Why is there Heisenberg's uncertainty principle?

Discussion in 'Physics & Math' started by litewave, Mar 2, 2008.

  1. litewave Registered Senior Member

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    Can anyone give me an intuitive explanation of the reason for Heisenberg's uncertainty principle? (rather than just "that's what the math says")

    I have read somewhere that it has to do with the fact that energy exists in elementary quantum amounts that cannot be further analyzed, and since these unanalyzable quanta stretch over time and space it is impossible to define the exact amount of energy or momentum within a very short period of time or very small space. With this explanation however it strikes me as weird that the uncertainty in energy or momentum can reach as great as infinite proportions (rather than just the proportions of an elementary quantum amount, I guess)...
     
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  3. kevinalm Registered Senior Member

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    I'll give it a try. You understand that the wavelength, energy and momentum of a photon are strictly interelated? (Well, anyway they are.) Now Heisenburg realized that the only way to locate a particle is by the electromagnetic interaction. This means that the acuracy of the position is limited by the wavelength of the photon used. This is a general property of e/m. In optics it makes an appearance as the Ralleigh Limit. (spelling?) Generally, the shorter the wavelength the smaller the error in position. But remember the shorter the wavelength the greater the energy and momentum of the photon, and the larger the induced change in the velocity of the measured particle. Basically, you could say the more precisely you measure the position of a particle the harder you had to "whack the sucker" to do it.

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  5. litewave Registered Senior Member

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    Well, this is the explanation based on the perturbation by measurement.
    But imagine that at time t1 I measure the position of a particle with total precision. That of course means that I have no information about its momentum at time t1 because of the perturbation. However, later at time t2 I can measure its momentum with total precision and since there was no perturbation to momentum between t1 and t2 I can conclude that this momentum is the same as it was at t1, can't I? Thus I have determined exact values of both position and momentum at t1 and can make precise predictions about the particle's future movement. And quantum mechanics doesn't allow this, does it? The uncertainty principle means that exactly defined position and momentum of a particle at the same time simply doesn't exist. It's not just a problem of perturbation by measurement, is it?
     
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  7. Reiku Banned Banned

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    One major implication of the Uncertainty Principle is that is dissallows the electron to move or fall into the nucleus - - which allows for stable nuclei and stable orbital references.
     
  8. AlphaNumeric Fully ionized Registered Senior Member

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    No, the wave properties of the electron forming particular energy levels does that. The Uncertainty Principle doesn't.
     
  9. Reiku Banned Banned

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    Not as i understand it. For an electron to move into a proton would define a path and a location. Dr. Wolf PhD makes this notion clear in his book:

    ''Parallel universes.'' - 1985
     
  10. D H Some other guy Valued Senior Member

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    Correct. Lay writing often misrepresents the uncertainty principle as meaning that one cannot measure anything precisely because doing so would involve perturbing that which is being measured. The uncertainty principle is a tale of two measurements, not one, and not just any two measurements. The measurements in question are of "canonically conjugate generalized coordinates", i.e., a pair whose product has units of energy. A particle does not have a specific position and momentum. A better view is to view a particle as a wave packet. This wave packet is the described mathematically by a wave equation. The particle does not have a specific position (this would entail the wave collapsing to a point) or a specific frequency (this would entail the Fourier transform of the wave equation collapsing to a point). There is no way to know both position and momentum precisely because the wave cannot simultaneously collapse to a point in the spacial domain and to a point in the frequency domain. Real measurements make things even worse.


    Listen to AlphaNumeric. That an electron does not "fall into" the nucleus is a consequence of the wave equation. Turn your argument around. Photons do interact with electron. Yet for a photon to move into a electron "would define a path and a location".
     
  11. Reiku Banned Banned

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    No i will not listen, and i qoute Dr Hawking in his book, black holes and baby universes:

    ''The electron is found not to fall into the nucleus because of the uncertainty principle.''
     
  12. Reiku Banned Banned

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    Now, if Alphanumeric, what a name, had said the wave function was involved within the applications of the uncertainty principle, then i would have agreed, since, the uncertainty principle implies that a particle of mass m behaves like a wave of wavelength of h/mc.
     
  13. litewave Registered Senior Member

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    Is this similar to saying that energy exists in an elementary quantum that occupies a nonzero length of space and time and since this quantum is indivisible the exact amount of energy cannot be determined within the stretch of space and time smaller than the stretch occupied by the whole quantum?

    I imagined the elementary quantum of energy as some tiny finite amount but now I realized that it can actually vary from zero to infinity, depending on frequency of vibration (energy of a quantum = Planck constant x frequency).
     
  14. AlphaNumeric Fully ionized Registered Senior Member

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    A proton is an extended object anyway. And as DH points out, interacting particles connect, that's how they interact.
    But then Dr Wolf, who you are obsessed with, says a lot of things.
    Which page is that?
    No, de Broglie's equation implies that. The uncertainty principle imples that the variance in simultaneous measurements of particular pairs of variables is never less than a certain non-zero constant.

    This means you can never localise a particle down to a particular point, unless you're willing to know nothing about it's momentum. Thus, in principle, you are not forbidden from localising the position of an electron down to an arbitrary accuracy, but you don't know it's momentum. The fact the particle has an associated wavelength isn't a problem.
     
  15. Reiku Banned Banned

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    But as i do believe, there is a limit on any path of a particle upon interaction with another particle. If de Broglies equation says this, which it does, then it implies very much of what i had said.

    But let us assume that the electron did move into the nucleus, this would still limit any particle with its path and location. The uncetainty p would then say that the electron cannot move into the nucleus, because everything would be defined through decoherence processes.
     
  16. Reiku Banned Banned

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    What page... gee... i would need to read it again.
     
  17. Reiku Banned Banned

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    Yeh... i am obsessed with Dr Wolf... He's only the best psychophsicist in the world, next to Penrose.
     
  18. Farsight

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    I can. It's quite simple actually, but note that this is not currently accepted physics: particles are extended entities with no actual surface. For example, an electron is not some tiny billiard ball "point" that generates a surrounding electric field. The electric field is part of what the electron is. If you want an analogy, think of a flat calm ocean. Introduce a whirlpool into the middle of the ocean. Now, I ask you a question: Where is the whirlpool located? You point to the centre of it, and I say Are you certain? You say yes, but then I tell you that all the whirlpool actually is, is water moving in a rotary fashion. And the water is in motion all around. As we move away from the centre there's less motion, but we don't find any actual cut-off point where the whirlpool has some kind of edge. In fact, the nearest thing to an edge is in the inner rim of the whirlpool. And within it, at the place you pointed to, is where there isn't any water in motion. Where you said the whirlpool was, it isn't! Now you're not so certain about where the whirlpool is. And now you understand it, you realise that the conceptual error was trying to pin down an extended entity in some particular location and trying to say with certainty that the whirlpool is here. We can't be certain, so we have to be uncertain. Anyhow, an electron is a little like this. It's a stress rather than a fluid flow, so don't take it the whirlpool analogy too literally. But it should be enough to give you an idea.
     
    Last edited: Mar 6, 2008
  19. BenTheMan Dr. of Physics, Prof. of Love Valued Senior Member

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    litewave----

    Please note this:

    Emphasis added.
     
  20. litewave Registered Senior Member

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    You seem to be talking about the wave aspect of electron. Since the wave is extended in space and time and the electron's energy and momentum depend on the wave - on the frequency of the wave (E=hf, p=hf/c), this leads to the conflict between localization of the electron in space/time and the very definition of its momentum/energy (if it's localized it has no defined frequency and hence no defined momentum/energy)?
     
  21. Pandaemoni Valued Senior Member

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    3,634
    I've heard the same explanation, back in college, That Heisenberg was thinking about why an electron with a known energy does not fall into the nucleus (given the electromagentic attraction and the fact that the electron was "orbiting" and so should lose energy because of its acceleration), and, thinking about the uncertainty principle, realized that the electron did not have a specific "position." As he calculated it, there was (always) a probability that the electron if pinpointed would be outside the nucleus (and also a small, but non-zero, chance that it would wind up inside the nucleus).

    When the electron winds up inside the nucleus, we see it as "electron capture" and it's much more likely to occur in some nuclei than in others.

    Then again, I've also heard wave theory explanations for why electrons don't fall...which I suspect are two somewhat conceptually different ways of describing the same thing. Remembering the uncertainty principle explains electron capture, though.
     
  22. kevinalm Registered Senior Member

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    Ok, at t1 you measured the position with 'infinite' precision. So you have no idea which direction and how fast it's moving. How can you tell that measurement at t2 is the same particle?
     
  23. litewave Registered Senior Member

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    And if it was the only particle in the world?
     

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