Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Jarek Duda on 18/07/2018 08:43:32

There is some confidence that fundamental particles are perfect points e.g. to simplify QFT calculations  what experimental evidence do we have, especially for electron?
Electron Wikipedia article (https://en.wikipedia.org/w/index.php?title=Electron#Fundamental_properties) only points argument based on gfactor being close to 2: Dehmelt's 1988 paper (http://iopscience.iop.org/article/10.1088/00318949/1988/T22/016/pdf) extrapolating (by fitting parabola to two points!) from proton and triton behavior that RMS (root mean square) radius (https://en.wikipedia.org/wiki/Charge_radius) for particles composed of 3 fermions should be ≈ g−2:
(https://i.stack.imgur.com/6BAG4.png)
Another argument for point nature of electron might be tiny crosssection, so let's look at it for electronpositron collisions:
(https://i.stack.imgur.com/WNP2i.png)
As we are are interested in size of resting electron (no Lorentz contraction), we should extrapolate the flat line sigma ~ 1/E^2 to resting electron, getting sigma ~ 100mb corresponding to ~2fm radius.
From the other side we know that two EM photons having 2 x 511keV energy can create electronpositron pair, hence energy conservation doesn't allow electric field of electron to exceed 511keV energy, what requires some its deformation in femtometer scale from E ~ 1/r^2:
Can we bound size of electron from above: gfactor or scattering experiments?
Is there other experimental evidence?

Another argument for point nature of electron might be tiny crosssection, so let's look at it for electronpositron collisions:
One thing that comes to (my very inexpert) mind is that this "tiny crosssection" would be detectable only after the electron had been observed. My understanding is that it qualifies as a pointparticle after observation, but we have no evidence that it is before being observed.

From Cross section Wikipedia (https://en.wikipedia.org/wiki/Cross_section_(physics)) : "When two particles interact, their mutual cross section is the area transverse to their relative motion within which they must meet in order to scatter from each other."
If they are perfect points (what would need infinite energy of electric field), where this area comes from?

As an electron has mass and charge, it cannot have zero radius as this would give it infinite density and a nearfield of infinite gradient.

As an electron has mass and charge, it cannot have zero radius
So far, so good.
as this would give it infinite density and a nearfield of infinite gradient.
Mathematically, no problem; but, surely, physically, if it has zero radius, it doesn’t exist, so how could it have any density?
I apologise if this is repetitive questioning, but the apology doesn’t mean I’ll stop asking. :)

From Cross section Wikipedia : "When two particles interact, their mutual cross section is the area transverse to their relative motion within which they must meet in order to scatter from each other."
This is probably not helpful in terms of your OP, but it must raise questions such as: "Do unobserved electrons scatter in the same way as observed electrons?"
How would we know?

Mathematically, no problem; but, surely, physically, if it has zero radius, it doesn’t exist, so how could it have any density?
As mentioned in the first post, the basic problem of point charge is density of energy of its electric field  which leads to infinite energy for a perfect point.
Some discussion: https://physics.stackexchange.com/questions/386760/theproblemofinfiniteenergyofelectronaspointcharge
Do unobserved electrons scatter in the same way as observed electrons?
I have to admit that I don't understand this "observation issue"?  scattering of electrons also happens e.g. in centers of stars, without any observer  the question is about objective size of electron.
For example is its electric field E ~ 1/r^2 down to r > 0, what means infinite energy ... or maybe it is somehow deformed?
Experimental suggestion for such deformation is running coupling (https://en.wikipedia.org/wiki/Coupling_constant#Running_coupling): that alpha ~ 1/137 coupling constant increases e.g. to alpha ~ 1/127 for 90GeV e+e scattering  there is some deformation from Coulomb interaction of perfect points.

From Cross section Wikipedia : "When two particles interact, their mutual cross section is the area transverse to their relative motion within which they must meet in order to scatter from each other."
This is probably not helpful in terms of your OP, but it must raise questions such as: "Do unobserved electrons scatter in the same way as observed electrons?"
How would we know?
Scattering counts as an observation.
With respect to the OP, I think that the "size" of the electron (or anything really) is not well defined aloneas it depends on how it is being measured...
For instance, as mentioned above, the "cross section" depends on both particles that are interacting, and if memory serves, there are some cases in which the apparent size ordering of two particles depends on the nature of the particle they are interacting with... I will have to look that up...

Scattering counts as an observation.
True; but if it is observed only when it is scattered, and that is what constrains it to "become" a particle, how could it be scattered if it did not exist as a particle before scattering?

With respect to the OP, I think that the "size" of the electron (or anything really) is not well defined aloneas it depends on how it is being measured...
Indeed definition of radius is a crucial and difficult question here.
For composite particles they use Root mean square (https://en.wikipedia.org/wiki/Charge_radius) radius  average over all building charges (e.g. three quarks) of r^2 * q.
Such "radius" can be even negative <r_n^2> ~ 0.1 fm^2 for neutron (http://www.actaphys.uj.edu.pl/fulltext?series=Reg&vol=30&page=119) as it has negative charge in larger distance.
For electron we definitely need a different definition of radius, we should rather define energy profile:
E(r) = energy inside radius r sphere around electron
We know E(r) ~ 511 keV for large r.
Reducing r we need to subtract e.g. energy of electric field, the big question is r > 0 behavior?
For charge being a perfect point, from electric field alone we would have E(r) > infinity for r > 0, what doesn't make sense (?)
We should rather expect E(r) > 0 for r > 0, allowing to define e.g. median radius: such that E(r) = 511/2 keV.
What order of magnitude should it have?
Scattering and energy considerations suggest ~ femtometer size (?)

Scattering counts as an observation.
True; but if it is observed only when it is scattered, and that is what constrains it to "become" a particle, how could it be scattered if it did not exist as a particle before scattering?
The "observation" business should not be taken too literally. In order for something to not exist until observed, it must retain a memory of what it will become when observed, and also an idea of what constitutes a legitimate observation. Therefore it must exist before it is observed, which contradicts the original statement. Observational models of quantum physics are simply mathematical attempts to predict what happens by analogy with mesoscopic physics.
Nor, for that matter, should we take waves and particles too literally. All we know about physics is that matter behaves like mathematical waves and particles. I can predict the behavior of my dog in a river because I know she swims and eats fish, but she isn't a shark!

Observation is a very sophisticated process like SternGerlach, or using CCD matrix ...
In contrast, these e.g. scatterings just objectively happen for example in the center of stars ...
All we know about physics is that matter behaves like mathematical waves and particles.
Exactly, we have waveparticle duality, e.g. electron is simultaneously (indivisible) fundamental charge and coupled wave.
For such objects: being corpuscles with coupled wave, already for classical ones ("walking droplets") they are now recreating "quantum" phenomena, e.g.:
1) Interference in particle statistics of doubleslit experiment (PRL 2006 (https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.97.154101))  corpuscle travels one path, but its "pilot wave" travels all paths  affecting trajectory of corpuscle (measured by detectors).
2) Unpredictable tunneling (PRL 2009 (https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.102.240401)) due to complicated state of the field ("memory"), depending on the history  they observe exponential drop of probability to cross a barrier with its width.
3) Landau orbit quantization (PNAS 2010 (http://www.pnas.org/content/107/41/17515.full))  using rotation and Coriolis force as analog of magnetic field and Lorentz force (Michael Berry 1980 (http://iopscience.iop.org/article/10.1088/01430807/1/3/008/pdf)). The intuition is that the clock has to find a resonance with the field to make it a standing wave (e.g. described by Schrödinger's equation).
4) Zeemanlike level splitting (PRL 2012 (https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.108.264503))  quantized orbits split proportionally to applied rotation speed (with sign).
5) Double quantization in harmonic potential (Nature 2014 (https://www.nature.com/articles/ncomms4219))  of separately both radius (instead of standard: energy) and angular momentum. E.g. n=2 state switches between m=2 oval and m=0 lemniscate of 0 angular momentum.
6) Recreating eigenstate form statistics of a walker's trajectories (PRE 2013 (https://journals.aps.org/pre/abstract/10.1103/PhysRevE.88.011001)).
But asking for objective radius of electron here, we are interested in its central indivisible fundamental charge  coupled wave carries relatively negligible energy, can be rather ignored here (?)

In order for something to not exist until observed, it must retain a memory of what it will become when observed,
Which would be impossible if it didn’t exist. (?)
Therefore it must exist before it is observed,
This is the point I reached after much thought. The main reason I started the “Copenhagen” thread was to try to find out if I was missing something.
Nor, for that matter, should we take waves and particles too literally.
Where would you stand on the idea that quons may be neither waves, nor particles; but something we cannot “experience”, other than by analogy, in the current state of our technology?

Exactly, we have waveparticle duality, e.g. electron is simultaneously (indivisible) fundamental charge and coupled wave.
This is exactly the kind of loose language that causes confusion!
The behavior of an electron can best be modelled by a charged particle or a wave. The electron is a distinct entity with mass m_{e} and charge e.

Where would you stand on the idea that quons may be neither waves, nor particles; but something we cannot “experience”, other than by analogy, in the current state of our technology?
Either you can infer the existence of x from observation , or you can't.
Occam says if you can't infer it from observation, it probably doesn't exist, though you may not have looked hard enough. Common sense says if you can infer it from observation it may exist, but science is inherently reductionist so don't bet your shirt on it.

The behavior of an electron can best be modelled by a charged particle or a wave.
Are you claiming that electron is switching between corpuscular and wave nature?
If so, please specify conditions for such switching, e.g. while free electron approaches free proton and they form hydrogen?
Or while they are stripping electrons from atoms before measuring their positions to get literally photos of orbitals by averaging over large numbers of positions of electrons: https://jonescollegeprep.org/ourpages/auto/2010/12/2/52195746/Imaging%20atomic%20orbitals.pdf
There is so called principle of complementarity (https://en.wikipedia.org/wiki/Complementarity_(physics)): "objects have certain pairs of complementary properties which cannot all be observed or measured simultaneously".
Sure, we cannot measure/observe both natures at once as measurements are extremely complex (e.g. SternGerlach, CCD) and limited procedures.
However, are there any reasons to conclude that particles objectively don't have simultaneously both natures?
We cannot measure/observe situation in the center of a star, but it does not prevent us from building selfconsistent models of what is objectively happening there.
Here is example of experiment where both corpuscular and wave nature of photons are simultaneously used: https://en.wikipedia.org/wiki/Afshar_experiment

The behavior of an electron can best be modelled by a charged particle or a wave.
Are you claiming that electron is switching between corpuscular and wave nature?
Absolutely not! An electron is and behaves like an electron at all times. We just don't have a single mathematical description that predicts it behavior under all circumstances.
If you insist that the world should be classical and continuous, that is a philosophical problem.
If you prefer to begin with observation and derive predictive mathematical descriptions of what actually happens, that's physics.
I really can't see why people get excited about quantum physics. A tabletop is a smooth surface when seen from a distance. As you get closer you can see wood grain, then wood cells, and eventually all sorts of different molecules. You wouldn't expect the same maths to describe a billiard ball, a fly, or a water molecule, interacting with a wooden table, nor do the cellulose molecules react differently to different mesoscopic stresses, but alcohol diffuses differently from water.

Indeed. People smear electron into quantum probability cloud, forgetting that objectively it is amazingly complex object: having fixed charge, magnetic dipole and angular momentum (allowing for acrobatics like Larmor precession or spin echo: https://en.wikipedia.org/wiki/Electron_paramagnetic_resonance#Pulsed_electron_paramagnetic_resonance )
and additionally some internal oscillation: zitterbewegung/de Broglie's clock, which has been observed experimentally: https://link.springer.com/article/10.1007/s1070100892251
(https://i.imgur.com/bBy41uT.png)
However, we don't understand even the electric charge part, as standard assumption of perfect point  supported experimentally only (?) through fitting parabola to 2 points, would mean infinite energy  nonsense.
It is time to finally stop hiding behind quantum mysticism and start asking the real missing basic questions.

Another argument for point nature of electron might be tiny crosssection, so let's look at it for electronpositron collisions:
One thing that comes to (my very inexpert) mind is that this "tiny crosssection" would be detectable only after the electron had been observed. My understanding is that it qualifies as a pointparticle after observation, but we have no evidence that it is before being observed.
Its helpful to know in these kinds of subjects that a quantum state remains in that state for a short time after its observed.

This is the point I reached after much thought. The main reason I started the “Copenhagen” thread was to try to find out if I was missing something.
No, you didn't miss anything. If you adhere to the Copenhagen definition, which has as much validity as anything else, then the two slit experiment clearly states that it is your choice of observation that defines the outcome. The wave particle nature is dual and co existing. You find people define it in different ways, but if we stay with just the experiment, not peoples conceptions of how to 'fit it' into what they expect nature to be, then a 'photon' is both a wave and a particle, and what defines it is you, your interaction with it. and the same goes for a propagation. A 'photon' is indeed not there until measured. It's not a ball.
When it comes to electrons they are tricky, if I remember right one can be f.ex. at two places at the same time. But they have a rest mass. https://en.wikipedia.org/wiki/Electron_rest_mass
https://www.sciencedaily.com/releases/2005/10/051013084257.htm
so it's not that simple
=
sort of weird :)
Was just looking for a refresher of my statement but the article contains the two slit experiment too, but with electrons. There are other experiments proving it too.

When it comes to electrons they are tricky, if I remember right one can be f.ex. at two places at the same time.
There is absolutely no need for such "bilocation" interpretation of interference, especially that it would require retrocausality to explain e.g. Wheeler's delayed choice experiment ( https://en.wikipedia.org/wiki/Wheeler's_delayed_choice_experiment ), confirmed e.g. by Aspect's group: which allows to choose between classical and quantum ("bilocation") behavior after such choice was already made.
In contrast, performing Madelung transformation: substituting psi = sqrt(rho) * exp(iS) to Schrodinger, we get continuity equation for density (rho), and HamiltonJacobi equation for the action (S), with horder correction from pilot wave: https://en.wikipedia.org/wiki/Pilot_wave_theory#Mathematical_formulation_for_a_single_particle
Such behavior was confirmed e.g. while measuring average trajectories of interfering photons: http://science.sciencemag.org/content/332/6034/1170.full
And it allows for a natural interpretation of e.g. double slit: particle travels one trajectory, its coupled (pilot) wave travels all trajectories, affecting trajectory of the particle
This way they have obtained interference also for classical waveparticle duality objects: http://dualwalkers.com/statistical.html
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fdualwalkers.com%2FIMAGES%2FDEVIATIONpost.jpg&hash=8b1d6e8be0b9115f3bd06b8dc9596451)

As I said Janek. you have a view of how you expect it to be.
=
But I'll side with Pete. The world have a way to put us upside down, questioning ourselves. But we're just as perfect as any other person.

Most of the things we decide are coming from our expectations, of what is a proper behavior, in this case of nature. If you wind that backwards you get to a place in where there are a few choices. It's magic, God exist. Not magic, God exist. Science and you just have to find the right questions, with or without a god. Can't say if you're right or wrong here, if science is your thing you will need further experimental proofs though.
=
And I better point out that in my case 'weak experiments/proofs' aint really my thing. Using that ones preconceptions comes into full bloom

Please take a look at title of this thread.
Instead of any trial to answer this crucial question, I see only general comments about mystery of QM ... or bilocation which also should remain in domain of religion.
Let's get back to science and try to understand e.g. configuration of electric field of fundamental charge  such that it does not exceed 511 keVs.

Please take a look at title of this thread.
Instead of any trial to answer this crucial question, I see only general comments about mystery of QM ...
And for good reason, too. QM is at the very heart of measurement of small quantities and any barrier to determining whether the electron is a point particle is related, at least in part, to QM. After all, that's why it hasn't be figured out yet and why it presents problems for QFT. In fact if the electron is a point particle then its self energy is infinite.

Don't get me wrong Janek. I answered Bill, not discussing your points. I don't really know. But I have a lot of respect of people thinking.

Sorry Janek, we're thinking though :)
Slightly abbreviated (eh inebriated), which makes my brain connect to a lot of different stuff.
But what I think makes us, is that we're not satisfied.
We want to know, whatever it takes.
=
really hate my spellchecker.
Still, it's life

And for good reason, too. QM is at the very heart of measurement of small quantities and any barrier to determining whether the electron is a point particle is related, at least in part, to QM. After all, that's why it hasn't be figured out yet and why it presents problems for QFT. In fact if the electron is a point particle then its self energy is infinite.
Once again, limitations of our measurements do not restrict objective values  the fact that we cannot measure parameters in the center of our sun does not mean that there objectively are no parameters there.
In contrast, for both center of sun and electron, we need a selfconsistent model of what is going on there  while we cannot directly measure them, we can test indirect consequences of such models.
For example it seemed we cannot measure wavefunction of atomic orbitals (until https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.165404 ), but we use selfconsistent model predicting values there (Schrodinger equation)  and confirm its far consequences like energy differences.
Regarding energy of electron, if we meet it with positron, we get just 2 x 511keV energy of electromagnetic wave  models predicting energy of electron above 511 keVs (like perfect point charge) just make no sense.

maybe Janek. You need to link your sources, and when you do you probably also need to explain the way you read them. If I would guess, which I do a lot, then I think you want 'forces'. as in 'action and reaction'. Am I right?
If you do, where do they come from?
=
I think you need to break it down, not linking to people using hard mathematics. You need to show me where you started and why you still think this is the way to go. I won't be a judge but I'm interested
=
Whether they are perfect points?
If what you have is a emanation decided by your experiment, does it need to be inside a geometry?
You do, I do, but we're macroscopic, What's called decoherence in physios
Another question if you consider this might be, what creates a geometry?

Arnold Neumaier has responded on stack ( https://physics.stackexchange.com/questions/397022/experimentalboundariesforsizeofelectron )  he has gathered many materials on this topic:
https://www.mat.univie.ac.at/~neum/physfaq/topics/pointlike.html
But still no clear argument that electron is much smaller then femtometer (?)
Anyway, to better specify the problem, define E(r) as energy in a radius r ball around electron.
We know that E(r) ~ 511keVs for large r, for smaller it reduces e.g. by energy of electric field. Assuming perfect point charge, we would get E(r) > infinity for r>0 this way. Where does divergence from this assumption starts?
More specifically: for example where is maximum of E'(r)  in which distance there is maximal deposition of 511keVs energy?
Or median range: such that E(r) = 511/2 keVs.
It is not a question about the exact values, only their scale: ~femtometer or much lower?

I like you man, keep on putting holes in the theories. I'll give you another thing to think of.
https://phys.org/news/201505electron.html
" When an electron splits in two "
Bill made me wonder this. ' (electron) how can a pointparticle be superimposed?'

There is now some blind faith the electrons are perfect points ... which turns out supported only (?) by Dehmelt's fitting parabola to two points ...
Because of it, we still don't know e.g. structure of EM fields around electron (standard assumption of perfect point would mean infinite energy), or charge quantization: that Gauss law can only return integer (maybe /3 or /2) charge.
These are extremely important basic ignored problem, which can be repaired e.g. by soliton particle models ( https://www.dropbox.com/s/aj6tu93n04rcgra/soliton.pdf ) ... physicists need to finally start asking these fundamental questions.
Thanks for the interesting article, but it probably can be explained with statistical interpretation: 1/2 charge as 1/2 probability.

Yes, but fractions are interesting in themselves :)
Still, physics never seem to end, which is what I like.

The problem is that current physics has fixed on adding new terms to standard model QFT ... which, due to mathematical difficulties, directly operates on perfect points, removing resulting infinities by hand: especially ultraviolet divergence and divergence of perturbative series say that in fact they are not perfect points  we wouldn't have these issues if they were.
It is not just a matter of natural further development of physics ... but rather of finally returning to ignored fundamental questions like structure of EM field of electron.

I know Jarek.
And I see your frustration. But a lot of current theories are about 'normalization'. And 'normalization' comes from statistics in my mind.

Doesn't really matter maybe, but in a wider sense all physics is about what the experiments and statistics tells you.

think you will find this one interesting Jarek
And weird :)
https://news.brown.edu/articles/2014/10/electron there's a link to the paper in it.