"Electron" computer simulation?

[Genady]

Can a computer program be made that fully and accurately simulates an electron?

[dimreepr]

23 minutes ago, Genady said:

Can a computer program be made that fully and accurately simulates an electron?

On one hand, doesn't a computer already do that? On the other, isn't an electron a fuzzy ball of probability?

TBH I'm not sure what you're asking.

Shor's algorithm would seem to qualify.

[Genady]

Something like this. The input is an electron's state and an interaction, if there is one, and the output is result of a measurement.

[dimreepr]

4 minutes ago, Genady said:

Something like this. The input is an electron's state and an interaction, if there is one, and the output is result of a measurement.

Shor's algorithm would seem to qualify.

[Genady]

5 minutes ago, dimreepr said:

Shor's algorithm would seem to qualify.

How?

[John Cuthber]

25 minutes ago, dimreepr said:

Shor's algorithm would seem to qualify.

Really?

[dimreepr]

31 minutes ago, John Cuthber said:

Really?

Probably not.

[Duda Jarek]

Electron is much more - quantized electric charge, somehow of finite energy (infinite for perfect point charge) ... plus magnetic dipole moment and angular momentum ... plus zitterbewegung/de Broglie clock - confirmed experimentally: https://link.springer.com/article/10.1007/s10701-008-9225-1

We can simulate some aspects of electron, but it seems we are still far from its complete understanding.

[Genady]

1 hour ago, Duda Jarek said:

Electron is much more - quantized electric charge, somehow of finite energy (infinite for perfect point charge) ... plus magnetic dipole moment and angular momentum ... plus zitterbewegung/de Broglie clock - confirmed experimentally: https://link.springer.com/article/10.1007/s10701-008-9225-1

We can simulate some aspects of electron, but it seems we are still far from its complete understanding.

Ignoring new physical effects that we don't understand, can we simulate everything we know well about electron? If not, what aspects we cannot simulate?

[Genady]

Imagine we have "an electron simulator", which simulates behavior of an electron in various conditions. Let's run two instances of the simulator and let them communicate with each other. Would they simulate an interaction between two electrons?

[Markus Hanke]

14 hours ago, Genady said:

Ignoring new physical effects that we don't understand, can we simulate everything we know well about electron? If not, what aspects we cannot simulate?

In relativity it is often wondered what it would be like to ride on a beam of light. One could ask a similar question here - what would it be like to ride on an electron, or any other quantum object for that matter? Can this be simulated? From a top-down vantage point, an electron is well described as a Dirac spinor living on a classical spacetime. But what if we reverse this? If an electron (or any other quantum object) were sentient, what would the rest of the universe look like to such an observer, given the validity of all of known quantum physics? How could one even describe such a vantage point mathematically? Are there fundamental reasons to assume that such observers cannot exist? How would a quantum observer describe a classical frame?

Or more generally put - is there a transformation between mathematical objects of some kind that maps a classical frame into the rest frame of a quantum system and vice versa (fully accounting for all quantum effects of course!), similar to how Lorentz transformations map between vantage points of different inertial frames?

Is this even a meaningful question?

PS. I understand of course that an electron isn't a 'little ball of matter' that one could ride on, but nonetheless I think the above is an interesting question to ponder.

[Genady]

6 hours ago, Markus Hanke said:

Or more generally put - is there a transformation between mathematical objects of some kind that maps a classical frame into the rest frame of a quantum system and vice versa (fully accounting for all quantum effects of course!), similar to how Lorentz transformations map between vantage points of different inertial frames?

I think that Bell theorem answers this question negatively.

[swansont]

On 5/10/2023 at 7:25 AM, Genady said:

Can a computer program be made that fully and accurately simulates an electron?

No, for two reasons.

A computer simulation rests on some algorithm, which would be based on quantum mechanics. Do all systems allow an analytic QM solution? No. Some require numerical solutions, which are not exact.

Does QM provide a full description of an electron? Also no. The uncertainty principle, for example.

 

[Genady]

7 minutes ago, swansont said:

No, for two reasons.

A computer simulation rests on some algorithm, which would be based on quantum mechanics. Do all systems allow an analytic QM solution? No. Some require numerical solutions, which are not exact.

Does QM provide a full description of an electron? Also no. The uncertainty principle, for example.

 

Re reason 1. A simulation could use numerical methods and calculate with precision according to a measuring instrument.

Re reason 2. Wave function provides a full QM description. The simulation could calculate eigenvalues with the associated probabilities and output an answer accordingly.

Wouldn't the above solve these two issues?

[swansont]

1 hour ago, Genady said:

Re reason 1. A simulation could use numerical methods and calculate with precision according to a measuring instrument.

Does that “fully and accurately” simulate an electron?

Any measuring instrument is limited in its precision.

1 hour ago, Genady said:

Re reason 2. Wave function provides a full QM description. The simulation could calculate eigenvalues with the associated probabilities and output an answer accordingly.

Does it? What about terms that are not eigenvalues, or do not commute?

And can you determine the wave function for all systems, and solve the equations analytically?

 

[Genady]

Let's reformulate the question then:

To what extent can a computer program approximately simulate QM behavior of electron?

Which aspects of it cannot be simulated in principle?

[Markus Hanke]

On 5/11/2023 at 2:36 PM, Genady said:

I think that Bell theorem answers this question negatively.

Yes, so this is the crux of the matter. Since Bell's theorem implies an absence of local realism, then in what sense is the concept of a 'rest frame' even meaningful for quantum systems such as electrons? At a minimum, being at rest wrt to something would imply that both position and momentum of that object are simultaneously known precisely, or else the notion of 'relative rest' is meaningless. But a vanishing commutator like this implies we are in a classical situation, so there's a contradiction.

So are we to understand that quantum systems do not possess any rest frame in the usual sense, except perhaps as a helpful approximation? 

[Genady]

2 hours ago, Markus Hanke said:

in what sense is the concept of a 'rest frame' even meaningful for quantum systems such as electrons?

It is a frame in which expectation value of the electron momentum vanishes.

[Markus Hanke]

On 5/13/2023 at 9:39 AM, Genady said:

It is a frame in which expectation value of the electron momentum vanishes.

Right, I see. So, what we are really talking about when we speak of the “rest frame” of a quantum system is a region of space V where:

\[\langle p\rangle =-i\hbar \int _{V} \psi ^{*}\frac{\partial }{\partial x} \psi \ d^{3} x=0\]

wherein x is to be understood as the appropriate collection of coordinates. Ordinarily the region V would need to be all of space, or at least large enough to ensure proper normalisation of the wave function. 

So in essence this is a statistical statement about a region of space, given by the volume integral of some (probability) density. This is remarkably different from the notion of “rest frame” as used in (eg) GR.

Just trying to develop a more intuitive grasp on the relationship between classical and quantum frames here.