Careful. Everett does not posit multiple universes, despite that imagery made popular by DeWitt.
Superposition is different than p & ~p. It requires the two states to interfere with each other, which has been demonstrated with macroscopic objects, but not a cat. The cat scenario isn't realistic, and it reduces to simply not knowing the state of the cat in the box.

I can't think of a paradox that can be easily resolved in the way you suggest. X is true here but false elsewhere isn't really a paradox in the first place. A thing in superposition of two states is not paradoxical since superposition is not a state of both X and ~X, again a wording often used in pop articles.

So how, for instance, would you resolve 'this statement is false' using multiple worlds? Is the statement true in one world and false in another? That doesn't work. Each would perhaps be referencing the other statement, but not 'this' statement.

Good points! I've always been suspicious of claims of so-called quantum weirdness, an interpretation that can trace it roots to the Schrödinger's cat gedankenexperiment. I only surmise this connection as highly probable.

However, as great a mind as Schrödinger's was of the view that the best translation of his equations was, macroscopically rendered, that a cat is both dead and alive. In other words, given the stature of the man who made the claim, quantum paradoxes should be taken seriously (as true paradoxes).

Anyway, the MWI seems to, whether deliberately or not is up for debate, rather cleverly resolve the Schrödinger's cat contradiction by proposing that the cat is alive in one universe and dead in the other.

From this it follows that any contradiction (p & ~p) can be compared to an observation in a quantum experiment vis-à-vis MWI - essentially causing the universe to divide into two, one in which p and the other in which ~p. As with Schrödinger's cat, the, any, contradiction melts away as the two incompatible propositions are now in two separate, logically independent universes. Picture two inimical men being housed in different rooms (violence, which, being mutually annihilatory, contradictions are, is averted).

How do I use Everett's technique on an actual paradox like the Liar sentence? Well, assume it is true - this is one universe. Then you reason (this is the counterpart of observation in quantum experiments) and conclude it is false - this is another universe. The same logic applies to all subsequent true and false sequences in the chain of reasoning. Either there are only two universes and you go back and forth between them OR it's a branching tree-like universe with every true and false state birthing daughter universes.

Superposition is different than p & ~p. It requires the two states to interfere with each other, which has been demonstrated with macroscopic objects, but not a cat. The cat scenario isn't realistic, and it reduces to simply not knowing the state of the cat in the box. — noAxioms

No, quantum states are transmutable, for the purpose of the experiment. The cat can be used in superposition. But the point is to deny that there's superposition.

Careful. Everett does not posit multiple universes, despite that imagery made popular by DeWitt. Superposition is different than p & ~p... — noAxioms

:100:

I've always been suspicious of claims of so-called quantum weirdness — Agent Smith

Oh it's still plenty weird, enough to have Everett need to change his thesis to something wrong, but more believable, like 'splitting' happens only occasionally.

an interpretation that can trace it roots to the Schrödinger's cat gedankenexperiment

I don't think it was born of the cat. The cat is simply something that everybody knows and showing how each interpretation deals with the scenario is quite useful in illustrating the differences. No, the root was the mathematics of quantum mechanics theory.

However, as great a mind as Schrödinger's was of the view that the best translation of his equations was, macroscopically rendered, that a cat is both dead and alive.

Again, in an unmeasurable superposition of being dead and alive, for the purpose of illustrating an absurd state. He also put the cat in a mere iron box, which reduced the cat to a single but unknown state. Remember that the wave equation back then was considered an epistemological thing: It described what we knew about a system. It was only later that people suspected that it described the system.

In other words, given the stature of the man who made the claim, quantum paradoxes should be taken seriously (as true paradoxes).

I would not agree to that. I see no paradox in quantum mechanics unless you introduce premises of classical law, which would be a mistake.

by proposing that the cat is alive in one universe and dead in the other.

OK, so you're not reading, comprehending, or caring about my posts. There's no mention of other universes in the theory. The theory posits only that an isolated system evolves according to Schrodinger's equation. The cat being dead is a valid solution. It being alive is another. The equation being linear, the sum of two solutions is also a solution, so the cat being alive/dead is also a valid solution, but a system measuring a live cat and the cat not being alive is not a valid solution to the equation.

How do I use Everett's technique on an actual paradox like the Liar sentence? Well, assume it is true - this is one universe.

It can't be, since it says it is false. It isn't talking about a statement in another world.

Ok! You sound like an expert, I'll have to take your word for it!

Paradoxes appear when one rejects the self-justifying nature of logic.

Regardless of how someone tries to "resolve" the apparent illogical nature of a superposition, the implication is always that all possible worlds are unified in one reality, and that one reality has the property of being able to mentally "select" collapses of state. In line with this, science has demonstrated the validity of quantum contextuality.

I'd reject the Many Worlds Interpretation on the basis that it adds ontic baggage without solving anything.

In a flight of philosophical fantasy, the sequence of contours that converge uniformly to the line segment [0,1] but increase in length toward infinity might approach a boundary point between two worlds. In one, the length is 1, in the other infinity. As one stares at the paradox one looks directly into the many-world environment. :cool:

I'd reject the Many Worlds Interpretation on the basis that it adds ontic baggage without solving anything. — Hallucinogen

Doesn't it present itself as a way of handling paradoxes? If I say p & ~p, p goes "this town ain't big enough for both of us" to ~p and vice versa - one has to go! However if p in one town and ~p in another, there's no issue at all. If I say life's bitter sweet, I mean bitter from a certain perspective and sweet from another. Perspectives/angles are simply different towns (worlds). There's this idiom "from another planet" which is to the point in my estimation.

If I say p & ~p, p goes "this town ain't big enough for both of us" to ~p and vice versa - one has to go! However if p in one town and ~p in another, there's no issue at all. — Agent Smith

Yes, but it adds the explanatory burden of new universes being created with every superposition collapse. An alternative that doesn't necessitate the creation of new domains is that superpositions are potentials, and with observation, a value is selected-in from the medium which does the selecting (which is the medium in which p or not-p are contraposed, e.g. the medium contains the logical syntax).

Yes, but it adds the explanatory burden of new universes being created with every superposition collapse. — Hallucinogen

Indeed, it does! On target, mon ami!

:up: and if we follow the explanatory burden, we find that it implies the existence of a shared reality, or medium, in which the rules of p or not-p are distributed and selected, just as the superposition in the "original" universe did, at which point we have to acknowledge that that medium is the true reality, making the Many Worlds superfluous.

Interesting!

There's no mention of other universes in the theory. The theory posits only that an isolated system evolves according to Schrodinger's equation. The cat being dead is a valid solution. It being alive is another. — noAxioms

"Superposition" is essentially linearity with regard to solutions of Schrodinger's equation. When modelling a physical phenomenon mathematically, frequently a differential equation is involved. These equations might have multiple solutions, linear combinations of one another. When a measurement is executed the proper solution crops up. In general, a math equation might have superfluous solutions.

For example, drop an object from a height of 100 feet. How long before it hits the ground (ignore air resistance)? Answer from acceleration due to gravity is t=2.5 and -2.5. Obviously the answer is t=2.5 seconds.

For example, drop an object from a height of 100 feet. How long before it hits the ground (ignore air resistance)? Answer from acceleration due to gravity is t=2.5 and -2.5. Obviously the answer is t=2.5 seconds. — jgill

Those solutions are true for parabolas and yet the line this object traces is a straight line.

Most interesting. — Ms. Marple

Can you explain? Please.

P. S. I fear I've forgotten the formula. Is it $s = ut + \frac{1}{2}at^2$?

Those solutions are true for parabolas and yet the line this object traces is a straight line. — Agent Smith

Nonsense. Start with $\frac{{{d}^{2}}s}{d{{t}^{2}}}=-32$ and use the height of 100 and initial velocity of 0 and solve & compute. You are confused because the formula becomes quadratic, like that for a parabola. I think you delight in raising hackles . . . :cool:

Ok!