Can an electron be in two places at the same time?

[Magneto_1]

Yes, but the fact a particle has mass does not imply it has volume, which is what you said.

Please stop giving out wrong information, and then closing post for no apparent reason, other than you don't like or agree with what is being written by the poster.

OnlyMe, is correct in stating that all mass has volume and mass density. In fact the person that defined "Mass" Isasac Newton defined it that way.

In the Principia Mathematica, written by Newton, he defines mass in terms of density, which naturally assumes a volume.

Look it up!

 

[Reiku]

There does seem to be a vagueness between volume, mass and density. I don't think many actually appreciate that a particle, which has a mass could even not have a volume... that is (outside the scientists group). Most scientists just appreciate that most tests on particles show them to be more or less pointlike.

Though, saying this, no matter how hard we have tried to measure a radius for an electron, it is sufficiently difficult. There are some tests at the moment which are trying to study the magnetic moment of an electron to determine whether it has any shape or size.

 

[Reiku]

I guess if it has a radius, it must be so tremendously small, that if it was any smaller by any fraction it would possibly be a pointlike system.

 

[Reiku]

The classical electron radius depends on the Compton Wavelength.

Actually I should be careful here. The classical radius actually technically depends on mass, it's charge and the speed of light.

$$\frac{e^2}{Mc^2}$$

What I meant by the Compton Wave length, is that it is as 1/137 big as the classical radius. The Compton wavelength on the other hand depends on $$\hbar$$, $$c$$ and $$M$$. The Compton Wavelength and the Classical Radius are related through the fine structure constant, that little number 1/137 we just covered.

In such a rush, need to go!

 

[Magneto_1]

There does seem to be a vagueness between volume, mass and density.

Vagueness with whom. It is very clear to me & Newton!

Most scientists just appreciate that most tests on particles show them to be more or less pointlike.

How do you measure a point?

Though, saying this, no matter how hard we have tried to measure a radius for an electron, it is sufficiently difficult. There are some tests at the moment which are trying to study the magnetic moment of an electron to determine whether it has any shape or size.

I am aware of these experiments, and I am waiting for the results that will describe the shape of the electron as a torus.

You are right in that it is sufficiently difficult measure the radius of the electron.

But, tell me which electron radius should they concentrate on, there appears to be three:

1) ~ 1x10^-13
2) ~ 2x10^-15
3) ~ 5.29x10-11

Which of the three electron radii do we look for?

 

[Reiku]

How do you measure a point?

You are right in that it is sufficiently difficult measure the radius of the electron.

But, tell me which electron radius should they concentrate on, there appears to be three:

1) ~ 1x10^-13
2) ~ 2x10^-15
3) ~ 5.29x10-11

Which of the three electron radii do we look for?

I don't have my figures with me at the moment. I think the classical electron radius is around $$3 \cdot 10^{-15}$$. As I said I have no fugures with me at the moment, so I might be off a factor or two. Anyway, we measure whether mass particles are like pointlike systems through scattering processes I'd presume.

I am going to make a guess, but maybe your three radii are in relation to the Bohr radius, Compton wavelength and the Classical electron radius?

Not sure, don't have my figures with me and I really need to rush now!!!!

 

[Magneto_1]

I am going to make a guess, but maybe your three radii are in relation to the Bohr radius, Compton wavelength and the Classical electron radius?

Not sure, don't have my figures with me and I really need to rush now!!!!

Yes. Precisely!

1) ~ 1x10^-13 (Compton/Brown Radius)
2) ~ 2x10^-15 (Classical Electron Radius)
3) ~ 5.29x10-11 (Bohr Radius)

 

[prometheus]

Vagueness with whom. It is very clear to me & Newton!

You're only about 400 years out of date. It is well known that newtonian physics doesn't work on very small scales - that's why we need quantum mechanics. Trying to treat particles as classical objects simply fails.

 

[OnlyMe]

You're only about 400 years out of date. It is well known that newtonian physics doesn't work on very small scales - that's why we need quantum mechanics. Trying to treat particles as classical objects simply fails.

Prometheus,

QM sets aside gravity, as insignificant at the involved scales. Given the equivalence principle and its association of gravity and inertia, if you were to also set aside inertia as far as QM is involved, would that not have some affect on the application of Newtonian mechanics?

I am not suggesting that is does. It just occurred to me that one of the problems in treating particle spin as clasical angular momentum might involve the inertial implications. If inertia were not involved, a particle spinning faster than c, would be of little concern. Especially if the OPERA FTL neutrino issue is at some point confirmed.

Are there other practical issues aside from the c limit and inertia?

 

[Reiku]

Prometheus,

QM sets aside gravity, as insignificant at the involved scales. Given the equivalence principle and its association of gravity and inertia, if you were to also set aside inertia as far as QM is involved, would that not have some affect on the application of Newtonian mechanics?

I am not suggesting that is does. It just occurred to me that one of the problems in treating particle spin as clasical angular momentum might involve the inertial implications. If inertia were not involved, a particle spinning faster than c, would be of little concern. Especially if the OPERA FTL neutrino issue is at some point confirmed.

Are there other practical issues aside from the c limit and inertia?

Actually, the math which describes particle spin in quantum mechanics is identical to the math which describes it in a classical sense as well.

 

[OnlyMe]

Actually, the math which describes particle spin in quantum mechanics is identical to the math which describes it in a classical sense as well.

I understand that. What I was thinking about was the issue involbing the FTL angular momentum required for the magnetic moment of an electron to be what it seems to be, if it were associated with angular momentum... And the debate that rises from that...

 

[Reiku]

I understand that. What I was thinking about was the issue involbing the FTL angular momentum required for the magnetic moment of an electron to be what it seems to be, if it were associated with angular momentum... And the debate that rises from that...

Oh right.

You are talking about what if the electron was an actual spinning object? Well as you note, that doesn't work for a pointlike particle because you would need to rotate it $$720^o$$ to get it back to it's original orientation. For a classical radius of course, objects can be easily rotated $$360^o$$ and find that they have been orientated back to their original starting point.

 

[Magneto_1]

You're only about 400 years out of date. It is well known that newtonian physics doesn't work on very small scales - that's why we need quantum mechanics.

The queston and my statements were not about Newtonian Mechanics in general, it was about mass, volume, and density; and this is very specific.

Are you claiming that Quantum Mechanics treats mass and density differently than say classical mechanics? Ignoring the mechanics and mathematics of Special Relativity.

Trying to treat particles as classical objects simply fails.

This is true, on the Atomic and Sub-Atomic scales there are particle-waves; and they not "point particles" or "marble" type particles in the classical sense. They are spread out in space or volume, spin, and have an energy density.

 

[Reiku]

This is true, on the Atomic and Sub-Atomic scales there are particle-waves; and they not "point particles" or "marble" type particles in the classical sense. They are spread out in space or volume, spin, and have an energy density.

yes but any attempt to measure this wave directly will result in a collapse of the wave function, as I am sure you aware of. You still end up with a pointlike particle?

 

[Magneto_1]

yes but any attempt to measure this wave directly will result in a collapse of the wave function, as I am sure you aware of. You still end up with a pointlike particle?

No, you collapse the wave function into a localized entity that is called a particle. There is no evidence that a particle-wave collapses into a point.

The wave function collapses to allow you to measure either position or momentum accurately; but not both simultaneously. Or the collapse will allow you to measure the energy and time of collapse; but not both simultaneously.

 

[Reiku]

No, you collapse the wave function into a localized entity that is called a particle. There is no evidence that a particle-wave collapses into a point.

I think you are beginning to favor your own view over experimental verification. Not only that, but you are arguing my point as if I am flawed. You are not really arguing me, you are arguing mainstream physics.

There is evidence a particle's wave will collapse to a point, if all experimental evidence suggests that particle behaves like a pointlike system.

 

[Magneto_1]

I think you are beginning to favor your own view over experimental verification. Not only that, but you are arguing my point as if I am flawed. You are not really arguing me, you are arguing mainstream physics.

If you are feeling flawed, then don't blame me.

There is evidence a particle's wave will collapse to a point, if all experimental evidence suggests that particle behaves like a pointlike system.

Point me to evidence that a particle's wave will collapse to a point.

Points represent a location in relation and relative to some inertial frame of reference. Now you can place a particle-wave at that point location. But a particle or wave is not a point. A point is a location, a point as a particle is a myth.

The reason that we have point particles is that they make for good simplifying of description of systems.

For example, I can describe an enclosed volume of space that is filled with Nitrogen gas. I can model the mathematics and describe: Pressure, Force, velocity, velocity squared inertia, and energy equation of state. Now I can describe entirely this system assuming the Nitrogen atoms are point particles. When in actually a Nitrogen atom is made of seven electons, seven protons, and seven neutrons.

You are mistaken the concept for point particles as being real entities, when the purpose for using point particles is for simplying the mathematics and description of the system. When you narrow your view down to one Nitrogen atom you will determine that it is not a point.

 

[prometheus]

The queston and my statements were not about Newtonian Mechanics in general, it was about mass, volume, and density; and this is very specific.

If you want to talk about fundamental particles then Newtonian mechanics is simply the wrong physics to use. It's like trying to hammer in nails with a kitchen knife - you're using the wrong tool for the job.

Are you claiming that Quantum Mechanics treats mass and density differently than say classical mechanics? Ignoring the mechanics and mathematics of Special Relativity.

For non relativistic QM, no. If you're considering quantum field theory as you should be to understand the interactions of fundamental particles then mass is treated as it is in relativity.

This is true, on the Atomic and Sub-Atomic scales there are particle-waves; and they not "point particles" or "marble" type particles in the classical sense. They are spread out in space or volume, spin, and have an energy density.

In an imprecise nutshell, that is what I said before.

 

[Reiku]

If you are feeling flawed, then don't blame me.



Point me to evidence that a particle's wave will collapse to a point.

Points represent a location in relation and relative to some inertial frame of reference. Now you can place a particle-wave at that point location. But a particle or wave is not a point. A point is a location, a point as a particle is a myth.

The reason that we have point particles is that they make for good simplifying of description of systems.

For example, I can describe an enclosed volume of space that is filled with Nitrogen gas. I can model the mathematics and describe: Pressure, Force, velocity, velocity squared inertia, and energy equation of state. Now I can describe entirely this system assuming the Nitrogen atoms are point particles. When in actually a Nitrogen atom is made of seven electons, seven protons, and seven neutrons.

You are mistaken the concept for point particles as being real entities, when the purpose for using point particles is for simplying the mathematics and description of the system. When you narrow your view down to one Nitrogen atom you will determine that it is not a point.

The fact science is telling us matter behaves at the fundamental level like pointlike particles is all the evidence I require to state that a wave function will collapse to a pointlike system. That is just how it works.

When you have figured a precise mathematical way to express classical terms for an electron in a way that reconciles quantum field theory, then I will apologize and hand you a certificate.

 

[wellwisher]

Electrons are both particles and waves, due to the wave-particle nature of matter. An interesting conceptual consideration is say we had two electrons, in relative motion, such that their waves were to cancel. The crests of one waves cancels the valleys of the other. Since the two waves cancel, would this disrupt the particle-wave duality, since all that remains will be two particles but no waves?