On Sun, Mar 8, 2020 at 11:54 PM smitra <[email protected]> wrote: > On 08-03-2020 11:56, Bruce Kellett wrote: > > > > Yes, I think the Carroll's comment was just sloppy. The trouble is > > that this sort of sloppiness permeates all of these discussions. As > > you say, probability really has meaning only in the 1p picture. So the > > guy who sees 1000 spin-ups in the 1000 trials will conclude that the > > probability of spin-up is very close to one. That is why it makes > > sense to say that the probability is one. The fact that this one guy > > sees this is certain in Many-worlds (This may be another meaning of > > probability, but an event that is certain to happen is usually > > referred to as having probability one.). > > > > The trouble comes when you use the same term 'probability' to refer to > > the fact that this guy is just one of the 2^N guys who are generated > > in this experiment. The fact that he may be in the minority does not > > alter the fact that he exists, and infers a probability close to one > > for spin-up. The 3p picture here is to consider that this guy is just > > chosen at random from a uniform distribution over all 2^N copies at > > the end of the experiment. And I find it difficult to give any > > sensible meaning to that idea. No one is selecting anything at random > > from the the 2^N copies because that is to how the copies come about > > -- it is all completely deterministic. > > > > The guy who gets the 1000 spin-ups infers a probability close to one, > > so he is entitled to think that the probability of getting an > > approximately even number of ups and downs is very small: > > eps^1000*(1-eps)^1000 for eps very close to zero. Similarly, guys who > > see approximately equal numbers of up and down infers a probability > > close to 0.5. So they are entitled to conclude that the probability of > > seeing all spin-up is vanishingly small, namely, 1/2^1000. > > > > The main point I have been trying to make is that this is true > > whatever the ratio of ups to downs is in the data that any individual > > observes. Everyone concludes that their observed relative frequency is > > a good indicator of the actual probability, and that other ratios of > > up:down are extremely unlikely. This is a simple consequence of the > > fact that probability is, as you say, a 1p notion, and can only be > > estimated from the actual data that an individual obtains. Since > > people get different data, they get different estimates of the > > probability, covering the entire range [0,1]; no 3p notion of > > probability is available -- probabilities do not make sense in the > > Everettian case when all outcomes occur. This is the basic argument > > that Kent makes in arxiv:0905.0624. > > It's not true that everyone concludes that their observed relative > frequency is > a good indicator of the actual probability. Precisely in cases where > there is a large deviation of the statistics from the actual probability > will this also be visible in the observed data.
You appear to assume that there is an actual probability in these situations. There is no evidence for that in Everett. > It's only when you > consider the case where the statistical fluctuation has affected all the > data in a self-consistent way that this becomes hidden. But, of course, > nothing limits that freak observer from doing a few more measurements. > I think you are referring to the possibility that sub-sequences of data do not reflect the overall probability. Yes, but that is always the case. Why do you think that experimenters at the LHC see so many apparently significant results that go away with more data? The experimenter does not know from his data that it is 'freak'. If he does more trials, or repeats the experiment, the data may converge to some result, or they may not. If Everett is correct, and there is no true probability, then the fact that the data appear to converge is just a miracle -- or Everett is wrong. I think the latter is more likely. Bruce The laws of physics may make it inevitable that there are observers who > will happen to observe such large statistical deviations that they'll > draw the wrong conclusions about the laws of physics. That fact is not > evidence for or against such laws of physics. Experiments can still > settle the question if the laws of physics are correct. Pointing to > freak observers is not a good argument, because all these freak > observers need to do is do more experiments to demonstrate that their > previous observations are a statistical fluke. > > One can then continue to select those observers who'll continue to see > statistical flukes. But the problem is then that these observers need to > stop at some point, being satisfied with their observations implying the > wrong theory. This means that not just the spin experiment, but > everything else must also have been a statistical fluke in such a way as > to imply the wrong theory in a consistent way. So, for centuries a large > number of independent physicists have done experiments that were > affected by statistical flukes that happened to point consistently to > the wrong theories. Those wrong theories then made sense, it fits in > well with all the data not just from rigorous laboratory experiments but > also all other available data. > > The alternative theories due to the astronomically unlike statistical > flukes then cannot explain the everyday observations the people make > about their environment, the Earth the Sun etc. You then need to invoke > fluke statistical effects that affect those observations as well. But > then we're moving away from having observers that can actually observe > anything at all. > > Saibal > -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAFxXSLQR2Z1HAH_pSX-Uv7sH9XjfyO4uR_d47KJoQpfKjLtGyw%40mail.gmail.com.
