Spooky action at a distance by electrons?

[Happiness]

Electrons are indistinguishable, but we may pretend that they are distinguishable if their wave functions do not overlap in space. For example, an electron "a" in Chicago and an electron "b" in Seattle would produce a zero integral in [5.20], and so their indistinguishablilty would not produce any different observable compared to those of distinguishable particles.

But any 2 electrons always overlap in space because their wave functions are never zero! For example, the radial wave functions of the hydrogen electron are all proportional to $e^{-kr}$, where $k$ is a constant. So, that makes [5.20] never zero. And from [5.22], we know the distance between the electrons (in fact, any 2 electrons in the Universe) change when any electron has its wave function altered. That means a change to the electron in Chicago instantaneously causes a change to the electron in Seattle. This is obvious if you consider the giant wave function encompassing all the electrons in the Universe. This giant wave function has to be antisymmetric (since electrons are fermions), and so any change to one electron must result in an instantaneous change to at least one other electron to keep the giant wave function antisymmetric.

This seems to enable faster-than-light communication, because I could instantaneously take measurements on the electrons at Seattle to know instantaneously whether or not there is a change to the one at Chicago. Also, this seems to violate locality, because just by moving my hands, I am changing the position of all the electrons in the Universe instantaneously.

Reference: Intro to QM, David J Griffiths, p208

 

[PeterDonis]

any 2 electrons always overlap in space because their wave functions are never zero!

The idealized wave functions, such as the one you give for a single electron in a hydrogen atom, are never zero, true. But that just means those idealized wave functions are approximations; we use them because they are mathematically tractable and because we don't know how to write down the true wave function of an electron in a hydrogen atom in Chicago which makes clear that it can't instantaneously affect another electron in Seattle.

This seems to enable faster-than-light communication

This seems to violate locality

Yes, and this should be a big red flag that the idealizations I referred to above are leading you astray. In fact, the strong empirical evidence that we can't communicate FTL and can't violate locality in the way you describe (note that many physicists describe things like EPR correlations that violate the Bell inequalities as "nonlocal", so the term "locality" requires some care in definition) is also evidence that, as above, the wave functions we use in our math (because it's the only way we know how to actually solve the math) are idealized and don't exactly represent the true wave functions of the electrons.

 

[DrChinese]

This seems to enable faster-than-light communication, because I could instantaneously take measurements on the electrons at Seattle to know instantaneously whether or not there is a change to the one at Chicago.

Suppose this is true (an instantaneous change). How does that allow you to communicate FTL? All Bob in Chicago is a random outcome. That is the case regardless of what Alice does in Seattle.

 

[Happiness]

the wave functions we use in our math are idealized and don't exactly represent the true wave functions of the electrons.

But we get them from solving the Schrodinger equation. How do you know that they are idealisations?

Also, if the wave function of an electron does indeed become zero and remain zero after a certain distance, then what distance would that be? Suppose that distance is 10 km, but why 10 km? There seems to be no reason for 10 km or such a magic number to appear. It seems more realistic that the wave function gets weaker and weaker but never reaches zero, as distance increases, just like how light and sound intensity does.

Could it be that FTL communication and non-locality are true but not yet achievable by current technology? Or maybe those wave functions are always non-zero, but there will be some difficulty stopping one from having FTL communication?

 

[Mentz114]

But we get them from solving the Schrodinger equation. How do you know that they are idealisations?

Also, if the wave function of an electron does indeed become zero and remain zero after a certain distance, then what distance would that be? Suppose that distance is 10 km, but why 10 km? There seems to be no reason for 10 km or such a magic number to appear. It seems more realistic that the wave function gets weaker and weaker but never reaches zero, as distance increases, just like how light and sound intensity does.
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Could it be that FTL communication and non-locality are true but not yet achievable by current technology? Or maybe those wave functions are always non-zero, but there will be some difficulty stopping one from having FTL communication?

Wave functions must be square-integrable.

https://www.physicsforums.com/threads/square-integrable-wave-functions-vanishing-at-infinity.889483/

Could it be that FTL communication and non-locality are true but not yet achievable by current technology? Or maybe those wave functions are always non-zero, but there will be some difficulty stopping one from having FTL communication?

No.

 

[PeterDonis]

we get them from solving the Schrodinger equation. How do you know that they are idealisations?

You are thinking of it backwards. We know the solutions are idealizations because, taken literally, they tell us things that are obviously contrary to experiment, like that an electron in Chicago could suddenly appear in Seattle.

Therefore, the Schrodinger Equation itself must be an idealization (or perhaps a better term would be approximation). And we already know that anyway because it's non-relativistic.

if the wave function of an electron does indeed become zero and remain zero after a certain distance, then what distance would that be?

Nobody knows; we can't do experiments precisely enough to figure this out.

Suppose that distance is 10 km

It would obviously be a lot smaller than that. Not only don't electrons jump spontaneously from Chicago to Seattle, they don't spontaneously jump from one side of your lab to the other. The kinds of distances we are talking about would be of the order of the size of ordinary objects like tables or chairs that have electrons confined in them.

 

[Happiness]

Suppose this is true (an instantaneous change). How does that allow you to communicate FTL? All Bob in Chicago is a random outcome. That is the case regardless of what Alice does in Seattle.

Since the giant wave function for all the electrons must remain antisymmetric, no change in Chicago produces no change in Seattle, and a change in Chicago produces a change in Seattle. (For simplicity, we assume all the electrons in the Universe are either in Chicago with Charlie or in Seattle with Sophie.)

Suppose Charlie has one electron in Chicago and Sophie has a large number of electrons, say 1 million. Sophie then set up all her electrons to spin up. That would fix Charlie's electron into some state. Charlie wants to communicate to Sophie the start of some special event. They have agreed that once that event in Chicago starts, Charlie would alter his electron.

What Sophie needs to do is to constantly measure her 1 million electrons, to see if they are all spin up. If they are, it means there is no change in Seattle, and so no change in Chicago, and so the event has not started. But once the event in Chicago starts, Charlie would alter his electron, and some of Sophie's electrons would spin down. Sophie then would be informed of the event before the news traveling at the speed of light could reach her.

 

[charters]

Any state of two electrons - |2> - is not the tensor product of two one particle states, and measurements cannot prepare strictly localized states. We can really only talk about physically possible configurations of the global electron field. In your case, the effectively localized state of the field has a high concentration lump in Chicago and a high concentration lump in Seattle and low elsewhere (but not strictly vacuum). So the low concentration region in Denver - is this the tail of the Chicago electron or the Seattle electron? The question is just ill-posed - its not the tail of either, just a tail region of the global |2> state. This indistinguishability is why even non-relativistic/first quantized "particle" quantum mechanics is really properly understood a field theory (though in a more general sense than QFT being a field theory).

Now, let's say the effectively localized state |2> only effectively localizes the two lumps relatively poorly, over the whole cities. You can then decompose |2> along a new basis which is a superposition of states that are (maximally) Compton localized in Chicago, but unaffected in Seattle. Decoherence along this basis is what we mean by measuring the electron in Chicago while leaving the Seattle electron alone.

Remember also only fermionic bilinears are observable. Measurement in a fermion-only theory, ie not coupled to gauge bosons, does not quite make sense.

 

[Happiness]

You are thinking of it backwards. We know the solutions are idealizations because, taken literally, they tell us things that are obviously contrary to experiment, like that an electron in Chicago could suddenly appear in Seattle.

But maybe it did suddenly appear in Seattle. But this happens exceedingly rarely, not totally impossible though. And when it did happen, nobody was actually looking. The people in Chicago did not keep track of all their electrons to realize that they lost one electron to Seattle on say, Sep 21, 1935.

 

[charters]

But maybe it did suddenly appear in Seattle. But this happens exceedingly rarely, not totally impossible though. And when it did happen, nobody was actually looking. The people in Chicago did not keep track of all their electrons to realize that they lost one electron to Seattle on say, Sep 21, 1935.

This type of argument assumes N particle states can be strictly localized in the first place, which is wrong, at least without a severe redefinition of vacuum states.

 

[Happiness]

Now, let's say the effectively localized state |2> only effectively localizes the two lumps relatively poorly, over the whole cities. You can then decompose |2> along a new basis which is a superposition of states that are (maximally) Compton localized in Chicago, but unaffected in Seattle. Decoherence along this basis is what we mean by measuring the electron in Chicago while leaving the Seattle electron alone.

Remember also only fermionic bilinears are observable. Measurement in a fermion-only theory, ie not coupled to gauge bosons, does not quite make sense.

Your points seem too advanced for me to understand. Could you explain without using terms like "decoherence" or "fermionic bilinears"? Or explain them further in simple concepts?

So what are the implications of your points? Is there spooky action at a distance? Is FTL communication or non-locality (faster-than-light causality) possible? I am guessing you are trying to say that these may be possible in theory but somehow would be impossible to be experimentally verified?

 

[charters]

There are "spooky" spacelike EPR correlations but there is nothing FTL associated with this. Your basic problem is you are thinking of a process like this:

1) I measure that the electron is exactly and perfectly and only right here in my Chicago lab.

2) The electron wavefunction would, immediately after this measurement, instantly grow tails infinitely far away.

3) These tails signify nonzero amplitude/detection probability in Seattle or Andromeda galaxy, so a measurement of the electron position in Seattle or Andromeda has a response rate above its vacuum expectation.

4) Therefore the electron jumped, FTL, from Chicago to Seattle or Andromeda.

The flaw is a too naive conception of measurement, in which anything ever gets strictly localized in the sense of steps 1 and 3. These exact position states are pathological. Realistic N particle states are only effectively localized, so they are more like Gaussians than delta functions or anything with compact support.

 

[PeterDonis]

Suppose Charlie has one electron in Chicago and Sophie has a large number of electrons, say 1 million. Sophie then set up all her electrons to spin up. That would fix Charlie's electron into some state.

Why?

 

[PeterDonis]

maybe it did suddenly appear in Seattle. But this happens exceedingly rarely, not totally impossible though. And when it did happen, nobody was actually looking

Now you are just waving your hands. We have no experimental evidence that this ever happens. The fact that one particular (approximate, non-relativistic) theory tells us it might happen is not a good reason to believe that it actually does happen. For such a belief we would need some evidence, and we have none.

 

[Happiness]

Why?

Because we are assuming these 1 million and one electrons are all the electrons in the Universe, and Charlie's electron must adopt a state that makes the giant wave function antisymmetric.

 

[PeterDonis]

So what are the implications of your points? Is there spooky action at a distance? Is FTL communication or non-locality (faster-than-light causality) possible?

No. More precisely, our best current theory, quantum field theory, says they're impossible. (Note that the Schrodinger Equation is not QFT; it's a non-relativistic approximation.)

 

[PeterDonis]

Because we are assuming these 1 million and one electrons are all the electrons in the Universe, and Charlie's electron must adopt a state that makes the giant wave function antisymmetric.

That does not come anywhere close to fixing the state of Charlie's electron. "Antisymmetric" does not mean "Charlie's electron has to have opposite spin". Antisymmetry applies to the entire, 1,000,001-electron wave function, including all degrees of freedom (position/momentum and spin) of each electron. Now try and write down all the possible 1,000,001-electron wave functions that are antisymmetric and have 1,000,000 of them located in Seattle and 1 of them located in Chicago. You will find there are a lot of them.

 

[DrChinese]

Since the giant wave function for all the electrons must remain antisymmetric, no change in Chicago produces no change in Seattle, and a change in Chicago produces a change in Seattle. (For simplicity, we assume all the electrons in the Universe are either in Chicago with Charlie or in Seattle with Sophie.)

Suppose Charlie has one electron in Chicago and Sophie has a large number of electrons, say 1 million. Sophie then set up all her electrons to spin up. That would fix Charlie's electron into some state. Charlie wants to communicate to Sophie the start of some special event. They have agreed that once that event in Chicago starts, Charlie would alter his electron.

What Sophie needs to do is to constantly measure her 1 million electrons, to see if they are all spin up. If they are, it means...

...What that means is that none are entangled with any other particle outside of Seattle. You can't both know an electron's spin AND it remain entangled on that basis.

Thus: whatever you do in Chicago, remains in Chicago.

 

[PeroK]

Your points seem too advanced for me to understand. Could you explain without using terms like "decoherence" or "fermionic bilinears"? Or explain them further in simple concepts?

So what are the implications of your points? Is there spooky action at a distance? Is FTL communication or non-locality (faster-than-light causality) possible? I am guessing you are trying to say that these may be possible in theory but somehow would be impossible to be experimentally verified?

There is another fundamental flaw in your reasoning. Suppose we have an electron in a box in Seattle and an electron in a box in Chicago.

There electrons are continually monitored. The two experiments carry on for some time.

Let's assume that every now and again the electron escapes from its box. The box isn't a perfect electron container. And every now and again another electron gets in, so you have two electrons in your box.

Let's finally suppose that one day the electron escapes from the box in Chicago and, at about the same time, a second electron appears in the box in Seattle.

As electrons are indistinguishable there is no way, theoretically or practically, to say that the electron from Chicago escaped to the box in Seattle.

The Chicago lab cannot ring up the Seattle lab and ask them to check if they've got the Chicago electron there.

Also, even if we accept that the Chicago electron could be found in Seattle, it is fantastically more likely that the Chicago electron escapes out into the Chicago lab and the second Seattle electron came into the box from the Seattle lab.

All you can really say is that the two experiments were ended by unwanted interaction with the rest of the universe.

 

[PeroK]

Because we are assuming these 1 million and one electrons are all the electrons in the Universe, and Charlie's electron must adopt a state that makes the giant wave function antisymmetric.

You haven't provided any information on your profile, but as you have been quoting Griffiths's book I assume you are seriously trying to learn QM.

There must be 100 threads on this site about why entanglement does not support FTL communication.

But, if you are a serious student, you must eradicate the fundamental misconceptions about QM that you currently have. Instead, you are doing what a lot of people do and attributing their misconceptions as a challenge to mainstream physics.

My advice is to forget entanglement, FTL communication and the hydrogen atom until you have fully understood the nature of quantum spin.