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Quantum Mechanics for Programmers

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Re: Quantum Mechanics for Programmers

#71

Post by monktastic1 »

tomonl wrote: post #54
monktastic1 wrote: post #34

Earlier quoted context omitted.

Tensor products only describe the separable (i.e., unentangled) states.

As I understand it, that is only true when dealing with density matrices. For example, |0>⊗|0> + |1>⊗|1> is entangled and has tensor products. I think that Xcelerate is correct in saying that all combinations of the basis vectors form the basis of the multi-particle Hilbert space, as a single-particle wavefunction is just a vector/ket.

Sure, the tensor product space has a basis that is formed by the tensor products of all pairs of basis elements. But this is different from saying that any particular vector in the space is a tensor product of elements from the individual spaces.

But I'm possibly just misunderstanding what you're saying.

Re: Quantum Mechanics for Programmers

#72

Post by monktastic1 »

doubleunplussed wrote: post #12
monktastic1 wrote: post #3

Hmm he seems to imply that MWI is the "right" interpretation, and that the measurement problem is solved. Most physicists would not agree. If you follow the link to his MWI description, there's this gem: > But fortunately, I knew computer science, which most physicists do not know, with the Church-Turing thesis, which roughly states that anything physical can be simulated by a computer. But that is not what the Churc…

I'm a quantum physicist (well, we don't say that, I'm an atomic physicist, but for anyone not aware it is 99% quantum mechanics we do all day), and the MWI isn't universally accepted, but it's not universally rejected either. Plenty of important physicists interpret quantum mechanics that way, and I do too (I am not important though). That's not to say I'm confident it's correct , just that it's the most sensible way…

Thanks for weighing in.

Decoherence is great at explaining the loss of interference. It may even address the "preferred basis" problem (though there seems to be good reason to believe that it might not). But ultimately what I want to know is why I experience just one outcome, and decoherence doesn't really help here.

MWI partially resolves that ("you don't just experience one; there are many of you!"), but not in a way that satisfies me.

Re: Quantum Mechanics for Programmers

#73

Post by aphextron »

krastanov wrote: post #13
aphextron wrote: post #10

The more I learn about physics and math, especially with regards to quantum theory, I start to get really freaked out. The amount of "neatness" to the universe is staggering. How there's no "inbetween" at the smallest scales. Everything is discrete. The fact that simple arrangements of symbols on a screen can perfectly describe this behavior is mind blowing. It leads me to think there's no possible way we're not livi…

Minor nitpick: We definitely do not know whether everything is discrete. There are plenty of quantum mechanical phenomena that do not have discrete spectra (you can have light of any wavelength for instance (with some caveats at the extremes of the energy scales)). We also do not have theoretical or experimental proof that space-time is discrete at the Plank length-scale - all we know is that our current theories bre…

Thanks for exposing my ignorance. I had an "aha" moment realizing that relativity makes it so that there can be no "final" level of energy.

Re: Quantum Mechanics for Programmers

#74

Post by n4r9 »

naasking wrote: post #67
AgentME wrote: post #37

Earlier quoted context omitted.

>Quantum Mechanics requires randomness, because determinism is scary. Isn't the many-worlds interpretation generally regarded as deterministic?

IIRC, it's deterministic in a sense that isn't equivalent to the way de Broglie-Bohm is deterministic. The latter is generally what people mean by deterministic, ie. it's a classical theory with an extra term to account for quantum influences.

Both theories model the universe as being in a definite, non-probabilistic state, and that the state at one time determines the state at all future times. But yeah there is some difference in the anthropocentric aspects, i.e. how our observation of probabilities actually arises.

Re: Quantum Mechanics for Programmers

#75

Post by codethief »

monktastic1 wrote: post #34
codethief wrote: post #25

Earlier quoted context omitted.

> Another professor […] once said that the single particle wave function is more fundamental than the multi-particle wave function. Nevermind […] his research […] where the molecular wave function can't be well approximated using a product of single particle wave functions Depends on what you mean by "multi-particle wave function". The way it is usually understood (I think), it includes all possible tensor products o…

Tensor products only describe the separable (i.e., unentangled) states.

Fair enough, I should have been more precise: By "all possible tensor products" I actually meant all elements in the tensor product space, including all linear combinations of tensor products of single-particle states.

Re: Quantum Mechanics for Programmers

#76

Post by akvadrako »

chriswarbo wrote: post #70
Xcelerate wrote: post #14

Earlier quoted context omitted.

> that decoherence does not completely solve the measurement problem It's kind of funny how the problem keeps getting pushed to higher levels of "meta": If you consider the experimenter and his system, measurements of (non-eigenstate) quantum systems appear indeterministic to him . However, the state of [experimenter + system] is governed by an entirely deterministic equation that follows a reversible, unitary path t…

Let's say I toss a fair coin; before I look at it, the outcome is indeterministic to me: there's a 50/50 chance of heads or tails. Once I look at it, I gain 1 bit of information. To another experimenter, the 'me + coin' system is indeterministic: it's either me seeing heads or me seeing tails. Once I tell that experimenter the outcome, they gain 1 bit of information. To a different experimenter, the two of us with th…

What you just described is a hidden variable model which cannot reproduce the behavior of entangled particles. For details look up Bell's theorem.

Re: Quantum Mechanics for Programmers

#77

Post by akvadrako »

platz wrote: post #68
adrianratnapala wrote: post #58

Earlier quoted context omitted.

The problem here is that very much of what we mean by "scale and mangitude" boils down to the frequency of particular outcomes when situations are repeated. So Decoherence only explains those things after you already have the Born rule (P ∝ |Ψ|^2). But that's the very thing we are trying to explain!

Maybe you are trying to explain the Born rule, but I was not claiming to explain that; I've already stated decoherence doesn't explain why we get certain outcomes instead of others.

It explains what we experience perfectly well. In the simple case of a 50/50 coin flip, there will be two equally real future versions of you. One will see heads, one tails.

You don't need to dive into quantum mechanics to understand this concept; instead, consider being cloned twice while you are asleep, then killing the original.

Your current self knows what will happen; you'll fall asleep and wake up as either one or the other, becoming both but never being both.

Re: Quantum Mechanics for Programmers

#78

Post by chriswarbo »

akvadrako wrote: post #76
chriswarbo wrote: post #70

Earlier quoted context omitted.

Let's say I toss a fair coin; before I look at it, the outcome is indeterministic to me: there's a 50/50 chance of heads or tails. Once I look at it, I gain 1 bit of information. To another experimenter, the 'me + coin' system is indeterministic: it's either me seeing heads or me seeing tails. Once I tell that experimenter the outcome, they gain 1 bit of information. To a different experimenter, the two of us with th…

What you just described is a hidden variable model which cannot reproduce the behavior of entangled particles. For details look up Bell's theorem.

Oh I'm well aware of Bell's theorem; I'm a trained Physicist :)

Bell's theorem rules out theories of local hidden variables. It says nothing about non-local hidden variables, or even something more mundane like determinism (sometimes referred to as "superdeterminism").

In any case, I'm not sure Bell's theorem has much impact on my question: why is one of these things (transfer of information from a coin toss) not a problem, conceptually; whilst the other (entanglement of quantum systems) is a problem, conceptually?

(Personally, I don't find either particularly troubling; just curious to know what the philosophical distinction is, without appeals to "quantum weirdness")

Re: Quantum Mechanics for Programmers

#79

Post by akvadrako »

chriswarbo wrote: post #78
akvadrako wrote: post #76

Earlier quoted context omitted.

What you just described is a hidden variable model which cannot reproduce the behavior of entangled particles. For details look up Bell's theorem.

Oh I'm well aware of Bell's theorem; I'm a trained Physicist :) Bell's theorem rules out theories of local hidden variables. It says nothing about non-local hidden variables, or even something more mundane like determinism (sometimes referred to as "superdeterminism"). In any case, I'm not sure Bell's theorem has much impact on my question: why is one of these things (transfer of information from a coin toss) not a p…

A classical analogue to entanglement is not problematic for causally connected processes and in some cases it's a good model, like with human reasoning or neural networks. QM is a generalisation of bayesian reasoning that can handle non-commuting variables.

Yet entanglement is observed non-locally, even backwards in time or between degrees of freedom that never co-exist. Nobody has been able to create a non-local model that doesn't require fine tuning and the idea goes against the spirit of special relativity.

Thus, I would agree with you, there is no "problem" with entanglement. Except non-locality.

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