Undergrad Quantum Tunneling Max Distance

[name123]

I was assuming that it is possible to repeatedly measure an electron's position, but that it was not possible to know the result of the subsequent measurement because of the uncertainty principle. What I was wondering was whether the maximum distance between the two measurements is limited by the speed of light, limiting the distance an electron can be measured to have tunnelled during the intermission?

 

[ZapperZ]

I was assuming that it is possible to repeatedly measure an electron's position, but that it was not possible to know the result of the subsequent measurement because of the uncertainty principle. What I was wondering was whether the maximum distance between the two measurements is limited by the speed of light, limiting the distance an electron can be measured to have tunnelled during the intermission?

Your question, and the scenario you presented here, are rather puzzling.

What exactly are you actually measuring? You mentioned "position", but position of what, and where?

How exactly are you expecting to measure this "position"?

If all you care about is to measure how far into the forbidden region that an electron can penetrate, then make a series of measurement on an ever-increasing barrier thickness. At some point, the tunneling current will be "low enough" that it will be below your defined cut-off measurement, and you can conclude that you've reached some level of maximum thickness and thus, you have arrived at the maximum tunneling distance. There is no need to make any measurement of electron "position" here.

Zz.

 

[name123]

Your question, and the scenario you presented here, are rather puzzling.

What exactly are you actually measuring? You mentioned "position", but position of what, and where?

How exactly are you expecting to measure this "position"?

I am not sure how I would be measuring the position of the electron. I thought there were ways though.

If all you care about is to measure how far into the forbidden region that an electron can penetrate, then make a series of measurement on an ever-increasing barrier thickness. At some point, the tunneling current will be "low enough" that it will be below your defined cut-off measurement, and you can conclude that you've reached some level of maximum thickness and thus, you have arrived at the maximum tunneling distance. There is no need to make any measurement of electron "position" here.

Zz.

I thought there was no limit to how far an electron could tunnel. I assumed there would be a limit to how far it could tunnel in a given amount of time though. I just wanted clarification that my assumption was correct.

 

[ZapperZ]

I am not sure how I would be measuring the position of the electron. I thought there were ways though.
I thought there was no limit to how far an electron could tunnel. I assumed there would be a limit to how far it could tunnel in a given amount of time though. I just wanted clarification that my assumption was correct.

There is also no limit on gravitational field, but do you detect the gravity from Alpha Centauri?

This is why I emphasized some pre-defined cut-off that you have to clarify. If the probability of something tunneling takes longer than the age of the universe, do you think it is realistic to consider that event to be possible? Just because the phase space of something happening isn't zero, it doesn't mean that it is realistic to consider that it is possible. Otherwise, we would have seen a broken vase reassemble itself into its original shape when we throw the broken pieces onto the ground.

Zz.

 

[PeterDonis]

I was assuming that it is possible to repeatedly measure an electron's position, but that it was not possible to know the result of the subsequent measurement because of the uncertainty principle.

No, the uncertainty principle doesn't come into play here. The uncertainty principle is involved when you are making measurements of observables that don't commute, such as position and momentum. But position commutes with itself, so the uncertainty principle places no limits on the results of repeated position measurements.

The issue that arises if you make repeated position measurements on an electron is that in all the cases I can think of, position eigenstates are not energy eigenstates, so they will change with time. That means that, if you measure an electron's position and thus put it into a position eigenstate (I'm oversimplifying here, but the main point stays the same when you add back all the complications), and then wait a little, the electron's state will have changed, so if you measure its position again, you are not certain to get the same result. This is not the uncertainty principle, but just ordinary time evolution, and it doesn't happen for all observables--for example, eigenstates of spin are also energy eigenstates, so they don't change with time; that's why, if you measure an electron's spin about some axis and then wait, and then measure its spin about the same axis again, you will get the same result--because the electron's state hasn't changed, so it's still in the same eigenstate of spin that the first measurement put it in.

 

[PeterDonis]

What I was wondering was whether the maximum distance between the two measurements is limited by the speed of light

The proper framework for answering this question is not ordinary QM, but quantum field theory. In QFT, this question becomes: given that I have measured an electron to be at a particular position at a particular time, i.e., that there is an electron definitely present at some particular event in spacetime, is there a nonzero amplitude for an electron to be present at some other event that is spacelike separated from the first? It turns out, counterintuitively, that the answer to this question is yes. Informally, we might describe this as telling us that electrons have a nonzero amplitude to travel faster than light; but one of the things you quickly learn when studying QFT is not to trust such informal descriptions.

 

[name123]

There is also no limit on gravitational field, but do you detect the gravity from Alpha Centauri?

This is why I emphasized some pre-defined cut-off that you have to clarify. If the probability of something tunneling takes longer than the age of the universe, do you think it is realistic to consider that event to be possible? Just because the phase space of something happening isn't zero, it doesn't mean that it is realistic to consider that it is possible. Otherwise, we would have seen a broken vase reassemble itself into its original shape when we throw the broken pieces onto the ground.

Zz.

Yes I consider that if something has a non-zero probability that it is possible. It might not happen, but it could.

I thought that a gravitational field only propagates at light speed.

 

[name123]

No, the uncertainty principle doesn't come into play here. The uncertainty principle is involved when you are making measurements of observables that don't commute, such as position and momentum. But position commutes with itself, so the uncertainty principle places no limits on the results of repeated position measurements.

If you knew the position at one point but not the momentum, how could you tell what the future measurement of position would be? I had assumed you would need to know both (though with quantum stuff I was not even sure that would allow accurate prediction).

 

[name123]

The proper framework for answering this question is not ordinary QM, but quantum field theory. In QFT, this question becomes: given that I have measured an electron to be at a particular position at a particular time, i.e., that there is an electron definitely present at some particular event in spacetime, is there a nonzero amplitude for an electron to be present at some other event that is spacelike separated from the first? It turns out, counterintuitively, that the answer to this question is yes. Informally, we might describe this as telling us that electrons have a nonzero amplitude to travel faster than light; but one of the things you quickly learn when studying QFT is not to trust such informal descriptions.

Why does that not count as faster than light travel, is the underlying field thought to absorb the electron at one point and produce another electron at another point? If so, and if it would balance out (same amount of electrons), would that be another case of "spooky action at a distance"?

Or is it that you think that it would be more accurate if the equations were modified to give a 0 probability to faster than light travel?

With a multi worlds theory, if there were to be a number of identical worlds created to explain why we find it more likely we observe more probable worlds, presumably there would have to be loads of more probable worlds, as there are events with very low probability.

 

[ZapperZ]

Yes I consider that if something has a non-zero probability that it is possible. It might not happen, but it could.

Then why even bother doing this experiment? Your expectation is not realistic.

Zz.

 

[name123]

Then why even bother doing this experiment? Your expectation is not realistic.

Zz.

I do not know what expectation you are referring to. I was just wondering what current theories suggested and PeterDonis answered.

The proper framework for answering this question is not ordinary QM, but quantum field theory. In QFT, this question becomes: given that I have measured an electron to be at a particular position at a particular time, i.e., that there is an electron definitely present at some particular event in spacetime, is there a nonzero amplitude for an electron to be present at some other event that is spacelike separated from the first? It turns out, counterintuitively, that the answer to this question is yes. Informally, we might describe this as telling us that electrons have a nonzero amplitude to travel faster than light; but one of the things you quickly learn when studying QFT is not to trust such informal descriptions.

Though I am not sure what he meant by not trusting the informal description. Do you think he was suggesting it was wrong?

 

[ZapperZ]

I do not know what expectation you are referring to. I was just wondering what current theories suggested and PeterDonis answered.

Though I am not sure what he meant by not trusting the informal description. Do you think he was suggesting it was wrong?

There is a problem here. What EXACTLY are you trying to find? You seem to be meandering all over the place.

I get back to the original question which is written in the topic. Is this truly what you are after, i.e. the "maximum tunneling distance"?

If it is, then this excursion into measuring the position of an electron is an unnecessary distraction in that goal.

Secondly, if you think that tunneling effect can be measured, no matter how infinitely SMALL it is, then ANY measurement that you make for ANY experiment will never satisfy you. Because, after all, where exactly is there a situation when a theory will definitely indicate that you'll get a zero value absolutely?

Finally, I've given you a rather straightforward outline on an experiment to measure such a distance. When one wants to measure something, the experiment should be as "simple" as possible, so that the measurement will require the LEAST amount of interpretation and analysis to get to the actual quantity that one wants. Invoking a measurement of a "position" of an electron to determine maximum tunneling distance introduces A LOT of complications, and unnecessary "middle men" along the way just to get to the value of "tunneling distance".

I did tunneling spectroscopy experiments (not just theory) for 4 years for my doctoral degree. I'm not simply stating all this out of thin air.

Zz.

 

[name123]

There is a problem here. What EXACTLY are you trying to find? You seem to be meandering all over the place.

I get back to the original question which is written in the topic. Is this truly what you are after, i.e. the "maximum tunneling distance"?
.

The original question was:

What I was wondering was whether the maximum distance between the two measurements is limited by the speed of light, limiting the distance an electron can be measured to have tunnelled during the intermission?

And while you seem to have found that unclear, I also quoted PeterDonis's rewording of it:

In QFT, this question becomes: given that I have measured an electron to be at a particular position at a particular time, i.e., that there is an electron definitely present at some particular event in spacetime, is there a nonzero amplitude for an electron to be present at some other event that is spacelike separated from the first?

And I pointed out that he answered it. The answer being "yes". What I was not clear of was what he meant in his last sentence

Informally, we might describe this as telling us that electrons have a nonzero amplitude to travel faster than light; but one of the things you quickly learn when studying QFT is not to trust such informal descriptions.

Were you thinking that QFT suggests that electrons have a nonzero amplitude to travel faster than light?

Secondly, if you think that tunneling effect can be measured, no matter how infinitely SMALL it is, then ANY measurement that you make for ANY experiment will never satisfy you. Because, after all, where exactly is there a situation when a theory will definitely indicate that you'll get a zero value absolutely?

I would not expect any measurement of an event with a very low probability amplitude because its low probability amplitude would indicate that such a measurement should not be expected. But I am concerned with what the theory states.

I am not clear on what you mean by your last question, but quantum theories aside, I assume theories such as Relativity give a 0 probability for observations at odds with what the theory would predict, and if such observations were made, the theory (as it was formulated) would be falsified.

 

[ZapperZ]

The original question was:
And while you seem to have found that unclear, I also quoted PeterDonis's rewording of it:
And I pointed out that he answered it. The answer being "yes". What I was not clear of was what he meant in his last sentence
Were you thinking that QFT suggests that electrons have a nonzero amplitude to travel faster than light?
I would not expect any measurement of an event with a very low probability amplitude because its low probability amplitude would indicate that such a measurement should not be expected. But I am concerned with what the theory states.

I am not clear on what you mean by your last question, but quantum theories aside, I assume theories such as Relativity give a 0 probability for observations at odds with what the theory would predict, and if such observations were made, the theory (as it was formulated) would be falsified.

Then all of these have nothing to do with "Quantum Tunneling Max Distance".

Zz.

 

[name123]

Then all of these have nothing to do with "Quantum Tunneling Max Distance".

Zz.

The question in the text was about the maximum distance for quantum tunnelling for a given time period. I did not think there room in the title for the question, and just used the title to indicate the area of physics that the question related to.

 

[PeterDonis]

Were you thinking that QFT suggests that electrons have a nonzero amplitude to travel faster than light?

QFT says electrons have a nonzero amplitude to be present at events that are spacelike separated. As I said, this is often described, informally, as electrons having a nonzero amplitude to travel faster than light, but that's not really a good description.

 

[PeterDonis]

If you knew the position at one point but not the momentum, how could you tell what the future measurement of position would be?

If you know the position at one event--meaning that you know the electron is in a position eigenstate at that event--then you can't know the momentum at that same event, because a position eigenstate is not a momentum eigenstate; it can't be since position and momentum are non-commuting observables. This is one way of stating the uncertainty principle.

However, if you know the electron is in a position eigenstate, then you know its state, and you can use that state to predict the results of future measurements of position, by using your knowledge of how that state evolves in time. This has nothing to do with the uncertainty principle, and it is what I was describing.

You appear to be trying to reason about all this using ordinary language, instead of using knowledge of the underlying math. That's not going to work well.

Why does that not count as faster than light travel

Because you can't use this effect to propagate causal influences faster than light.

is the underlying field thought to absorb the electron at one point and produce another electron at another point?

In QFT, you can't say that an electron at one event is "the same electron" as the electron at another event. All you can say is that there is an electron at one event and an electron at another event--more precisely, that the electron field is in a particular state at each event.

is it that you think that it would be more accurate if the equations were modified to give a 0 probability to faster than light travel?

No, it would be less accurate. The equations as they are, with a nonzero amplitude for electrons to be present at spacelike separated events (note carefully how I'm phrasing this, which is not the way you keep phrasing it), accurately predict the results of experiments. If we made that amplitude zero, they would not.

With a multi worlds theory

Nothing that I have said depends on picking any particular intepretation of QM. Many worlds is not a separate theory; it's an interpretation of QM. And it's a hard one to understand; trying to adopt it here is not likely to help you.

I am not sure what he meant by not trusting the informal description. Do you think he was suggesting it was wrong?

To the extent that it leads you to make incorrect inferences and predictions, yes.

 

[PeterDonis]

I would not expect any measurement of an event with a very low probability amplitude because its low probability amplitude would indicate that such a measurement should not be expected.

That's not what low probability amplitude means. It means the result happens rarely; it doesn't mean it never happens.

The question in the text was about the maximum distance for quantum tunnelling for a given time period.

No, it wasn't. Your question about "maximum distance between two measurements", which I rephrased, is much more general; it applies to any measurements, not just measurements involved with tunnelling experiments. That is what @ZapperZ is trying to tell you.

 

[name123]

In QFT, you can't say that an electron at one event is "the same electron" as the electron at another event. All you can say is that there is an electron at one event and an electron at another event--more precisely, that the electron field is in a particular state at each event.

With the prediction of an electron position that you mentioned (once knowing its position eigenstate), if the prediction turned out to be correct could you not assign a probability to it being the same electron?

The reason I ask, is that if you could, then could you not do the same with electrons at two spacelike separated events?

 

[PeterDonis]

if the prediction turned out to be correct could you not assign a probability to it being the same electron?

No. "The same electron" makes no sense in QFT.

 

[name123]

That's not what low probability amplitude means. It means the result happens rarely; it doesn't mean it never happens.

I realized that, and did not state that it means it never happens.

The question in the text was about the maximum distance for quantum tunnelling for a given time period.

No, it wasn't.

The question was:

What I was wondering was whether the maximum distance between the two measurements is limited by the speed of light, limiting the distance an electron can be measured to have tunnelled during the intermission?

So it was about whether the maximum distance an electron could tunnel during the intermission (the time period) was limited by the speed of light.

 

[name123]

No. "The same electron" makes no sense in QFT.

So when you wrote:

However, if you know the electron is in a position eigenstate, then you know its state, and you can use that state to predict the results of future measurements of position, by using your knowledge of how that state evolves in time.

The prediction was not based on how the position of that particular electron was going to evolve?

 

[PeterDonis]

it was about whether the maximum distance an electron could tunnel during the intermission (the time period)

You used the word "tunnel", yes. But nothing you actually asked about has anything to do with tunneling. You were just describing two successive position measurements, and asking about what happens if the measurement events are spacelike separated. No tunneling is required for such an experiment.

The prediction was not based on how the position of that particular electron was going to evolve?

No, it was based on how the state of the quantum field--the electron field--was going to evolve. But even "evolve" is not really the right word in the QFT context. A better way to describe it would be that, given the knowledge that the electron field is in a particular state at a particular event, what are the amplitudes for it to be in some other particular state at some other event?

 

[Nugatory]

The prediction was not based on how the position of that particular electron was going to evolve?

Because of the general fuzziness of English-language descriptions I can't be sure exactly what you mean... But it sounds very much as if you are muddling together ordinary non-relativistic quantum mechanics, in which we can speak of "the" electron and the evolution of "its" wave function to describe how "its position" changes, and the quantum field theoretic description in which none of those concepts make sense.

Finding conflicts between non-relativistic quantum mechanics and relativity is not surprising, and just tells you that you're using the non-relativistic theory outside its domain of validity. As PeterDonis said back in post #6, "The proper framework for answering this question is not ordinary QM, but quantum field theory".

 

[name123]

No, it was based on how the state of the quantum field--the electron field--was going to evolve. But even "evolve" is not really the right word in the QFT context. A better way to describe it would be that, given the knowledge that the electron field is in a particular state at a particular event, what are the amplitudes for it to be in some other particular state at some other event?

Ah ok thanks. Might I just ask, does QFT have a field for each fundamental particle type?

 

[Nugatory]

Ah ok thanks. Might I just ask, does QFT have a field for each fundamental particle type?

Yes

 

[name123]

Yes

Thanks :)

 

[Good Elf]

Surely there is no theoretical limit to the distance an electron or anything else existing in a single quantum state could tunnel? Leo Susskind (and also Juan Maldacena) suggest that "wormholes" are simply special cases of quantum entanglement. Others (eg: Dirac Medal winner - Ashoke Sen) suggested earlier that there is a close relationship between black holes and elementary particles. See article: ‘Elementary particles may be thought of as small black holes’ - The Hindu - 24 August 2014. There is an easy read by Leo Susskind here: Dear Qubitzers, GR=QM - 10 August 2017. I realize that such tasks have not been performed yet but developments with Quantum Computers are suggested to be fertile grounds for future research in the next couple of years. Arguments about whether the "transferred" particle is the same as the original particle could be discussed somewhere else. Long Distance Teleport protocols have been recently shown to be effective in China for photons, as well as being practical over many hundreds of kilometers, and that was contrary to every previous source.

Of course an electron actually has considerable mass and currently that is a counter indication for an unlimited range. But the limits of non-locality are not yet determined (if ever). Susskind appears to suggest that a traversible wormhole is not impossible, and these phenomena are closely related to Black Holes and Elementary Particles. So what is not "actually" proscribed in physics is usually permissible. QFT is partially out of it's league when dealing with non-locality. Apparently this topic has been bogged down here previously in highly complex argument. I can only point to the experiments which show that not only photons can "teleport" but also neutrons in helium nucleii in close proximity and in the same quantum state can pull it off using the Hong-Ou-Mandel Phenomena. See: Measuring Optical Tunneling Times using a Hong–Ou–Mandel Interferometer. - NIST - 24 September 2008. Or this see: Like Magic! Tiny Particles Can Pass Through Long-Distance Barriers - Live Science - 12 June 2014. Of course these Cesium atoms tunnel under "duress" using active biassing of the energy barrier, that general principle seems good to me..

However, "the tunneling process becomes slower and slower the farther the atoms have to hop. This does not bode well for scaling such interaction-shifted tunneling resonances to a larger number of lattice sites," Simon told Live Science. "Fortunately, developing intuition for the quantum dynamics of even five or six particles is already exciting and important."

If there is a limiting range it still has not been found. For quantum mechanics using statistical methods, you may need to wait a long while but if the alternative states could be suppressed, if entanglement can be maintained and if the barrier energy could be suppressed using external physical phenomena, promoting the quantum frustration of other states doe the electron, then perhaps it might happen instantly. Suggested is the range depends on how far entanglement can be coupled between two identical quantum states then the "particles" will tunnel. How long is a "wormhole" or what is the limiting distance for quantum entanglement? In many ways the Universe appears to be a kind of open waveguide and the transfer of states appears to obey rules like those found in microwave circuitry by way of Complex electrical condition matching at either end matching source to sink. Much is to be said for intuition and actual experiments, and not to blindly invoke general statistical methods to apply to actual controlled bench-top experiments. So I don't know... but I would certainly like to.

 

[PeterDonis]

Surely there is no theoretical limit to the distance an electron or anything else existing in a single quantum state could tunnel? Leo Susskind (and also Juan Maldacena) suggest that "wormholes" are simply special cases of quantum entanglement.

Quantum entanglement is not the same thing as tunneling.

Long Distance Teleport protocols

Quantum teleportation (which is a misleading name for the phenomenon) involves entanglement, not tunneling. Your post is irrelevant to the topic of this thread.

 

[PeterDonis]

The OP question has been answered. Thread closed.