You Will Not Tunnel Through a Wall - Comments

[ZapperZ]

ZapperZ submitted a new PF Insights post

You Will Not Tunnel Through a Wall

Continue reading the Original PF Insights Post.

 

[gianeshwar]

Thanks ZapperZ.I have a better understanding now!

 

[Markus Hanke]

Good insight article, very well spoken !

 

[Drakkith]

So I'm not going to tunnel through my chair and into the core of the Earth. Good to know!

 

[maline]

Does the differencebetween the proton & electron actually make the tunneling probability lower, or just much more difficult to calculate? if so, why?

 

[vanhees71]

Very nice Insight!

 

[ZapperZ]

Does the differencebetween the proton & electron actually make the tunneling probability lower, or just much more difficult to calculate? if so, why?

Look at the difference in the CHARGE! One sees it is a "barrier", while the other sees it as a "well". This means that the transmission probability for each one of them will be different!

This is not an issue of tunneling of individual particles. It is the tunneling of ALL the particles together, simultaneously, and coherently. We have not seen such a thing yet. The best that we have is the tunneling of alpha particles, which is nothing more than a clump of two protons (and notice that each of them making up the composite particle has the same charge and the same charge sign) while the neutrons have no charge.

Until we can show of tunneling phenomenon by whole atoms and molecules, tunneling by macroscopic object is practically impossible at this moment.

Zz.

 

[maline]

This means that the transmission probability for each one of them will be different!

Would you mind putting in a word about what effect this has on the final probability?

 

[ZapperZ]

Would you mind putting in a word about what effect this has on the final probability?

I'm not exactly sure what you are looking for here. One particle has to tunnel through a barrier, while the other one has to "jump" over a "hole in the ground". Is it not obvious that the transmission probability will be different for each one of them?

So if you want just "a word", it is "DIFFERENT"!

Zz (who thinks explaining physics using "a word" is impossible).

 

[maline]

What I'm not getting is why the difference in the separate transmission probabilities necessarily leads to a lower probability that for the transmission of two particles with similar individual probabilities.
Thanks for your patience.

 

[ZapperZ]

What I'm not getting is why the difference in the separate transmission probabilities necessarily leads to a lower probability that for the transmission of two particles with similar individual probabilities.
Thanks for your patience.

Because they won't get through the barrier with equal probability! Your right hand might go through, but your left hand stayed behind! (Sorry, but I had to resort to THAT ridiculous analogy.) So ALL of you didn't get through the barrier at the same time! To me, the probably of all of you to tunnel through the barrier is then ZERO.

Goodbye left hand!

Zz.

 

[maline]

If they did get through with equal probability, as in the case of alpha particles, how does this increase the probability for them both to get through at once?

 

[ZapperZ]

If they did get through with equal probability, as in the case of alpha particles, how does this increase the probability for them both to get through at once?

Did you not pay attention to my description of the SIGN of the charges?

Zz.

 

[maline]

I have no problem with the fact that the two individual transmission probabilities are different. But what does this have to do with the joint probability of both particles being transmitted?

p.s. with all due respect, I don't think I'm the one who's "not paying attention" here!

 

[ZapperZ]

I have no problem with the fact that the two individual transmission probabilities are different. But what does this have to do with the joint probability of both particles being transmitted?

p.s. with all due respect, I don't think I'm the one who's "not paying attention" here!

Then I don't understand why you were using the alpha particle example, especially when clearly it doesn't apply to the "they" in your Post #12, if you are paying attention.

Whether you buy my argument or not, here's a fact: we have no experimental evidence of the tunneling of whole atoms and molecules.

If such an event can't be achieved, then there's no hope of tunneling whole watermelons.

Zz.

 

[kmm]

I have no problem with the fact that the two individual transmission probabilities are different. But what does this have to do with the joint probability of both particles being transmitted?

p.s. with all due respect, I don't think I'm the one who's "not paying attention" here!

Maline. I would think of it like this. The probability of flipping a coin heads is 1/2. The probability of flipping two heads consecutively is 1/2*1/2=1/4. This is analogous to a the probability of a composite particle tunneling. So if you have an electron that has some probability X of tunneling through some potential barrier, and you have a proton with some probability Y of going through the barrier. Then the composite particle consisting of one electron and one proton will have a probability X*Y of tunneling and since Y<1, X*Y<X. That's what I expect anyway..

 

[kmm]

I have no problem with the fact that the two individual transmission probabilities are different. But what does this have to do with the joint probability of both particles being transmitted?

p.s. with all due respect, I don't think I'm the one who's "not paying attention" here!

Maline. I would think of it like this. The probability of flipping a coin heads is 1/2. The probability of flipping two heads consecutively is 1/2*1/2=1/4. This is analogous to a the probability of a composite particle tunneling. So if you have an electron that has some probability X of tunneling through some potential barrier, and you have a proton with some probability Y of going through the barrier. Then the composite particle consisting of one electron and one proton will have a probability X*Y of tunneling and since Y<1, X*Y<X. That's what I expect anyway..

I should note, I don't think X*Y is the exact probability of electron and proton tunneling at the same time, but I expect the actually probability to have a similar form.

 

[maline]

Sure, two particles tunneling is less probable than one! But Zapper's statement was that a hydrogen atom is less likely to tunnel than an alpha particle, because of the fact that the proton & electron have different individual transmission probabilities. In your terms, we're comparing X*Y vs Z*Z. With classical probability, it would be completely irrelevant whether X=Y or not. So why is this aspect important here?

 

[DaveC426913]

I have no problem with the fact that the two individual transmission probabilities are different. But what does this have to do with the joint probability of both particles being transmitted?

Because the condition for success is that you (all of you) pass through the wall. Otherwise, none of you does. You encounter an impassible barrier.

Think of a mesh bag full of dice. Shake the bag, and each die has an individual chance of falling out of the bag.

But imagine if all the dice were stuck together with strands of gooey gum. Now, no die can literally fall out of the bag onto the floor, and the entire glop of dice will never fall out of the bag no matter how long and how hard you shake it. The chance of the entire glop of dice falling through are virtually zero, because it is a the sum of all the individual chances, which is a very small number.

 

[maline]

Yes, I got all that from the start! But for the seventh time, how does the fact that the individual probabilities are different come into this?

 

[Drakkith]

Does the differencebetween the proton & electron actually make the tunneling probability lower, or just much more difficult to calculate? if so, why?

Yes, I got all that from the start! But for the seventh time, how does the fact that the individual probabilities are different come into this?

Are you asking if/why the probability for electron + proton is less than proton + proton or electron + electron?

 

[DaveC426913]

Dang. Crossed onto page 2.

@maline, read post #17.

 

[maline]

Are you asking if/why the probability for electron + proton is less than proton + proton or electron + electron?

Yes. I thought that was clear.

@maline, read post #17.

Absolutely, the tunnelings of the two particles are not uncorrelated. That is why I didn't use formulas like X*Y from the beginning. But it remains true that in classical probability, the question of whether two different events (correlated or not) have the same probability has no bearing on the probability of them both happening.

 

[kmm]

@maline I wasn't trying to show that the probability was merely less than one. I was attempting to show why the probability of transmission of the electron is higher than the transmission probability of electron + proton. But I think I see your concern now. In the OP it was stressed that the reason it's tougher to have an H2 molecule tunnel is because the protons and electrons have different probabilities of transmission. I think you understood this as implying that if the protons and electrons had equal probabilities of transmission, they would be more likely to tunnel, and you want to know why. Is that correct?

 

[maline]

sorry, I meant "less than for one particle".
yes, now you got my Q right.

 

[Derek Potter]

Does tunneling shift the phase of the wavefunction? Because if it does then the probability of Harry Potter running through the wall of Platform Nine and Three Quarters and retaining coherence (in this independent-particle toy model) would be precisely zero, not zero FAPP. His state would rotate in phase space and he would emerge with a rather different, and probably terminal, configuration on the other side.

Harry could, of course, be thinking about Humpty Dumpty. Where all the King's horses and all the King's men couldn't put Humpty together again, environmental decoherence would give Harry a sporting chance of being recohered - at least sufficiently so to survive. Harry of course can use his wand to impose superselection of favourable outcomes but the rest of us must calculate - as Harry Hill says "What are the chances of that happening?"

But I'm shooting in the dark here as I have a sneaking suspicion that tunneling does not impose a phase shift so we're back to maline's question. Or perhaps more usefully, we should ask can we treat a highly entangled system as a collection of independent particles? Why *does* a tunelling alpha particle stay in one piece? DaveC's answer may apply because of binding energy... So perhaps the scenario of Zapper splinching his left hand is not a viable one.

FAPP, of course.

 

[stevendaryl]

Does tunneling shift the phase of the wavefunction? Because if it does then the probability of Harry Potter running through the wall of Platform Nine and Three Quarters and retaining coherence (in this independent-particle toy model) would be precisely zero, not zero FAPP.

Well, FAPP, there is no difference between zero and zero FAPP.

 

[maline]

if/why the probability for electron + proton is less than proton + proton or electron + electron?

I hope someone actually addresses the question before the thread gets closed!

 

[Derek Potter]

Well, FAPP, there is no difference between zero and zero FAPP.

Then the term FAPP is meaningless FAPP. Thanks for making that clear FAPP.

 

[stevendaryl]

Then the term FAPP is meaningless FAPP. Thanks for making that clear FAPP.

I was sort of joking, but I don't see how one can say that any transition that doesn't violate a conservation law has rigorously zero probability, which is what I think you are saying about Harry Potter tunneling. Or maybe it's just a matter of definition--because of the phase differences, the event where Harry Potter is on one side of the wall one moment and on the other side another moment (and the wall remains unbroken) would not be considered "Harry Potter tunneling through the wall".

 

[Drakkith]

I hope someone actually addresses the question before the thread gets closed!

I don't think the probability of electron + proton is necessarily less than either proton + proton or electron + electron. My guess is that it depends on the type of barrier.

 

[Derek Potter]

I was sort of joking, but I don't see how one can say that any transition that doesn't violate a conservation law has rigorously zero probability, which is what I think you are saying about Harry Potter tunneling. Or maybe it's just a matter of definition--because of the phase differences, the event where Harry Potter is on one side of the wall one moment and on the other side another moment (and the wall remains unbroken) would not be considered "Harry Potter tunneling through the wall".

No, I wasn't saying it is rigorously zero. I first argued that the phase difference made it rigorously zero because whatever emerges the other side is definitely not HP (maybe HP Sauce?) but then I noticed the re-coherence loophole. That's two independent FAPP zeros so I won't be buying shares in the Tunneling Transporter just yet :)

 

[jeffery_winkle]

I attended the April 2000 APS Meeting at Long Beach, CA, and even though I already graduated, I went to a lunch for undergraduates. There was a girl undergraduate physics major there, and she was relating a conversation she had with her mother, where she was trying to convince her mother that you could walk right through a wall, without leaving a hole in the wall behind you, without being injured, without damaging the wall. Quoting herself, she was saying, "MOM! It's true!" After the girl told the story, all the physics undergraduates at this lunch all had a big laugh, basically laughing at this girl's mother.

Part of the problem is that in undergraduate classes, they frequently approximate macroscopic objects as point particles. For example, if they are calculating the Earth revolving around the Sun, they approximate the Earth as a point particle. Well, obviously, the Earth is not a point particle. If they are calculating the probability of something barrier tunneling, they also approximate it as a point particle, which might be sufficient for an electron but not for a person. There are more differences between a person and electron than simply the difference in mass.

Aside from the stupendously low probability for this happening, let's say all the subatomic particles in your body, successfully barrier tunnel through the barrier. There is no reason to assume that after that, they would all reform the exact same atomic and molecular bonds that they had before. Even if you do successfully tunnel through the barrier, in the process, you will be converted into a plasma of subatomic particles.

This is also relevant to the black hole information problem. Let's say you have a bound state of two fundamental particles, say a positronium, which is a bound state of an electron and positron. Let's say, it is passing through the event horizon of a black hole. Well, one particle has to pass through first. So, then you have an electron inside the event horizon, and a positron outside the event horizon. Obviously, they can no longer be bound together when they are on opposite sides of the event horizon. Then the positron passes through the event horizon. After that, there is no reason to assume they will reform the same bond they had before. And that's for the most simple example of a bound state of two particles. Now imagine, if a person, which contains complicated organic molecules such as DNA, were to pass through the event horizon of a black hole. They will be converted into a plasma of subatomic particles simply by passing through the event horizon of the black holes. Obviously, all of these subatomic particles are not going to spontaneously reassemble into DNA after they are on the other side of the event horizon. Simply by passing through the event horizon of a black hole, you will be converted into a plasma of subatomic particles.

This was implicit even in the earliest formulation of black holes going back to Schwarzschild, but nobody seemed to recognize it because they were so used to approximating things as point particles, especially in general relativity. However, recently, this idea was independently rediscovered as a solution to the black hole information problem, where it was called the "firewall". Even after the firewall solution to the black hole information problem was proposed, some critics complained that it contradicted the general relativity assumption that "nothing special happens at the event horizon".

 

[stevendaryl]

Let's say you have a bound state of two fundamental particles, say a positronium, which is a bound state of an electron and positron. Let's say, it is passing through the event horizon of a black hole. Well, one particle has to pass through first. So, then you have an electron inside the event horizon, and a positron outside the event horizon. Obviously, they can no longer be bound together when they are on opposite sides of the event horizon...

The physics of black holes is certainly beyond my expertise, but I don't think that's quite right. You can set up an approximate local inertial coordinate system in the vicinity of the electron-positron pair, and to first approximation, the metric looks the same as the Minkowski metric, and so the usual two-particle bound state wave function should be approximately correct for this coordinate system. So to first approximation, falling through the event horizon shouldn't do anything to the positronium. (I'm sure there are higher-order effects that will take into account the possibility of the electron falling through while the positron escapes capture...)

 

[maline]

I don't think the probability of electron + proton is necessarily less than either proton + proton or electron + electron. My guess is that it depends on the type of barrier.

Because they won't get through the barrier with equal probability! Your right hand might go through, but your left hand stayed behind!

Okay, we have a bona fide disagreement here! Can anyone settle this?