fet2105 said: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.
fet2105 said: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 said: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.
If it's the best and most objective answer, what grounds do you have for disagreeing with it?No-where-man said:The best and most objective answer, indeed.
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.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 said: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.
Ok, but what these "quantum microscopes" are looking at are atomic orbitals, not the internal structure of an electron.No-where-man said:
No-where-man said:
An elementary particle is an excitation of a quantum field, but it is created at a point and annihilated at a point.Maui said:It's superior to treat elementary particles as their respective fields and detections as their excitations.
Bill_K said:Ok, but what these "quantum microscopes" are looking at are atomic orbitals, not the internal structure of an electron.
RGauld said: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 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.No-where-man said: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.
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.nikkkom said:So, an electron is never in a point. So any other particle.
Am I missing something?
Maui said:It's superior to treat elementary particles as their respective fields and detections as their excitations.
Is this what you are trying to say?
fet2105 said: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
Bill_K said: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.
No-where-man said: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.
fet2105 said:the article posted seems to allude to the idea that point particles are like little traffic lights
Bill_K said: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. said: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.
nikkkom said:So the "point-like" is a misnomer, "point-like electron" does not mean that electron has (or can have) zero size.
Jano L. said: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.
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.Jano L. said: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.
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 said: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.)
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.
These are quantum numbers, not degrees of freedom.
Jano L. said: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.
No-where-man said: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
bhobba said: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. 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.No-where-man said: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.
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.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.