What is the current scientific consensus on the shape of an electron?

[Buckeye]

Does String (M) theory predict a shape for the electron? If so, what shape or shapes are proposed so far?

 

[rtharbaugh1]

String theory has been criticized for not predicting anything, so I would think the answer must be, NO.

In general, the electron itself is not thought to have any shape, because its boundaries fall under the scale where quantum processes predominate over the statistical processes which give us our common idea of shape of objects. In one sense, the shape of an electron is the shape of the orbital it inhabits, because we cannot say that it is located at any moment in one part of the orbital or in another, or even that it is strictly located in the orbital at all. This interpretation of the shape of an electron makes the electron much larger than the proton, for instance, and it is not a standard approach to the idea of size of an electron.

Instead, we consider the measureable energy of an electron, and use a calculation to determine its Compton wavelength. This measure gives us an idea of the size of the region of space in which an electron might be likely to interact with some other particle which happens to inhabit the same region.

In general, the idea of shape at the scale of the electron is not clearly defined. String theory uses six or more compact dimensions at small scales, and it is a commonly stated legend in physical circles that humans cannot imagine any shape in more than three or maybe four dimensions.

I personally hold some hope that human imagination may not be so limited, but even so I cannot give you any idea of what a six dimensional electron might look like, in string or M or any other theory.

Hope this helps...

Richard

 

[Buckeye]

String theory has been criticized for not predicting anything, so I would think the answer must be, NO.
In general, the electron itself is not thought to have any shape, because its boundaries fall under the scale where quantum processes predominate over the statistical processes which give us our common idea of shape of objects. In one sense, the shape of an electron is the shape of the orbital it inhabits, because we cannot say that it is located at any moment in one part of the orbital or in another, or even that it is strictly located in the orbital at all. This interpretation of the shape of an electron makes the electron much larger than the proton, for instance, and it is not a standard approach to the idea of size of an electron.
Instead, we consider the measureable energy of an electron, and use a calculation to determine its Compton wavelength. This measure gives us an idea of the size of the region of space in which an electron might be likely to interact with some other particle which happens to inhabit the same region.
In general, the idea of shape at the scale of the electron is not clearly defined. String theory uses six or more compact dimensions at small scales, and it is a commonly stated legend in physical circles that humans cannot imagine any shape in more than three or maybe four dimensions.
I personally hold some hope that human imagination may not be so limited, but even so I cannot give you any idea of what a six dimensional electron might look like, in string or M or any other theory.
Hope this helps...
Richard

If free electrons do not have a shape, then how does the Klystron microwave beam manage to transfer momentum to the electrons in a synchrotron when the beam operator needs to rebalance the load?

And why do so many researchers still struggle to define the charge based radius of the electron (Mac Gregor, Malcolm H. "The Enigmatic Electron". Boston: Kluwrer Academic, 1992)
Rc = 3.86 x 10-11 cm
Rqmc = 6.64 x 10-11 cm to 6.70 x 10-11 cm

 

[rtharbaugh1]

It sounds like you already feel you have an answer and are asking rhetorical questions to provoke a response.

I did not say electrons do not have a shape, I only replied to your question about predictions from string theory, which AFAIK are none, at least about the shape of the electron. Perhaps someone else here will have something more about this.

Your new question about momentum transfer seems to suppose that momentum transfer is related to shape. Could you say more about this? It seems you have some kind of special knowledge about it. It could be quite interesting, imho, if momentum transfer were linked to shape somehow.

My imagination tells me that electrons are possibly affected by microwaves in much the same way as larger objects are affected by larger waves. Standing microwaves might generate a slope down which electrons might accelerate. However I am only trying to understand these things myself and do not offer this as an authority but only in the interest of conversation.

Also, if this is any help to you, researchers study many things, some of which turn out to be justified by results, most of which do not. Basic reaseach is usually not designed to produce a predetermined result. In any case, the 'charge based radius' sounds to me like it has to do with the effective range in which an electron might be expected to react to a given charge. 10^-11 cm is smaller than the radius of a proton, and IIRC is very close to the quantum limit of measurment.

Perhaps you know that quantum effects begin to predominate at about this scale. Under these conditions it becomes impossible to say exactly where an object is if you know its momentum exactly, or if you know its position exactly at any time, it becomes impossible to know anything about what its momentum is. Momentum would be affected by charge in this case, so I believe.

Good luck in your study.

Richard

 

[Buckeye]

Apologies if I wrote in a gruff way. Not my intent. There are several difficult people in this forum, so...

It sounds like you already feel you have an answer and are asking rhetorical questions to provoke a response.

I'm working on understanding a few things, yes. An answer, no, not yet.

I did not say electrons do not have a shape, I only replied to your question about predictions from string theory, which AFAIK are none, at least about the shape of the electron.

In general, the electron itself is not thought to have any shape...

I guess I misinterpreted this quote...Yes-No?

Your new question about momentum transfer seems to suppose that momentum transfer is related to shape. Could you say more about this? It seems you have some kind of special knowledge about it. It could be quite interesting, imho, if momentum transfer were linked to shape somehow.

Sorry, no special knowledge regarding shape and momentum.

In any case, the 'charge based radius' sounds to me like it has to do with the effective range in which an electron might be expected to react to a given charge. 10^-11 cm is smaller than the radius of a proton, and IIRC is very close to the quantum limit of measurment.

Hopefully, the newly developed "intense" source of gamma rays will help.

Perhaps you know that quantum effects begin to predominate at about this scale. Under these conditions it becomes impossible to say exactly where an object is if you know its momentum exactly, or if you know its position exactly at any time, it becomes impossible to know anything about what its momentum is.

Heisenberg's supposition (HUP) was useful in its time, but time has past, and it is time for new methods to determine if HUP is meaningful or simply an outcome of the limits of measurement available at that time .

 

[rtharbaugh1]

I am pleased to continue discussion with you.

In general, the electron itself is not thought to have any shape. In general, because there may be someone somewhere who wants to insist on a shape. However in the past three years I have been reading about the geometry of very small spaces, and I can say that my sampling of the common opinion leads me to believe, always open to correction, that very few if any current researchers are unwilling to accept the idea that the electron is a point charge, hence zero dimensional, hence without measurable shape.

That is my impression of what people I imagine to be better informed than myself are thinking. Of course, nature is hardly democratic, and truth has often turned out to contradict commonly held beliefs, so I retain some doubt.

As for the HUP, my impression is that it is firmly established and unlikely to be overturned anytime soon. Which high energy gamma ray observations do you have in mind? And in what way do they provide a challenge to HUP?

My reading leads me to believe that HUP cannot be upended by any improvements in our ability to measure. It is founded on the idea that there is a fundamental relationship between the idea of location and the idea of momentum, such that any improvement in precision of measurement of one idea results in loss of information about the other. I am pretty sure that any supportable challenges to HUP would be big news.

Wikipedia has a nice summary of HUP at

http://en.wikipedia.org/wiki/Uncertainty_principle

Wiki also has information about Klystron tubes at

http://en.wikipedia.org/wiki/Klystron_tube

Enjoy your study.

Thanks,

Richard

 

[Buckeye]

I am pleased to continue discussion with you.
In general, the electron itself is not thought to have any shape. In general, because there may be someone somewhere who wants to insist on a shape. However in the past three years I have been reading about the geometry of very small spaces, and I can say that my sampling of the common opinion leads me to believe, always open to correction, that very few if any current researchers are unwilling to accept the idea that the electron is a point charge, hence zero dimensional, hence without measurable shape.

The problem with a point charge is that the Charge/Radius value goes to infinity forcing QED to invoke Renormalization to justify the covenants of QED.

That is my impression of what people I imagine to be better informed than myself are thinking. Of course, nature is hardly democratic, and truth has often turned out to contradict commonly held beliefs, so I retain some doubt.

Information comes in two flavors: Dis- and Pro-, and then there was the Pope who denied Galileo, and Kepler who hid in fear. I prefer to be the doubter, the antagonistic dreamer of a better level of knowledge.

As for the HUP, my impression is that it is firmly established and unlikely to be overturned anytime soon. Which high energy gamma ray observations do you have in mind?

Linear and circularly polarized gamma rays with enough intensity can interact with either free or bound electrons of light elements, (H, He...) and will provide more insight on the sizes of the fields of the electron. Crossed beams of femto-sec lasers UV and higher eV range have the potential to test HUP's supposition that we can not determine momentum and position at the same time if IMHO I am foreseeing the future clearly. If however, we are "unlucky" enough to develop a gamma-ray laser, which is in progress, the HUP will surely be tested because the cross-section is small enough.

 

[rtharbaugh1]

I was under the impression that we can measure the charge density distribution in an electron field, but that it is everywhere greater than zero. Since the energy is essentially distributed infinitely, the charge density of the field is nowhere infinite. There are no sharp boundaries to the field, it is isotropic. A smaller probe would find the edge, if there were one, but HUP says there isn't any edge. There is only an area, thicker in the middle and thinner as you progress outward. No edge in sight. Maybe it is a Riemann surface.

R

 

[Buckeye]

I was under the impression that we can measure the charge density distribution in an electron field, but that it is everywhere greater than zero. Since the energy is essentially distributed infinitely, the charge density of the field is nowhere infinite. There are no sharp boundaries to the field, it is isotropic. A smaller probe would find the edge, if there were one, but HUP says there isn't any edge. There is only an area, thicker in the middle and thinner as you progress outward. No edge in sight. Maybe it is a Riemann surface.
R

Hmmm, let me take a different tact. A single hydrogen atom with one proton and one electron has a radius of 0.53e-8 cm while the classical radius of the electron is 2.8e-11 cm. How do we get a particle with a classical radius of 2.8e-11 cm to convert into a QM particle with a radius of 0.53e-8 cm?

 

[selfAdjoint]

Hmmm, let me take a different tact. A single hydrogen atom with one proton and one electron has a radius of 0.53e-8 cm while the classical radius of the electron is 2.8e-11 cm. How do we get a particle with a classical radius of 2.8e-11 cm to convert into a QM particle with a radius of 0.53e-8 cm?

What classical radius are you quoting? None of these numbers mean anything in the field theory of the electron; due to the uncertainty principle it doesn't have a well defined position or trajectory and its "amplitude cloud" does, in certain eigenstates, intersect the proton. This is all handled in the theory and extremely accurate experimental predictions are made.

 

[Buckeye]

What classical radius are you quoting? None of these numbers mean anything in the field theory of the electron; due to the uncertainty principle it doesn't have a well defined position or trajectory and its "amplitude cloud" does, in certain eigenstates, intersect the proton. This is all handled in the theory and extremely accurate experimental predictions are made.

Sorry 'bout that. Your right of course.
I'm trying to learn what happens to a free electron that is captured by a free proton.
I am confused when I think about the beam of electrons in a synchrotron and the how they might be considered within HUP. The same goes for a bolt of lightning. Guess I'm up to my eyeballs in confusion just now.

 

[DM]

In general, because there may be someone somewhere who wants to insist on a shape. However in the past three years I have been reading about the geometry of very small spaces, and I can say that my sampling of the common opinion leads me to believe, always open to correction, that very few if any current researchers are unwilling to accept the idea that the electron is a point charge, hence zero dimensional, hence without measurable shape.

Unfortunately "someone somewhere who wants to insist on a shape" happens to be all physics and chemistry books. The electron has been given a spherical shape for many years, it seems all illustrated books have adopted this belief. The latter part of your statement is also correct. The majority of books and people conceive the electron not to have a measurable shape due to its infinitesimal geometrical shape. However, isn't this idea somewhat misleading? In my mind, all geometrical shapes, irrespective of how big or indeed how small they are known to be, must have a measurable size. So I'd like to raise a small question to you, Sir. Are you implying that shapes such as that of an electron cannot be measured due to its size OR as I believe you mean, cannot be measured due to the absence of an apparatus capable of measuring such shape?