Quantum tunneling - Questions about some pop-science claims

[Jeronimus]

This might become a series of questions, but let me begin with the most essential one.

According to QM/QFT, would it be true that there is a non-zero chance for an object on Earth to instantaneously tunnel to the moon for example?

Like let's say a paper with a note on it. Could this paper, given we waited an arbitrary long time period, suddenly tunnel/teleport to the moon instantaneously?If yes, could you elaborate on the instantaneous part?

Let's say we have two synced clocks, one of which is on Earth and the other on the moon. Let's say the tunneling event would occur at x=0 t=5s. The moon is roughly 1 lightsecond away from earth.

Would the tunneling object appear at x=1ls t=5s, or could it also appear at t=5.5s or even below 5s?

follow up questions related to SR will follow possibly, depending on how the above are answered.

 

[vanhees71]

The problem about "tunnel times" is pretty involved and, as far as I know, no consence among quantum physicists is reached about how to define and, most importantly how to measure them.

What's clear from the very foundations of relativistic QFT is that there's no faster-than light "traveling" possible. This class of theories is constructed in such a way that the socalled linked-cluster principle holds, i.e., experiments done at space-like distances are (or appear) always uncorrelated. There is no causal influence across space-like distances (also by construction).

 

[Jeronimus]

The problem about "tunnel times" is pretty involved and, as far as I know, no consence among quantum physicists is reached about how to define and, most importantly how to measure them.

What's clear from the very foundations of relativistic QFT is that there's no faster-than light "traveling" possible. This class of theories is constructed in such a way that the socalled linked-cluster principle holds, i.e., experiments done at space-like distances are (or appear) always uncorrelated. There is no causal influence across space-like distances (also by construction).

So according to you, physicists in various pop-science docus are outright lying. I could link several documentaries where they clearly state that if you waited a very very long time, an object like a ball etc could tunnel instantaneously to a far away place. Not likely at all to happen, but possible according to QM.
That's not making science easier accessible to the public, but is misleading.

 

[DarkBabylon]

In principle, yes, although through the numerical solutions of the schrodinger equation, one can see that it is not simply let an object sit:
a) It must not be measured, or interact with anything, EVER.
b) The wavefunction spreads with finite speed, so in a sense the object is already on the moon...and at the same time on Earth.
c) Information still does not travel faster than c.

However, this is ignoring the fact there is a gravitational potential with the Earth not allowing you to go any deeper than you already are. So should it spread, it will *in principle* have a non zero chance to be on the moon (a decaying function would never reach zero until you reach infinity). However, unlike mathematics, physics takes into consideration how significant something is, and chances are, although the probability is non zero, we'd go through quite a lot of zeroes after the 0.000... before we reach a non zero digit writing the probability. Experimentalists will tell you that it might as well be zero because you can't measure it AND be sure it was a quantum tunneling at work, and Theorists would suggest to ignore such effect due to its insignificance.

The following to demonstrate the tunneling and its dependence on time:
Here is a little numerical simulation of a simple Gaussian wave packet and Barriers tunneling.
Here is another with a bit of a run down and a Dramatic Orchestral music.

EDIT: I shall add that most likely scenario you'd have to wait until the heat death of the universe to see such a result as a paper "teleporting" to the moon.
EDIT2: Correction, mathematicians do also consider how significant something is, but they tend to be careful with omitting anything from a problem. To be fair, they might also consider 1 over sextillion of a chance to be zero if it is not as significant as a chance for something else to happen.

 

[A. Neumaier]

Could this paper, given we waited an arbitrary long time period, suddenly tunnel/teleport to the moon instantaneously?

Only when you are prepared to trust the model in which you calculate to be valid for a huge multiple of the lifetime of the universe - the mean time predicted by QM is this large.

 

[Jeronimus]

Maybe one last question to clear things up.

In principle, yes, although through the numerical solutions of the schrodinger equation, one can see that it is not simply let an object sit:
a) It must not be measured, or interact with anything, EVER.
b) The wavefunction spreads with finite speed, so in a sense the object is already on the moon...and at the same time on Earth.
c) Information still does not travel faster than c.

However, this is ignoring the fact there is a gravitational potential with the Earth not allowing you to go any deeper than you already are. So should it spread, it will *in principle* have a non zero chance to be on the moon (a decaying function would never reach zero until you reach infinity). However, unlike mathematics, physics takes into consideration how significant something is, and chances are, although the probability is non zero, we'd go through quite a lot of zeroes after the 0.000... before we reach a non zero digit writing the probability. Experimentalists will tell you that it might as well be zero because you can't measure it AND be sure it was a quantum tunneling at work, and Theorists would suggest to ignore such effect due to its insignificance.

The following to demonstrate the tunneling and its dependence on time:
Here is a little numerical simulation of a simple Gaussian wave packet and Barriers tunneling.
Here is another with a bit of a run down and a Dramatic Orchestral music.

EDIT: I shall add that most likely scenario you'd have to wait until the heat death of the universe to see such a result as a paper "teleporting" to the moon.
EDIT2: Correction, mathematicians do also consider how significant something is, but they tend to be careful with omitting anything from a problem. To be fair, they might also consider 1 over sextillion of a chance to be zero if it is not as significant as a chance for something else to happen.

I was asking specifically for __instantaneous__ tunneling which you seemingly agreed on is possible, but then went on to contradict yourself as it appears to me.

This means that if that note is next to you at x=0, t=0 (you placed yourself in the middle of the coordinate system), with your stopwatch showing a clock count of 10 seconds for example,
then someone who is at the moon, with a stopwatch synced to yours with the same clock count at 10s at x~300000km, t=0, would see the note appear at his place at x~300000km, t=0s, exactly when his stopwatch has a count of 10s while the note disappears from your location at at x=0,t=0 10s on your watch.
That is what instantaneous means.

An even better thought experiment might be a note with a clock attached, since we would need to also know which instance of the note/clock tunneled there instantaneously.

If for this observer on the moon, the note would appear at >11s on his stopwatch, then it would not be instantaneous but the "tunneling" would have happened at about c or <c.

If the tunneling does happen instantaneous as described, then information was transferred FTL which would inevitably lead to the possibility of sending information and or objects back in time if we were to apply special relativity. Any transfer of information at higher than c in one reference frame, will in some reference frames be observes as traveling at negative time.

 

[Jeronimus]

Only when you are prepared to trust the model in which you calculate to be valid for a huge multiple of the lifetime of the universe - the mean time predicted by QM is this large.

So basically, if I am interpreting this comment correctly, there are many different models of QM which give different predictions when it comes to tunneling, plus we do not have any experimental data (we can trust) related to tunneling which could tell us if or not particles/molecules/larger objects can or cannot tunnel from one place to another __instantaneously__.

Then my question would be. Are there any experiments about to happen which would settle this question, or hasn't anyone thought of a feasible experiment to settle this question yet?

 

[DarkBabylon]

I was asking specifically for __instantaneous__ tunneling which you seemingly agreed on is possible, but then went on to contradict yourself as it appears to me.

Alright so let me phrase myself better. The act of tunneling itself is what I am in agreement with, but not instantaneous, as that can't happen.

Thing is particles behave like waves in the quantum world, so their wave function always spread. THAT'S why you have to wait a really long time.

The instantaneous part is the act of measurement, which causes a wave function collapse. Basically, the wave function of a particle is what you know about it, and when it spreads to the moon and measure, and find it at the moon the wave function was already there, which also did not get there at super luminal speeds.

 

[PeterDonis]

instantaneously

This word is meaningless when relativity is taken into account, since "instantaneous" is frame dependent.

In QFT, i.e., quantum mechanics + relativity, the key condition that enforces causality is that measurements at spacelike separated events must commute, i.e., the results can't depend on the order in which the measurements are made. But any "tunneling" of the kind you describe, where information is transmitted, can't meet this condition: the ordering is crucial, since it determines the flow of information. So no, you can't tunnel information faster than light.

 

[Jeronimus]

This word is meaningless when relativity is taken into account, since "instantaneous" is frame dependent.

In QFT, i.e., quantum mechanics + relativity, the key condition that enforces causality is that measurements at spacelike separated events must commute, i.e., the results can't depend on the order in which the measurements are made. But any "tunneling" of the kind you describe, where information is transmitted, can't meet this condition: the ordering is crucial, since it determines the flow of information. So no, you can't tunnel information faster than light.

I don't understand why you say that instantaneous becomes meaningless in the context of SR/GR, just because it is frame dependent. Simultaneous is also frame dependent in SR but not meaningless.

I can observe someone traveling to the moon at 0.5c, reaching the moon in 2 seconds. Another at 0.25c, reaching the moon at 4 seconds. Which word should I use for if I observed someone "teleporting" from Earth to the moon in zero seconds? I would use instantaneous, and yes, it would be instantaneous only as observed from within my frame of reference.As I understand the rest of what you wrote, it is simply not possible to have an _instance_ of a particle "vanish" at my location on earth, with my clock being synced to Bob's clock on the moon, displaying 10s at the moment of the disappearance, and have that instance of the particle appear next to Bob with his clock displaying 10s as well, or less than <11s if you will.

Is that what the maths in QM tells us, no matter which accepted interpretation of QM without any heavy weights in the scientific community disagreeing on this?

Are there any experiments which actually can measure tunneled particles "disappear" and "appear" times and locations accurately enough to ensure that no FTL was involved in the actual particle disappearing and appearing at another location?

 

[A. Neumaier]

I was asking specifically for __instantaneous__ tunneling

Nothing ever happens instantaneously. The latter, if used in physical arguments, is always a convenient approximation only, ignoring shorter scale physics than what is modeled. Thus your question is based on a misunderstanding.

 

[PeterDonis]

Which word should I use for if I observed someone "teleporting" from Earth to the moon in zero seconds?

"Impossible".

Is that what the maths in QM tells us

It's what QFT tells us. Ordinary QM does not incorporate causality the way QFT does, because ordinary QM is not relativistic. But ordinary QM breaks down for cases like the one you are considering.