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How do we know it's random?

  1. Nov 27, 2004 #1
    Is there a reason other than statistics that forces randomness into quantum mechanics? Have people just done test after test and found the positions of things, etc, to be random? Is it still possible that there is some sort of particle or process or thing that is small or insignificant enough that with trillions of them around or doing what they do they could give a result that looks very close to what randomness should look like? Like saying planets are always circular. Really we see this as being from quintabillions of atoms with forces acting in such a way to CAUSE the spherical planets. Could something be causing this "randomness" or if true pseudo-randomness?
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  3. Nov 27, 2004 #2

    The answer is no. What you are talking about are hidden variables. Bell showed that no hidden variable theory can explain all quantum phenomena (Bell particularly meant entanglement here).

  4. Nov 27, 2004 #3
    Without knowing what Bell did to show this, I don't see how any experiment could show this for certain...

    Plus, why does entanglement say that the outcome is randomness?
  5. Nov 28, 2004 #4
    randomness basically explains alot of phenomena we see in experimentation, and is a big part in the copenhagen interpretation. There are other more deterministic interpretations of quantum mechanics, but if I'm not wrong, very few of them have had any popularity.

    But if you ask me, I think whether randomness is really a fact of nature, stuff like that, and disputes over QM should be in the philosophy forum or something.
  6. Nov 28, 2004 #5
    well, I think it is impossible to make a real "one by one" experiment with QM systems. If so, you could do an individual experiment on an electron.
    But there are lots of statistical experiments that shows the correctness of QM. fpr example the diffraction phenomena of electron. We treat with lots of electrons. But we can still speak about "one electron" in our extended theorem.
  7. Nov 28, 2004 #6


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    Gerard 't Hooft doesn't think that Bell inequalities and EPR-type experiments is a good enough reason do dismiss the possiblility of an underlying deterministic theory.

    This is a quote from an article he wrote, with the title "How does God play dice? (Pre-)determinism at the Planck scale":

    Of course I am aware of the numerous studies regarding the difficulties in devising hidden variable theories for quantum mechanics. Deterministic theories appear to lead to the famous Bell inequalities 2 , and the Einstein-Rosen-Podolsky paradox 3 . There are various possible reasons nevertheless to continue along this avenue. Generally speaking, we could take the attitude that every “no-go theorem” comes with some small-print, that is, certain conditions and assumptions that are considered totally natural and reasonable by the authors, but which may be violated in the real world. Certainly, physics at the Planck scale will be quite alien to us, and therefore, expecting some or several of the “natural” looking conditions to be violated is not so objectionable. More specifically, one might try to identify some of such conditions. One example might be the following: turning some apparatus at will, in order to measure either the x- or the y -component of an electron’s spin, requires invariance of the device under rotations, allowing the detector to rotate independently of the rest of the scenery. This is unlikely to be totally admissible in terms of Planck scale variables.
    Last edited: Nov 28, 2004
  8. Nov 28, 2004 #7
    Shouldn't there be some sort of experimentally shown "accuracy" of the randomness? I mean, couldn't you say how sure in some sort of measurement that the randomness is really randomness?

    I agree that a lot of discussions about randomness in QM should be in the philosophy forums but I'm only talking about the experiments that were done to make people think things are random.
  9. Nov 28, 2004 #8


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    From a purely formal point of view quantum mechnics is inherently random (i.e. the postulates of quantum mechanics talk speicfically about probality), but as has been mentioned earlier this doesn't necessarily mean it cannot be explained by deterministic explnations, i.e. so-called hidden variable theories (HVTs).

    What Bell did was to show that for any HVT to consistently explain the quantum formalism it must be a non-local hiddenvariables theory (NLHVT).There are NLHVTs such as Bohm's pilot wave theory that that do explain the quantum formalism in a consistent manner, but NLHVTs are problematic in that they are very hard to square with special relativty, even though quantum mechnaics itself is relatively (excuse the pun) easy to square with special relativity, plus any hidden variables theory must postulate the existance of artifacts that can never be experimentally tested for.
  10. Nov 28, 2004 #9


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    Testing for randomness is a simple statistical matter. When you see things like gaussian distributions in photon dispersal patterns, it is pretty obvious the pattern is random even without doing the math.
  11. Nov 30, 2004 #10
    I'd strongly disagree with the idea that 'testing for randomness is a simple statistical matter' as it isn't. You can't say anything is random, you can only postulate that it is. Just becuase a distribution looks random or normal for that matter will ultimately be derived from deterministic relationships, and the only reason we use the work random is becuase our models can't cope with the level of detail necessary to build a fully inclusive model.

    A great example is flipping a coin. Some people would call the outcome random. But if you know enough about the force applied, starting position, direction of movement and any other forces acting upon the coin during motion then you can accurately predict the outcome, therefore is it actually a random event.

    Quantum mechanics makes use of probability distributions because current physical techniques and knowledge dont know enough about dynamics and the atomic level..... well thats just my opinion I guess/
  12. Nov 30, 2004 #11


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    Yep such statsical tests can never prove conclusively that it is random.

    My opinion is that if it is objectively random then we should probably call it random; what QM say is that it's not just that we DON'T know enough to describe it deterministically, it's that we can NEVER know enough to decsribe it determinsitically, not even in principle, so by any objective standard it is random.
  13. Nov 30, 2004 #12


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    As like everything else, this thing keeps popping back like a bad zit.

    If you equate the "randomness" in flipping a coin with the "randomness" in QM, then you have not understood QM. Why? Because there is a DISTINCT difference between the two, and a MEASURABLE one at that!

    If I have the superposition of two basis state such as

    |psi> = a1|u1> + a2|u2>

    before a measurement, the system is simultaneously in both basis state! How do I know this? Hydrogen molecule, the SQUID experiments, NH3, etc.. etc. The presence of an energy gap between the parity of bonding and antibonding states clearly indicate that the Schrodinger Cat-type situation exists! There is NO analogous situation such as this in coin flipping. You do not get an "energy gap" of the superposition of "head" and "tail" outcomes that intermix to create an unusual, non-classical observation! Coin-flipping is a completely different beast than QM superposition.

    Now, upon a direct measurement of the system, you will get either a state corresponding to |u1> or |u2>, but NOT both in a single measurement. The fact that you cannot unambiguously determine which state will be measured IS what is commonly cited as the "randomness" in QM. The formulation makes NO such determination, nor does it explain/describe the mechanism of which state will be the one that is measured.

    While we know what all the possible outcomes are, and while we can in fact deterministically obtain the average result of many, many such measurement (where most of our world operates), we have no way of determining the outcome of a single measurement. Now you may speculate all you want that QM is incomplete, not random, deterministic, etc... etc.. But they are all just speculation because we have (i) no formulation that is accepted that explain the "underlying" nature of such measurement and (ii) no experimental observation to indicate that there IS one.

    I really do not care if people believe QM is inherently random or not. However, please, please, please... do NOT equate the apparent randomness in QM with the randomness of coin-tossing, dice-throwing, etc, etc. Give us physicists SOME credit into having realized this already and that we have thought about it enough to know these two are NOT the same!

  14. Nov 30, 2004 #13
    ZapperZ, I just want you to know that when I started this thread I didn't have an intent of convincing myself it isn't random or deterministic. I was trying to figure out why it's thought to be random. I can't imagine how someone could tell the difference between a truely random and a coin flipping experiment or even that there could be a difference. It's probably because I don't understand much about QM yet, but I can't imagine any way of knowing and I've never heard an explanation that made me think that we could know. Again, I have much to learn before I can argue one way or the other. If anyone could explain the difference in different words, maybe it would help.
  15. Nov 30, 2004 #14


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    I actually have no issues with your question. I am just a bit annoyed with the coin-flipping connection being force onto QM's picture.

    When people use that, they seem to forget that the PHYSICS itself indicates that we can know, in principle, all the mechanics of a coin toss and thus, it is NOT random. We only put in randomness due to our "laziness" of trying to know all those intricate detail.

    Such "underlying" principle is complete ABSENT in QM. There are NO PHYSICS to tell us that, even in principle, and even if we're not lazy, there is an underlying mechanism that causes one outcome to turn up instead of the other. The superposition is REAL, and the consequences of such superposition have been verified! I have explained this at length in my previous post.

    It is the absence of such underlying mechanism that causes us to, at the very least, indicate that we have no way of telling the outcome of a single measurement. If this is called "randomness", so be it. However, do not be fooled into thinking that this "randomness" is identical to coin-flipping, because it isn't!

  16. Dec 1, 2004 #15
    Does this imply that there is no "rule" about the distribution of where the particle is when measured? I always assumed that because people were saying it's random that it had a normal distribution. I'm sure statistics have shown that it looks normal but is there any principal in QM against it not normal?
  17. Dec 2, 2004 #16
    I have to add some comments to ZapperZ post concerning the coin-flipping explanations as I do not agree with this apparently extreme position concerning QM and classical statistics even if I agree with core of ZapperZ’s previous post.

    The common mistakes, I have encountered with QM concern the interpretation of the born rules (the statistics and measurements) and the basic interpretations (out of the context of application) of several theorems (bell’s theorem, no-go theorem, etc …).

    The classical randomness of a coin-flipping may be described by QM. We can always do that: this is the de brooglie-Bohm (DBM) modelling. It is the selection of a peculiar observable (the coin faces) with a fixed quantum state, say 1/sqrt(2)(|odd>+|even>) (or the density matrix |odd><odd|+|even><even| corresponding to a different QM state) that defines the statistics. The observation of the results gives the known statistics (50%, 50%). In this experiment, we have the same results both in classical and QM (property of the observables that induce a probability law on their spectrum set).
    Now, we can apply the DBM model and say (quickly), yes my coin as an unknown trajectory q(t) that complies with the statistics. Therefore, what davidmerritt says in its post is also correct to some extent (i.e. we must know the context).
    This is what I want to underline. It is a matter of choice and context. We must not forget that these two descriptions (QM and “DBM Classical”) give the same statistical results because we are using the same observable (the coin faces) and the born rules.
    One important result of the born rules (and QM measurement) comes from the simple fact that any measuring experiment the values of an observable gets *only* one result (e.g. odd or exclusive even for the coin face observable): this is the connection between classical and quantum probability.
    It is a very strong assumption. It also means that to measure (to see) a superposition of states we need the adequate observable (and the adequate apparatus to measure it). Thus, the measurement of a superposition a states of a coin requires a specific experiment that is different from looking at the faces once the coin has stopped.

  18. Dec 2, 2004 #17
    Concerning the deterministic or statistical approach of physics, in my modest opinion, it is only a matter of choice of 2 equivalent mathematical models (selecting a measure or a probability law to compute fields or whatever we want).

    We are used to considering physics with the a priori deterministic approach: this is due, I think, to the Newton mechanics model that is taught first.
    However, it is important to understand that is an a priori selection. And any deterministic model may be re-thought as a statistical model: this is the application of the weak large number law:
    The random variable sn=1/N sum_i si where xi are independent variables with the same variance and mean value converges to <x> when N becomes large. We have a deterministic result from a statistical source.

    For example, let’s take the coulombian interaction at a point ro: V(ro)=sum_i V(ri-ro).
    Now let’s assume (for the demo purpose) that the ri sources are independent random variables.
    We have: V(ro)=n.(1/n.sum_iV(ri-ro))=n.sn

    Thus si=V(ri-ro) are also independent random variables. Now when n becomes large we have V(ro)=n.<V(ro)> where <V(ro)> is the mean value of any random variable V(ri-ro).

    Now, with this result, we have the “deterministic” coulombian interaction value at point ro that is now the result of random sources. <V(ro)> is now the local density source that is constant in our current model: we have to multiply <V(ro)> by the number of sources to recover any V(ro).
    For example, we can choose V(ro)=k/(ra-ro)=n.<V(ro)>, n large. This is a statistical model of a coulombian interaction at a point ro created by a "deterministic" point charge. It is easy to generalise to any distribution of charges (the superposition of different sets of random variables with a given mean value : V=n1<V1(ro)> +...+ nk<Vk(ro)>=V1(ro)+...+Vk(ro))

    Thus, we can model the deterministic results of em by statistical results: we are just applying the same mathematical model: a set with a sigma-algebra and a measure.

    Therefore to the question “how do we know it is random?”, well, I can say it is a simple point of view.

  19. Dec 2, 2004 #18


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    I will admit that I didn't quite get the point you are trying to make.

    The classical randomness of coin-flipping is the randomness in the 'statistics' of the outcome. It is not due to an underlying randomness in the mechanics or the dynamics of coin-flipping. We can't say that for a "quantum coin-flipping". While there ARE distinct, orthorgonal states that are well-defined before measurement (|head> and |tail>), unlike the classical coin-flipping, these states are (i) mixing with one another to produce very non-classical effects and (ii) no one can use anything to definitely make a prediction of a single outcome.

    I very much hesitate to use the word "randomness" to describe this. The word carries stronger connotations to the system which, I believe, isn't accurate. However, if "randomness" as used in this context means "no physical means to make definite predictions of a single outcome", then I'll use that word. However, the issue here is that there is definitely a clear distinction between classical coin-flipping and QM coin-flipping, no matter what kind of QM interpretation one uses to look at it.

  20. Dec 2, 2004 #19
    Note that, as you say, we have just a coin-flipping experiment: the output experiment result and the probability law that only describes the probability output of the experiment. The coin-flipping statistics does not suppose that the coin has travelled classically along the table to stop at the end of the experiment, just that we have a probability law with a 50/50% distribution on the 2 possible outcomes. This is exactly what says the born rules.
    The coin-flipping experiment outputs may be viewed as the measurement of the observable “coin faces”, we still have the same probability distribution as a classical probability.

    It is one of the point I want to underline when we speak about QM: we need to distingish the unitary evolution of the states and the born rules: this is the same thing as in statistical Newtonian mechanics. We have an equation of motion that modifies the probability density over the time (Liouville equation) in classical mechanics and in QM we have the Schroedinger equation. These equations are the deterministic part. Now both have the same source of randomess: the initial or final distribution law (it is only boundary conditions). Both do not explain the source of the probability distribution, just the deterministic update of it during time.

    Now, in my opinion a common mistake in QM is to see the QM state more than a QM probability state: a probability distribution for the spectrum of an observable. When you say that there are distinct QM states before the measurement, you are in fact saying that you have an initial probability distribution for any given observable.
    As in classical probability, you are just considering two initial probability distributions (the distribution associated to |head> and the distribution associated to |tail>). In the case of the measurement of the coin face, these two initial density probabilities correspond to the probability law “100% head”, 100% tail”, but you must not forget that you do not know the initial velocity state probability distribution for the classical probability distribution or the initial interaction in QM case (before the coin becomes a “free falling” system).

    Now once the coin is thrown, you have a deterministic mechanical evolution in both models (SE or Newton equation – I am not saying they are the same, just they are deterministic), at the end of the time evolution, you have a new probability distribution law that depends on a not well know initial probability distribution (the source of “randomness”).
    Only this final distribution counts in the experiment results not the initial distribution. Thus, whatever the quantum effects occur during the path of the coin, this is not important, only the final probability distribution may be analysed in this experiment. We still have the final statistical result 50% head, 50% tail: thus we must have at final state |psi> that verifies these 2 results. Using the born rules, once again, implies that the probability distribution over the spectrum (the classical probability) of the coin face observable is 50/50 whatever entangled the state |psi> is.

    If you accept to separate the source of the randomess from its deterministic time evolution, you will have a simpler view of why QM model is different from the classical statistical mechanics: both models does not explain the source of randomness, just its probability distribution evolution in time.

  21. Dec 2, 2004 #20


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    OK, so I'm getting even MORE confused than before of what you are saying. Let's first get a few things clear:

    1. The TIME EVOLUTION of the Schrodinger wavefunction is deterministic. I don't think I've said anything contrary to that.

    2. Then the only possible source of discrepancy between my explanation and yours, is the "preparation" of the state. At least, this is what I have gathered.

    If that's the case, let's examine this.

    In the QM case, let's say we have a Schrodinger Cat-type situation with a superposition of two orthorgonal states before a measurement. Now, what would be the equivalent or analogous situation for a classical case? My answer to that would be a coin that has been flipped and tumbling through the air and before it lands for the rest of the world to see the outcome.

    Would this be an acceptable comparison?

    If it is, then I clearly do not see how you can argue that, just because they both evolve "deterministically" with time, that they are identical to each other. The classical flipping is being described with only one thing in mind : that the outcome can only be EITHER head or tail. I cannot, for example, make a measurement (before it lands) of a non-commuting observable to see a result that tells me that there is this weird mixture of "head+tail" outcome. I can, however, do that for the QM case. I can look at the energy difference of the bonding-antibonding states, which clearly is the result of the mixing of these two results.

    To me, that in itself indicates a profound difference between the "dynamics" of the classical and QM coin-flipping. At no time in the classical case is there any ambiguity about the "either-or" nature of the evolution of the system. Yet, in the QM case, there is! Only upon measurement of that particular observable is the ambiguity of that observable removed. This indicates that they are not of the same beast.

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