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97

The theory of probability used in QM is intrinsically different from the one commonly used for the following reason: The space of events is non-commutative (more properly non-Boolean) and this fact deeply affects the conditional probability theory. The probability that A happens if B happened is computed differently in classical probability theory and in ...


73

“Observe” oftentimes causes a lot of confusion for this exact reason. It doesn’t actually refer to some conscious entity making an observation. Rather, think about how we actually make an observation about something. You have to interact with the system in some way. This can be through the exchange of photons, for example. This interaction is what ...


68

I'm not a quantum cosmologist, but I am an early-universe cosmologist, so I can give you my opinion after having read this paper. The article claims that Bohmian trajectories is a valid replacement for geodesics. This was claimed in the very beginning of the paper and not much is offered in the way of defense for this assumption. That's not to say that it's ...


50

The assumption that a measurable property exists whether or not we measure it is inconsistent with the experimental facts. Here's a relatively simple example. Suppose we have four observables, $A,B,C,D$, each of which has two possible outcomes. (For example, these could be single-photon polarization observables.) For mathematical convenience, label the two ...


48

You're right; the Schrödinger's equation induces a unitary time evolution, and it is deterministic. Indeterminism in Quantum Mechanics is given by another "evolution" that the wavefunction may experience: wavefunction collapse. This is the source of indeterminism in Quantum Mechanics, and is a mechanism that is still not well understood at a fundamental ...


47

No, it doesn't. For example, since charge is conserved, every "world" in the wavefunction must have the same charge. This goes for any other conserved quantity, too. (This doesn't rule out you being a rockstar, though.)


40

Interpretation is whatever people don't have to agree on to have the same accurate predictions about the observable. Classical mechanics is empirically wrong in ways quantum mechanics isn't. For example, only quantum mechanics predicts discrete energies for atomic electrons, and discrete changes in these energies from the absorption and emission of ...


34

First of all, "loopholes" is no disrespect. It's standard nomenclature. Given a law, a "loophole" is a way to circumvent it. Bell's inequalities, in their mathematical formulation, are laws that prevent superdeterminism, so if we believe it should exist, we have to find loopholes in the assumptions. It might be that the loophole is so big that the whole law ...


34

The Copenhagen interpretation isn't an essential part of quantum mechanics. It isn't required in order to make physical processes happen. It's just a way of describing what seems to happen when an observer makes a measurement. It's not even the only way of describing what it seems like to the observer. However, according to the Copenhagen interpretation, ...


31

There are two problems here, one on the quantum mechanical side and one on the relativistic side. Interpreting quantum mechanics First, you seem to be imagining that quantum particles "really" are classical, with well-defined trajectories which we simply can't measure because of the uncertainty principle. That is, you treat quantum mechanics as just ...


30

The crucial word is "interpretation". In physics it means that the results of calculations, hard numbers to be checked with data for interactions and processes that we can measure in the lab, are the same in all interpretations of a theory. There is no difference in the hard data. One can see the integrals as "many worlds splitting off", but it is just ...


29

I realize I'm late to this discussion. For whatever it's worth, I disagree in the strongest terms with Ron Maimon and Dmytry, when they criticize Yudkowsky for being "too conceptual." As I see it, that's exactly what you should and must do if your goal is to explain QM to an audience of non-physicists! Indeed, most popularizations of QM go off the rails ...


29

The idea of my latest paper is simple. I experienced in other blogs that most people refuse to go with me all the way. I'll give my argument step by step and you may choose where you want to step out. Consider superstring theory, in its original, completely quantized version. Many people believe it might have something to do with the world we live in. It ...


28

While this work certainly investigates an interesting point, I think simply replacing geodesics in GR with similarly looking quantum trajectories does not solve the issues here. Finding the Friedmann equations while assuming large-scale homogeneity and isotropy is no surprise to me. There are a number of people working on so-called Big-Bounce Cosmologies. ...


25

Until we have an accepted solution of the Measurement Problem there is no definitive definition of quantum measurement, since we don't know exactly what happens at measurement. In the meanwhile, measurement is simply defined as part of the postulates and recipe associated with the notion of a quantum observable. Mostly an observable is thought of as an ...


22

No. Shor's algorithm isn't demonstration of MWI. MWI is a way to think about Shor's algorithm, just like other interpretations of QM. Deutsch advocates MWI as a way to think about quantum algorithms because it is an easy way. where else did all the exponentially many combinations happen? Why do you need many worlds for exponentially many combinations to ...


22

In the many worlds interpretation, measurement devices (i.e. including things like the "conscious" (whatever that means) you) are equally part of the quantum system along with the putative "quantum system" that is under your measurement. During the "measurement", nothing remarkable happens: the whole quantum system (i.e. you and the studied system) remain ...


21

The statistical interpretation of quantum mechanics is alive, healthy, and very robust against attacks. The statistical interpretation is precisely that part of the foundations of quantum mechanics where all physicists agree. In the foundations, everything beyond that is controversial. In particular, the Copenhagen interpretation implies the statistical ...


20

Great question! I don't think there is anything obvious at play here. In quantum mechanics, we assume that that state of any system is a normalized element of a Hilbert space $\mathcal H$. I'm going to limit the discussion to systems characterized by finite-dimensional Hilbert spaces for conceptual and mathematical simplicity. Each observable quantity ...


19

Bell's theorems indeed rule out simple theories where hidden variables obey local equations. However, no matter how you reason, it's always at some point where you need another assumption. In its simplest form, it is the assumption that two observers, Bob an Alice, have the "free will" to choose along which axis they will measure the spin of a particle (...


19

I'm not sure its more complicated than the fact that the Copenhagen Interpretation is the oldest and most widely taught. Couple this with the fact that many physicists don't spend too much time worrying about things like Quantum Interpretation, and you're left with a population that, when pressed, say they follow the Copenhagen one. This is not to say this ...


19

It might help to cite your source: I found this one here - is this what you speak of? Anyhow, actually this kind of idea has had considerable, if not mainstream attention over the years. Many people who have worked with quantum mechanics will have at least heard of the following: it's just that it doesn't make it into many QM courses (being an equivalent ...


18

Yes, the density matrix reconciles all quantum aspects of the probabilities with the classical aspect of the probabilities so that these two "parts" can no longer be separated in any invariant way. As the OP states in the discussion, the same density matrix may be prepared in numerous ways. One of them may look more "classical" – e.g. the method following ...


18

This is not a settled question. Just as it is still debated whether or not there is wavefunction collapse, so is it debated what exactly we should understand by a measurement. In the following, we will go through the ideas behind the von Neumann measurement scheme, which is one way to try and talk about measurement in quantum mechanics. An interaction ...


17

Unfortunately, physicists and philosophers disagree on what exactly the preferred basis problem is, and what would constitute a solution. Wojciech Zurek was my PhD advisor, and even he and I don't agree. I wish I could give you an objective answer, but the best I can do is state the problem as I see it. In my opinion, the most general version of the ...


17

Why is the Copenhagen interpretation the most accepted one? I would say the answer is this: it's the oldest more or less "complete" interpretation hence you'll find it in many (all?) early text books, which is basically from where people writing modern text books copy from. the overwhelming majority of physicists doesn't really care about the interpretation,...


17

When dealing with a single quantum mechanical particle, both the wavefunction and the electric field appear to belong to the familiar class of "fields", both $\mathbf{E}(x)$ or $\psi(x)$. This analogy completely breaks down when you consider multiple particles, in which case the wavefunction depends on all of the particle coordinates, i.e. $\psi(x_1,x_2,x_3,\...


17

You will see all outcomes, because "you" are part of the universe. The idea that it is random is actually more in line with the Copenhagen interpretation than MWI. The real issue is a philosophical one. You are used to defining the concept of "you" in a way that makes sense in a classical world. The "you" which makes sense in a MWI point of view must ...


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