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A common sense objection to tunneling?

  1. Mar 3, 2008 #1
    My understanding of the phenomenon: Occasionally a particle will tunnel through a solid barrier rather than bounce off. Theoretically the same is true for larger, more complex structures, it is just a matter of this happening to enough particles simultaneously. So, If you lean against a wall, as time approaches infinity, you find yourself "falling through" it.

    Should this not be observable on an every day basis? Where I am typing this, I see a finite yet very large amount of distinct particle groupings which this could happen to. I see a monitor and keyboard able to fall though my desk, a dozen pens, a soda bottle, a mouse, and so on. Going beyond the obviously huge amount of particles in these things, I see what is probably a few thousand grains of dust on my keyboard.

    So, lets call the amount of objects that a single person is observing (and would notice if it tunneled) at any given time N. There are 6.6 billion N's out there. I am not sure long a time it would take for an object to tunnel through, although I am sure it is minuscule. Let us call the amount of "chances" an object has in tunneling through something within one second for T. Now multiply this with the amount of seconds passed since 1928 (yeah yeah, don't nitpick).

    Even with very conservative numbers for N and T, this number is very big. No match for infinity, of course, but I would think that it is large enough to get SOME sort of observable phenomenon out if it? So why is it not?

    Please enlighten me if you have the time and inclination.

    k
     
  2. jcsd
  3. Mar 3, 2008 #2

    ZapperZ

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  4. Mar 3, 2008 #3

    Andy Resnick

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    It does happen- every single transistor in your computer has leak current due to tunneling.
     
  5. Mar 3, 2008 #4
    Thank you, that did help somewhat. Although the bits where a few people that know very much about the subject started discussing technicalities confused me.

    The "common sense objection" was against the popular example of leaning against the wall, the gut reaction is that this is nonsense or we would observe it. (There is an awful lot of small-yet-macroscopic things constantly leaning on others).

    So, what I got from that thread is this:

    The "leaning against the wall" example is horrible and should not be used to explain things in layman terms, since physicists themselves do not really agree that quantum behavior carries over to the macroscropic world.

    The Copenhagen interpretation says that you will lean against the wall for infinity and not fall through.

    Although I have problems understanding how a particle has behavior A, and a bundle of X particles suddenly looses that behavior. I guess it would be something akin to the abillity of a single football to pass through a window, while it simply will not happen when you glue a thousand of them together. The glued blob is just a collection of balls, but the behavior that emerges from that collection will be different.

    Thanks for pointing out the thread.

    k
     
  6. Mar 3, 2008 #5

    russ_watters

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    Define "an awful lot" in terms of the actual probability of such an event and you'll have your answer to why we don't observe it on an every-day basis with macroscopic objects.

    In order for the thought process to involve "common sense", it must start with the facts and then derive conclusions through logic. Just because an idea that is devoid of factual content sounds good in your head, that doesn't automatically make it "common sense". In fact, that's pretty much exactly the opposite of what common sense is.
     
    Last edited: Mar 3, 2008
  7. Mar 3, 2008 #6
    Probability of tunneling is connected to decrease of wave function through the potential obstacle.
    In area where the energy of a particle is lower than potential energy, wave function decreases as exp(-k*x).

    Formula for k is:

    k=sqrt(2*m*(V-E))*(2*Pi/h)

    h is Planck constant, which is very small: 6.6*10^-34

    Since h is so small, -k*x can be a normal size number only if m, (V-E) and x are small (like atomic masses, energies, sizes).
    In case of an object in normal life k*x will be very large.

    Then you calculate exp(-very large number). What do you think you will get?
     
    Last edited: Mar 4, 2008
  8. Mar 4, 2008 #7
    Russ: Ok. Fair enough, it should be "gut reaction" rather than "common sense".

    Lojzek: You sort of lost me on some of the constants there. Anyway I did some "research" (as in google :p) and discovered that the average amount of atoms in a spec of dirt is around 5 hundred quadrillion. So the probability gets kind of tiny, even compared to the amount of observed dust-specs times the chances in a second times the seconds since the fenomena became known.

    But that doesn't really matter now, I find the Copenhagen interpretation reassuringly simple. Why should a collection of something exhibit the same properties as individual objects anyway, it sure isn't like that with anything else.

    k
     
  9. Mar 4, 2008 #8

    Demystifier

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    It is well known that quantum mechanics (QM) contradicts "common sense". However, some interpretations of QM contradict "common sense" more than the others. The interpretation of QM that seems to be the closest to the "common sense" (which, of course, does not necessarily imply that it is "the best" interpretation) is the Bohmian interpretation. In the Bohmian interpretation there is an additional non-classical force on the particle, which provides a "common sense" explanation of tunneling.
     
  10. Mar 4, 2008 #9
    Aye, not necessarily looking for the best, but rather the easiest to initially wrap your head around if you are a lay person new to the ideas :)

    k
     
  11. Mar 4, 2008 #10

    vanesch

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    As others pointed out, in as far as quantum mechanics is valid for macroscopic objects, if you estimate roughly the probability for, say, your pen to fall through your desk, you get RIDICULOUSLY small probabilities. Things like, say, 10^(-2000000000). That's a number you cannot even write out in decimal notation on a piece of paper that would fit in the visible universe ; worse, it is a number that is so small that you cannot even write on a piece of paper that fits in the observable universe, how many universes you would need to fit the paper in on which you wrote the number :bugeye:

    So your meager 10^9 objects or so are not going to fall through the desk....

    and yet, regularly, MY pen falls through my desk and even through the floor, and disappears! :smile:
     
  12. Mar 4, 2008 #11
    Vanesch: I just read somewhere that 1 planck equals 10^-20 the diameter of a proton, yet the radius of the known universe is ~ 10^61p. Clearly I am underestimating the power of powers :)

    Thank you for caring, I'll go back to my basic books now and let these issues I'm having lay until I'm better equipped to deal with them!

    k
     
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