The problem of induction 3.2

The meaning of induction is that

we regard, for example, that

“AAAAA –> the sixth is also A”

is more likely than

“AA –> the second is also A”

 

We use induction to find “patterns”. However, the induced results might not be true. Then, why do we use induction at all?

There is everything to win but nothing to lose.

— Hans Reichenbach

If the universe has some patterns, we can use induction to find those patterns.

But if the universe has no patterns at all, then we cannot use any methods, induction or else, to find any patterns.

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However, to find patterns, besides induction, what are the other methods?

What is meaning of “pattern-finding methods other than induction”?

— Me@2012.11.05

— Me@2018.12.10

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2018.12.10 Monday (c) All rights reserved by ACHK

The problem of induction 3

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In a sense (of the word “pattern”), there is always a pattern.

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Where if there are no patterns, everything is random?

Then we have a meta-pattern; we can use probability laws:

In that case, every (microscopic) case is equally probable. Then by counting the possible number of microstates of each macrostate, we can deduce that which macrostate is the most probable.

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Where if not all microstates are equally probable?

Then it has patterns directly.

For example, we can deduce that which microstate is the most probable.

— Me@2012.11.05

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2018.11.19 Monday (c) All rights reserved by ACHK

Relational quantum mechanics

EPR paradox, 10

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Relational quantum mechanics (RQM) is an interpretation of quantum mechanics which treats the state of a quantum system as being observer-dependent, that is, the state is the relation between the observer and the system. This interpretation was first delineated by Carlo Rovelli in a 1994 preprint, and has since been expanded upon by a number of theorists. It is inspired by the key idea behind special relativity, that the details of an observation depend on the reference frame of the observer, and uses some ideas from Wheeler on quantum information.

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Relational solution

In RQM, an interaction between a system and an observer is necessary for the system to have clearly defined properties relative to that observer. Since the two measurement events take place at spacelike separation, they do not lie in the intersection of Alice’s and Bob’s light cones. Indeed, there is no observer who can instantaneously measure both electrons’ spin.

The key to the RQM analysis is to remember that the results obtained on each “wing” of the experiment only become determinate for a given observer once that observer has interacted with the other observer involved. As far as Alice is concerned, the specific results obtained on Bob’s wing of the experiment are indeterminate for her, although she will know that Bob has a definite result. In order to find out what result Bob has, she has to interact with him at some time {\displaystyle t_{3}} in their future light cones, through ordinary classical information channels.

The question then becomes one of whether the expected correlations in results will appear: will the two particles behave in accordance with the laws of quantum mechanics? Let us denote by {\displaystyle M_{A}(\alpha )} the idea that the observer {\displaystyle A} (Alice) measures the state of the system {\displaystyle \alpha} (Alice’s particle).

So, at time {\displaystyle t_{2}}, Alice knows the value of {\displaystyle M_{A}(\alpha )}: the spin of her particle, relative to herself. But, since the particles are in a singlet state, she knows that

{\displaystyle M_{A}(\alpha )+M_{A}(\beta )=0,}

and so if she measures her particle’s spin to be {\displaystyle \sigma }, she can predict that Bob’s particle ( {\displaystyle \beta } ) will have spin {\displaystyle -\sigma }. All this follows from standard quantum mechanics, and there is no “spooky action at a distance” yet. From the “coherence-operator” discussed above, Alice also knows that if at {\displaystyle t_{3}} she measures Bob’s particle and then measures Bob (that is asks him what result he got) — or vice versa — the results will be consistent:

{\displaystyle M_{A}(B)=M_{A}(\beta )}

Finally, if a third observer (Charles, say) comes along and measures Alice, Bob, and their respective particles, he will find that everyone still agrees, because his own “coherence-operator” demands that

{\displaystyle M_{C}(A)=M_{C}(\alpha )} and {\displaystyle M_{C}(B)=M_{C}(\beta )}

while knowledge that the particles were in a singlet state tells him that

{\displaystyle M_{C}(\alpha )+M_{C}(\beta )=0.}

Thus the relational interpretation, by shedding the notion of an “absolute state” of the system, allows for an analysis of the EPR paradox which neither violates traditional locality constraints, nor implies superluminal information transfer, since we can assume that all observers are moving at comfortable sub-light velocities. And, most importantly, the results of every observer are in full accordance with those expected by conventional quantum mechanics.

— Wikipedia on Relational quantum mechanics

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2018.10.22 Monday ACHK

Universal wave function, 20

The physical (synthetic) universal wave function logically cannot be found by any local observers.

The definition of “universe” is “all the things”. So there is no outside.

A global observer has to be outside the universe.

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However, a mathematical (analytic) universal function is possible.

It applies to theoretical/model universe, which can be used to develop interpretations of quantum mechanics and successively approximate the physical universe.

— Me@2012-04-16

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2018.07.21 Saturday (c) All rights reserved by ACHK