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    Empirical Probability Versus Classical Fair Meta-Randomness
    By Sascha Vongehr | July 26th 2011 02:55 AM | 8 comments | Print | E-mail | Track Comments
    About Sascha

    Dr. Sascha Vongehr [风洒沙] studied phil/math/chem/phys in Germany, obtained a BSc in theoretical physics (electro-mag) & MSc (stringtheory)...

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    Lets gamble; participating costs you only 50 cents per game. The odds are in your favor! Two out of three times, you win and get a dollar. So we start playing, and it seems as if we walk along time, every game we get to a point in the road where it splits into three paths, two of them are winning one-dollar branches, one is the zero-dollar branch, there we toss a three sided fair die, then we ‘find ourselves’ in one of the three branches. However, I cheated.


    I used a quantum die. Although the classical probabilities are V0 = 1/3 and V1 = 2/3, the zero-dollar branch itself branches into three more. If you believe in classical physics, then such branching does not make any difference. You go with probability 2/3 into one of the winning branches. The zero dollar branch may as well split into a million more; since we only get there with probability 1/3 in the first place, it does not matter.



    You happen to lose maybe, but then you want to play again of course – after all, the game seems in your favor. After two runs, you have a good chance of having won two dollars already and the ticket fee is only one dollar for two trials. The classical probability of getting two dollars is V11 = 4/9, and the other classical probabilities are V10 = 2/9, V01 = 2/9, and V00 = 1/9. Thus, you expect to break even or win in 8 out of 9 cases. Except for one little problem: the die is a quantum die, and the zero-dollar branch always splits into three more.


    After a while, you will maybe believe in having bad luck (or preferably accept quantum mechanics). What happened? Well, we do not walk along time and then come to junctions in the road and then have some meta-randomness with meta-fairness that lets us go this or that path.


    Space as such does not reside inside some meta-space. If time is put down as a t-axis, it should not be discussed as if there is a ‘now-moment’ creeping along the axis, as if there is a meta-time that allowed such movement. One rejects such meta-levels (this is discussed generally in detail here), because describing them would require another ‘meta-meta’ level, leading to infinite regress or at least regress without definite termination.


    With the zero-dollar path being there three times, there are after the first run already five outcomes, and three of them got zero dollars, only two branches won. After two trials, the outcome numbers are N11 = 4, N10 = 6, N01 = 6, and N00 = 9 (total 25, as you can easily check in the picture). In twelve of these parallel worlds, you just break even, but in nine you paid the ticket fee and I gave you nothing in return.


    It does almost not matter what the classical probabilities V are. We find probabilities by repeating an experiment many times and then judging from the past record. In the overwhelming number of world branches in which you remember to have played the above game many times, you will also find that the probabilities are the quantum probabilities P0 = 3/5 and P1 = 2/5, not the classical V.


    Consider the branching tree of the potential outcomes of coin tosses. There is no meta level on which we throw a fair meta-coin whenever we reach a branching point. Classical “meta-probability” can be represented as a (phase space) volume V. A random vector Real may then select the actual outcome without bias for any points in that space: The more volume V a branch has, the more likely it will be selected. Statistical mechanics similarly assumes fair meta-probability via the ergodic hypothesis. Instead of the whole being already fully described by the tree alone, the meta-probability V makes Real behave properly. Such meta-coin tosses are unnecessary and lead to difficulties especially in cosmology, where also space-in-space and time-of-time are most problematic.


    In a true many-worlds model, all outcomes are actualized relative to their own branch. You do not advance into the ‘heads’ instead of the ‘tails’ branch with meta-probability Vheads = 50%; both futures exist equally. Most outcome branches of several tosses will observe close to 50% heads. The probability P of an outcome is proportional to the number N of branches with that outcome, which can only in a classical many worlds model be replaced by V.


    Nothing selects any branches or needs to count the parallel branches in order to establish P. The branches remember their past, that is enough.


    To understand the above is the next step on the path of making the Many Worlds Wiener Sausage resolve the Einstein-Podolsky-Rosen paradox. Remember, it can produce the correct quantum factors, but we also saw that although it is a many worlds model with parallel universes and all that, it is not a quantum world! Simply introducing the “Real” direction turned it completely classical. Now we see how to fix what is wrong: The volume V of the sausage is the classical meta-probability and Real does the meta-fair meta-coin toss, i.e. it lands somewhere inside V without bias. If we want to make it a mature quantum model, we necessarily need to grow new worlds, not just cut the one that is there into small pieces.



    Adding a single little arrow “Real” (short "DR") clarifies that the sausage model is fundamentally a local realism and thus cannot violate Bell’s inequality. No such model can possibly describe quantum physics.



    S. Vongehr: "Many Worlds Model resolving the Einstein Podolsky Rosen paradox via a Direct Realism to Modal Realism Transition that preserves Einstein Locality" arXiv:1108.1674v1 [quant-ph] (2011) UPDATE: This reference is the first paper on the possibility of such models, but the models have now actually been constructed and are much better explained in S. Vongehr: “Against Absolute Actualization: Three "Non-Localities" and Failure of Model-External Randomness made easy with Many-Worlds Models including Stronger Bell-Violation and Correct QM Probability” http://arxiv.org/abs/1311.5419 (2013)

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    Comments

    The Stand-Up Physicist
    This statement confused me (along with others, but such are my own limitations):
    Space as such does not reside inside some meta-space. If time is put down as a t-axis, it should not be discussed as if there is a ‘now-moment’ creeping along the axis, as if there is a meta-time that allowed such movement. One rejects such meta-levels, because describing them would require another ‘meta-meta’ level, leading to infinite regress or at least regress without definite termination.
    Going back to good old special relativity, space is not able to live on its own. Rather, space is married to time to form spacetime. I would not refer to spacetime as a meta-space since I don't know what that means. Spacetime is a place that gets filled up with events. If spacetime has no events, then it is the vacuum. I sometimes make dull animations this way. 

    The space parts of spacetime have a pointiness to them, or a vector quality. The space part of spacetime will uses axes of one's choosing. The time part of spacetime does not have that pointiness because it is a scalar. There is no axis to point to for time, such is the life of a scalar. Any and all events need 4 types of information, the 3D location and a time. I would agree, there is no now-moment, only things like now-here and a now-there, and a future-moment-behind the couch. Nothing meta in that as far as I can see.

    It could be that folks who work on many worlds ignore Minkowski's edict on spacetime. If many world workers are toiling in branching spaces without time formally folded into its foundations, I could live with that by rejecting the thesis.
    vongehr
    I would not refer to spacetime as a meta-space since I don't know what that means
    Meta-space for example is the space that would contain the Einstein-ether in which the SO(1,3) symmetry we observe is emergent (if such were the case). It could also mean the space that people often assume the universe must expand into during cosmic inflation or accelerated metric expansion. It is the space that contains space. Similar to the time that allows time to flow, phenomenal consciousness that makes us conscious of being conscious, or here randomness that makes randomness random, these meta-levels are mostly (I did not claim always) merely everyday concepts applied to areas where they are not applicable.
    Ok, I'm less confused about why we see quantum probabilities. But now I'm confused about why we see classical probabilities given that we live in a quantum world. Or maybe I'm confused about what I'm confused about.

    vongehr
    why we see classical probabilities given that we live in a quantum world
    We don't. In the huge majority of states of minds, we remember empirical evidence consistent with the quantum probabilities. Maybe what confuses is how I set up the game. I assumed a physical situation where the classical description (which my hypothetical player believes in) leads to probabilities that are different from the correct quantum description (which I assumed the gambler does not accept). This is easily done with particles having spin (so called Clebsch Gordan coefficients) or say with help of the EPR setup that I discussed so much in the previous weeks. If you look at the Quantum Randi Challenge, the classical description predicts different probabilities and it is indeed a later world branching that leads to different quantum probabilities.
    If I were to set up a game (e.g., $0.50 per turn, payoffs of $0.00 or $1.00 contingent on event X yielding outcome 0 or 1) in which the quantum probabilities for X promised that playing offered a positive expected value for you, and a negative value for me, while the classical probabilities for X promised the reverse, would you play?

    If the answer is no, what have I misunderstood?

    vongehr
    Let's play. As many times as possible. When, where, how. I want to do it as soon as possible. I bring all my money.
    Could you please describe an example of a physical implementation of such a game?

    The answer may be seem clear enough from your post, but to perfectly clarify my understanding, I’d benefit from a concise description in the form of an algorithm with implementable, physically determined inputs (the quantum die), specified conditional actions, and outputs of 0 or 1.

    vongehr
    We could use the EPR setup for this quite easily.

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