What's the Force Acting on an Isolated Electron at (0,0,0)?

[SpectraCat]

If you have a string bound at both sides oscillating as a standing wave and you put your hand somewhere on it and hold until the energy from the wave is absorbed into your hand you could say

"I found the energy right here where I placed my hand and now if I place my hand anywhere else on the string I do not find any energy"

Ok, that seems grossly oversimplified, but let's run with it ... you could also do another experiment where you made two separate measurements at two points in space x and x', where 1/4 of the energy was measured at point x and 3/4 was measured at x'. This is of course possible because the energy of the string is a continuous variable.

The point Matterwave and I have been trying to drive home is that you cannot do the analogous experiment for an electron. It is a discrete particle (as far as we know), and no experiment has succeeded in measuring a fraction of an electron.

Your points seem to reduce to "there is no explanation for quantum phenomena in the framework of classical physics", which of course we will all agree to. You have indicated a personal preference to emphasize the wave-nature of quantum systems as somehow being more significant than their particle nature. I have been trying to show that there is not a general consensus within the physics community that such emphasis is justified.

 

[LostConjugate]

Ok, that seems grossly oversimplified, but let's run with it ... you could also do another experiment where you made two separate measurements at two points in space x and x', where 1/4 of the energy was measured at point x and 3/4 was measured at x'. This is of course possible because the energy of the string is a continuous variable.

Ok let's say you did this experiment. You setup a measuring device at two different points on the string. Now each device must collapse this standing wave and absorb the energy in order to make a measurement but let's say with this string there is only enough total kinetic energy in the string to make a single recording.

This may be a very fragile system with huge limitations in the measuring devices but so is measuring an electron.

 

[SpectraCat]

Ok let's say you did this experiment. You setup a measuring device at two different points on the string. Now each device must collapse this standing wave and absorb the energy in order to make a measurement but let's say with this string there is only enough total kinetic energy in the string to make a single recording.

This may be a very fragile system with huge limitations in the measuring devices but so is measuring an electron.

This is a red herring AFAICS. Even if one allows perfect, noise free, ideal instrumentation with infinite sensitivity, there is no experiment one can propose, consistent with the laws of Q.M. as we understand them, which can measure a fraction of an electron. So the issue of measurement precision doesn't enter into it.

For your example of the energy of the string, in the ideal case you can just say, "improve the sensitivity of the experiment until you can measure the fractional energy in two places". Since you are assuming a purely classical system with a continuous energy variable, this will always work.

 

[LostConjugate]

This is a red herring AFAICS. Even if one allows perfect, noise free, ideal instrumentation with infinite sensitivity, there is no experiment one can propose, consistent with the laws of Q.M. as we understand them, which can measure a fraction of an electron. So the issue of measurement precision doesn't enter into it.

For your example of the energy of the string, in the ideal case you can just say, "improve the sensitivity of the experiment until you can measure the fractional energy in two places". Since you are assuming a purely classical system with a continuous energy variable, this will always work.

But for two measurements some time dt must be present between each measurement. I have never heard of the wave function taking time to collapse.

 

[eaglelake]

I see what you mean, eaglelake.
But I'm sorry to say you probably misunderstand what I said in #11.
Because the reduced mass in #11 is used also in the hydrogen solution of the Schroedinger equation (this is the same as the Bohr model.)

Bohr's 1913 calculations are erroneous in many ways, as you know. He did not use Schrodinger's equation. Bohr's 1913 solution is not the same as Schrodinger's equation, which does gives the correct solution for the the Hydrogen atom.

As you know, if you don't use this form of the reduced mass, the correct energy levels of the Schroedinger equation would not be obtained. This is a well-known fact. But if you want to arrive at this equation of the reduced mass, you have to think about the classical rotaion of the electron. Do you know some other ways of getting this \mu=m_{e}m_{p}/(m_{e}+m_{p}) using only quantum mechanics?

If you know more about the Bohr model, see this thread.
I think the historical parts (in 1920's) are not explained in detail in the ordinary QM textbooks.

You are correct: the reduced mass should be used. But, the significant thing here is that what we now call quantum mechanics uses Schrodinger's equation. The reduced mass, on the other hand, is not an essential concept in quantum mechanics. I am puzzled why you put so much emphasis on it.

The old quantum mechanics that existed prior to 1927 is now understood to be a mess that erroneously tried to modify classical mechanics to explain quantum events. Every new problem required ad hoc assumptions to make it work. We do ignore it today, because that is not how we do quantum mechanics. Today, when we say "quantum mechanics", it is understood to be 1927 and later.

 

[eaglelake]

But then the particle states of which the waves are a superposition would need to be described in the position basis and once again would become a particle of waves. So the particle is a particle of waves of particles of waves of particles of waves...

Is it the chicken or the egg?

This is a common misconception - that somehow the particle is a wave, or a superposition of waves, This is not true! The fallacy occurs when we confuse the particle, which is a part of the experiment, with the state function, which is a mathematical thing that we use to determine probabilities. The state function is a probability amplitude defined in a linear function space. The state function does not describe the behavior of the particle as it traverses through the experimental apparatus. Nor does the state function propagate in 3-space, as the particle does. Particles interact with particle detectors, state functions do not. No experiment has ever revealed a state function moving along with the particle.

The quantum mechanical explanation of tunneling is thus: If the momentum state is an eigenstate of momentum, i.e. we have prepared particles with a known momentum, then there is an infinite uncertainty in the particles position. That means we have no idea where the particle will be found when we make a position measurement. The experimental results verify this. Position measurements find some particles in front of the barrier, while other measurements find it behind the barrier, as if it had somehow penetrated (tunneled?) through the barrier. But such a view is a classical picture that has no connection with the results of this experiment. All we know is that, in the tunneling experiment, some particles are found beyond the barrier, and with the state function, we can predict the probability of this happening. Neither quantum theory nor the actual experiment gives a mechanism for such behavior. There is no answer to the question, "how did the particle get beyond the barrier"? Quantum mechanics doesn't tell us, and we know classical mechanics doesn't work.
Best wishes

 

[meopemuk]

All we know is that, in the tunneling experiment, some particles are found beyond the barrier, and with the state function, we can predict the probability of this happening. Neither quantum theory nor the actual experiment gives a mechanism for such behavior. There is no answer to the question, "how did the particle get beyond the barrier"? Quantum mechanics doesn't tell us, and we know classical mechanics doesn't work.
Best wishes

This is exactly right. QM is not designed to provide mechanistic explanations of "why" and "how" things happen. QM is only a mathematical formalism that allows us to predict results of measurements.

The endless debates about "interpretations" of quantum mechanics and "is electron a particle or a wave?" cannot be resolved by scientific means. These debates result from unrealistic expectations that physics must give us detailed mechanisms of everything happening in nature, including things that happen when no observations are made. One can invent dozens of such mechanisms, including such bizarre ideas that the whole world splits into infinite number of copies once an electron touches a measuring device. These ideas cannot be checked by experiments, so they do not belong to science.

Feynman was right that one should not ask too many questions about QM. "Shut up and calculate!"

Eugene.

 

[ytuab]

Bohr's 1913 calculations are erroneous in many ways, as you know. He did not use Schrodinger's equation. Bohr's 1913 solution is not the same as Schrodinger's equation, which does gives the correct solution for the the Hydrogen atom.

You are correct: the reduced mass should be used. But, the significant thing here is that what we now call quantum mechanics uses Schrodinger's equation. The reduced mass, on the other hand, is not an essential concept in quantum mechanics. I am puzzled why you put so much emphasis on it.

The old quantum mechanics that existed prior to 1927 is now understood to be a mess that erroneously tried to modify classical mechanics to explain quantum events. Every new problem required ad hoc assumptions to make it work. We do ignore it today, because that is not how we do quantum mechanics. Today, when we say "quantum mechanics", it is understood to be 1927 and later.

eaglelake, SpectraCat, thanks for your reply.

But I think this thread is about "whether the force is influencing the momentum or not in QM".
You said "There is no force acting. Force is a classical concept." in #10.
Of cource I see what you mean. But the reduced mass is an essential concept in QM.
If you don't use the nuclear movement, the energy error would be greater than the relativistic energy error.
If you think the reduced mass is not related to the nuclear movement(this is the same as the electron movement), the equation of the reduced mass as I said above would not be obtained. Here I mean the electron movement is the classical rotaion or the classical oscillation by the classical force.

If we do m_{p} \to \infty, the reduced mass \frac{m_{e}m_{p}}{m_{e}+m_{p}} \to m_{e}. this means the reduced mass is related to the nuclear (or electron) movement.
Using only the QM methods or only the Coulomb potential (not force) we can't ariive at this equation of the reduced mass.

 

[LostConjugate]

Whew... well at least I proved my point that its not for fact a particle. I see your point about how a wave function in an infinite LVS is not the same as waves in 3-space. Will keep it in mind.

 

[SpectraCat]

eaglelake, SpectraCat, thanks for your reply.

But I think this thread is about "whether the force is influencing the momentum or not in QM".
You said "There is no force acting. Force is a classical concept." in #10.
Of cource I see what you mean. But the reduced mass is an essential concept in QM.
If you don't use the nuclear movement, the energy error would be greater than the relativistic energy error.
If you think the reduced mass is not related to the nuclear movement(this is the same as the electron movement), the equation of the reduced mass as I said above would not be obtained. Here I mean the electron movement is the classical rotaion or the classical oscillation by the classical force.

If we do m_{p} \to \infty, the reduced mass \frac{m_{e}m_{p}}{m_{e}+m_{p}} \to m_{e}. this means the reduced mass is related to the nuclear (or electron) movement.
Using only the QM methods or only the Coulomb potential (not force) we can't ariive at this equation of the reduced mass.

Look, reduced mass has NOTHING to do with QM or CM per se ... it is not somehow essential, as you seem to be making out to be. Yes, the H-atom levels are wrong if you don't take the finite mass of the nucleus into account ... why should that be surprising?

Reduced mass is simply a transformation to an inertial frame of reference that is more computationally convenient. It is probably possible to work out all of these solutions in an inertial frame where the motion of each particle is considered independently, but AFAIK nobody bothers to do that because it is WAY harder, and would anyway be equivalent to the known solutions using reduced mass.

 

[SpectraCat]

Whew... well at least I proved my point that its not for fact a particle. I see your point about how a wave function in an infinite LVS is not the same as waves in 3-space. Will keep it in mind.

Who said it was just a particle? I never did ... I said that experiments designed to measure particle properties do exactly that, and likewise for experiments designed to measure wave properties.

Another poster said it was a particle *with an associated probability wave*, which is just a casual description of the deBroglie-Bohm picture of Q.M., which is also completely consistent with available experimental evidence.

Oh .. and I also said, "An electron is neither a particle nor a wave, and it is both." ... which is a phrasing I came up with and like a lot, but probably has already been said by someone before me.