electron is very hard.

I suppose the question is: where do the theories that treat electrons as point particles fail? Is it possible that these theories are describing electrons from some particular point of view in which they are indeed correctly treated as point particles . . . similar to how particle physics describes particles as though measurements are being performed in a freely falling frame of reference?

 

[bhobba]

I suppose the question is: where do the theories that treat electrons as point particles fail?

It fails in the case of particles with EM fields because it becomes infinite as you approach the particle. This is the rock bottom cause of the reed for renormalisation. The field creates a screening effect as you get closer to the particle leading to the absurdity of an infinite charge that the 'trick' of renormalisation solves. This means almost certainly the theory is wrong at small distances with the prime candidate being its not a point - but maybe something like a string.

Thanks
Bill

 

[BruceW]

yeah. QFT is an effective field theory, right? But wikipedia seem to imply that QED is not an effective field theory. http://en.wikipedia.org/wiki/Effective_field_theory where they say "...they are not generally renormalizable in the same sense as quantum electrodynamics which requires the renormalization of only three parameters." Maybe they are just saying that QED is a special case of an effective field theory. Anyway, it must be an effective field theory surely, since it is not valid at length scale less than the Planck length.

 

[bhobba]

yeah. QFT is an effective field theory, right? But wikipedia seem to imply that QED is not an effective field theory.

QED is a renormaliseable theory right from the gecko.

QFT theories exist that do not need to be renormalised.

For theories that are not renormalizeable like gravity you can find a theory that is valid up to some scale beyond which it isn't necessarily valid eg:
http://arxiv.org/pdf/1209.3511v1.pdf

Renormalizable theories are effective theories of a very special type. They are effective in the sense we know there is some cutoff beyond which it's not valid but the value of the cutoff doesn't appear in most calculable quantities. Effective Field theory is usually reserved for theories that are not renomalizable and are approximated in a certain region by a theory one can extract finite predictions from.

Thanks
Bill

 

[Nugatory]

QED is a renormaliseable theory right from the gecko.

Gotta love autocorrection... My iPad will never let go of the idea that bodies with non-zero rest mass move with "timely worldliness".

 

[andrien]

Actually there are problems if one close take a look at quantum electrodynamics.For example,one modifies the photon propagator as δ_μv/k² to δ_μv/k²(λ²/k²+λ²) so that it behaves properly in low energy limit and vanishes as energy becomes very large(for k>>λ case) but if one will see it closely then one can write it simply as (δ_μv/k²)-(δ_μv/k²+λ²).If one see the second term one finds that the coupling for that term must be imaginary(because of - sign) and so there should be a non hermitian term in S-matrix which will give non unitarity.One just use different regulators which can fix some of these but nevertheless there are prblems.Also some theories which are non renormalizable turn out to be renormalizable if one goes to lower dimensions like fermi four interaction which is renormalizable in 1+1 dimension.These theories are treated within effective field theory.

 

[bhobba]

Actually there are problems if one close take a look at quantum electrodynamics.

I am not sure I see your point, but I am hardly an expert on QED or renormalisation.

My understanding is in QED fixing an energy scale means fixing the renormalised parameters so all quantities come out finite regardless of energy scale (except of course the renormalised parameters which change as you change energy scale). Providing of course one stays well clear of the Landau pole so that perturbation theory is a reasonable thing to do.

Thanks
Bill

 

[BruceW]

Renormalizable theories are effective theories of a very special type. They are effective in the sense we know there is some cutoff beyond which it's not valid but the value of the cutoff doesn't appear in most calculable quantities. Effective Field theory is usually reserved for theories that are not renomalizable and are approximated in a certain region by a theory one can extract finite predictions from.

ah, right. thanks for explaining. I definitely need to learn more about this subject before I fully understand.

 

[No-where-man]

As far as you know means from everyday experience. But the quantum world may be different.

There are however well known issues with point particles in classical physics such as a-casual runaway solutions in EM. It is fixed in QM but requires that device called re-normalization which while not wrong is a bit sneaky. It probably means at a deeper level we aren't dealing with point particles -strings maybe - but really right now its up in the air.

Thanks
Bill

Yes, I forgot this is quantum physics we're dealing with, I don0't know how could I miss this.

 

[No-where-man]

Yes. He did explain everything. And a proton is point-like (with some very small size). And an electron is a point particle. It really does have zero size, no matter how far you zoom in on it. Relativistic quantum electrodynamics requires it.

I just hope scientists will be able to experimentally 100% prove that an electron is truly a point!
Who knows...

 

[No-where-man]

Its the well known problem with the Lorentz-Dirac equation:
http://arxiv.org/pdf/gr-qc/9912045v1.pdf
'Even though the applied force is constant, the acceleration grows exponentially with time. This is the problem of runaway solutions, which occurs also in the general case'

It is thought the cause is the point particle model it is based on, which means its field grows infinitely large the closer you get, although the physicality of such solutions is open to question.

Thanks
Bill

Wow, this is very interesting.

 

[Nugatory]

I just hope scientists will be able to experimentally 100% prove that an electron is truly a point!
Who knows...

It's unlikely that we will ever see that sort of experimental proof. All experiments can do is set a new and smaller upper limit of the size of something - they can never establish that the size is zero. That's why Bill_K was so careful in the way that he phrased his answer in #15 of this thread ("pointlike to less than 10^-17 cm").

 

[BruceW]

he was talking about the proton I think (which definitely has non-zero size, since it is a structure made of other things). But yes, you are right that experimentally, we can only say for certain that the electron is as small as our smallest measuring equipment can tell us. We can only give an upper bound, experimentally.

edit: blech, oh no, he was talking about the electron. wow, 10^-15 doesn't seem like a very precise limit. I guess it is hard to make measuring equipment that can probe that scale!

 

[fet2105]

It fails in the case of particles with EM fields because it becomes infinite as you approach the particle. This is the rock bottom cause of the reed for renormalisation. The field creates a screening effect as you get closer to the particle leading to the absurdity of an infinite charge that the 'trick' of renormalisation solves. This means almost certainly the theory is wrong at small distances with the prime candidate being its not a point - but maybe something like a string.

Thanks
Bill

What becomes infinite as you approach the particle?

 

[DrDu]

I think it is also interesting to consider the results of axiomatic quantum field theory (AQFT) like, e.g. the Reeh-Schlieder theorem
http://en.wikipedia.org/wiki/Reeh–Schlieder_theorem
which shows that sufficiently localized measurements will lead to the generation of field excitations arbitrarily far from the measurement region. Hence there are limits on the localizability of a particle.

 

[bhobba]

What becomes infinite as you approach the particle?

Classically the field becomes infinite via Coulomb's law.

QM wise as you approach the particle you are probing shorter distances which requires higher and higher energies. What QED tells us is the charge (specifically the coupling constant) actually depends on the energy scale you probe with - and in fact becomes infinite at what is called the Landau pole:
http://en.wikipedia.org/wiki/Landau_pole

However before that energy is reached the electroweak theory takes over and it is thought that gives way to another theory at even higher energy (string theory maybe). The bottom line is there are issues with current physics and quite possibly its pointing to we are not dealing with point particles.

Thanks
Bill