Probability of Hand Going Through Table?

[Mozart]

I was watching a show called Daily Planet a while back when some author of a Science book said something like, "There is a probability that my hand will go right through this table."

I started thinking about what he said, and I rememberd hearing one of my Science teachers 2 years ago saying atoms are 99% empty (I don't know if this is true or not I may have rememberd wrong). I was also thinking about how matter isn't continuous and it contains gaps. So what is in my head is the following. Imagine each period is a single atom


Finger----> . . . . . . . . . . . . .
. . . . . . . . . . . . . .
. . . . . . . . . . . . . . . .
. . . . . . . . . . . . .

Table ------> . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . .
. . . . . . . .. . . . ... . . . . . . .

So by looking at that very awkward depiction of atoms it seems that there is a chance that your finger will go through the table. Maybe it will go through until it becomes blocked by other atoms. So is this a proper way to think about the chances of matter going right through matter? Oh, and what about the electrons? Is it because they are bosons that they just pass right through each other without disturbing its orbital path?

 

[nmondal]

There is a probability and that too is 100% is that, the Guy who said it is MAAD.

:yuck:

People, without appropriate context should not talk like that.
In the mean time the picture you drew is a waste, as that shifting never happens in the solids. Any kind of solids.

Ok...
Here is the case...it CAN NEVER HAPEN.
No SOLID exists in the world for which this can happen, it happens for ice with sharp edged object into it.

Why?
In case of ice, that answer does not require a real innovation.
Why the thing mentioned above never happen?

There exist something called an electron, and something called bonding.

So by the property of solids, we just do not have to worrry about the scenario that you mentioned.
If the other thing happens, then do not call the thing a solid.
A table is always solid.

 

[inha]

yeah that was more likely just an pop-sci analogy for tunneling. maybe mindboggling but also horribly inaccurate.

 

[Gokul43201]

So by looking at that very awkward depiction of atoms it seems that there is a chance that your finger will go through the table. Maybe it will go through until it becomes blocked by other atoms. So is this a proper way to think about the chances of matter going right through matter?

No, it's not. You can not think of quantum mechanical phenomena classically, especially if one doesn't know the QM involved.

Oh, and what about the electrons? Is it because they are bosons that they just pass right through each other without disturbing its orbital path?

No. Electrons are NOT bosons. They are Fermions and they certainly repel each other through the Coulomb interaction.

 

[hexhunter]

this might be in reference to branes, in that documentary on the string theory the guy starts talking about how all posibilities have a chances of being the outcome, i'll ahve to watch that bit again... i think it was around the bit where he starts with branes and the 11 dimensions...

 

[PIT2]

this might be in reference to branes, in that documentary on the string theory the guy starts talking about how all posibilities have a chances of being the outcome, i'll ahve to watch that bit again... i think it was around the bit where he starts with branes and the 11 dimensions...

I think that's in the video called 'the quantum cafe' on this site:

http://www.pbs.org/wgbh/nova/elegant/program.html

 

[hexhunter]

yup, that's it...

 

[Spastik_Relativity]

mozart,
ive got to say that that is ludacris. the strong nuclear force will repel you if your hand was to have any penetration aanyway

 

[LURCH]

I am sure that the statement was indeed a reference to tunneling, which is a verified phenomenon, a result of Uncertainty. The statement is correct as stated, "there is a probability...". However, one must understand that in this context the use of the word "probability" merely means that the chances are not mathematically zero. The only questionable turn he uses his the phrase "pass through", since tunneling would be more accurately described as his hand getting from one side of the table to the other without passing through it.

After all, the man's hand is a material object, and matter is made of Quantum articles. The location of anyone of these particles as a degree of uncertainty to it. Included within the "possible" locations of each of these particles is a location on the far side of the table. However, the distance from the top of the table to the underside is so great (in Quantum terms) that the probability of anyone particle occupying this location is extremely low. The probability of all of the particles in the man's hand existing on the far side of the table can be found by taking the odds against one particle making such a jump, and multiplying it by the number of Quantum particles in the man's hand. The result is still >0, but a probability so very low that, if the man were to strike the table with his hand five times per second since the beginning of the universe, he would still just be hitting the table and stopping every time.

But, given an infinite number of tries, there would be some occasions on which the hand is found on the far side table, giving the appearance that it had "passed through".

 

[Hans de Vries]

But, given an infinite number of tries, there would be some occasions on which the hand is found on the far side table, giving the appearance that it had "passed through".

Since the laws of Quantum mechanics are not infinitely mathematical perfect
one can savely say that the chance is absolutely zero, zero, zero.

Not zero is for instance is the chance that one acquires a genetic disorder,
spontanously grows wings, and then becomes the first man or woman to fly
around the world using them.

Luckely, popular Bio.science programs do not seem to need stuf like this.
For the time being at least...

Regards, Hans

 

[learningphysics]

Since the laws of Quantum mechanics are not infinitely mathematical perfect
one can savely say that the chance is absolutely zero, zero, zero.

If Quantum mechanics were "perfectly true", then would there be a non-zero probability?

 

[Hans de Vries]

If Quantum mechanics were "perfectly true", then would there be a non-zero probability?

The QM effect in general is about how particles can temporary (for a short
time) have some extra energy to tunnel through a barrier. The longer the
time needed or the higher the energy required the less likely it becomes.

1) A single atom in your hand would need to acquire a large amount of extra
energy for a very long time: very unlikely but maybe not zero.

2) Now all the atoms in your must acquire a huge energy all at the same time:
extremely unlikely. The general result would be that your hand explodes.

3) Now the real miracle must happen: Your hand should not explode but
by sheer chance all atoms should bang in perfect concert through the
table and appear at the other side at exactly identical relative positions.

4) Next miracle is that all the atoms lose the extra energy in perfect
concert to stop as if nothing has happened. Yet another required miracle
is that the table remains unharmed by all of this.

The recipe for mindless extrapolation:

Electron tunnels through barrier => Hand tunnels through barrier
just replace sound "electron" by sound "hand" and make sure not
to think any further.

Regards, Hans.

 

[Pengwuino]

One of my professors said this was possible though. He's example was his hand passing through a wall and he said that its possible except that you'd ahve to wait a few of the universes current lifespans before it would ever happen but he made it clear that there is a mathematical possibility.

 

[ohwilleke]

There is a similar hypothetical that involves nothing but classical gas kinetics.

There is some possibility, exceedingly remote to the point of being so unlikely that it will probably never happen, that the molecules of oxygen in your bedroom could all end up in the part of the room where your mouth and nose are not, for some period of time. If that period of time was long enough, you could suffocate and die.

But, the law of averages applies viciously with a large population of gas molecules. There are 6*10^23 molecules of oxygen in 16 grams of the stuff. Air is about 21% oxygen at sea level (the nitrogen and nobel gases that make up most of the rest is essentially inert for breathing purposes). Air weights about 1 gram per liter. Nitrogen is 7/8th the weight of oxygen, so oxygen is about 23% of air by weight. A typical bedroom might have 10,000 liters of volume. This means that there are about 1.4*10^27 oxygen molecules in a typical bedroom.

Normally, 1.4*10^22 oxygen molecules are going to be in the general vincinity of the 1 liter of your bedroom containing your mouth and nose. The odds of most of those oxygen molecules going to some other part of the room for any extended period of time are astronomical.

To apply the law of large numbers rather crudely, and say that each oxygen molecule has a 1/10,000 chance of being in that liter of air and that you apply this 1.4*10^27 times, the number of molecules of air in that liter is going to hover very close to the mean expected number of molecules.

Also, 1/10,000 chance is really something that ought to be applied at a frequently roughly comparable to the time it takes a molecule of air to travel a decimeter (since a liter is a cubic decimeter). Air molecules at room temperature move at 500 m/s on average. http://www.Newton.dep.anl.gov/askasci/chem03/chem03448.htm

Thus, you really need to recalculate the the number of air molecules around your head about 5000 times per second.

Since you would have to be deprived of oxygen for perhaps 2 seconds to even notice the effect, this means that you'd basically have to beat the law of large numbers 10,000 times to have even a noticeable effect, and in each case this means that one has to come from applying the 1/10,000 determination about 1.4*10^27 times and come out far from the mean. And, that is just to notice it.

To get a real scare and be without oxygen for say 2 minutes, this deviation has to take place 600,000 times. In other words, an event with a 1/10,000 chance of happening has to happen at a frequency significantly different from the average frequency when repeated an 8.4*10^32 virtually independent occassions. The standard deviation is roughly 10^14 and the mean is roughly 10^22. Thus, 95% of the time (i.e. roughly 2 standard deviations), the number of oxygen molecules in the 1 liter of your bedroom that contains your head will be within 2*10^-6 percent of normal. At 50% reduction in the number of air molecules around your head for two minutes is at z=10^13 or so on the normal distribution curve. Converting that z score into an ordinary probabilty is off the chart of most computer programs designed to do that. A probability of this event happening every two minutes of once or twice in 10^15 would be once in the time period from the Big Bang to now. The probability of something with this z score happening is less than .01^z or on a comparable order of magnitude. In short it is so improbable that it will never happen.

Anyway, the hand through the table quantum mechanics example requires events with probabilities on an order of magnitude less probable. In short, these are events are so rare that they will never happen.

 

[PIT2]

The result is still >0, but a probability so very low that, if the man were to strike the table with his hand five times per second since the beginning of the universe, he would still just be hitting the table and stopping every time.

Someone should test this in an experiment :rofl:

 

[learningphysics]

I believe there is a vast difference between saying that something is impossible according to a theory, and something is exceedingly improbable. Practically it may make no difference. But conceptually there is a great difference.

 

[ZapperZ]

I believe there is a vast difference between saying that something is impossible according to a theory, and something is exceedingly improbable. Practically it may make no difference. But conceptually there is a great difference.

Can you elaborate, or give an example, on how such a knowledge can make a "great" conceptual difference?

Zz.

 

[Pengwuino]

Can you elaborate, or give an example, on how such a knowledge can make a "great" conceptual difference?

IMHO, impossible vs. insanely improbable means a physical object can be modeled in 2 different ways. With a hugely improbable situation like this, we might assume that atoms are not full solid components. If it were absolutely impossible, we would have to model atoms in a way that it was physically impossible for something to pass through which would present a different model then the previous one.

 

[learningphysics]

Can you elaborate, or give an example, on how such a knowledge can make a "great" conceptual difference?

Zz.

If it is improbable (if the probability is nonzero), then given an infinite amount of chances the event will happen. However if it is impossible, the event will never happen. So there is a conceptual difference. With one scenario the event happens... with the other it doesn't (not in the real world, but within the conceptual framework)

It would be like saying that tunneling is exceedingly improbable according to classical mechanics as opposed to saying that it is impossible according to classical mechanics.

Let me ask a different question. If a hand were to go through a table, then is QM necessarily violated?

 

[ZapperZ]

IMHO, impossible vs. insanely improbable means a physical object can be modeled in 2 different ways. With a hugely improbable situation like this, we might assume that atoms are not full solid components. If it were absolutely impossible, we would have to model atoms in a way that it was physically impossible for something to pass through which would present a different model then the previous one.

But you stated that there is a great conceptual difference. These are not "conceptual", are they? They are more... er... "technical", and honestly, as someone who has done tunneling spectrum AND had to deal with modelling of band structure, I don't see any great technical difference between "infinite barrier" and "very, very, very, large barrier", the same way I don't see any technical difference between "very, very small gravitational field from alpha centauri" with "no gravity from alpha centauri".

Zz.

 

[Pengwuino]

Well what's the conceptual difference though? I don't know anything about the gravity situation but don't you think the whole idea of gravity would be conceptually different if there were absolutely 0 gravity coming from alpha centauri?

 

[ZapperZ]

If it is improbable (if the probability is nonzero), then given an infinite amount of chances the event will happen. However if it is impossible, the event will never happen. So there is a conceptual difference. With one scenario the event happens... with the other it doesn't (not in the real world, but within the conceptual framework)

Note that we are not talking about something that simply has a non-zero chance. We're talking about something that is not likely to happen even during the lifetime of a universe! The chances of a vase, that has been broken into a hundred pieces, reassmbling itself into the original vase when I throw it onto the floor is also non-zero. But has anyone ever seen such a thing? The phase space for such an event is so miniscule, we dismiss it as being impossible. This changes nothing, nor does it affect our description of the universe by adopting for such a thing.

It would be like saying that tunneling is exceedingly improbable according to classical mechanics as opposed to saying that it is impossible according to classical mechanics.

Let me ask a different question. If a hand were to go through a table, then is QM necessarily violated?

The problem here, and I see this WAY from the beginning of this thread, is the absence of a careful analysis of the physics of this phenomenon. A single particle, such as an electron (or a stream of "free" electron) does not need to tunnel as a whole, or together. However, once you involve an object consisting of various entity (be it cooper pairs, buckyball, a hand), then various parts of that entity must be in COHERENCE with each other in such a way that a single wavefunction can be used to describe the WHOLE entity. Only then can the whole object has any reasonable probability of tunneling through the barrier. Somehow, this issue has either been ignored, or haven't been clearly emphasized.

So it isn't just the probability of tunneling a HUGE object that's the issue, there is an added complication to the whole matter that makes it even MORE unlikely. I would not hesitate one second to say it is IMPOSSIBLE.. and I can model it accurately using that as a starting point. I do not see why conceptually it should make any difference, and anyone who has paid any attention to my view on this would immediately know that "conceptual understanding" always follows the mathematical formulation.

Zz.

 

[ZapperZ]

Well what's the conceptual difference though? I don't know anything about the gravity situation but don't you think the whole idea of gravity would be conceptually different if there were absolutely 0 gravity coming from alpha centauri?

Well, I dunno. You were the one who said there is a "great" conceptual difference between the two. That's why I asked for you to elaborate. To me, it makes no "conceptual difference" especially when the model/mathematics makes no difference.

Zz.

 

[ZapperZ]

Er.. I seem to have overlooked to whom I was replying to and didn't realize that both Penguino and learningphysics were replying to me as the same time. So if I mix up who said what when, please blame it on my onset of senility. Oy.

Zz.

 

[learningphysics]

Note that we are not talking about something that simply has a non-zero chance. We're talking about something that is not likely to happen even during the lifetime of a universe! The chances of a vase, that has been broken into a hundred pieces, reassmbling itself into the original vase when I throw it onto the floor is also non-zero. But has anyone ever seen such a thing? The phase space for such an event is so miniscule, we dismiss it as being impossible. This changes nothing, nor does it affect our description of the universe by adopting for such a thing.



The problem here, and I see this WAY from the beginning of this thread, is the absence of a careful analysis of the physics of this phenomenon. A single particle, such as an electron (or a stream of "free" electron) does not need to tunnel as a whole, or together. However, once you involve an object consisting of various entity (be it cooper pairs, buckyball, a hand), then various parts of that entity must be in COHERENCE with each other in such a way that a single wavefunction can be used to describe the WHOLE entity. Only then can the whole object has any reasonable probability of tunneling through the barrier. Somehow, this issue has either been ignored, or haven't been clearly emphasized.

So it isn't just the probability of tunneling a HUGE object that's the issue, there is an added complication to the whole matter that makes it even MORE unlikely. I would not hesitate one second to say it is IMPOSSIBLE.. and I can model it accurately using that as a starting point. I do not see why conceptually it should make any difference, and anyone who has paid any attention to my view on this would immediately know that "conceptual understanding" always follows the mathematical formulation.

Zz.

So if the event did happen, would that mean that QM was false?

 

[ZapperZ]

So if the event did happen, would that mean that QM was false?

Why would it be false when the whole phenomenon came out of QM in the first place?

Now, if it happens 20 times a day without any effort, then yes, there's something VERY wrong with QM.

Zz.

 

[learningphysics]

Why would it be false when the whole phenomenon came out of QM in the first place?

Now, if it happens 20 times a day without any effort, then yes, there's something VERY wrong with QM.

Zz.

I'm talking about the hand going through the table. Would QM be false if that happened?

 

[ZapperZ]

I'm talking about the hand going through the table. Would QM be false if that happened?

And that's what I was replying to also. If it happens 20 times a day without any effort, then yes, QM would be seriously wrong.

Zz.

 

[Pengwuino]

Well, I dunno. You were the one who said there is a "great" conceptual difference between the two. That's why I asked for you to elaborate. To me, it makes no "conceptual difference" especially when the model/mathematics makes no difference.

Zz.

learningphysics made the statement that it would make a "great" conceptual difference. I feel there's no telling how big or small the conceptual difference might be if we thought it was impossible.

 

[learningphysics]

And that's what I was replying to also. If it happens 20 times a day without any effort, then yes, QM would be seriously wrong.

Zz.

That's what I meant by conceptual difference between saying it is improbable and saying it is impossible.

When I started reading this thread, most were saying that it was impossible. I took this to mean that if the event did take place... then it violated QM.

Later on, people were saying that it was highly improbable but not impossible according to QM... I took this to mean that if the event did take place... then it did not necessarily violate QM.

So if such an event took place... an understanding like:
"According to QM the event cannot happen" would lead to the conclusion "QM is false".

But an understanding like:
"According to QM the event is highly improbable" does not lead to the same conclusion.

This is the difference I was referring to. We reach different conclusions depending on what the understanding is... impossibility or improbability.

If you tell a lay person that it is impossible for a hand to go through a table according to QM... they will take it to mean that if the event does take place, then QM is violated, because that's what impossible means. But this is a misunderstanding of QM right? Isn't it a significant misunderstanding?

 

[ZapperZ]

That's what I meant by conceptual difference between saying it is improbable and saying it is impossible.

When I started reading this thread, most were saying that it was impossible. I took this to mean that if the event did take place... then it violated QM.

Later on, people were saying that it was highly improbable but not impossible according to QM... I took this to mean that if the event did take place... then it did not necessarily violate QM.

So if such an event took place... an understanding like:
"According to QM the event cannot happen" would lead to the conclusion "QM is false".

But an understanding like:
"According to QM the event is highly improbable" does not lead to the same conclusion.

This is the difference I was referring to. We reach different conclusions depending on what the understanding is... impossibility or improbability.

If you tell a lay person that it is impossible for a hand to go through a table according to QM... they will take it to mean that if the event does take place, then QM is violated, because that's what impossible means. But this is a misunderstanding of QM right? Isn't it a significant misunderstanding?

Ah, but here comes the PROBLEM. This same lay person considers my broken vase scenario to be "impossible". Yet, thermodynamics says it can happen!

So, by saying to this layperson that it isn't impossible for a hand to tunnel through a table, and yet, this person would consider the vase reassemblying itself to be impossible, what have you done? You have conveyed to this person that QM is weird, mysterious, maybe mystical, or worse still, nonsense! And I will bet you that there are other things that even you would not accept would happen that physics would consider to be possible, even in the most remote sense.

This has nothing to do with "conceptual" issues. It has everything to do with being reasonable within the CONTEXT of the situation. You can only describe things in relation to other things if this is what you are truly trying to do.[1]

Zz.

[1] http://arxiv.org/abs/physics/0503229