A Physicist Trying to Fix Quantum Mechanics
nytimes.com
nytimes.com
[1]https://en.wikipedia.org/wiki/Ghirardi%E2%80%93Rimini%E2%80%...
Why? Measurement is just a photon you shoot at something. Or electron. Wikipedia is saying we cannot define what an observer is and what constitutes “measurement” - sure we do, measurement interacts with the quantum mechanical system because we need to use something - a photon or an electron or some particle to see how it interacts with the system.
In classical mechanics, adding a 3rd filter between the two would have no effect since already no light is getting through.
However with quantum putting a 3rd filter between your two original filters at 45 degrees will allow half of the photons to pass through all 3 filters. This is where things get strange and measurement is not very well defined. Are any of the 3 filters now performing a measurement? We know that half the photons will pass through but have no way of determining which will and which won't.
This experiment works with polarized sunglasses btw, quantum in the palm of your hands.
Ask a grad student or even a professor of physics what is essentially different about QM verses classical mechanics.
I almost always get one of two answers.
QM has operators acting on a Hilbert space (rigged HS). It's so mysterious because we have to replace everything with operators. well...
Have they heard of the Koopman–von Neumann formulations of classical mechanics? It's CM formulated using HS and ops.
https://en.wikipedia.org/wiki/Koopman%E2%80%93von_Neumann_cl...
Another answer is uncertainty. QM has uncertainty. Well... so does classical mechanics!
So what is different? That's a very long answer but one thing is the Exclusion principle.
Besides the KvN formulation is it possible to do QM using the equations of CM in the same form?
yes, it is. The Wigner Moyal Weyl formulations of QM. Look it up or Moyal star products.
Lastly, the collapse of the wave function.
Already done long, long ago by John von Neumann in his book on Quantum Mechanics. The correct formulation involves the subtle concept of decoherence. Von Neumann's trace operators are used in extreme cases where standard calculations (which involve a tiny bit of cheating) won't work, e.g. black hole entropy.
What's wrong with QM? So far nothing! It's possible someone might find a flaw but it hasn't happened.
The problem is mostly US. We don't understand all the implications of what we already possess. The enormous amount of myth making and lack of understanding surrounding QM obfuscates what the true problems are which in 99% of cases is the most physicists simply haven't studied von Neumann carefully enough.
It’s like physicists (collectively) have PTSD from a few decades of trying to understand QM, which then crystallized into the maxim “shut up and calculate”. What we’re seeing is the resulting learned helplessness.
The trouble is that decoherence only explains part of the story. With decoherence you end up with the probability density converging into multiple outcomes. But decoherence does not in any way explain that the choice is made to pick one of these outcomes.
As for what is wrong with QM, the main issue for me is the measurement process, which is just posited axiomatically. How measurement works should be explained by the theory but it is just posited. They assume a classical device that does the measurement. Decoherence explains bits of it but much is left hanging loose.
As you mention, the probability density converges to multiple outcomes, but then I believe that you're in more of an Everett Many Worlds between the outcomes, rather than a "choice."
In practice, it seems like all of the Many Worlds scenarios statistically converge into one world sooner or later anyways (would love this to be formally shown, but have never seen it, so it's just conjecture from me). For example, if you flip a quantum coin, splitting the universe in two in a Many Worlds Interpretation, who cares? Does the Sun notice? Does someone in a town a mile away?
You've created a small bubble of "two universes," in a Many Worlds sense, but that bubble will pop. Quantum mechanics is ambivalent about the direction of time, so it sure seems like worlds are joining as fast as they're splitting, keeping us statistically around one effective universe.
Quantum mechanics is just statistics, but operations preserve the 2-norm instead of the 1-norm. Instead of case weights (probabilities) adding up to 1, the squares of case weights (amplitudes) add up to 1. Everything else (the uncertainty principle, measurement mattering, no cloning, Bell inequalities, etc, etc, etc) follows.
Did Aaronson provide a source for that?
"Statistics but with the 2 norm" is really just a succinct way of stating the postulates of quantum mechanics, and obviously all effects of quantum mechanics are determined by the postulates. So you shouldn't really see this as a statement that's controversial at all.
The uncertainty principle follows via doing signal analysis on Fourier-transformed wavefunctions. A fun professional treatment from Baez et al. is [0], and 3blue1brown has an excellent two-video visual explanation [1][2]. The uncertainty principle turns out to be a special case of the sampling theorem (yes, that one! [3]), which itself turns out to be a special case of a result in sheaf theory [4].
Measurements matter because "observables don't commute"; taking linear operators on the complex numbers or other Hilbert spaces can have lasting effects which can't easily be undone. Combine this with "conservation of probability", which is formally mostly abstract nonsense [5], and we get mostly to Aaronson's point of view. (I would go further using the Free Will Theorem. [6])
When Aaronson says that the no-cloning principle is provable using probability, but for complex numbers, he's referring to the standard proof [7]. There are two connections to draw to typical probability theory. The first, and bigger, connection is that random variables can't be cloned in typical probability theory either! The second, deeper, connection is that Hilbert spaces give linear logics, which imply conservation laws for the information representing the particles to be cloned.
Finally, for the Bell inequalities, again there is a standard proof on Wikipedia [9] using typical probability theory. I'd like to mention the overlooked Kochen-Specker theorem [8], which forms the backbone of the Free Will Theorem [6]. Measuring a particle is like taking a sample of a random variable: We decide how we want to ask the particle, and the particle chooses a response that is both allowed by its probability distribution and also correctly represents its context.
[0] http://math.ucr.edu/home/baez/photon/schmoton.htm
[1] https://www.youtube.com/watch?v=spUNpyF58BY
[2] https://www.youtube.com/watch?v=MBnnXbOM5S4
[3] https://en.wikipedia.org/wiki/Nyquist%E2%80%93Shannon_sampli...
[4] https://arxiv.org/abs/1405.0324
[5] https://en.wikipedia.org/wiki/Probability_current
[6] https://en.wikipedia.org/wiki/Free_will_theorem
[7] https://en.wikipedia.org/wiki/No-cloning_theorem#Proof
[8] https://en.wikipedia.org/wiki/Kochen%E2%80%93Specker_theorem
https://physics.stackexchange.com/questions/10230/trace-of-a...
Wait what? I mean sure, at scale CM is not feasible to compute (eg. n body problem). But our inability to precisely compute the otherwise completely predictable events is not the same as QM which can give true randomness.
No it isn't. Even with perfect information and unlimited compute resources you cannot determine the outcome of a simple Bell Test https://en.wikipedia.org/wiki/Bell_test_experiments
The same is not true for CM. QM absolutely allows for true randomness. This has been proven time and time again. I encourage you and the original author to read the above. Look at the Feynman lectures. There are no hidden local variables. This is true randomness.
Namely that when an observer observes a quantum mechanical system, you get a quantum mechanical system that can be described as a superposition of parallel observers who each think that they saw something different. Those parallel observers cannot meaningfully interact thanks to thermodynamic considerations.
Of course accepting this description involves believing in quantum mechanics a little more than most feel comfortable believing in it...
There is a wonderful lecture by Harvard Professor Sidney Coleman, called "Quantum Mechanics in Your Face"[1]. In it, he essentially leads into precisely this. It's what happens when you take quantum mechanics seriously.
My issue is that I can't take quantum mechanics seriously, or expect that it's interpretational issues can be sorted out within itself. The problem is that quantum mechanics is "merely" an extremely excellent approximation to quantum field theory. It can be thought of as an "effective theory" in a very similar way to QFTs as low-energy versions of other QFTs. Which means naturally that we should expect the framework of QFT to answer the interpretational issues, especially to provide guidance as to how the changes due to the approximations change the interpretation.
This is all a fine idea, but quantum field theories have even worse interpretational problems.
But there could be non-local ones. The Bohm theory, which is perfectly consistent with standard QM, is fully deterministic.
Important point. It is quite unfair to say "nya nya local hidden variable theories cannot replicate QM", when QM is itself radically non-local.
No. The standard formulation of QM posits a measurement using a pseudo-classical device which generates a probabilistic outcome. This is at the very core. Source: any text on QM.
The wave function evolution is deterministic but that is only a part of the theory.
Fundamentally, QM is just some special subset of algebra with certain properties. Just like other algebras aren't "physics", QM isn't really physics. It's just a bag of tools with the right algebraic features to solve a wide category of problems physicists often have.
This is fine, but first think of ordinary algebra. It has some interesting implications that took a while for people to wrap their head around. The zero wasn't a widely accepted concept for thousands of years. Negative numbers are already a squirrelly concept. How can you have negative three apples? That was an easy abstraction hurdle to get across, eventually, and now even children understand that the implication of this is that you owe three apples. If you're give five apples, you have to return three to whomever you borrowed apples from, and now you're left with two.
QM is firmly in the group of abstractions where we haven't worked out the mental models quite yet. Talking about complex-valued probabilities makes most people raise their eyebrows quizzically. It doesn't matter how many different ways you demonstrate that the algebra works out, it's still a very difficult concept to internalise.
One interesting mental model I've come across is that classical probabilities are the products of two things, we just haven't noticed. Quantum Mechanics undoes this multiplication, making it in some sense the "square root of classical probabilities", which is not a probability, but something... "else". It's mysterious because in ordinary life we only ever observe the (else×else) products, never the "roots", even though the latter is more fundamental.
I've never heard anyone take this kind of thought all the way to its conclusion. My current extremely tentative notion is that the "roots" represent probabilities in a kind of continuous alternate universe space, along the lines of MWI. Neither the "observer" nor the "observed" are in any one such universe, but smeared across them in some distribution. Their interactions require their many-worlds-distributions to be multiplied to produce a "real" result, which is still a distribution, but now the one we're used to in CM. Self-interactions such as a resonator in a potential well require self×self products, which are simplify to self^2. Quantum mechanics just undoes this squaring in order to model to underlying behaviour across parallel worlds.
But note how to get even this far, this tentative explanation already required a nearly complete rethinking of what QM really is. It's never going to be sufficient to shuffle the algebra around on a page, because algebra isn't physics. Physics is. Quantum Mechanics is still in the "a bunch of algebraic tricks" stage and needs to be dragged kicking and screaming into a form that people can intuitively understand in terms of physical concepts, not just mathematical ones.
Some physicists claim it's inevitable because we don't have direct sensory access to quintessential quantum behavior -- we can only have intuitive models for classical physics. I don't buy it -- the human imagination is quite powerful.
I suspect that a superior theory (1) will be mathematically equivalent to QM (2) may suggest obvious extensions that are not equivalent, leading to testable predictions (3) won't result from merely reshuffling equations -- it'll take some serious inspiration.
Another hunch: the decoherence approach is barking up the wrong tree. The lesson of Schroedinger's cat is that realism doesn't emerge from a non-realistic theory. It seems like locality has a better chance of being an emergent property.
A lot of things in physics (or in other model in science, for that matter) have cannot be measured directly. (I think "has no meaning" is a stretch here.)
I can go for ages talking about things in physics that are less intuitive than simple, non-relativistic, quantum mechanics (Poynting vector, anyone?)
But think about something simple and concrete: electric potential. You cannot measure it. But you can measure its difference.
Except to explain our everyday experience of a single classical world. Then something in QM has to give.
Which the parent says is explained via decoherence. Why do you feel that decoherence does not account for the observed phenomenon?
No, that's not what the parent says. The parent says:
"The idea that quantum mechanics stops working at macroscopic scales is totally unnecessary..."
which is true, with the one exception that I noted:
> Except to explain our everyday experience of a SINGLE classical world [emphasis added]
You can get from QM to multiple worlds without any ad hoc assumptions, but you cannot get to a SINGLE classical world that way. You have to give up either linearity or superposition.
http://blog.rongarret.info/2019/07/the-trouble-with-many-wor...
It isn't. To take a simple example, suppose we measure the spin of a single spin-1/2 particle that is in a state such that there is a 50-50 chance of either possible result. Decoherence can explain why the total system--particle plus measuring device plus observer plus environment--ends up in a superposition of "particle with spin up, measuring device measures spin up, observer observes spin up" and "particle with spin down, measuring device measures spin down, observer observes spin down"--in other words, why the interference terms between those two alternatives go away. But decoherence cannot explain why only one of those two results actually occurs.
MWI is consistent with decoherence, but the choice of MWI vs. other interpretations is not based on decoherence; it can't be, because decoherence is consistent with all QM interpretations, not just the MWI, so decoherence can't possibly be the basis for choosing any one QM interpretation.
> no extra assumptions are required to derive the MWI
Yes, there are; you have to assume the Born rule. Various attempts have been made to derive the Born rule in the context of the MWI, but none of them have gained general acceptance as having been successful.
Epicycles did work for the solar system. But the modern solution was much simpler.
https://www.google.com/search?q=angelo+bassi+site%3Aarxiv.or...
This one seems relevant to the topic of the NY Times article:
The probabilities in QM should be viewed as subjective, but physicists hate subjectivity, so they talk about hypothetical ensembles. It baffles me that Everett took those ensembles and decided they were real universes.
When the universe splits at two distant measurements it isn’t until those outcomes are brought into contact that the matching of worlds needs to happen.
Does the universe split every time the wave function collapses in any form, for all measurements of all atoms in the universe? Isn't that essentially infinite? And how would you prove it if any of this was real?