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

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Offline PmbPhy

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I've seen the question
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Can an electron be in two places at the same time?
poised a great number of times and in almost all cases the responder says "yes" where in fact the answer is "no." I'm looking for the source of such assertions because I want to write a paper on the subject. Can someone find the source of this question and the answer as well? Thanks.

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Offline evan_au

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Re: Can an electron be in two places at the same time?
« Reply #1 on: 12/09/2014 23:41:00 »
An extreme case of this is Richard Feynman's conjecture that there is only one electron in the universe - we just see it in many places at once.
See: http://en.wikipedia.org/wiki/One-electron_universe

However, the question seems to be more aimed at the double-slit experiment conducted with electrons, where the interference fringes suggest that a single electron has passed through both slits at the same time before hitting a target.

This is just like laser light, which can pass through two slits at once, causing an interference pattern - even if the light intensity is so attenuated that only one photon is in transit at once.

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Offline chiralSPO

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Re: Can an electron be in two places at the same time?
« Reply #2 on: 13/09/2014 00:02:15 »
I believe that the misconception has to do with the fact that an electron is usually not localized. There can be two (or infinitely many) positions in which something has an equal probability of interacting with the electron...

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Offline lightarrow

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Re: Can an electron be in two places at the same time?
« Reply #3 on: 13/09/2014 11:10:02 »
It depens on how you define "an electron"   [:)]
Defined as the wavefunction which represents it, the answer is yes; defined as the properties of its detection the answer is no.
Defined as "an irreeducible representation of an Hilbert space on the Poincarè Group with charge -e, mass 9.11*10-31 kg and spin ħ/2" I would have some difficulty to answer.

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Offline JohnDuffield

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Re: Can an electron be in two places at the same time?
« Reply #4 on: 13/09/2014 16:22:58 »
Can someone find the source of this question and the answer as well? Thanks.
I can't find the source, but the answer is yes. The electron has a wave nature. A wave is not some point-particle thing. It's quantum field theory, and the electron's field is what it is. It's always in more than one place at once.   

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Offline PmbPhy

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Re: Can an electron be in two places at the same time?
« Reply #5 on: 13/09/2014 20:30:27 »
Can someone find the source of this question and the answer as well? Thanks.
I can't find the source, but the answer is yes. The electron has a wave nature. A wave is not some point-particle thing. It's quantum field theory, and the electron's field is what it is. It's always in more than one place at once.

As is the case too many times John, you're wrong. It most certainly is not the case. As I said in the OP in fact the answer is "no." so if you have another opinion I have no interest in hearing it.

I wrote about this to a physicist I know. He got his PhD at Princeton and worked as a physics professor at Harvard.
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The statement is nonsense.  It arises from the mistaken idea that an electron is a little spinning object (made out of ...?).  An electron is much more subtle than that.

A similar confusion exists with respect to the photon.  While teaching the course from which my book Newton to Einstein emerged, I coined the sentence, "Light travels as a wave but departs and arrives as a particle."  No classical concept--electromagnetic wave or tiny solid particle--corresponds to the truly novel nature of light.

Similarly, no classical concept can capture all the attributes of what we call "an electron."

My friend at Boston University, whose also a world renown physicist, also confirmed this for me too (since I always knew it but enjoy having things confirmed before I talking about them in forums).

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Offline jeffreyH

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Re: Can an electron be in two places at the same time?
« Reply #6 on: 13/09/2014 22:35:14 »
I agree with you Pete but out of interest how does this relate to the double slit experiment. Is it a wave disturbance in the electromagnetic field that causes interference? Like an echo?
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Offline PmbPhy

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Re: Can an electron be in two places at the same time?
« Reply #7 on: 14/09/2014 07:26:35 »
Quote from: jeffreyH
I agree with you Pete but out of interest how does this relate to the double slit experiment. Is it a wave disturbance in the electromagnetic field that causes interference? Like an echo?
Thanks buddy! :) The particles have a specific energy and that energy is used to determined the de Broglie wavelength. Then we have particles moving along different trajectories and as such they have a different phase when they get to the screen. That difference in phase causes an interference pattern to form.

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Offline JohnDuffield

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Re: Can an electron be in two places at the same time?
« Reply #8 on: 14/09/2014 10:54:44 »
As is the case too many times John, you're wrong. It most certainly is not the case. As I said in the OP in fact the answer is "no." so if you have another opinion I have no interest in hearing it.
I'm not wrong about this. Your friend must have misunderstood what you were asking. The electron is not some little point-particle thing. We make electrons (and positrons) out of light waves in pair production. We can diffract electrons. In atomic orbitals electrons "exist as standing waves". The electron has a magnetic dipole moment, and the Einstein-de Haas effect demonstrates that "spin angular momentum is indeed of the same nature as the angular momentum of rotating bodies as conceived in classical mechanics." And when we annihilate the electron with a positron, we typically get two light waves. The evidence is rock-solid, the wave nature of matter is not in doubt. And waves are not point-particles. Again, the electron is not some point particle thing that has a field, its field is what it is. And that field is always in two places at the same time.

I rather fear your friend gave you the brush-off with this. You should contact him referring to the above evidence, and perhaps he'll give you a considered response.

The particles have a specific energy and that energy is used to determined the de Broglie wavelength. Then we have particles moving along different trajectories and as such they have a different phase when they get to the screen...
They have a wavelength and a phase because they are waves.
« Last Edit: 14/09/2014 10:59:03 by JohnDuffield »

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Offline PmbPhy

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Re: Can an electron be in two places at the same time?
« Reply #9 on: 14/09/2014 11:50:48 »
I agree with you Pete but out of interest how does this relate to the double slit experiment. Is it a wave disturbance in the electromagnetic field that causes interference? Like an echo?
I see from John's misunderstanding how you might have also misunderstood something too.

I think you confused a moving electron's electric and magnetic field as being an electromagnetic field that causes interference. That's not the case at all.

What electromagnetic field are you talking about? Is it the EM field of electron? No. It's the wavelength and phase of the wave function of the electrons.

As I said earlier. The frequency is due to the wave function. The electric and magnetic field of a moving electron doesn't have a frequency to it. However the location of the slits are related to the phase of particles as I recall.

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Offline JohnDuffield

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Re: Can an electron be in two places at the same time?
« Reply #10 on: 14/09/2014 13:19:43 »
Pmb: have a read of Ehrenberg and Siday's 1949 paper The Refractive Index in Electron Optics and the Principles of Dynamics . This is the paper that predicted the Aharonov-Bohm effect, see figure 2 on page 19 which depicts the phase being "advanced" by the solenoid. It's a paper that talks of optics and potential and waves, not point particles. In QED the electron is described as an excitation of the electron field. QFT stands for quantum field theory. Not quantum point-particle theory. Also have a look at weak measurement work by Aephraim Steinberg et el and by Jeff Lundeen et al

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Offline yor_on

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Re: Can an electron be in two places at the same time?
« Reply #11 on: 16/09/2014 14:33:25 »
Pete, I don't agree there. The electron is normally defined as some sort of probability cloud. Doing so you can define it to anywhere inside that 'cloud', before a measurement. After a measurement it is different though, as seen by the photographs made by Lund university of a 'electron orbiting' :)

"To demonstrate the quality and value of the triplets, researchers tested local realism—finding evidence that, as quantum theory predicts, entangled particles do not have specific values before being measured.* Researchers also measured one of each of a succession of triplets to show they could herald or announce the presence of the remaining entangled pairs. An on-demand system like this would be useful in quantum repeaters, which could extend the range of quantum communications systems, or sharing of secret data encryption keys." http://phys.org/news/2014-09-charm-nist-detectors-reveal-entangled.html#ajTabs

It's just a example of the principle I think is there.
==

Also I had some papers defining the possibility of finding electrons existing in different places 'simultaneously', and experimentally so, but it's been some time since? I know I linked them here though, but maybe a year or two ago?
« Last Edit: 16/09/2014 14:53:54 by yor_on »
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Offline yor_on

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Re: Can an electron be in two places at the same time?
« Reply #12 on: 16/09/2014 14:59:20 »
Logically it shouldn't be possible to a 'real time' measurement of a 'same electron' though, in two 'places' so if that is what you mean I will agree. But the probabilities, and possibilities, of a electron affecting outcomes even without that observer measuring seems very high, I would call it a certainty that it could, assuming it to exist. And as it is that cloud?
=

You can do the interference pattern using just one 'photon' at a time, and the only way that singular 'photon' can create that 'wave pattern', as I know? is for it to be assumed to somehow interfere with itself, passing both slits simultaneously. Alternatively define it as a product of a field, observed. There is no real problem to this if we define under a arrow though. Under a arrow you should only find one outcome at a time, measuring. At least I think it should be that way, although it might also depend on how you define that outcome, aka setting your 'system'.
« Last Edit: 16/09/2014 15:30:24 by yor_on »
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Offline Bill S

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Re: Can an electron be in two places at the same time?
« Reply #13 on: 16/09/2014 19:29:31 »
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It depends on how you define "an electron"

It also depends on how you define “place”.  In general it must be defined as a position in space.  Space must be restricted to the three dimensions that we experience.  Any additional dimensions that may be suggested are mathematical concepts which may, or may not, bear any relation to reality. 

The question that must arise is: “Can we restrict a quantum object (quon) to the dimensions of the observable – macro – Universe?”

Quantum mechanics works, but no one really knows why.  There is something about QM that eludes the best efforts our scientists and mathematicians.

Infinity has similar features.  Mathematicians have shown that infinity can be a valuable concept, but there is always something about it that cannot be tamed.

Perhaps looking for a link here is fanciful.  Perhaps it should be left to philosophers, but, on the other hand, if it could lead to a clearer understanding of reality; if it could throw some light on some of the apparent paradoxes of the Universe, surely it is worth considering.
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Offline JohnDuffield

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Re: Can an electron be in two places at the same time?
« Reply #14 on: 16/09/2014 19:52:03 »
Yor_on, Bill: IMHO if you read up about weak measurement, you come to appreciate that the Copenhagen Interpretation is old hat, and the photon really is a wave. Have a look at an ocean wave:



Look under the surface. That wave isn't some localized point-particle thing. It's always in two places at the same time. So is the photon. It's a wave in space, where there is no ocean surface, and it genuinely goes through both slits. But when you detect it at one slit, something like an optical Fourier transform occurs and the photon is transformed into a dot. This goes through one slit only. Then when you detect it at the screen, something like an optical Fourier transform occurs and the photon is transformed into a dot. Simple mundane stuff, no magic, and no multiverses.

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Offline David Cooper

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Re: Can an electron be in two places at the same time?
« Reply #15 on: 16/09/2014 21:25:15 »
For something to be in one place, the whole of it must be in that place. If some of it is not in that place, that part is in a different place. To say that anything is in two places at the same time is wrong unless the whole of it is in both places at the same time. If a green apple is in two places at the same time, it could be sitting on one side of a set of scales while also being in a fruit bowl on a table some distance away. It would be able to balance a red apple on the other side of the scales, an apple of the same mass but which is only located in one place. That doesn't happen though, because when we're dealing with the quantum world we would have to say that the green apple is both sitting on one side of the scales while balancing the red apple AND it's sitting in the fruit bowl while not balancing the red apple, though that then spoils things because it means the red apple has to be sitting on balanced scales and sitting lower down on unbalanced scales at the same time as well.

So, it's complicated stuff, and it's easy for people to disagree while actually believing the same thing and talking at cross purposes. Tighten up your use of language and you might resolve the issue.

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Offline jeffreyH

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Re: Can an electron be in two places at the same time?
« Reply #16 on: 16/09/2014 21:27:02 »
Yor_on, Bill: IMHO if you read up about weak measurement, you come to appreciate that the Copenhagen Interpretation is old hat, and the photon really is a wave. Have a look at an ocean wave:



Look under the surface. That wave isn't some localized point-particle thing. It's always in two places at the same time. So is the photon. It's a wave in space, where there is no ocean surface, and it genuinely goes through both slits. But when you detect it at one slit, something like an optical Fourier transform occurs and the photon is transformed into a dot. This goes through one slit only. Then when you detect it at the screen, something like an optical Fourier transform occurs and the photon is transformed into a dot. Simple mundane stuff, no magic, and no multiverses.

I can very much appreciate that point of view.
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Offline Bill S

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Re: Can an electron be in two places at the same time?
« Reply #17 on: 16/09/2014 21:44:06 »
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So, it's complicated stuff, and it's easy for people to disagree while actually believing the same thing and talking at cross purposes.

Absolutely!  I think that's very common.
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Offline Bill S

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Re: Can an electron be in two places at the same time?
« Reply #18 on: 16/09/2014 21:52:31 »
Arguing that a wave is not in more than one place at a time unless the whole wave is in two places at once seems very reasonable.  I would certainly agree with that if the wave is finite; but what if the wave is infinite?  Does that make any difference?
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Offline jeffreyH

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Re: Can an electron be in two places at the same time?
« Reply #19 on: 16/09/2014 21:59:57 »
I think the magnetic flux through a surface external to the source of the field is an important consideration.

http://en.wikipedia.org/wiki/Meissner_effect
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Offline alancalverd

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Re: Can an electron be in two places at the same time?
« Reply #20 on: 16/09/2014 22:50:07 »
Go back to the double slit experiment. When we detect a single photon or electron, we find a single-point interaction with the detector. But if we look at the spatial distribution of many such single events, it looks as though each photon or electron has interfered with itself.

It's nonsense to say that a photon or even an electron is a particle or a wave. It is an entity whose behaviour can be modelled by wave and particle equations. Models are not reality, only a convenient approximation to it. 
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Offline jeffreyH

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Re: Can an electron be in two places at the same time?
« Reply #21 on: 16/09/2014 23:17:02 »
When considering the path of the magnetic field around a superconductor we see a disturbance of the normal behavior. A field is not a particle but we can split it in two. What happens if we fire a photon or an electron at a superconductor? We think we already know the answer but has anyone actually tried this? Also what happens to an electric field in the vicinity or a superconductor?
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Offline Bill S

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Re: Can an electron be in two places at the same time?
« Reply #22 on: 16/09/2014 23:18:18 »
I need some help here, please.  I don't see the connection between the Meissner effect and the possibility of a quon being in more than one place at a time.
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Offline jeffreyH

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Re: Can an electron be in two places at the same time?
« Reply #23 on: 16/09/2014 23:44:53 »
The electric field arises from particle charge. If this can be split by a superconductor then if an individual particle is very close to a superconductor what happens to its field lines? If the field from an individual particle can be split in two what does that say about the properties of particles?
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Offline yor_on

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Re: Can an electron be in two places at the same time?
« Reply #24 on: 17/09/2014 02:22:02 »
Tried to search for it Pete, but there's too many posts nowadays :)
Found this though: http://www.mpg.de/511738/pressRelease20051011

It's not the exact same as I was thinking of though, but it is interesting.
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Offline JohnDuffield

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Re: Can an electron be in two places at the same time?
« Reply #25 on: 17/09/2014 09:30:12 »
For something to be in one place, the whole of it must be in that place. If some of it is not in that place, that part is in a different place. To say that anything is in two places at the same time is wrong unless the whole of it is in both places at the same time...
That's the mistake. Imagine a magnet's magnetic field. It isn't like the green apple. It doesn't have an outside surface. Instead there is no point where it stops. Think of the electron as something like that, minus the magnet in the middle. It's quantum field theory, in QED the electron is an excitation of the electron field. It's "just field", and whilst there might be a middle to it like a hurricane has an eye, it just doesn't make sense to claim that all of it is in one place.

If a green apple is in two places at the same time, it could be sitting on one side of a set of scales while also being in a fruit bowl on a table some distance away. It would be able to balance a red apple on the other side of the scales, an apple of the same mass but which is only located in one place. That doesn't happen though, because when we're dealing with the quantum world...
...we're dealing with quantum field theory. Everything is fields and waves, and these things just don't have a surface.

So, it's complicated stuff, and it's easy for people to disagree while actually believing the same thing and talking at cross purposes. Tighten up your use of language and you might resolve the issue.
I don't think it is complicated actually. I think people make it complicated because they think in terms of billiard balls rather than waves in space.

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Offline evan_au

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Re: Can an electron be in two places at the same time?
« Reply #26 on: 17/09/2014 12:49:58 »
A slight diversion:
Quote from: jeffreyH
When considering the path of the magnetic field around a superconductor we see a disturbance of the normal behavior. A field is not a particle but we can split it in two.
If you can split something in two (and detect that it is split in two) but without changing its nature then you are not dealing with a fundamental object, but with a composite object.

For example, you can split a liter of nitrogen in two without changing its nature, but if I split a nitrogen molecule in two, it has very different properties - so I have reached the fundamental unit of nitrogen gas (at standard temperature & pressure).

There is a fundamental quantised unit of magnetic flux that is found when you cool a superconducting doughnut below its critical temperature in a steady magnetic field. The Meissner effect expels the magnetic field from the superconductor, and the magnetic field through the hole is quantised.

If you had two holes, you could detect this quantised flux in one hole or the other - and it will stay "pinned" there until the superconductor heats up again.

Before you measure the flux, there is uncertainty about where the flux resides - but this is classical uncertainty (ie I don't know where it is because I haven't looked yet), not quantum uncertainty (ie I don't know where it is because it is delocalised).

The magnetic fields we normally deal with are far larger than one magnetic flux quantum, giving the illusion that a magnetic field is infinitely divisible (plus, most of us don't deal with superconductors on a daily basis - except maybe alancalvard).
« Last Edit: 17/09/2014 21:30:15 by evan_au »

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Offline PmbPhy

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Re: Can an electron be in two places at the same time?
« Reply #27 on: 17/09/2014 14:02:31 »
Quote from: Bill S
Quote
It depends on how you define "an electron"
Hi Bill,

Where did you get this to quote it from? May I request that from now on you let us know whom you're quoting? It makes it easier to let us know who and what you're referring to. Thanks buddy! :)

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Offline PmbPhy

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Re: Can an electron be in two places at the same time?
« Reply #28 on: 17/09/2014 14:05:06 »
Quote from: JohnDuffield
..we're dealing with quantum field theory.
The purpose of this thread is quantum mechanics, not quantum field theory. The subject of this thread is about location of particles in space and not fields. If you wish to talk about QFT then please start your own thread. Please don't usurp mine.

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Offline Bill S

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Re: Can an electron be in two places at the same time?
« Reply #29 on: 17/09/2014 15:49:14 »
Hi Pete,

Sorry, that was a genuine oversight.  I was not rashly assuming that those in the thread would necessarily have read it. :) The quote was from Lightarrow: #3.
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Offline JohnDuffield

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Re: Can an electron be in two places at the same time?
« Reply #30 on: 17/09/2014 17:23:20 »
The purpose of this thread is quantum mechanics, not quantum field theory. The subject of this thread is about location of particles in space and not fields. If you wish to talk about QFT then please start your own thread. Please don't usurp mine.
It isn't a matter of usurping your thread, it's a matter of getting the physics right. A photon is not a point particle. It has an energy E=hf or E=hc/λ. It has a wavelength. The electron is not a point-particle either. Again, we make electrons (and positrons) out of light waves in pair production. We can diffract electrons. In atomic orbitals electrons "exist as standing waves". The electron has a magnetic dipole moment, and the Einstein-de Haas effect demonstrates that "spin angular momentum is indeed of the same nature as the angular momentum of rotating bodies as conceived in classical mechanics." And when we annihilate the electron with a positron, we typically get two light waves. The evidence is rock-solid, the wave nature of matter is not in doubt, in QED the electron is said to be an excitation of the electron field. It isn't some point particle thing that has a field, its field is what it is. And like the magnet's field, it isn't like an apple. It's always in two places at the same time.

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Offline David Cooper

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Re: Can an electron be in two places at the same time?
« Reply #31 on: 17/09/2014 22:09:37 »
What is there in an apple that isn't just like an electron or photon? The whole thing can be turned into photons. Every part of the the apple is spread across multiple locations (possibly ranging across the entire universe), but they're all tied together in such a way that they hold together collectively as an apple, and in an extreme case it could be possible for the probabilities relating to each component of the apple to be in agreement with each other that the whole apple is essentially occupying just two apple-sized locations with high probability while occupying all other possible locations with extremely low probability. Each fundamental component of the apple then is spread over a wide area, but there are two tightly defined locations where it is more probably going to interact with other things if it is forced to narrow down its range at any time.

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Offline yor_on

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Re: Can an electron be in two places at the same time?
« Reply #32 on: 17/09/2014 22:15:20 »
Well, I would say it is a duality. If you check out the article I linked last, then that is one of the conclusions.

"In its totality, nature is therefore dual. None of its constituents can be considered as only a particle or a wave. To reconcile this duality, in 1923 Niels Bohr proposed his Complementarity Principle: simply put, every component in nature has particle-like, as well as wave-like character, and which character is observed at a given time depends only on the observer. In other words, the experiment determines which characteristic one is measuring - particle or wave."

One point here that I find nice is what I read as a wider definition of what a 'observer' should be seen as. "In other words, the experiment determines which characteristic one is measuring - particle or wave.""

There's a big difference between assuming that you need consciousness for the outcome to be set one way or another, and defining it such as the experiment, observer included', all play a part for what the outcome will be. My assumption here though is that retracting any observer, once the experiment is set up, should change nothing in most cases, unless the observer is a integral part of the experiment.

It's a interesting article.
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Offline alancalverd

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Re: Can an electron be in two places at the same time?
« Reply #33 on: 18/09/2014 06:58:14 »
Each fundamental component of the apple then is spread over a wide area, but there are two tightly defined locations where it is more probably going to interact with other things if it is forced to narrow down its range at any time.

As Eddington said, if a physicist fell through the floor and materialised in the room below, he wouldn't consider it a miracle, just a lucky observation of an extremely rare event.

If we make the physicist very small and the floor very thin, we get a tunnel diode - as stocked by most electronics suppliers!
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Offline alancalverd

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Re: Can an electron be in two places at the same time?
« Reply #34 on: 18/09/2014 07:10:14 »
A photon is not a point particle.
Oh yes it is. You can capture a single photon on a phtographic plate and it's all there in one place.

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electrons "exist as standing waves".
no, their distribution can be modelled as standing waves.

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"spin angular momentum is indeed of the same nature as the angular momentum of rotating bodies as conceived in classical mechanics."
No, spin can be adequately modelled as angular momentum but unlike classical angular momentum it is quantised.

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The evidence is rock-solid, the wave nature of matter is not in doubt, in QED the electron is said to be an excitation of the electron field. It isn't some point particle thing that has a field, its field is what it is.
No, the behaviour of matter on an atomic scale can be modelled as waves.

Waves and particles are convenient descriptors of things we observe, but the description is not the object and since neither completely describes the behaviour of electrons or photons, neither can be said to be "true" - whatever that means.

I can describe the motion of a car with a Euclidean vector, but it doesn't mean a car is a vector.
« Last Edit: 18/09/2014 07:13:28 by alancalverd »
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Offline JohnDuffield

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Re: Can an electron be in two places at the same time?
« Reply #35 on: 18/09/2014 12:22:22 »
What is there in an apple that isn't just like an electron or photon?
Opposite charge. Simplify the apple to a hydrogen atom. You made this from an electron and a proton. At some distance from either of them their field is readily detectable, and you remember it's QFT and that "the electron is field". But when the electron and the proton come together their opposite fields largely cancel. Now at some distance from the hydrogen atom, the field isn't so readily detectable. 

The whole thing can be turned into photons.
Yes. And the photon is a wave that isn't localized, like a seismic wave it travels many paths. If you use pair production to convert photons into an electron and positron, you can say that the electron's widespread field isn't localized, and is akin to the many paths. But when you combine the electron with a proton the fields aren't so widespread.

Every part of the the apple is spread across multiple locations (possibly ranging across the entire universe),
You can argue that the electron's electromagnetic field is what it is, so the apple's gravitational field is part of what it is. But it has a definable surface, you can pick it up, and throw it, and eat it. People won't accept your argument. 

but they're all tied together in such a way that they hold together collectively as an apple, and in an extreme case it could be possible for the probabilities relating to each component of the apple to be in agreement with each other that the whole apple is essentially occupying just two apple-sized locations with high probability while occupying all other possible locations with extremely low probability. Each fundamental component of the apple then is spread over a wide area, but there are two tightly defined locations where it is more probably going to interact with other things if it is forced to narrow down its range at any time.
IMHO you should forget about probabilities.

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Offline JohnDuffield

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Re: Can an electron be in two places at the same time?
« Reply #36 on: 18/09/2014 12:35:06 »
Oh yes it is. You can capture a single photon on a phtographic plate and it's all there in one place.
Absorbing a wave at some location doesn't mean the wave wasn't an extended entity. Nor does performing an optical Fourier transform on it. 

no, their distribution can be modelled as standing waves.
Not so. It means they are standing waves. That's why you can diffract them. 

No, spin can be adequately modelled as angular momentum but unlike classical angular momentum it is quantised.
Again not so. The Einstein-de Haas effect is hard scientific evidence that spin angular momentum is of the same nature as classical angular momentum.

No, the behaviour of matter on an atomic scale can be modelled as waves.
You can diffract electrons, you can diffract protons, and neutrons, and buckynalls. Not because they can be modelled as waves, but because of the wave nature of matter.

Waves and particles are convenient descriptors of things we observe, but the description is not the object and since neither completely describes the behaviour of electrons or photons, neither can be said to be "true" - whatever that means.
The evidence for the wave nature of matter is overwhelming. 

I can describe the motion of a car with a Euclidean vector, but it doesn't mean a car is a vector.
But I can make an electron (and a positron) out of electromagnetic waves. Then I can diffract them. Then I can annihilate them, and I've got electromagnetic waves again. That's nothing like describing the motion of a car with a vector. 
« Last Edit: 18/09/2014 12:36:52 by JohnDuffield »

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Offline lightarrow

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Re: Can an electron be in two places at the same time?
« Reply #37 on: 19/09/2014 12:07:08 »
It depends on how you define "an electron"
It also depends on how you define “place”.
  In general it must be defined as a position in space.  Space must be restricted to the three dimensions that we experience.
Ok.
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Any additional dimensions that may be suggested are mathematical concepts which may, or may not, bear any relation to reality. 
If you think that only a three-dimensional world is "real" because "we experience this one only", and that the 4-dimensional world of GR (for example) is "just an idea", then you are wrong: it simply depends on how you interpret your perceptions; even "three-dimensional" is a concept just in our minds, "the reality" doesn't exist.
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The question that must arise is: “Can we restrict a quantum object (quon) to the dimensions of the observable – macro – Universe?”
Quantum mechanics works, but no one really knows why. 
And instead why classical mechanics works? I can simplify my question to the question: why Hamilton's principle of mechanics works? (As you know, all most important things of mechanics come from that principle).
In QM there are more than one principle; so who asks why QM works should ask "why do those principles works?" Or the problem is the fact that here there are more than one principle? Then you should better ask: "Is it possible to find an unique principle for QM as there is in classical mechanics?"

It was this the real question?

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Offline David Cooper

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Re: Can an electron be in two places at the same time?
« Reply #38 on: 19/09/2014 17:02:03 »
IMHO you should forget about probabilities.

Why would I want to forget about probabilities? The probabilities are determined by the distribution of the item that is spread out across a space, dictating how likely it is that that item will appear as a point particle at any position within that space if it is forced to choose a location to do so. Until it is forced to choose, it is able to maintain multiple possibilities as to where that point will be based on its distribution. Things are spread out while they keep the possibilities open, but there are times when they are forced to narrow down that range (though not necessarily to a single possibility). The result is that when a photon or electron is forced to interact with something in a way that requires it to have a tightly constrained location, it will then appear to exist at that single location. We can work out where it is most likely to do so based on probabilities, but is fully entitled to take us by surprise by selecting the most improbable option and appear at the other side of the universe instead. The apple can do the same thing, but the odds are stacked rather more heavily against it appearing anywhere other than where we most expect it to be, to the point that we can confidently state where it is with a practical guarantee (though not an absolute one) of being right.

Now, you seem to have decided that when an electron and proton get together (let's go the whole hog and combine them to make a neutron), the fields cancel out and result in something that is no longer spread out in the way that an electron is, but can that really be so? An experiment has been done in which an object made up of many atoms was oscillating in two opposite directions at the same time, and by that I mean that it was moving from right to left to right to left while also moving from left to right to left to right at the same time. I forget the details as to how the scientists proved that it was doing this, but it was held up as a demonstration of quantum effects with objects on the macro scale. That means we have large physical compound objects (not unlike an apple) behaving as if they are spread out and wavy. If you interact with the thing, you then force it to reduce the range of what it is doing and to pick only one of the two options, but up to that point it was doing both, and at many points along the way the end of this oscillating thing was "in two different places at the same time", in much the same way as Schrödinger's cat is both alive and dead at the same time (one walking around while the other is lying still), and in much the same way as my apple was in two places at the same time.

Everything I've just said may be hogwash, of course, because I'm not an expert in this at all. I merely listen to what more knowledgeable people say, probably misunderstand a great deal of it, try to build a model of what I think they mean in my head, and then I come to places like this to see if people who know more than I do can spot the points where I've gone wrong, and then I hopefully improve my understanding as a result. So, I'm always delighted to be shown to be wrong.

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Offline alancalverd

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Re: Can an electron be in two places at the same time?
« Reply #39 on: 19/09/2014 17:06:46 »
But I can make an electron (and a positron) out of electromagnetic waves. Then I can diffract them. Then I can annihilate them, and I've got electromagnetic waves again. That's nothing like describing the motion of a car with a vector. 

So you are now asserting that electromagnetic waves have mass?
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Offline jeffreyH

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Re: Can an electron be in two places at the same time?
« Reply #40 on: 19/09/2014 18:29:49 »
If the electron can be in two places at once then the two places can be anywhere including right next to each other. If they are right next to each other the Pauli Exclusion principle makes them into entirely different electrons. They are then not identical. If every electron in the universe can be considered to be in two places at once then all pairings become unique. So what is to stop these two unique objects from also being in two places at once. On and on ad infinitum.
« Last Edit: 19/09/2014 18:31:20 by jeffreyH »
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Offline JohnDuffield

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Re: Can an electron be in two places at the same time?
« Reply #41 on: 19/09/2014 18:31:14 »
So you are now asserting that electromagnetic waves have mass?
No. I'm referring to pair production.


Quote from: David Cooper
Why would I want to forget about probabilities?
Because weak measurement work by Aephraim Steinberg et al and by Jeff Lundeen et al demonstrate that wavefunction is real and that the Copenhagen interpretation is passé. See this:

"With weak measurements, it’s possible to learn something about the wavefunction without completely destroying it. As the measurement becomes very weak, you learn very little about the wavefunction, but leave it largely unchanged. This is the technique that we’ve used in our experiment. We have developed a methodology for measuring the wavefunction directly, by repeating many weak measurements on a group of systems that have been prepared with identical wavefunctions. By repeating the measurements, the knowledge of the wavefunction accumulates to the point where high precision can be restored.

So what does this mean? We hope that the scientific community can now improve upon the Copenhagen Interpretation, and redefine the wavefunction so that it is no longer just a mathematical tool, but rather something that can be directly measured in the laboratory."


Quote from: David Cooper
The probabilities are determined by the distribution of the item that is spread out across a space, dictating how likely it is that that item will appear as a point particle at any position within that space if it is forced to choose a location to do so. Until it is forced to choose, it is able to maintain multiple possibilities as to where that point will be based on its distribution. Things are spread out while they keep the possibilities open, but there are times when they are forced to narrow down that range (though not necessarily to a single possibility).
The item is wavefunction, it's distributed in space, and it's real, not some abstract probabilistic thing. 

Quote from: David Cooper
The result is that when a photon or electron is forced to interact with something in a way that requires it to have a tightly constrained location, it will then appear to exist at that single location.
No problem with that. When you detect the photon at one of the slits it's as if you've done an optical Fourier transform so it goes through that slit only. When you detect it at the screen again it's as if you've performed an optical Fourier transform, and you see a dot on the screen. But the photon always had its E=hf = hc/λ wave nature.   

Quote from: David Cooper
We can work out where it is most likely to do so based on probabilities...
And underlying those probabilities is something real. The Copenhagen interpretation basically says "you can never hope to understand it". Well, we can.

Quote from: David Cooper
Now, you seem to have decided that when an electron and proton get together (let's go the whole hog and combine them to make a neutron), the fields cancel out and result in something that is no longer spread out in the way that an electron is, but can that really be so?
Yes. That's why the hydrogen atom mass is less than that of the free electron plus that of the free proton. The fields don't quite cancel, but because they largely cancel, the hydrogen is more localised than either the electron or the proton.   

Quote from: David Cooper
An experiment has been done in which an object made up of many atoms was oscillating in two opposite directions at the same time, and by that I mean that it was moving from right to left to right to left while also moving from left to right to left to right at the same time.
That's what a photon in a cavity does. It's a wave thing.

Quote from: David Cooper
I forget the details as to how the scientists proved that it was doing this, but it was held up as a demonstration of quantum effects with objects on the macro scale. That means we have large physical compound objects (not unlike an apple) behaving as if they are spread out and wavy. If you interact with the thing, you then force it to reduce the range of what it is doing and to pick only one of the two options, but up to that point it was doing both, and at many points along the way the end of this oscillating thing was "in two different places at the same time", in much the same way as Schrödinger's cat is both alive and dead at the same time  (one walking around while the other is lying still), and in much the same way as my apple was in two places at the same time.
Schrödinger devised his cat to demonstrate the stupidity of the Copenhagen interpretation. But it got hijacked by people who promote quantum mysticism.

Quote from: David Cooper
Everything I've just said may be hogwash, of course, because I'm not an expert in this at all. I merely listen to what more knowledgeable people say, probably misunderstand a great deal of it, try to build a model of what I think they mean in my head, and then I come to places like this to see if people who know more than I do can spot the points where I've gone wrong, and then I hopefully improve my understanding as a result. So, I'm always delighted to be shown to be wrong.
Some of what you're saying is somewhat outdated. The thing is that some "expert" who's been banging on about the Copenhagen Interpretation for forty years isn't going to tell you about the weak measurement work. It was awarded the top two slots in the Institute of Physics "physicsworld" breakthroughs of 2011. But even now hardly anybody has heard about it.

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Offline jeffreyH

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Re: Can an electron be in two places at the same time?
« Reply #42 on: 19/09/2014 18:43:05 »
From John Duffield.

"Schrödinger devised his cat to demonstrate the stupidity of the Copenhagen interpretation. But it got hijacked by people who promote quantum mysticism."

It's about time people realized this!!
Fixation on the Einstein papers is a good definition of OCD.

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Re: Can an electron be in two places at the same time?
« Reply #43 on: 19/09/2014 20:13:58 »
Weak measurements is an assumption of being able to measure on a system without the parts of it, that you aren't allowed to measure on, noticing. It redefine action and reaction to something you can ignore, if you just do it weakly. I'm not happy about that John. You can give photon paths etc etc, but the reality is still that there is no 'photon' unless you measure.
=

Myself I consider it a try for a Newtonian world image, in where we have guaranteed forces that act upon us, a clock work universe. Which makes it doubly ironic to presume that action and reaction isn't there in the measurement.
« Last Edit: 19/09/2014 20:30:09 by yor_on »
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Re: Can an electron be in two places at the same time?
« Reply #44 on: 19/09/2014 20:40:18 »
Logically it shouldn't work, to measure on something you need a way to communicate with it. Doesn't matter if you do it through some 'middleman'. The act of communication should disturb its 'pure state', even though our tools may be too crude to define how. And when it comes to repeated measurements on 'identical' particles', proving for example a 'path' you introduce even more assumptions, or presumptions, for how the universe should work.
« Last Edit: 19/09/2014 20:43:01 by yor_on »
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Offline PmbPhy

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Re: Can an electron be in two places at the same time?
« Reply #45 on: 19/09/2014 21:01:14 »
From John Duffield.

"Schrödinger devised his cat to demonstrate the stupidity of the Copenhagen interpretation. But it got hijacked by people who promote quantum mysticism."

It's about time people realized this!!
That's always been the case, Jeff. E.g. on page 431 of Introduction to Quantum Mechanics - Second Edition by David Griffiths, (2005) the author writes
Quote
Schrodinger regarded this as patent nonsense, and I think that most physicists would agree with him. There is something absurd about the very idea of a macroscopic object being in a linear combination of two palpably different states. An electron can be in be in a linear combination of spin up and spin down, but a cat simply cannot be in a linear combination of alive and dead.
I recommend that you read the entire section of this book on the topic rather than a mere "sound bite". It's in section 12.4, pages 430 to 431.

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Re: Can an electron be in two places at the same time?
« Reply #46 on: 19/09/2014 21:05:17 »
If the electron can be in two places at once then the two places can be anywhere including right next to each other. If they are right next to each other the Pauli Exclusion principle makes them into entirely different electrons. They are then not identical. If every electron in the universe can be considered to be in two places at once then all pairings become unique. So what is to stop these two unique objects from also being in two places at once. On and on ad infinitum.
Not so. Two electrons can't be in the same quantum state. That means that no two electrons can have overlapping wave functions and the same spin and be in the same state. Besides, that only applies to electrons. I merely used electrons as an example for the thread. People claim that this whole idea applies to any two identical particles whatsoever.

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Re: Can an electron be in two places at the same time?
« Reply #47 on: 19/09/2014 21:18:02 »
Quote from: alancalverd
So you are now asserting that electromagnetic waves have mass?
Although I rarely, if ever, agree with John and I don't think that's what he's saying, there's nothing intrinsically wrong with the notion that EM waves have mass. Einstein himself proved this a long time ago. Are you not familiar with his paper on the subject? If not then please see

http://home.comcast.net/~peter.m.brown/sr/einsteins_box.htm

It's based on the article The Principle of Conservation of the Center of Gravity and the Inertia of Energy, Albert Einstein, Annalen der Physik, 20 (1906): 626-633.
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…, if one assumes that any energy E possesses the inertia E/c2, then the contradiction with the principle of mechanics disappears. For according to the this assumption the carrier body of mass E/c2, while it transports the amount of energy E from B to A; and since the center of gravity of the entire system must be at rest during this process according to the center-of-mass theorem the cylinder K undergoes during it a total shift S’ to the right.. If we assign the electromagnetic field too a mass density [tex](\rho_e)[/tex]

Consider also what Einstein said in is 1916 paper on GR too
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We make the distinction hereafter between "gravitational field" and "matter" in this way, that we denote everything but the gravitational field as "matter." Our use of the word therefore includes not only matter in the ordinary sense, but the electromagnetic field as well.
...
The special theory of relativity has led to the conclusion that inert mass is nothing more or less than energy, which finds its complete mathematical expression in a symmetrical tensor of second rank, the energy tensor.

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Offline yor_on

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Re: Can an electron be in two places at the same time?
« Reply #48 on: 19/09/2014 21:40:42 »
“Little Nudges from Light – Measuring the Recoil of Photons” from 2009.

“Prof. Dmitri Petrov in collaboration with colleagues from the Moscow State University were the first to measure this effect.  To measure the effect the researchers use a photonic force microscope (PFM) to trap a small metal covered dielectric sphere in a laser beam. The surrounding liquid contains fluorescent molecules that attach to the surface of the sphere. Excited by the light of the laser the molecules themselves start to emit light. Just like a soldier feels the recoil of his gun after firing a projectile, the small molecules pass their momentum they get from light emission on to the sphere. During this process the scientists measure two values: the forces acting on the bead (described by a tiny dithering in the trap) and the intensity of light generated by the molecules coating the bead's surface. As the intensity of the emitted light fades over time due to bleaching the scientists can observe a decline of the recoil as well.

What initially was the set-up for a different experiment turned out to deliver the first direct proof of the correlation between light emission and recoil and also allowed the calculation of the power of light emitted. In their experiment the researches measured a force of 240 femtonewtons, which equals a power coming from the bead of 1 microwatt. "Until now it has been really difficult to say how much light eventually comes off this material", says Dmitri Petrov from ICFO, “but by looking at the recoil we have a completely new approach to quantify light emission by a mechanical force”. Possible applications of the PFM-setup could be to offer a more precise way of measuring the efficiency and intensity of other light-emitting molecules, including the bleaching of fluorescent dyes.”

Let us put it this way John, assume that the 'force carriers' in your weak experiments are photons, there has to be something that communicate a 'nudge' or whatever it is one want to measure or influence. Above is an example of action and reaction, created in the interaction of matter and photons.

you can explain it different ways, it could be seen as a necessary symmetry, which I like, instead of a proof of a 'path'. But, no matter how I like to define it, it still is a example of 'action and reaction' to me, and the recoil defined to a photon. So what communicates in those weak experiments?
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Offline David Cooper

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Re: Can an electron be in two places at the same time?
« Reply #49 on: 19/09/2014 22:03:20 »
The item is wavefunction, it's distributed in space, and it's real, not some abstract probabilistic thing.

I never said it wasn't real. The probabilities are real too, dictated by a real mechanism which I have never denied (because I have never believed in magic and have never been a fan of the Copenhagen interpretation). Recent advances are enabling the mechanism to be detected, as anyone on this forum can't fail to have noticed, but it makes no change whatsoever to the issue of whether something is in two places or not at the same time. A thing can be spread across multiple places, but it cannot in totality be in two places at the same time.

So, I'm still trying to determine whether there's a real issue in conflict between what you're saying and what I've been led to believe. Brian Cox recently discussed a diamond in a locked box and the possibility of it suddenly appearing outside the box because the probability of this unlikely event occurring is supposedly not quite being zero. This would, I assume, depend on the diamond behaving in a wavy way such that every part of it too is spread out across space and all of those parts could spontaneously decide that they are outside the box instead of in it. So, do you disagree with him and think the diamond is so localised that it cannot get out of the box in such a way at all? The whole diamond is wavefunction and it enables the diamond to show itself as being located outside the box even though it was seen as being located inside it when it was locked in there: mechanism and probabilities intact.
« Last Edit: 19/09/2014 22:05:33 by David Cooper »