On 03-05-2022 19:47, Brent Meeker wrote:
On 5/3/2022 4:48 AM, smitra wrote:On 28-04-2022 07:23, Brent Meeker wrote:Any human observer is arguably implemented by an algorithm run by a brain.On 4/27/2022 10:38 AM, smitra wrote:On 27-04-2022 04:08, Brent Meeker wrote:On 4/26/2022 5:32 PM, smitra wrote:On 27-04-2022 01:37, Bruce Kellett wrote: On Tue, Apr 26, 2022 at 10:03 AM smitra <smi...@zonnet.nl> wrote: On 24-04-2022 03:16, Bruce Kellett wrote: A moment's thought should make it clear to you that this is not possible. If both possibilities are realized, it cannot be the case that one has twice the probability of the other. In the long run, if both are realized they have equal probabilities of 1/2.The probabilities do not have to be 1/2. Suppose one million peopleparticipate in a lottery such that there will be exactly one winner.The probability that one given person will win, is then one in a million. Suppose now that we create one million people using a machine and then organize such a lottery. The probability that one given newly created person will win is then also one in a million. The machine can be adjusted to create any set of persons we like, it can create one millionidentical persons, or almost identical persons, or totally differentpersons. If we then create one million almost identical persons, theprobability is still one one in a million. This means that the limitof identical persons, the probability will be one in a million.Why would the probability suddenly become 1/2 if the machine is settocreate exactly identical persons while the probability would be onein a million if we create persons that are almost, but not quite identical?Your lottery example is completely beside the point.It provides for an example of a case where your logic does not apply.I think you should pay more attention to the mathematics of the binomial distribution. Let me explain it once more: If every outcome is realized on every trial of a binary process, then after the first trial, we have a branch with result 0 and a branch with result 1.After two trials we have four branches, with results 00, 01, 10,and 11; after 3 trials, we have branches registering 000, 001, 011, 010,100, 101, 110, and 111. Notice that these branches represent all possible binary strings of length 3. After N trials, there are 2^N distinct branches, representing all possible binary sequences of length N. (This is just like Pascal's triangle) As N becomes very large, we can approximate the binomial distribution with the normal distribution, with mean 0.5 and standarddeviation that decreases as 1/sqrt(N). In other words, the majorityof trials will have equal, or approximately equal, numbers of 0s and 1s. Observers in these branches will naturally take the probability to be approximated by the relative frequencies of 0s and 1s. In other words, they will take the probability of each outcome to be 0.5.The problem with this is that you just assume that all branches are equally probable. You don't make that explicit, it's implicitly assumed, but it's just an assumption. You are simply doing branch counting.But it shows why you can't use branch counting. There's no physicalmechanism for translating the _a_ and _b_ of _|psi> = a|0> + b|1>_ into numbers of branches. To implement that you have put it in "by hand" that the branches have weights or numerousity of _a _and _b_.This is possible, but it gives the lie to the MWI mantra of "It's justthe Schroedinger equation."The problem is with giving a physical interpretation to the mathematics here. If we take MWI to be QM without collapse, then we have not specified anything about branches yet. Different MWI advocates have published different ideas about this, and they can't all be right. But at heart MWI is just QM without collapse. To proceed in a rigorous way, one has to start with what counts as a branch. It seems to me that this has to involve the definition of an observer, and that requires a theory about what observation is. I.m.o, this has to be done by defining an observer as an algorithm, but many people think that you need to invoke environmental decoherence. People like e.g. Zurek using the latter definition have attempted to derive the Born rule based on that idea.I.m.o., one has to start working out a theory based on rigorous definitions and then see where that leads to, instead of arguing based on vague, ill defined notions."Observer as an algorithm" seems pretty ill defined to me. Whichalgorithm? applied to what input? How does the algorithm, a Platonicconstruct, interface with the physical universe? Decoherence seems much better defined. And so does QBism.Plus sensors, plus environment....you call that "well defined"??
What matters is that it's well defined in principle. That in practice it looks like a big mess is irrelevant.
So, for any given observer at some time, there exists a precisely defined algorithm that defines that observer. In practice we cannot provide for any such definition, but from the point of view of the theory, it's important to takr into account the way an observer should be rigorously defined.Decoherence should be irrelevant to this issue. It's a process that happens at the macroscopic scale that is associate with observation. But ultimately observation is just the entanglement of the state of the observer with the measured system, it doesn't matter of that information also leaks out to an astronomically large number of other degrees of freedom.The brain already has a bazillion degrees of freedom. Without decoherence the entanglement is reversible and nothing ever really happens...and probability is meaningless. You can only talk this way because you've artificially bounded the observer-algorithm as though it's an isolated system...which is OK FAPP...but then you want to treat the evolution as though it's pure. This is just muddling the CI problem of Heisenberg's cut, not solving it.
Even with decoherence, everything is still reversible. So, the idea that reversibility implies that nothing can happen, must be wrong. Locality means that even in case of an open system, all the interactions involved in an observation involve only a finite number of degrees of freedom. A process that takes 10 seconds can only involve the degrees of freedom inside a radius of 10 light seconds.
It's true that probability is a problematic concept, it's perhaps better interpret probability as information. So, in case of a branching where some branches have low probability, then this low probability means more information needed to describe the observations compared observations in high probability branches.
Saibal
BrentSaibalBrent
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