Fun story. Jack Vance wrote “Rumfuddle” which also explores the idea…and ends with the protagonist beating the odds on infinity!
Exactly so. Quoted for truth, accuracy, and insight.
Not necessarily. For one thing, “somewhere” is absolutely isolated from us, in every possible way. It doesn’t “exist” in any meaningful sense. You can’t get there from here, nor communicate nor observe it.
It’s much more like noting that the square root of two provides two answers: 1.4142 and -1.4142. The additional answer “exists” mathematically, but go ahead and show me piece of cardboard -1.4142 inches on a side!
HMHW and Giraffe: I don’t know what the two of you are talking about, but I’ve ususually heard the issue raised in the context of Bell’s inequalities. MW is, from what I’ve gathered, one way of dealing with the issue of non-locality and still avoiding hidden variables. Phenomena are still non-local, just non-local “someplace else.”
Exactly. If you can come up with a series of events that would have led to Jim Carrey being President, then those events occurred on some world and he’s President Carrey there.
But there’s no possible chain of events that would lead to a world just like ours except that a Canadian comedian was elected President of the United States. So in an infinite number of worlds, you’ll never find one like that.
An infinite number of possibilities does not mean all possibilities. An example I’ve used in the past is Pi. The sequence of Pi is infinitely long - but you’ll never find the letter A in it.
Also, and not really very relevant, Larry Niven’s story overlooked probability density. He treated getting snake-eyes on two dice as equally likely as getting “7” on two dice. He didn’t describe the fact that universes where the latter happens are six times as common as universes where the former happens. Universes where unlikely things occur would be rare, or, more specifically, would be represented less densely in the continuum of events, but Niven treated them on an equal basis. It undermined the point of the story, just a little.
It’s not something you really need to have an opinion on if all you’re interested in is the science. I’m going to play this fast and loose even by my standards, but hopefully I won’t butcher it too badly.
Quantum mechanics is a little like Satan telling you that you can go fishing but that you have to choose between beer and bait - can’t have both. Except here the choice is between causality and reality. So either everything can have a proximate and identifiable cause (locality) or everything can have objective reality (counter-factual definiteness). But you don’t get to have both.
This is just one of a whole laundry list of things that pissed people like Einstein off about QM and a lot of them are still pissed. Part of the motivation - at least this is my personal belief - behind things like the many worlds interpretation of QM is it that sort of lets you believe that QM isn’t the bad acid mind fuck that it actually is.
It doesn’t MATTER what QM means or whatever. Just shut up about it and calculate, and you’ll be good to go. Interpreting it is as meaningful as reading tea leaves or believing in God.
No, you can’t sharply differentiate between when to use one process, and when to use the other (and just as a pointer, when you say ‘mixed state’, you should say ‘superposed state’—the two terms have very different meanings in quantum mechanics, mixed states essentially just being states in which one just doesn’t know what the state actually is). For some observers, some interaction can be a measurement, while for others, it ought to be modeled by the unitary dynamics.
If you have a measurement device, then the interaction between it and the measured system is in principle unitary, but if you read out its value, you must invoke the collapse. However, you could in principle decide randomly between two different procedures. First, you have the measurement apparatus measure the system. Then, you do either of two things: 1) You read out the recorded measurement, or 2) you perform another measurement, designed to measure the self-interference of the system+measurement apparatus. In 1), you would have to invoke the projection to correctly describe the interaction between system and measurement apparatus, while in 2), you need to evoke the unitary evolution. So the same physical interaction, depending on just what you plan to do with it further downwards, needs to be modeled according to the two different processes.
Now, this typically involves distinctions too small to currently measure, but it’s important that they exist conceptually. You can modify the dynamics in order to get a theory that ‘spontaneously collapses’ once systems reach a certain ‘macroscopicity’, but these are very difficult to make coherent, and so far, nobody knows for instance how to square them with special relativity.
Non-locality is really a different issue from the measurement problem, though it’s true that different interpretations say different things about it. The positions at variance here are realism (the possibility to describe the world with variables that have a well-defined value at all times, roughly) and locality (the nonexistence of ‘action at a distance’). Now, realism is a possible answer to the measurement problem: if you have certain ‘hidden’ variables, then measurement just ascertains their value. It’s at this point then that Bell’s inequalities kick in and tell you, OK, you can have realism, but then you have to give up locality (actually, you have to give up more, making this an unpalatable possibility to most, but this would take us too far right now). An interpretation that takes this course is Bohmian mechanics.
Except if I’m reading you correctly, the only time you get to have counterfactual definiteness under MW, is when it doesn’t matter - i.e, when there’s no chance of bifurcation. But I’m probably missing something as per usual and since there are so many things that actually DO matter that I don’t even begin to understand, I will leave your brains unpicked - for now.
Look…the many worlds interpretation may not make sense HERE, but quantum theory tells us that somewhere is another universe where it makes perfect sense, so we’re OK.
Another short story I liked on the subject (whose title I don’t recall unfortunately) had scientists accidentally apparently simultaneously demonstrating that the universe is a false vacuum, and that the Many Worlds Interpretation is true.
They were trying to run an ultra-high energy physics experiment, but no matter what they did the equipment always failed, sometimes through wildly implausible events. One of them finally realized that there was an explanation - the universe is a false vacuum, the MW Interpretation is true, and every time the experiment worked it collapsed the false vacuum and the universe was destroyed. They kept having all these wild coincidences prevent the experiment from working, because only the tiny minority of universes where such random occurrences stopped the experiment still existed.
It was a Quantum Suicide experiment on a universal scale, and they didn’t realize they’d been doing it.
Knowing how to apply the mechanics of a system is separate from understanding why it works that way, or what it means. It does not follow that there is no reason or meaning.
Everytime I see that word I read it as Bohemian mechanics (which if I was doing quantum mechanics that would probably be about how sophisticated I be go about doing it).
And thanks everyone for the good posts and short stories. Made for an interesting evening of reading and mild brain hurting.
Thanks for the tip, but mixed state is the correct term in this context. And there’s no decision about using one process or another: they are both just descriptions of how quantum systems evolve in different conditions. Just like you model a baseball flying through the air with one set of equations and bouncing off a wall with a different set – you aren’t switching between starkly different processes so much as applying all relevant interactions and constraints of the system as a whole. The tricky bit is that quantum particles act so much stranger in “free flight”. But once they hit the wall, they hit the wall.
This is completely wrong. Your reading of the measurement makes no difference whatsoever. Any measurement apparatus capable of interacting with the system in such a way as to gather information from it is going to remove any superposition. Recording or conveying that information makes no difference. (In a similar vein, Schrodinger’s Cat is never in a superposition. It is either 100% dead or 100% alive regardless of when or whether you open the box.)
The danger of thought experiments like this is that you can find yourself proposing things that aren’t possible, e.g. measurement apparatuses that entangle with systems while gathering information.
No. The measurement problem is the reduction of a superposed, pure state to the eigenstate of some observable. If the system were in a mixed state prior to measurement, there would not be any more of a problem than if you didn’t know whether there’s a red or green ball in the box, you look, and find a green one.
But there’s a unified description capturing both the flight and the bouncing of the ball; there’s no such thing in quantum mechanics (and in fact, such a thing is proven to be impossible).
No, at least not on the traditional account of quantum mechanics. In principle, I should be able to apply the unitary dynamics to the whole process, and measure interference terms indicating the presence of a superposition even if a measurement has taken place. As I said, it’s possible to change the dynamics such that your account would hold for systems that are ‘macroscopic enough’, and it’s also possible to stipulate a ‘buck stops here’-measurement device, but both are modifications of the usual account. Wigner conceived of the possibility that it might be consciousness that finally and ultimately destroys the superposition in his famous thought experiment, a variation of which (without the consciousness causes the collapse part) I basically gave in my last post.
If the cat and the box are sufficiently shielded from environmental influences, that’s simply wrong.
