Alright point taken, but the question is whether the Schrödinger equation is describing the real state of the particle before it's measured, or it just has predictive power as a useful tool, and the reality is something else. Afterall, what the hell is a probability wave supposed to be? — Marchesk

The wavefunction is NOT a probability wave! It's not even a probability amplitude wave! According to Copenhagen, it does not exist. According to Binney it seems to not exist either.

According to the only known REALIST interpretation that agrees with QM, the wavefunction is an element of reality, but exactly what? The mathematical properties of the wavefunction correspond to features of reality, and the only way to make sense of this is to accept that the wavefunction represents a branching (and occasionally recombining) world-density function.

It turns out that under realist QM - i.e. the sort where the only dynamics is UNITARY evolution of the wavefunction, then probability is not part of the theory, it is not required. That is not to say that probability is not an extremely useful MODEL in most circumstances.

In context of Binney and HMI, if the reality would be our epistemic uncertainty about the complex state of the measuring device having a large influence on the particle it's detecting. — Marchesk

For Binney, quantum mechanics is not a physical theory. If you ask me, everyone else in the discussion section of the video you posted was embarrassed into silence. It was a car-crash. At least he does not believe in objective propability - i.e. his version of QM is a stochastic theory of human ignorance.

If MWI is the case, then probability wave is a description of other worlds. Or it could be pilot waves guiding the particle. But then again, perhaps reality is a jumble of possibilities when we're not looking? Question is why does measurement make it classical? Why is our lived experience mostly classical? — Marchesk

For systems of more than one particle, QM takes place explicitly in Hilbert space - not in the space-time. This should at least indicate that the idea of "probability waves" flying around is wrong. In fact, under the Heisenberg picture, the wavefunction is stationary - it does not change - and all dynamics is contained within the observables! Why does no one talk about observables flying around?

If MWI is the case, then probability wave is a description of other worlds. Or it could be pilot waves guiding the particle. But then again, perhaps reality is a jumble of possibilities when we're not looking? Question is why does measurement make it classical? Why is our lived experience mostly classical? — Marchesk

Decoherence.

If I thought I'd "invented theories and what have you", I'd probably want to try out my ideas in a forum before inflicting them on busy professionals.

That said, I do follow several philosophers on Twitter.

The experiments are primary, not the math. Math is used to model and predict experimental results. Schrodinger's equation exists because of the double slit experiment and others like it.

So a natural question to ask is whether the math fully takes everything relevant into account. In this interpretation, the unknown quantum state of the measuring device is a potential source of something important not being taking into account. — Marchesk

That is not historically accurate, and you really need to stop pretending quantum mechanics is a "model", it's not, it's a theory i.e. a statement about what exists in reality, how it behaves and why.

The Schrödinger equation dates from ~1925. The first double-slit experiment with particles (ignoing photons) was not performed until 1965! Entanglement wasn't observed until ~1984, "macroscopic" superpositions ~1990s, and decoherence was discovered in 1970s, but I don't think it has been observed. Then of course is the yet-to-be-realised quantum computer.

All of these phenomena, and many more besides, are deductions from the theory!

1. To any possible state of a system (collection of particles) there corresponds a unique set of information about it, called a 'quantum state', which is uniquely represented by a mathematical object called a 'ket' which is part of a collection of such objects, called a 'Hilbert Space'. [Later on, this is generalised so that kets are replaced by operators, in order to allow for non-pure states, but we won't worry about that here] — andrewk

So, the laws of physics operate the "unique set of information" and not on the actual physical system?

2. To every aspect of the system that can be measured as a number - called an 'observable' - there corresponds a unique mathematical object called a 'Hermitian operator' — andrewk

But what does the operator operate on?

3. If a system is in state s, to which corresponds ket S, and a measurement is made of observable m, which corresponds to Hermitian operator M then, immediately after the measurement is made, the particle will be in a state s' whose associated ket has the mathematical property of 'being an eigenket of the Hermitian operator M', and the value observed from the measurement will be a number that is 'the eigenvalue of that eigenket'. Further, as assessed prior to the measurement, the probability of the state after the measurement having ket S' is proportional to the square of the 'inner product' (another maths term) of S with S'. — andrewk

None if this is a necessary axiom to do quantum mechanics though. Why not drop it?

4. The ket associated with a system evolves over time according to a known differential equation, called Schrodinger's Equation. — andrewk

Except when a measurement is made according to 3.

The MWI proponent conceded to Binney that MWI would be totally unnecessary if the measuring device is the culprit, but doubted that having more exact knowledge of its quantum state would make the uncertainty disappear. — Marchesk

Sure, if there was no such thing as the measurement problem, there would be no need to solve it.

It is a common misconception that the 'state' of a system is a specification of the exact value of every observable of the system - location, momentum, spin, energy, etc. But the Heisenberg Uncertainty Principle - which is core QM, not interpretation - tells us that for any pair of dual observables - of which position and momentum are the most commonly cited - a state that has a narrow range of possibilities for one of the observables must have a very wide range of possibilities for the other. This has nothing to do with the practical ability to make measurements and is instead based on what 'state' means in QM. It is a purely theoretical, mathematical result. To reject that result we would have to radically alter, or even jettison, QM, not just choose another interpretation. — andrewk

But that does not seem to be what Professor Binney is saying. He is claiming that the uncertainty principle is epistemic due to the large number of states available to the measuring apparatus. i.e. the uncertainty principle is entirely due to our ignorance of interactions between apparatus and the system being measured.

I don't think that was the case. He repeated himself a lot, and was rather adamant. He doesn't except certain postulates as being anything more than useful modelling tools. Also, becuase the other speaker conceded that MWI would be unnecessary if the measuring apparatus is the culprit of the wave function probability distribution. — Marchesk

I'd ask him to explain the Elitzur-Vaidman bomb tester - a device that can identify whether a photon-detecting trigger attached to a bomb is operational, by NOT interacting with it.

You didn't address the point. Putting it another way - the evidence for 'other worlds' can only ever be indirect. — Wayfarer

So, you've got "direct" evidence for the Higgs boson or gravitational waves? How about direct evidence for particles turning into waves when no one is looking? Maybe you have direct evidence for any fundamental particle, and how it behaves Maybe you have direct evidence for the force of gravity?

But of course you must have direct evidence of wavefunction collapse surely?

Some prefer to have a good explanation, which is possible, to direct evidence, which is impossible. This really is philosophy of science 101.

Binney's view of the wavefunction is that it's a really useful and powerful tool, given our limited knowledge, but it has unreal properties, such as superposition. He thought the notion of a superposed cat to be absurd, like Schrodinger did. Basically, Binney thinks all the other interpretations of QM go wrong because they took the wave equation to be something more than a useful tool. — Marchesk

Now it seems as if he is defending Copenhagen.

I'll restate it briefly. There wavefunction is not real. Rather, our uncertainty about the exact quantum state (which is classical in Binney's interpretation) is translated to the particle or particles in these experiments. If we could take into account the exact state of the measuring device, then the uncertainty of the particle's property in question would dissipate, and thus there would be no need for the wavefunction. — Marchesk

Hidden variable theories are ruled out. I have absolutely no idea why people still cling to them. Well actually I do - they wand quantum mechanics to be about reality, but are desperate to avoid the implications.

I think I found the video you were referring to. Have only had time to watch a few minutes, so far I'm deeply alarmed.

When you say 'MWI is a testable prediction', what you mean is that the results are compatible with the many worlds explanation; the results appear to support the idea that there are many worlds. But you can never actually detect 'the other worlds' directly, except by way of inference. Is that the case? — Wayfarer

Just to cover the most important point first, so it can be ignored immediately: Copenhagen Interpretation does not even begin to explain reality, so should be ruled out as a scientific theory.

The Copenhagen Interpretation claims that at some time after a measurement has taken place, a certain rule must be applied which assigns to all possible outcomes a probability, and that one of these outcomes will happen. This is a can of worms, which turns out to be a normative theory, not a scientific one!

The Copenhagen Interpretation also suffers from a class of inconsistencies called the "Measurement Problem".

Yet people prefer a non-explanatory, normative, and inconsistent theory to a scientific one!

Anyway, certain, not yet feasible, tests under which Copenhagen and Everett make different predictions have been put forward. And, when the first quantum computer becomes operational, Copenhagen will be over.

Sure, what I mean is that it's a pretty big metaphysical bullet to bite. — Marchesk

It's not metaphysical in the slightest, it's the real physical situation. And, the other worlds are required to explain what we see in this world in terms of interactions with them - i.e. it is a testable prediction.

That's the motivation for Many Worlds, btw. It removes the collapse issue, but at a cost of postulating a vast number of branching worlds that we can't interact with. But if you're willing to roll with that, it works. — Marchesk

That's not a postulate of Everettian QM, it's an inevitable consequence.

There's also Pilot Wave theory which removes the non-determinism and collapse issue, but at the cost of non-locality. The theory is quite simple in that it supposes that each particle interacts with a guiding field. So, say, the particle always passes through one of the slits in the double slit experiment, but the wave passes through both and hence interferes with the particle's motion. — Agustino

There are bigger costs than non-locality. The theory doesn't work. It can't be made relativistically invariant, requires absolute time, and is restricted to the position basis. Now, there are attempts to get round these (and other) issues, but as things stand quantum field theory doesn't work in this interpretation.

There is also a slew of results that refute hidden-variable theories of any kind, not least the Free Will Theorem.

Gravitons, I would presume. And space has quantum foam, where virtual particles pop in and out of existence, creating energy that supplies most of the mass for particles. — Marchesk

You presume too much. Gravitons are a nice idea, but there is zero evidence for them. As far as we can tell, physics takes place in a space-time.

Yeah, but part of science is asking why phenomena appears the way it does. What's going on behind the scenes? Imagine if Newton and Einstein had stopped at an equation for gravity and told everyone to shut up about the reality behind the equation. — Marchesk

Absolutely! My view is that Copenhagen Interpretation should be discounted as a scientific theory because it is non-explanatory. But then I adhere to the conception of science as a purely explanatory endeavour. Instrumentalists strongly disagree!

The related concern is why should Schrodinger's equation work at all? Just saying that it fits experimental data is no answer at all. I was watching a video last night where Brian Green brought in four people to discuss the various interpretations of QM. One of them summed up the measurement problem as asking the question: what sort of world do we live in to get the sort of results that the double slit experiment gives us? — Marchesk

A more difficult question to answer is "why should the Heisenberg equation work at all?".

I would suggest that you follow through some of the many derivations of the Schrödinger equation on the web. QM is actually intimately associated with deep classical theories, particularly Hamiltonian-Jacobi mechanics. The ONLY difference is the the commutator is non-zero!

There's an easy (yet correct) answer to this: no. Mathematics isn't the cause of anything. Mathematics is simply an invented language for thinking about relations abstractly. — Terrapin Station

So mathematics is a by-product of laws of physics which permit the representation of one physical system by another - i.e. laws that permit abstraction. Mathematics, apart from being extremely terse and efficient, also expresses physical laws in a manner most amenable to testing i.e. we have a powerful apparatus with which to make deductions from conjectured theories.

And, because there is no special physics unique to the human brain, we are able to automate much of the mathematical reasoning by instantiating the abstractions that interest us on a computer.

1. What determines a measurement? Even molecules can exhibit the same behavior that electrons and photons do in the double-slit experiments. — Marchesk

It doesn't matter what determines a measurement. All that matters is that you can predict probabilities associated with whatever you decide to measure.

2. How does a quantum property transition from possibility to a single value? This would be the issue of the so-called wave function collapse. — Marchesk

As you said, wavefunctions are not real - they are not elements of reality - so they don't really collapse either. Wavefunctions are purely epistemic.

3. Why is the probability distribution wave-like? If it's not real, then how does the math work out? What makes the wavefunction descriptive? How are mere possibilities interfering, cohering, entangling, etc? — Marchesk

Most integrable functions of position (or whatever basis you prefer) look a bit like waves, or wave-packets. Probability distributions are just another well-behaved wave-like function. Wavefunctions however are not probability distributions, but probability amplitudes, and in general they don't look like waves because they exist in Hilbert space as a ray of unit length.

Your other questions are meaningless. Shut up and calculate instead. If you don't like being told what to do, tough! Probabilities are normative.

4. Do normal, macro-scale objects exist when we're not "looking"? I recall reading that Bohr and Einstein debated whether the moon was still there when they turned their backs. Bohr, being the champion of the Copenhagen Interpretation, argued it was just a range of possible states. — Marchesk

Not so sure about that. Copenhagen requires the existence of classical physics, particularly as a place for probabilities to be calculated. It's called "Complementarity".

5. Early enough in the universe, everything would have been on the scale of subatomic particles, so how did the macro-scale universe where measurements take place come to exist? If the Copenhagen interpretation is correct, then the early Big Bang was just a probability space, not something real. Does that mean a measurement took place? — Marchesk

I'm not sure that these questions have any meaning under instrumentalist theories like Copenhagen.

6. Does gravity have a wavefunction? Is mass only discrete when measured? What would the implication of that be for GR? — Marchesk

Gravity? You mean space-time curvature I hope, and no, space-time is real.

If there are any normative moral relativists out there, I'd be fascinated to hear from them, since it seems to me that the putative worldview of this straw man category is self-contradicting. — andrewk

Isn't Angela Merkel one of those?

It is undoubtedly counter-intuitive, particularly as there is a great deal of work that indicates that for a classical Turing machine, operating under classical physics this could not be possible. I think the culprit is classical physics.

As I mentioned, the Bekenstein bound cannot apply to what is going on in a quantum computer. This implies that the state of a quantum computer, even its output in general, is not an observable.

So a universal computer could compute the result of itself being sucked into a black hole and having contact with the interior (singularity or whatever lies there). — Marchesk

We've got a pretty good idea of what it is like to fall into a black hole, so I don't see why you could not in principle do this - any finite system can be simulated to arbitrary accuracy by finite means.

Although, this seems unfair. I'm guessing the idea of simulating precludes the thing doing the simulating, otherwise we have regress and self-referential issues. I might as well ask if the computer can simulate itself itself being introduced to a really strong magnet, or whatever would disrupt a QC. — Marchesk

A quantum computer has got to be isolated from its environment. This can never be perfectly achieved, but there seems to be ways around the technical issues involving extra qubits and error correction. It's thus perhaps not too much of a stretch to think of the QC as a black box, with which there is no interaction save for setting inputs and reading the output.

Haven't thought this through, but this feature of the QC might solve any perceived problems with regression etc. The QC is actually in its own Hilbert space!

The visible universe could hold ~10¹²⁴ bits of information if it were a black hole of the same size. I've seen arguments that the the number will be of the order ~10⁹⁰ for a realistic non-black hole universe.

So, you need at most ~2⁴¹² bits of information to describe the universe. (I hope I did the change of base correctly i.e. 10^124 ~ 2^412)

A 1000 qubit quantum computer in a maximally entangled state, would require 2¹⁰⁰⁰ bits to describe it!

Whatever is going on in a quantum computer, the Bekenstein bound does not apply!

I don't see how having a computer, quantum or otherwise, that can store enormous volumes of information helps in simulating the universe, if the computer is in the universe. Let the info storable by the computer be A and the info in the universe outside the computer be B. Then, as long as B is nonzero, for the computer to simulate the universe it has to store at least volume A+B which, no matter how mind-bogglingly large A is, will be more than the computer can store. — andrewk

Simple question:

How many bits of information are required to fully describe the visible universe?

How many states are available to a quantum computer comprising 1000 qubits?

Do you think that a few hundred qubits could completely simulate a black hole? And by that, I mean the object itself, not just the effect on things outside the event horizon. — Marchesk

It depends on the size of the black hole. If the black hole is smaller than the visible universe, then yes. More interestingly, a universal computer inside a black hole could simulate the black hole.

False physics.

OK, perhaps that's a bit of an overstatement. There exists a very strange interpretation of quantum mechanics, that is compatible with that one-world determinism. It goes by the name "Super-Determinism". As far as I can tell, there are 3 people who hold that view, one being extremely famous.

Abstractions/concepts are particular, concrete phenomena in brains. Mentality is simply specific dynamic brain states. — Terrapin Station

Despite being surrounded by abstractions instantiated in all sorts of physical systems, from DNA to computers, you simply deny this and assert that the only physical system of instantiating abstractions is the (human) brain.

Denial is always an option.

Your link doesn't work.

However, whatever you think determinism implies or otherwise, what can and cannot happen in the universe is solely determined by the laws of physics.

I strongly suspect that the paper you have tried to link to deals with classical computation, operating under the laws of classical physics - i.e. an outmoded conception of computation operating under false physics.

If such prediction is impossible however, than I would say let's live in the illusion of a non-deterministic world, regardless of wether we do or not. — John Frostell

Such a prediction is impossible for false physics under an out-dated conception of computing.

How would the computer computer the future of the universe without being the entire universe? And if the entire universe isn't computing ahead such that we know the future, then you can't have a computer inside the universe doing so. — Marchesk

Surprisingly, according to the laws of physics, simulating the entire visible universe is indeed possible using a universal computer, from within the universe.

The visible universe is thought to contain about 10¹²³ bits of information. A rudimentary quantum computer containing only a few hundred qubits vastly outstrips that!

Why, in your view, (a) would information theory be a waste of time, (b) would technology based on information theory not be possible, (c) would computation not exist, and (d) would virtual reality be impossible just in case concepts/abstractions are purely mental? — Terrapin Station

If abstractions were purely mental (whatever you might mean by that) then they could not be instantiated in physical reality by physical objects like DNA molecules.

Abstractions, by the way, are strictly mental. Any properties abstractions have is simply properties of the concept we've formulated. — Terrapin Station

So, Information Theory is a complete waste of time, rather than an explicitly counterfactual theory of a type of abstraction, underlying much of technology? Computation doesn't happen, and in particular virtual reality is impossible?

You've got it the wrong way round. What we can know about the necessary truths of abstractions is limited to how closely we can instantiate, or model abstractions physically.

Not all mathematicians are platonists. At any rate, I'm definitely not a realist on mathematics. — Terrapin Station

But there exist necessary truths about the set of primes. Some of these truths have been set out in proofs. So what is going on if the subject of these proofs does not exist?

A proof is a type of computation that models the properties of an abstract entity (e.g. the set of primes) and establishes that the abstract entity has a certain property. So we can grant the abstract entity a list of properties, but not the property of existence?

Are you going to give the cicadas the bad news?

That's not at all the case. I just don't think that they're something other than particulars. — Terrapin Station

What is mathematical proof for then? Given that there are thousands of books and papers on properties of the primes, which have been discovered, you might be forgiven for thinking (as mathematicians do) that they are about something real.

When do you consider the theory of quantium entanglement to start--with the EPR paper? Schrodinger's response to it? — Terrapin Station

Start wherever you want. But remember, we need a set of observations from which to induce the theory an an unexpected observation if you want to abduce the theory. Since these are purported to be part of the methodology of science, I trust you will be able to do both in this case.

If I may interject, I find it hard to distinguish between "predictable regularities" and "real laws of nature." In other words, I don't see how "real laws of nature" explain rather than differently refer to the same predictable regularities. Do we not experience the order we find as a "brute fact"? — R-13

Why don't you propose a principle of "Predictable Regularity", then we can use it to describe the universe from the big-bang to the heat-death, with a brief interlude for life on earth? All so predictable and regular after all!

Right, but the question is how we can know that a counterfactual claim is true, if - as the nominalist asserts - there are no real laws of nature, just individual things and events. — aletheist

Under real deterministic natural law, counter-factuals can be regarded as meaningless. In the block-universe of general relativity, there is no room for them it seems.

We have been testing counterfactuals for centuries - that is what experimentation is, and this is precisely what Peirce called "induction." It is not the same thing that Popper rejected, since both men affirmed that theories are never verified, only corroborated (or falsified). — aletheist

If general relativity is wrong, and we don't inhabit a block space-time, then perhaps, but have we really been testing counter-factuals? We have been reasoning about them, but if we had tested them, they wouldn't be counter-factual.

Peirce committed the error of seeking to justify a theory, or render it more probably via "induction". Didn't he claim:

The true guarantee of the validity of induction is that it is a method of reaching conclusions which, if it be persisted in long enough, will assuredly correct any error concerning future experience into which it may temporarily lead us

It rather seems dubious to me that there are any scientific theories that are not arrived at via a combination of inductive, abdutive and deductive reasoning, with the first two being more prominent than the latter--after all, a deductively-arrived-at theory would at best only need experimentation to confirm its premises, otherwise it's not deductive at all. — Terrapin Station

Quantum entanglement provides a straight-forward example. What series of observations resulted in the induction of the theory? What was the "surprising observation" that resulted in its abduction?

Given that both induction and abduction are purported by some to be part of the method of science, it doesn't seem unreasonable to ask for an example of them being used?

but my question boils down to why induction is so successful as a mode of inference. — aletheist

So successful that you can't give a single example of a scientific theory arrived at by that method.

I know that this is getting repetitive, but I still would like to know - on your view, what warrants our confident predictions that particulars will "behave" in the future as they have in the past? — aletheist

In general the future does not resemble the past, and it is the role of science to explain the regularities and irregularities.

There is no such principle in science (or anywhere else that I am aware of) that "the future will resemble the past".

Are we ever justified in making law-like counterfactual claims about circumstances that may never actually occur? — aletheist

Justified? Why would you seek justification? Our knowledge permits us to make counterfactual claims. Interestingly, we can even test counterfactuals these days.

Temperature is completely out of control: