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A very basic question about Heisenberg Uncertainty

  1. Dec 8, 2014 #1
    So I understand that Heisenberg Uncertainty states that we cannot know the position and velocity of an electron at the same time.

    Although I haven't go through its proof and assumptions, I have read on couple place that thats because if we are able to observe it, that means it have to reflect at least couple photons to us. That means by the time we saw it, it already have changed its direction and position. Is this the main reasoning?

    If so, my question is as follows,

    How can someone claim that something cannot be known, if he couldn't find a way to know it himself. I mean yeah, we cannot observe the electron by directly measuring the photons on it. But you know maybe someone in the future will just do it by another way. Maybe he will measure the magnetic field of a single electron or maybe he will calculate the deviation depending on the angle he receive the photon reflected on the electron or maybe something more complex and bright.

    I mean, how can we build an entire physics on an argument that assumes impossibility of measurement. Isn't that a bit odd that everyone is comfortable with it? I haven't found an electron yet with its exact speed and position but I don't know if someone will say "here it is" tomorrow. Just because something is incredibly hard or sensitive doesn't mean claiming of impossibility is logical. This ought to be science not engineering. Am I missing something or does entire physics world really thinks thats our limit.
     
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  3. Dec 8, 2014 #2
    This is not the reason for the Heisenberg uncertainty principle. It may be the popular presentation of it, and Heisenberg himself initially interpreted it this way before later realizing how much more fundamental it is, but you're describing a separate phenomenon called the "observer effect". The uncertainty principle is about how precisely the position and momentum (or, more generally, any pair of incompatible observables) can even be defined for a particle. This makes no assumption about the nature of how a measurement is done, or even whether a measurement is made at all.

    That said, the HUP does certainly have implications for the precision of our measurements, however the popular understanding that ##\Delta p \Delta x \geq \hbar/2## means that if you measure momentum to precision ##\Delta p## then you necessarily disturb the position by at least ##\hbar/(2\Delta x)## is wrong. There is, however, a minimum amount of disturbance you can derive from HUP, called Ozawa's inequality. That the precision of incompatible measurements can exceed the bound a naïve application of the HUP was experimentally verified by Steinberg in a landmark experiment two years ago. Unfortunately, do the popular misconception I've mentioned, this was widely reported in the press as "physicists break the Heisenberg uncertainty principle". In any case, Ozawa's inequality, like the HUP, also does not make any assumptions about how a measurement is performed. The limitation to measurement precision that it implies comes not from a technological assumption but from our understanding of what quantum states are at a fundamental level. So if someone comes out tomorrow and says, "Hey, I've got this cool technique to measure the position and momentum of a particle simultaneously to arbitrary precision," and it turns they're right, then they haven't "just" made an engineering breakthrough. They'd have refuted quantum mechanics itself.
     
  4. Dec 8, 2014 #3

    atyy

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    In fact it can be shown that a particle in quantum mechanics cannot have simultaneously well-defined position and momentum (except in special cases). Since these quantities do not simultaneously exist, they cannot be simultaneously measured.

    But it doesn't matter. A measurement is a procedure that yields a probability distribution of outcomes. Measurements of position and momentum are simply different procedures, requiring apparatuses that cannot be in the same place at the same time. What quantum mechanics does is predict the distribution of outcomes for a given procedure.

    You may object that this is not "measurement", which is fine objection. Just treat "measurement" as a technical term meaning "experimental procedure". These procedures are called position and momentum measurements because in the classical limit of quantum mechanics, the classical definitions are recovered.
     
    Last edited: Dec 8, 2014
  5. Dec 9, 2014 #4
    So thats actually about the way quantum mechanics assume an object is. Nothing is ever certain until it happens. But seems pretty vague again, we can just say "well that was another possibility of position and momentum." for anything happened. I mean just stating that everything is possible but there are more probable things than others cancels out the entire causation logic. You only depend on numerous experiments but there is no good explanation after all.

    For example with this logic, its possible that 1 seconds later half of my atoms will appear 1m left and the rest at 1m right, ripping me apart. And quantum would say: "thats quite a low possibility but why not?"

    Is there any better reasoning in this "quantum randomness" that I am missing out? It feels like people just come up with this because they weren't able to find good explanations in microscopic level and they came up with a cool probability trick depending on experiments.
     
  6. Dec 9, 2014 #5

    phinds

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    Welcome to reality.
     
  7. Dec 9, 2014 #6
    Thats not reality thats just tragic if people really believes the thing I just said.
     
  8. Dec 9, 2014 #7

    Nugatory

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    That statement is in fact correct, and you don't need quantum mechanics to make it. This is bone stock classical statistical mechanics that has been known for better than a century now; Boyle's Law and thermodynamic concepts such as heat and temperature are all derived from these statistical analyses.

    Quantum mechanics is weird at the microscopic level, but the lack of observable weirdness at the macroscopic level is no more weird than the way that ##10^{26}## iron atoms flying in close formation while each one individually obeys Newton's laws can be modeled as a single giant particle called a "cannon ball" or "roundshot".
     
  9. Dec 9, 2014 #8

    phinds

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    No, it's tragic if you plan a career in science and can't face reality.
     
  10. Dec 9, 2014 #9
    Its okay to generalize stuff, anticipate results by statistics and all. But considering it as a fundamental science is not.

    You can't face reality as you don't admit you just don't know or derive the actual dynamics.
     
  11. Dec 9, 2014 #10

    atyy

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    The important point is that quantum mechanics does not say this. Quantum mechanics does not say what an object is. Quantum mechanics predicts the distribution of outcomes of experimental procedures.

    However, we can also say that whatever an object is, if quantum mechanics holds exactly, then the properties of an object cannot be simultaneously position and momentum. It is possible for the property to be position and some other property that is different from the non-commuting canonically conjugate momentum, and it is possible for particles to have trajectories. That is not ruled out by quantum mechanics. However, because there are many possible hypotheses for the properties of an object that can be consistent with the predictions of quantum mechanics, we will need experiments that go beyond quantum mechanics in order distinguish these hypotheses.

    I should also note that determinism versus randomness is not the true problem. If you prefer to think that randomness is fundamental, you can always imagine a deterministic theory emerging from a theory with randomness. If you prefer to think that determinism if fundamental, you can always imagine that a random theory is emerging from a deterministic theory. The main conceptual problem in quantum mechanics is that it appears that if we believe in common sense reality, the wave function of quantum mechanics cannot describe all of it.

     
    Last edited: Dec 9, 2014
  12. Dec 9, 2014 #11
    So for now, does it just suggest that existence of matter properties appear and disappear depending on some conditions? Like if speed is reduced to an interval, physical positions probable interval is widened. So it never assumes something is physically somewhere at a particular speed in the first place? Its not about how we measure or statistics, it says matter has a different nature than classical physics defends?
     
  13. Dec 9, 2014 #12

    atyy

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    No. Quantum mechanics is simply not about matter properties. Quantum mechanics is about the distribution of outcomes when you make a measurement.
     
  14. Dec 9, 2014 #13
    So didn't anyone tried to explain the reason for this distribution of outcomes?
     
  15. Dec 9, 2014 #14

    Nugatory

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    But we do know the actual dynamics and it's these dynamics that allow us to derive the uncertainty principle (instead of accepting the "oops - moved it when we bounced a photon off it" misconception that you started the thread with). It's unfortunate that these dynamics don't conform to your sense of what a respectable physical theory should look like, but then again people had similar objections to the Copernican model of the solar system when it first came out.

    PhysicsForums is here to help people understand modern physics. We can help you understanding what science says and why it says it, but we are not a platform for arguing against modern physics.
     
  16. Dec 9, 2014 #15

    atyy

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    Yes. In non-relativistic quantum mechanics, one family of possibilities is Bohmian Mechanics. There are probably other possible reasons for the distribution of outcomes. However, because all these possibilities lead to the same experimental predictions as quantum mechanics, we cannot tell at present whether any of these reasons are correct.

    The question of whether there is an explanation for relativistic quantum mechanics is still only partially solved.
     
  17. Dec 9, 2014 #16

    Nugatory

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    Yes. You actually are in good company in your reluctance to accept QM the way it is - google for "EPR paper" and you'll find Einstein arguing that there ought to be some deeper theory underlying QM, and that allowed the statistical distributions of outcomes that QM predicts. David Bohm gave it a good try (google for "Bohmian mechanics") but ended up just replacing statistical measurement results with statistical initial conditions. Gerard 't Hooft (google for "superdeterminism") has another approach, but it is even more bizarre and harder to swallow than QM.

    Einstein did not live long enough to see John Bell's proof (google for "Bell's Theorem") and the subsequent experimental confirmation that no theory of the sort that you are asking for and the hoped to find could exist.

    (Warning: "no such theory could exist" is an oversimplification verging on misstatement, but the subtleties are beside the point here. Everyone who knows what I'm talking about here... please restrain yourself from pointing them out... we don't need another journey down the rabbit hole :) ).
     
  18. Dec 9, 2014 #17
    Well its good that we at least can do some stuff by memorizing and generalizing experimental results. I don't know what you understand by the word science but people don't just believe in it. Just because its widely accepted or just because some objected arguments were correct in the past does not mean quantum also is. You might be the one arguing against reality in this case. Im just saying that my question is scientific, I want to understand the clear claim and discuss it scientifically. I am not randomly objecting everything I hear.

    I think there is nothing wrong with what I do but if that don't conform your sense of what a respectable physics forum should be a) delete this post along with my account if you have the authorization b) just go off the page.

    Thanks thats basically the kind of answer what Im looking for. But on overall, can my arm still appear 1m away on any time according to quantum principles no matter how low the possibility is?

    Whats wrong with going down the rabbit hole in a physics forum?
     
  19. Dec 9, 2014 #18

    Ken G

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    There's nothing wrong with going down the rabbit hole, so long as you understand it is a rabbit hole and not some other kind of hole. In physics, the rabbit hole is the place where you to be able to account for the outcomes of experiments. Once you have successfully accounted for those outcomes, that's the end of the hole. Searching for why the experiments came out the way they did is no different from being able to say what will happen. Anything more is not physics any more, it's a different rabbit hole-- more like metaphysics. But above all, we do not start with metaphysical assumptions, and try to make the physics fit them.
     
  20. Dec 9, 2014 #19

    atyy

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    Yes.


    I want to stress that the main conceptual problem in quantum mechanics is not that it is random. The main problem is something called the measurement problem, and has to do with the difficulty of using the wave function to describe all of reality, even though we do not know of any deviation from quantum mechanics at the moment, even at very large scales.
     
  21. Dec 9, 2014 #20

    Nugatory

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    Nothing. We already have hundreds if not thousands of posts discussing this particular topic, many of them in very great detail and at a fairly advanced level, and many containing pointers to excellent outside resources. I've suggested a number of google search terms that will bring some of these up, and allow you or anyone else to explore the exact boundaries of the class of theories that are excluded by Bell's theorem and its successors. (While you're at it, "Kochen-Sprecher" would be another good search term).

    However, all theories of the sort that would have satisfied Einstein and (judging by the arguments you're making) you fall far inside those boundaries. Thus, the modern subtleties about exactly where the boundaries lie are just going to derail this thread, which is still discussing stuff that was discovered fifty years ago or more
     
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