The existence of point particles and an infinite universe

[fet2105]

It seems to me that the question as to whether the universe is infinite or not carries the same validity as the question as to electron, quarks, etc. being infinitesimal or otherwise stated being modeled as point particles. It seems to me that these two quandaries are linked and perhaps can justify one another.

 

[phinds]

It seems to me that the question as to whether the universe is infinite or not carries the same validity as the question as to electron, quarks, etc. being infinitesimal or otherwise stated being modeled as point particles. It seems to me that these two quandaries are linked and perhaps can justify one another.

Is there a question here or did you just need to get that off your chest?

If you are asking if your idea is valid, I don't see how they have anything at all to do with each other.

 

[fet2105]

I suppose a question I could form to go with my statement would be relative to what are point particles considered to be infinitesimal?

 

[Nugatory]

I suppose a question I could form to go with my statement would be relative to what are point particles considered to be infinitesimal?

In our experiments to date, there is no detectable spatial extent or evidence of internal structure. So the best answer to your "relative to what?" question is "relative to the limits of our measurements".

It is not a priori impossible (although also not likely) that observations at higher energies than we can reach today might give us a different answer. Unless and until that happens, there's not a lot of point in wondering whether we're dealing with point particles or non-point particles whose behavior is in every respect indistinguishable from point particles.

 

[No-where-man]

In our experiments to date, there is no detectable spatial extent or evidence of internal structure. So the best answer to your "relative to what?" question is "relative to the limits of our measurements".

It is not a priori impossible (although also not likely) that observations at higher energies than we can reach today might give us a different answer. Unless and until that happens, there's not a lot of point in wondering whether we're dealing with point particles or non-point particles whose behavior is in every respect indistinguishable from point particles.

The best and most objective answer, indeed. But I wouldn't say true point-like particles exist, because if you can magnify them with some quantum microscope than they are not points at all.

 

[Bill_K]

The best and most objective answer, indeed.

If it's the best and most objective answer, what grounds do you have for disagreeing with it?

But I wouldn't say true point-like particles exist, because if you can magnify them with some quantum microscope than they are not points at all.

Quantum microscopes do not exist - when you invent one, be sure and let us take a look. Until then, experiment and theory indicates that elementary particles are indeed point-like.

 

[No-where-man]

If it's the best and most objective answer, what grounds do you have for disagreeing with it?Quantum microscopes do not exist - when you invent one, be sure and let us take a look. Until then, experiment and theory indicates that elementary particles are indeed point-like.

You're wrong, quantum microscopes do exist:
http://physicsworld.com/cws/article/news/2013/may/23/quantum-microscope-peers-into-the-hydrogen-atom
http://www.newscientist.com/article/mg21829194.900-smile-hydrogen-atom-youre-on-quantum-camera.html

 

[Bill_K]

You're wrong, quantum microscopes do exist:
http://physicsworld.com/cws/article/news/2013/may/23/quantum-microscope-peers-into-the-hydrogen-atom
http://www.newscientist.com/article/mg21829194.900-smile-hydrogen-atom-youre-on-quantum-camera.html

Ok, but what these "quantum microscopes" are looking at are atomic orbitals, not the internal structure of an electron.

 

[Maui]

You're wrong, quantum microscopes do exist:
http://physicsworld.com/cws/article/news/2013/may/23/quantum-microscope-peers-into-the-hydrogen-atom
http://www.newscientist.com/article/mg21829194.900-smile-hydrogen-atom-youre-on-quantum-camera.html

It's superior to treat elementary particles as their respective fields and detections as their excitations.

Is this what you are trying to say?

 

[Bill_K]

It's superior to treat elementary particles as their respective fields and detections as their excitations.

An elementary particle is an excitation of a quantum field, but it is created at a point and annihilated at a point.

 

[Maui]

Yes. There is no all-embracing classical-like concept. I have yet to find what the op was attempting to say.

 

[RGevo]

I believe your 'question' does have some importance.

At some high energy (some small distance) scale, if particles cease to become point like (which I expect at some scale they will) then we have to abandon the use of quantum field theory as we know it.

We would require something else to describe what is going on. This isn't too surprising since incorporating gravity into our current theory of elementary particles is rather difficult.

So, understanding how particles behave at this small distance may also tell us about gravity at very small scales and perhaps information about inflation etc. who knows.

 

[No-where-man]

Ok, but what these "quantum microscopes" are looking at are atomic orbitals, not the internal structure of an electron.

I'm not so sure, they have just begun with this technology, I wouldn't be surprised if they will be able to detect and actually see an electron directly.

 

[No-where-man]

I believe your 'question' does have some importance.

At some high energy (some small distance) scale, if particles cease to become point like (which I expect at some scale they will) then we have to abandon the use of quantum field theory as we know it.

We would require something else to describe what is going on. This isn't too surprising since incorporating gravity into our current theory of elementary particles is rather difficult.

So, understanding how particles behave at this small distance may also tell us about gravity at very small scales and perhaps information about inflation etc. who knows.

I wonder what is below quantum level. if particles cease to become point-like (which would happen eventually), than we would have sub-quantum field and sub-quantum physics.
And we will know what and how are created those point-like particles?

 

[Bill_K]

I'm not so sure, they have just begun with this technology ["quantum microscopes"], I wouldn't be surprised if they will be able to detect and actually see an electron directly.

I guess you haven't given it much thought in that case. The size of an atomic orbital is about 10^-8 cm, while the electron is already known to be pointlike to less than 10^-17 cm, or nine orders of magnitude smaller. Resolving power is directly proportional to energy, so you would need to use a probe whose energy was nine orders of magnitude greater, at least in the 10 TeV range.

 

[nikkkom]

Hmmm. I just realized that I don't quite understand what "point-like" actually means wrt quantum systems. Electrons, for instance.

An electron is never localized to a exact known location (for it would have infinite impulse uncertainty, thus infinite impulse, thus infinite energy... not good).

We have an experimental proof that this happens - we are quite sure electorn-degenerate matter in white dwarfs and neutron stars exists. The matter where electrons are forced into ever smaller spatial regions, and they do acquite energy which resists further cramping.

So, an electron is never in a point. So any other particle.

Am I missing something?

 

[Bill_K]

So, an electron is never in a point. So any other particle.
Am I missing something?

Yes. This has nothing to do with the Heisenberg uncertainty principle, and the particle does not need to be "localized". The particles we talk about in ordinary Schrodinger quantum mechanics are also point particles. Likewise for the Dirac Equation.

The issue is whether the particle has internal structure, that is, does an electron have parts. Is it extended in space, does it have internal degrees of freedom - can it come apart, can it vibrate, etc. If the answer was yes to any of these, you'd have a hard time writing down a theory that was Lorentz invariant. String theory says yes, ordinary quantum field theory says no.

 

[fet2105]

With reagrd to Maui's and Bill's latest thoughts:

It's superior to treat elementary particles as their respective fields and detections as their excitations.

Is this what you are trying to say?

I found this to be very helpful: http://www.fnal.gov/pub/today/archive/archive_2013/today13-02-15_NutshellReadMore.html

 

[No-where-man]

With reagrd to Maui's and Bill's latest thoughts:

I found this to be very helpful: http://www.fnal.gov/pub/today/archive/archive_2013/today13-02-15_NutshellReadMore.html

But shouldn't point-like particle be infinitely small, so when you magnify it's always of the same size-I thought that's impossible, although I was never sure.

 

[No-where-man]

I guess you haven't given it much thought in that case. The size of an atomic orbital is about 10^-8 cm, while the electron is already known to be pointlike to less than 10^-17 cm, or nine orders of magnitude smaller. Resolving power is directly proportional to energy, so you would need to use a probe whose energy was nine orders of magnitude greater, at least in the 10 TeV range.

But if you are able to magnify electron even though with so much energy, than it is not a point-like particle!?

 

[fet2105]

But shouldn't point-like particle be infinitely small, so when you magnify it's always of the same size-I thought that's impossible, although I was never sure.

the article posted seems to allude to the idea that point particles are like little traffic lights

 

[fet2105]

. . . I like this excerpt:"Point-like particles are mathematical abstractions with zero size. But even zero-size particles have an extended effect, due to the effect of the field surrounding them . . . The point-like particle is the mathematical abstraction at the center of the particle, but the extended field in essence makes even a point particle not so point-like."

for the sake of being dilligent~quote taken from: http://www.fnal.gov/pub/today/archive/archive_2013/today13-02-15_NutshellReadMore.html

 

[bhobba]

the article posted seems to allude to the idea that point particles are like little traffic lights

Well actually String Theory says they are not points.

It's quite likely particles will not turn out to be points but as of now every experiment we have done indicates that position is an operator, meaning whenever we set out to measure the position of a particle we get an answer to whatever resolution the apparatus we are using has. That's the real reason we treat them as particles.

Thanks
Bill

 

[nikkkom]

Yes. This has nothing to do with the Heisenberg uncertainty principle, and the particle does not need to be "localized". The particles we talk about in ordinary Schrodinger quantum mechanics are also point particles. Likewise for the Dirac Equation.

The issue is whether the particle has internal structure, that is, does an electron have parts. Is it extended in space, does it have internal degrees of freedom - can it come apart, can it vibrate, etc.

So the "point-like" is a misnomer, "point-like electron" does not mean that electron has (or can have) zero size.

 

[Jano L.]

So the "point-like" is a misnomer, "point-like electron" does not mean that electron has (or can have) zero size.

No, "point-like particle" means that the particle is like a point, i.e. has no extension in space, so its position with respect to other bodies can be described by merely three numbers. It was meant that way in classical theory and this meaning was inherited by the quantum theory as well.

What puzzles you is probably the fact that in quantum theory, the wave function of electron in hydrigen atom $\psi(\mathbf r)$ is never point-like. That is alright, because the wave function is not the electron. The wave function is just an abstract probabilistic description of electron's position. This becomes obvious when you have wave function for two or more particles - there are many electrons, but only one wave function, which describes them in a probabilistic way.

The internal degrees of freedom are a different matter - the particle can have them even while being point-like. For example, we can assign spin projection number, mass or charge or any other additional variable to a point-like particle.

 

[No-where-man]

No, "point-like particle" means that the particle is like a point, i.e. has no extension in space, so its position with respect to other bodies can be described by merely three numbers. It was meant that way in classical theory and this meaning was inherited by the quantum theory as well.

What puzzles you is probably the fact that in quantum theory, the wave function of electron in hydrigen atom $\psi(\mathbf r)$ is never point-like. That is alright, because the wave function is not the electron. The wave function is just an abstract probabilistic description of electron's position. This becomes obvious when you have wave function for two or more particles - there are many electrons, but only one wave function, which describes them in a probabilistic way.

The internal degrees of freedom are a different matter - the particle can have them even while being point-like. For example, we can assign spin projection number, mass or charge or any other additional variable to a point-like particle.

I actually thought that wave function is proven experimentally as natural phenomenon.
Regarding electron, someone here on the forums said that the size of an electron is 10^-17 cm, which means that an electron does have size, it's not point-like, which means with enough powerful microscope you could magnify it to see it.

 

[Bill_K]

So the "point-like" is a misnomer, "point-like electron" does not mean that electron has (or can have) zero size.

No, "point-like particle" means that the particle is like a point, i.e. has no extension in space, so its position with respect to other bodies can be described by merely three numbers. It was meant that way in classical theory and this meaning was inherited by the quantum theory as well.

I thought the definition of these terms was clear, but apparently not.

A point particle is one that has zero size.

A point-LIKE particle is one whose (possible) size is unknown, but smaller than the current experimentally observable limit.

A proton is an example of a particle which is not pointlike, having a size of about 1 fm. Within that radius it has a distribution of charge density and spin density, resulting of course from its constituent quarks and gluons.

The internal degrees of freedom are a different matter - the particle can have them even while being point-like. For example, we can assign spin projection number, mass or charge or any other additional variable to a point-like particle.

These are quantum numbers, not degrees of freedom. A degree of freedom has an associated coordinate and canonical momentum, and can be dynamically excited. An example of an internal degree of freedom would be a radial oscillation. Molecules as well as nuclei have rotational and vibrational degrees of freedom.

Regarding electron, someone here on the forums said that the size of an electron is 10^-17 cm, which means that an electron does have size, it's not point-like, which means with enough powerful microscope you could magnify it to see it.

No, it's pointlike. 10^-17 cm is an upper limit. (And you not only have to see it, you have to see inside it.)

 

[No-where-man]

I thought the definition of these terms was clear, but apparently not.

A point particle is one that has zero size.

A point-LIKE particle is one whose (possible) size is unknown, but smaller than the current experimentally observable limit.

A proton is an example of a particle which is not pointlike, having a size of about 1 fm. Within that radius it has a distribution of charge density and spin density, resulting of course from its constituent quarks and gluons.These are quantum numbers, not degrees of freedom. A degree of freedom has an associated coordinate and canonical momentum, and can be dynamically excited. An example of an internal degree of freedom would be a radial oscillation. Molecules as well as nuclei have rotational and vibrational degrees of freedom.
No, it's pointlike. 10^-17 cm is an upper limit. (And you not only have to see it, you have to see inside it.)

Question: Ok, but 10^-17 cm is still a size, when you say a point, it means no matter how much you magnify it, an electron will always be a point-like, but if it has a size, that size no matter how small it is, it is 100% possible to magnify it with enough powerful microscopes and other instruments.
If electron is not point-like, than you would be able to magnify no matter what the size it is.

And also if the electron is a true point you can't penetrate inside the electron-since an point-like electron is dimensionless (points are dimensionless in math), so what's the catch, here?

But if you said:
"A point particle is one that has zero size.
A point-LIKE particle is one whose (possible) size is unknown, but smaller than the current experimentally observable limit."

Than I guess you explained everything with this post.
Thanks again.

 

[Jano L.]

A point particle is one that has zero size.

A point-LIKE particle is one whose (possible) size is unknown, but smaller than the current experimentally observable limit.

An interesting distinction. I always thought point particle and point-like particle were the same thing, since many authors use one or another when discussing the same subject.

But since we do not know whether the electrons have zero or non-zero size, it is best to use the term point-like - we treat them as points, but still we admit they may have some small spatial extension.

These are quantum numbers, not degrees of freedom.

I'd rather not go into semantics. What I wanted to say is that internal degrees of freedom are not necessarily connected to position of something; the word "internal" includes all possible variables, not just spatial coordinates.

 

[No-where-man]

An interesting distinction. I always thought point particle and point-like particle were the same thing, since many authors use one or another when discussing the same subject.

But since we do not know whether the electrons have zero or non-zero size, it is best to use the term point-like - we treat them as points, but still we admit they may have some small spatial extension.



I'd rather not go into semantics. What I wanted to say is that internal degrees of freedom are not necessarily connected to position of something; the word "internal" includes all possible variables, not just spatial coordinates.

As far as I know, in a real world, a point no matter how small it is, it's still has a size and diameter, and you can magnify it, I don't think experiments will show that point-like particles are any different, but you never know, I'd be happy if experiments would prove me wrong.

 

[bhobba]

As far as I know, in a real world, a point no matter how small it is, it's still has a size and diameter

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

 

[fet2105]

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

could you expand on the casual runaway solutions in EM? thanks

 

[bhobba]

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

 

[BruceW]

Question: Ok, but 10^-17 cm is still a size, when you say a point, it means no matter how much you magnify it, an electron will always be a point-like, but if it has a size, that size no matter how small it is, it is 100% possible to magnify it with enough powerful microscopes and other instruments.
If electron is not point-like, than you would be able to magnify no matter what the size it is.

And also if the electron is a true point you can't penetrate inside the electron-since an point-like electron is dimensionless (points are dimensionless in math), so what's the catch, here?

But if you said:
"A point particle is one that has zero size.
A point-LIKE particle is one whose (possible) size is unknown, but smaller than the current experimentally observable limit."

Than I guess you explained everything with this post.
Thanks again.

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.

 

[Jano L.]

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.

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.

 

[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?