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Randomness in Quantum Physics

  1. Nov 17, 2008 #1
    "Randomness" in Quantum Physics

    I am interested in whether "randomness" actually exists in physics. I'm not very familiar with the math involved, but I understand that some quantum theories (one in particular that was created by Richard Feynman that uses canceled infinities) and also the Heisenberg's Uncertainty Principle with respects to observing particles which some people cite as being an example of the inherent randomness of our physical world.

    But I am confused whether these examples, or others, signify actual, legitimate randomness in the physical universe. Are they just mathematical tricks, an indication that our physical theories are lacking or something more significant?

    My question is, where does true randomness occur and are there restrictions to these random elements (that is, are the random values held only to natural number values, etc.)? Also, is it understood that this randomness signifies anything?
     
    Last edited: Nov 17, 2008
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  3. Nov 17, 2008 #2

    mgb_phys

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    Re: "Randomness" in Quantum Physics

    As far as we know the randomness (or unpredicatbility) is real.
    Of course you can't prove that there aren't hidden mechanisms determining the behaviour that we don't currently understand.
     
    Last edited: Nov 17, 2008
  4. Nov 17, 2008 #3
    Re: [Q] "Randomness" in Quantum Physics

    Randomness is a word that people think they understand, but actually have no clue about. It is often used as if it had a well understood, universal definition. But it doesn't.

    In mathematics, when two things are equal, they may be replaced with each other without changing the truth of a statement. But equal is a very strong condition, and in natural language, we often use "same" to mean something much less precise than "equal".

    To many people, 'random' means that the same event can have two different outcomes. But if two events are equal, by definition, they must have the same outcome. So "same" here means something more like "similar" or "equal in a few important aspects."

    Part of the weirdness in QM is that some of the "important aspects" things can be equal are inherently unknowable. The result is events which look absolutely identical by all experimental observation, but yield different results.
     
  5. Nov 17, 2008 #4
    Re: [Q] "Randomness" in Quantum Physics

    Very interesting although I'm not sure if I grasp all of what you said in it's entirety. You're saying that human capacity limits our ability to understand what is random? That something appears random when in fact it is relatively equal to the previous outcome?

    EDIT: What I meant by random, like you said, is that the situation can be identical and yield results that aren't just different, but sometimes wildly different. My underlying question was if these so-called "random" events actually exist in reality or only a result of our mathematics?
     
    Last edited: Nov 17, 2008
  6. Nov 17, 2008 #5
    Re: [Q] "Randomness" in Quantum Physics

    That's not quite what I meant.

    My main point was that "random" is a word that most people think they understand, but never really sat down to give it a rigorous definition. Is randomness something simply is or isn't? Are there different magnitudes of random? Is randomness a property of something which can be measured and compared?

    Which sequence is more random? "abcdefg" or "yuiop"? Most people would say the first, because those are the first few letters of the alphabet. But on a QWERTY keyboard, they are positioned all over the place. The second sequence seems random, but on the keyboard, it's just the 6 letters your right hand can reach above the home row. They are all in a line, and nicely ordered.

    So, again, randomness doesn't mean what you think it does.



    You can take any even with two possible outcomes and make the outcomes "wildly different" by putting a cat in a box with a vial of poison =-D

    It's not clear what you mean by "actually exists" and "a result of mathematics". When does something actually exist versus just regular exist? When is a physical theory an accurate description of reality and when is it "just a result of mathematics"?
     
  7. Nov 17, 2008 #6
    Re: [Q] "Randomness" in Quantum Physics

    This is turning more into a philosophical discussion than what I meant...

    For instance, if you throw a football with given parameters, it is possible to accurately judge where it will land. My question was that, in some of QM, some results equivalently have the football landing in an infinity of different positions given the same parameters. I don't think I know enough about QM to make this a just analogy, but I'm attempting my best to frame the question as I've originally intended.
     
  8. Nov 17, 2008 #7

    mgb_phys

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    Re: "Randomness" in Quantum Physics

    There are two types of 'random' in QM.
    The first is the uncertainty principle, basically there are limits to how well you can measure some properties (however good your equipment) because measuring it disturbs it. This even applies to macroscopic objects like a football, you cannot measure both it's position and it's motion perfectly accurately. There are good reasons to think this is true.

    The second kind of random is the 'hidden variable' kind. We cannot measure anything about the state of eg. an unstable atomic nucleus to know which atom is going to decay next. It is perhaps possible there may be some physical effect (the hidden variable) that we could measure if we knew how. There is no evidence that it is anything but random - but we have no way of proving that there isn't somethign we don't know about!
     
  9. Nov 17, 2008 #8
    are quantum fluctuations caused?

    I often here people refer to "uncaused" quantum events like quantum fluctuations... but i'm a little unclear as to whether they are actually uncaused or whether there is some unidentified condition that is forcing them to arise.

    For example i've read that these particles arise from the uncertainty principle:


    The uncertainty principle in the form ΔEΔt>/= h/2pi implies that in the vacuum one or more particles with energy ΔE above the vacuum may be created for a short time Δt. These virtual particles are included in the definition of the vacuum.
    http://en.wikipedia.org/wiki/Vacuum_state

    I aslo read this"
    "The fact that the Universe exists should not be a surprise in the context of what we know about quantum physics. The uncertainty and unpredictability of the quantum world is manifested in the fact that whatever can happen, does happen (this is often called the principle of totalitarianism, that if a quantum mechanical process is not strictly forbidden, then it must occur). " http://zebu.uoregon.edu/~js/ast123/lectures/lec17.html

    This seems to suggest that all non-forbidden quantum process are somehow forced to occur, which seems to indicate that if a particle can be created within the vacuum, then it MUST be created.

    is this true?

    If all occuring quantum process MUST occur (as a result of not being forbidden), then how is there any uncaused quantum process?
     
  10. Nov 18, 2008 #9
    Re: "Randomness" in Quantum Physics

    This leads me to wonder if maybe we have had a bit too much acceptance of 'randomness'. We obviously haven't proven determinism, but on that same page cant we claim that we also have not proven non-determinism. Todays general science readers for the laymen spend a lot of time claiming that randomness is the ultimate reality. Shouldnt we fear that the next generation of physicist will have a predisposition to accept non-determinism and shun models that offer deterministic explanations of QM phenomenon?
     
  11. Nov 18, 2008 #10
    Re: "Randomness" in Quantum Physics

    Good question....Yes to all three!! There is no simple answer.

    Some things, say rolling dice, or flipping a coin, are inherently "random"....Many others are just "uncertain". Mathematical "tricks" with predictive ability are deemed "good". Some math reflects this world, a lot does not...the "trick" is figuring out which is which...

    Try starting with Wikipedia on randomness: Is this definition what you meant??

    http://en.wikipedia.org/wiki/Randomness

    A few sections from the Top you'll notice RANDOMNESS IN SCIENCE....check those...

    Your post is eliciting, perhaps, incomplete answers because its an impossibly large area to discuss in one or two paragraphs.

    Also try UNCERTAINTY...You may be thinking of either randomness or uncertainty or both.


    These are examples of what are believed to be two different situations. Feynman did not know what do do with infinities because the math was clearly insufficient to provide "reasonable" answers...his own descriptions of this are quite funny.(as is he) So he decided to group infinities together and assume they did not count. Then he used measured values for other constants and voila...he obtained answers from the remaining math which matched experimental results. I believe this represents incomplete understanding and hidden aspects of science. But good enough for many predictions.

    Heisenberg "uncertainty" may not be so much random as an accurate reflection of our world which is "uncertain", somewhat indeterminate, on small scale. Wiki says: (http://en.wikipedia.org/wiki/Quantum_uncertainty)
    "The only kind of wave with a definite position is concentrated at one point, and such a wave has an indefinite wavelength."
    It says you can't theoretically measure certain correleated parameters with complete precision (even if your observation instruments were perfect) say position and momentum, energy and time. It appears these restrictions reflect fundamental aspects of the small world, but we definitely do NOT know all we'd like.
    (If this makes no sense to you, try reading about Planck scale and the inherent "foam" (energy) encountered. There may be no mass, time, distance below Plank scale, just energy!! The closer to planck scale, the more "hazy" our understanding and measurements.)

    Vacuum energy or zero point energy might also be of interest to you regarding your question.

    In large scale, measurements often appear "random"....say the length of a road between two telephone poles....yet very close...every time you stretch a tape, you'll get a slightly different answer...the "uncertainty" has a bell shaped curve...not really "random" but imprecise....we can get close to the "real" answer, but not exact. Use a laser transit and you get closer, but never exact due to always imperfect measuring devices. On cosmic scales due to general relativity (differences in time and scale between distant points) "distance" becomes even more ambiguous...there is no "correct" answer even theoretically....all the scales are "curved" by gravity...different observers see thing differently...


    For questions like:
    see wikipedia http://en.wikipedia.org/wiki/Measurement_(quantum_mechanics)


    It's generally true. Radioactive decay and quantum tunneling in general, say black hole radiation, would be examples. A roughly equivalent view is parallel worlds...EACH quantum event in EVERY world may stimulate a new world!!.
     
    Last edited: Nov 18, 2008
  12. Nov 18, 2008 #11

    DrChinese

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    Re: "Randomness" in Quantum Physics

    As mentioned already, true randomness can be seen in radioactive decay of an ensemble of atoms; also in the values of some measurements in which the uncertainty principle comes into play (i.e. when there are non-commuting observables). A common one is electron spin: once you know the x spin component of an electron, the y and z components are completely indeterminate and their observed values will be completely random (in the normal sense that they pass the mathematical tests which measure degrees of randomness).

    Now the big question (and the one you may be asking) is: is there an underlying explanation for the random values you get this way? Are there "hidden" causes which yield random values for observations, but is a fully causal mechanism? There is no scientific evidence that there is an underlying cause, and no amount of research has really ever pointed towards the existence of such potential cause. If there were, then quantum mechanics would be incomplete as well. However: no one actually knows the answer to this question at this time, so your guess is as good as anyone else's.

    Now, regarding the possible incompleteness of quantum mechanics: You are probably familiar with Bell's Theorem (1964), which addressed the original 1935 EPR paper's assertion that QM was incomplete. Bell showed that no local realistic model could be introduced to replace QM. So the upshot is essentially: you must abandon either locality or realism (causality). In other words, if there is an underlying cause to the randomness, expect it to be non-local.
     
  13. Nov 18, 2008 #12
    Re: "Randomness" in Quantum Physics

    kdgloeckner, you've already gotten some really good replies, but here's my two cents:

    Yes, it does. Randomness means unpredictability.

    Saying that our physical world is inherently random vis quantum theory might be a little misleading in that quantum theory isn't really designed to say much about the deep nature of our physical world. It would be more accurate to say that the physical basis of our apprehension of the deep nature of our physical world, such that it is, depends to a large extent on necessarily random individual quantum experimental events. According to the Copenhagen interpretation (mainly Heisenberg and Bohr) of the theory, the randomness of individual quantum experimental phenomena is due to the existence of a fundamental quantum of action (Planck's constant), and hence the uncertainty relations of Heisenberg and the principle of complementarity of Bohr, constraining quantum experimental probings of the deep nature of our physical world. This necessary randomness of individual results allows only a probabilistic, statistical accounting of them -- and we can never know their deep nature.

    Randomness means unpredictability. Except for individual quantum experimental results, what is random to one observer might not be random to another, more knowledgable, observer. However, where individual quantum experimental results are concerned, the randomness that they exhibit is, according to the theory, irreducible.

    This is the question explored by advocates of hidden variable, and other, supplements to, or reformulations or interpretations of the quantum theory. So far, none of them diminish the randomness of individual quantum experimental results.

    This irreducible randomness occurs in the accumulation of individual quantum experimental results, and is formalized in the mathematical theories and models based on the existence of a fundamental quantum of action. The probabilities calculated by these theories and models do have physical meaning, but only with regard to large accumulations of individual results.

    For example, Heisenberg's uncertainty relations say that the product of the statistical spreads of the accumulated results of two related measurements (like position and momentum) must be greater than or equal to the fundamental quantum of action (Planck's constant, which is 6.626069 x 10^-34 Joule seconds).

    As has been noted, they exist in reality as individual quantum experimental events and as elements of the mathematical formalisms associated with them.
    Of course, there are some things which have been predicted which haven't been observed yet, or which can only be indirectly observed, or which can never be observed. But the random individual quantum events which have been recorded are real enough. They're not just mathematical fictions.

    Any unpredictable event is, vis the definition of randomness, a random event. But the only random events that are (and must remain according to the quantum theory) irreducibly random for everyone, are individual quantum experimental results. So, in that sense, it's ok to call them 'truly random' or 'random in principle', because, according to the principles of the quantum theory, their deep nature must remain off limits to us.

    One might logically presume that quantum theory is just incomplete. The catch is that quantum theory is the deepest theory of our physical world, and it puts limits on what we can know about our physical world. These limits are a necessary consequence of the ways in which we're forced (due to the scale of our physical existence and the limitations of our sensory faculties) to probe and apprehend the deep nature of reality -- and there's no way around them.
     
  14. Nov 21, 2008 #13
    Re: "Randomness" in Quantum Physics

    It takes us back to Epicurus (350 BC) who, using logic, concluded that there must be a smallest object (later, became known as an atom) otherwise objects on reduction (continous halving for example) would go 'out of existence'. And since objects do not go 'out of existence', there must be a smallest sized particle (the atom). In fact, if Epicurus and Democritus had considered what happens below the atom limit they would have unearthed quantum theory. Its now shown that Special Relativity could have been discovered by Galileo if he had considered rotational symmetries - c pops out as an ordinary mathematics constant. (see Mitchell Feigenbaum brilliant paper on google)

    We are now discussing sizes smaller than that limit set by Epicurus, where objects become defined by 'states' which in turn, can only be observed in a probabalistic way. Again, my 10 cents worth is to suggest there must be an entirely logical explanation (a la Epicurus) to explain the random nature that occurs for 'things' below the 'existence in the Universe' size limit.
     
    Last edited: Nov 21, 2008
  15. Nov 21, 2008 #14
    Re: "Randomness" in Quantum Physics

    There's no such thing as random in the sense of something external to you. Random just means you don't have the capacity to predict the outcome.

    Eg. We use the idea of a pair of dice being thrown as a random outcome but it is only random because you don't have enough informational capacity on the event to predict it. If you knew every parameter and trajectory and force etc it wouldn't be "random"

    By the way there is also no such thing outside of your own perception as "death" or "chaos" or "chance" or "accident" or "coincidence" or darkness etc....... because they are all expressions of the lack of something. Not an actual thing. The absence of light, the absence of pattern recognition, the absence of a higher perspective of consciousness in which to percieve the situation.....
     
  16. Nov 21, 2008 #15
    Re: "Randomness" in Quantum Physics

    Maybe irreducible was a poor choice of words on my part. Inevitable or inescapable might be better.

    I'm not familiar with Epicurus' stuff. Did he equate existence with amenability to sensory perception? Halving something always leaves something -- however small -- but not being able to sense it's existence in any way is, for all practical purposes, equivalent to it not existing.

    This might not be quite the same as the randomness imposed on experimental results due to a fundamental quantum of action. Or maybe it is.

    Maybe I missed your point. :smile:
     
  17. Nov 21, 2008 #16
    Re: "Randomness" in Quantum Physics

    Good points. The only way that quantum randomness differs from dice, or any other sort of, randomness is that, if the the principles of the quantum theory are true, then there's absolutely no way to know the things that you'd have to know, or do the things that you'd have to do to make individual quantum experimental results predictable.
     
  18. Nov 21, 2008 #17
    Re: "Randomness" in Quantum Physics

    Yes, your logic does not quite hang together (philosophically speaking!). try this:

    Epicurus postulated that objects cannot go 'out of existence' (also the difference between a void and nothing - in that one cannot place an object into nothingness, but one can place an object into a void - actually an interesting difference even today I'd say, wouldn't you?)

    So, assunimg that objects (gas, solid or liquid) cannot simply dissappear out of the Universe, it 'follows' that an object could not be infinitely reduced without it dissappearing. Voila - atoms. -there was other logical evidence too (thought evidence).

    There followed centuries of debate about irreducibility and its logical consequences.

    One could 'prove' atoms today like this: if matter were infinitely reducible then heat would simply vanish because the degrees of freedom would be infinite. Therefore there must be a lower sized limit (atoms) that can hold the heat energy.
    Its another fundamental truth based on logic and a bit of evidence. See the power of our consciousness now?

    So I am saying that the randomness of state observations in the quantum world could well have an explanation that it *must be* that - nothing else would be correct just from logic (and mathematics, of course - which is a form of logic). I'm sure that if it was not random, then absurdities would be the result (not the Schr cat please!).




    I nearly had a psychic girlfriend once, but she left me before we met.
     
  19. Nov 21, 2008 #18
    Re: "Randomness" in Quantum Physics

    Do you believe the Universe needs a 'machine' to produce its random observables? We have great trouble producing truly random numbers - must use look up tables or something like atomic decays.
    Or is it just some mathematics that the Universe has no problem with?
     
  20. Nov 21, 2008 #19
    Re: "Randomness" in Quantum Physics

    "Random" can't be thought of correctly as a state in which something can be in, but rather a specific function of perspective\perception; that is, on the part of the observer.
    eg. It's not the signal that is random it is the lack of pattern recognition by the observer. The receptive half of the signal.

    If you viewed a small section of a fractal you might deduce that it is chaotic and random when in actual fact it is a very coherant pattern it's just that you don't have the perspective to percieve that pattern. Therefore labelled; "random", "chaotic".....
     
  21. Nov 22, 2008 #20
    Re: "Randomness" in Quantum Physics

     
    Last edited: Nov 22, 2008
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