But in other theories (those termed "realist"), such as Pilot Wave or Superdeterminism, the uncertainty principle is exactly an artifact of measurement. A particle has an exact position, momentum, energy, spin etc, but they can't be reliably measured all at once.
In the end, these are philosophical positions, outside of our current mathematical and physical tools. Perhaps in time we will be able to settle these questions, but for now there are no definitive answers.
Not really. Realist theories are actually just rhetorical sleight-of-hand. Bohmian positions, for example, are supposedly "real" but they cannot actually be measured, and this inability to measure them is not a technological limit, it is an inherent part of the interpretation. Bohmians essentially take the randomness, hide it in the infinite digits of a real (no pun intended) number, call that number "the actual position of a particle" and claim that, because it's "the actual position of a particle" that it is somehow "real". Well, it's not real. You can't measure it. You've just hidden the randomness behind some clever rhetoric.
> the reality is that we do not know
Yes, we do. The Bell inequalities and concomitant experiments show that quantum randomness is fundamental. You can hide it or sweep it under the rug but you can't get rid of it because it's actually part of our reality.
Now, Bell's inequalities show that any theory of local hidden variables independent from the measurement apparatus is inconsistent with QM and with experimental observations. However, that still leaves the possibility of non-local hidden variables possible, and it also leaves open the possibility that the experiments have been flawed - that the measurement decision was somehow correlated with the result.
The Copenhagen interpretation is BOTH non-real and non-local, so I don't find a real non-local theory a priori problematic. Whether pilot wave theory can be made consistent with at least special relativity is still open as far as I know, but perhaps there is some equivalent of the no-communication theorem that will be found.
Superdeterminism is also seeing a resurgence - I can't claim to understand how it could be made into a real scientific theory, but perhaps there is something that is escaping me and we will see a successful theory come out of it.
Now, the matter of whether something can be considered "real" but fudamentally un-measurable (as opposed to just being practically un-measurable) is in the end a problem of definitions.
I would also note that there is no fundamental quantum randomness - quantum phenomena behave according to a linear equation, so they are fundamentally deterministic. It is only measurement (the interaction between quantum systems and classical systems) that introduces randomness - the superposition of all the solutions to the Schrodinger equation is replaced with a single position&momentum with some probability, and with error bars that are subject to the uncertainty principle.
It can be made consistent, namely, adding a foliation (a notion of a canonical present moment) makes it work out fine. The foliation is not detectable, it gives the right predictions, it is mathematically sound, etc.
But it does feel philosophically sketchy and not fundamentally relativistic. However, there is a paper https://arxiv.org/abs/1307.1714 which explores how to derive foliations from the wave function itself and thus would be as relativistic as in theory involving the wave function.
The article also points to other articles with a variety of ideas how to deal with nonlocality in Bohmian mechanics.
No, they don't. The uncertainty principle applies just as much to grains of sand as it does to electrons. The only reason they appear to have definite position and momentum is that their masses are large, so a very small velocity produces a very large momentum which gives them a very small wavelength, much smaller than their physical extent. But the uncertainty principle still applies. With the right technology you could do a two-slit experiment on grains of sand. See: https://www.wired.com/story/even-huge-molecules-follow-the-q...
Still, the point was about a classical model, not about physical reality being classical or quantum. To rephrase, my point was that even in a classical model there are quantities that can't practically be measured (even though classical mechanics as a model assumes all objects have definite positions and momentums), and that doesn't stop us from accepting in such a model that they are 'real'. So, the idea of property that is 'real' but not really measurable already exists in classical physics, it is not an invention of exotic interpretations of QM.
In the Bohmian model world, particle positions would be real. They may not be measurable to the inhabitants to infinite precision (assuming quantum equilibrium, i.e., the particles are distributed according to psi-squared), but the particles have definite postions in this world. It has in it no need to postulate anything about measurement. Observables and all that are deduced from the theory.
It is important to ask what in a model has a fundamental existence, what has an implied existence, and what is just a useful term for something secondary to all that. In Bohmian mechanics, particles (things with position) have a fundamental existence, the wave function has an implied existence because that is how the particles move about, and spin has a secondary existence since it does not have a separate existence from either of those two objects, being solely deduced from the motion of the particles.
The Bohmian model is well-defined and has an easy correspondence between the entities that are real and our experience (stuff has position). It does not require observers to be complete. A Bohmian world could happily exist without PhDs, humans, mammals, life forms, etc.
What's real in CI? Not really sure, but I guess the wave function and measuring devices? It does require something that corresponds to measurements and the evolution of that classical world is distinct and separate.
This is the context of calling BM a realist theory. I would just call it an actual theory.
Bohmian mechanics illuminates the quantum randomness, allowing it to be analyzed. The theory happens to be deterministic (ignoring creation/annihilation), but it derives the apparent randomness from all that and it clarifies the meaning of psi-square.
The wave function and any of its behaviors are not considered Real in CI, quite the opposite. CI posits that the wave function / schrodinger equation is just a mathematical tool that can be used to model the behavior of quantum phenomena - it is merely a tool that we can use, together with the Born rule, to predict the outcome of measurements. The measurements are the only things that are real. That's why CI is also sometimes summarized as "shut up and calculate" :).
So the programmer who wrote the simulation program took a shortcut. "No one will ever look at reality at this granular of a level, we should be good." Figures.
Seriously though, great explanation.
I find it very "triggering" when people use this metaphor of uncertainty as a programming shortcut, when my life (currently working on simulating quantum systems) would be substantially (exponentially) easier if reality was classical.
I consider it a universal warning sign when your physical theory postulates that reality works a certain way underneath, and then conspires to keep you from exploiting this way. Superluminal collapse, for instance, or closed timelike curves; it seems to my intuition that these are clearly flaws in the theory rather than properties of reality. In a sense, the sci-fi concept of the ansible, where quantum collapse effects are exploited for FTL signaling, is more plausible than the view where quantum systems collapse instantly, but cannot be exploited for FTL. If your theory requires FTL in the "backend" to operate, it shouldn't end up with FTL just happening to not be exploitable in the "frontend". So I expect that when we find the true ToE, it's not going to end up with traits where the data structure in principle allows a certain capability, but coincidentally doesn't give us access to it; all limitations of that theory would follow directly from its structure, so that illegal operations cannot even be expressed. So when we find a practical limitation to the exploitation of a physical theory, then this seems to me to require, barring very good theoretical reasons to the contrary, a genuine underlying property of the universe that justifies this limit.
As such, it seems to me, purely from an intuitive view, that of those three claims:
- reality is quantum
- quantum mechanics requires exponential cost to simulate
- quantum mechanics cannot be exploited for exponential computation
One has to be false! If reality requires exponential cost to simulate, we shouldn't expect it to then turn around and hide that capability from us. God famously doesn't play dice with the universe; but I doubt he's playing Poker either. Personally, I suspect quantum mechanics is cheaper than is widely believed.
Idk, am I missing something obvious?
As far as we know for now, [a variant of [0] ] this one is the wrong claim: we do have algorithms (Shor's, Grover's) that are faster on Quantum Computers than any known classical algorithm.
Of course, we do not yet have any proof that a faster classical algorithm can't exist, so the possibility remains open that this claim remains true. BUT, if this claim turns out to be true, then it is extremely likely that either one or both of the other 2 claims will immediately turn out to be wrong.
[0] I would note that the "exponential" part is somewhat of a red herring. If there is any kind of asymptotic speed-up that QCs fundamentally have over classical computers, even if it's just quadratic, then the larger point will remain valid.
> In a sense, the sci-fi concept of the ansible, where quantum collapse effects are exploited for FTL signaling, is more plausible than the view where quantum systems collapse instantly, but cannot be exploited for FTL.
This is also what rubs me the wrong way about entanglement, and seems a very tantalizing thread to pull at if one wanted a more fundamental theory. The other thread of course is the measurement problem.
The Schrodinger equation almost always predicts that a particle has some particular amplitude at many different locations. However, if you try to detect a particle, you will never find it at more than one location. Furthermore, once the particle is detected at one particular location, you need to update the Schrodinger equation to give it amplitude 1 at that location and 0 everywhere else - if you don't perform this nonlinear update and instead use the old wave-function, the predictions for further experiments will be completely off.
Now, the physical interpretation of this collapse varies wildly between different interpretations of QM, but some variant of it is always required - otherwise, the observations simply do not match the math. We don't yet have any theory consistent with QM that can make predictions without applying the Born rule.
The current consensus (at least among people I speak to) is that a quantum computer will probably be able to solve some problems which are in NP (and not in P), but will probably not be able to solve an NP-hard problem.
Your intuitive view is appealing, but I don't think one should get too hung up on intuition. Our intuition was honed for millions of years to avoid large wild animals and avoid falling out of trees in prehistoric Africa. It generally sucks pretty badly at making guesses about the fundamental nature of the universe (or at least mine does).
Edit: by the way a faster than light communication "ansible" is functionally equivalent to a machine that sends messages back in time. I disagree with your view that such a machine is more plausible than the view that some ftl stuff happens on the "backend" but is hidden from the "frontend". Having said that my view is that there is no ftl stuff on the back or front end, this is consistent with something like the many worlds interpretation of quantum mechanics, which is entirely local and causal (no ftl stuff).
Disagreeing again with the "Ansible is unrealistic" view: I agree it's unrealistic in a global sense, I just think all of its unrealism comes from the use of FTL in the backend. FTL + relativity produces timetravel, yes. I just think it's implausible to expect a physical universe to first provision the mechanics for FTL, then provision a system that gives you timetravel when exposed to FTL, and then very carefully separate those two systems so that they computationally never touch, even though in theory they could! and so in a sense, this physical theory implies that this universe has to be prepared, in principle, to allow time travel and account for it, and having gained this capability has elected to specifically not use it. It just stinks of a massive Occam violation - the potential for time travel is an "entity without necessity", and the theory is bloated by it twice over; once by its inclusion in the physical logic and once again by the additional exclusion mechanism that makes it unusable in every reachable state. And so the ansible universe pays slightly less cost just by leaving out the global censor.
Am I saying "no correct theory can look like this"? No! I am saying it enters the race with a huge handicap.
My understanding is that that is a yes - with a quantum computer, quantum simulations [are expected to] run in linear time instead of the current exponential time.
Then you give me two numbers a and b (with some technical constraints) and ask me whether the ground state energy of H is between a and b.
This problem is QMA-complete as long as k >= 2, and known to be QMA-hard even for some pretty nice looking Hamiltonians. Here QMA stands for Quantum Merlin-Arthur which is the complexity class equivalent to MA (Merlin-Arthur) for classical computers. You can think of MA as being related to BPP in the same way that NP is related to P, and this is the same way that QMA is related to BQP.
Basically QMA problems are not expected to be solved efficiently by a quantum computer.
That is, if we think that the universe is a simulation running on a classical computer, then quantum effects such as the uncertainty principle CAN'T be a "shortcut" to make the simulation easier - as in fact they make the simulation literally exponentially harder. If we assume that the universe is a simulation running on a quantum computer, then quantum effects are fundamental anyway.
Of course, everyone understands that this is a simple joke. Still, it's interesting that it goes completely against our intuitions as computer simulation designers.
PBS Spacetkme has a great video on pilot wave.
Getting rid of all the messy probability issues is amazing.
Quantum mechanics forms a consistent theory without any concept of randomness or wave function collapse, and decoherence explains how this evolves into a classical observation when things get "big". There is nothing fundamentally random about this evolution. We still use random numbers (wave function collapse) to approximate observations, because in many cases quantum calculations for macroscopic objects would be intractable, and because they give the same answer to any precision we can hope to measure.
Every experiment that demonstrates quantum entanglement is essentially just showing that quantum mechanics still applies on systems that were previously thought to behave classically. And none of these experiments have demonstrated a mechanism for wave function collapse beyond what we already understand from decoherence.
Decoherence does explain why macroscopic systems can't (normally) exhibit self-interference and some other quantum effects.
However, decoherence doesn't in any way solve the other aspect of the measurement problem: why the object is only ever found entirely at one location instead of appearing with different amplitudes at multiple locations, as the Schrodinger equation predicts. That is the source of the "fundamental randomness" and it is not explained by decoherence.
For a slightly more mathematical (but still very understandable) explanation of what decoherence solves and what it doesn't solve, I recommend this article [0] by Sabine Hossenfelder.
[0] https://backreaction.blogspot.com/2020/08/understanding-quan...
So decoherence either fails to solve the measurement problem or solves it by saying the universe is weird.
Nevertheless, you will NEVER see both detectors detect the same particle. You know with 100% certainty that if one detector "saw" the particle, the other one didn't (this is true regardless of how far apart the detectors are).
Furthermore, imagine an experiment like this:
1. A particle P1 is fired, and it has some amplitude at locations Det1 and Det2.
2. At location Det1, a second particle P2 is made to collide with P1; the collision will throw P2 towards location Det3.
Now, the correct probability of finding P2 at location Det3 depends on whether Det1/Det2 are activated. If Det1 detects P1, the probability for P2 to reach Det3 is 0, but this is inconsistent with the Schrodinger equation for P1 and P2. To make the results consistent with observations, you must update the wave function for P1 and P2 after Det1 has detected P1.
Now, the MWI tries to circumvent this by postulating that both results happen at the same time, just in different worlds; and that Det3 becomes entangled with Det1, so their results are perfectly correlated. But that runs into other problems, both philosophical (how could the other worlds be "real" if they are fundamentally undetectable) and formal (e.g. it is not yet agreed that a consistent, non-circular definition for probability in the face of many worlds can be given that is consistent with the observed probabilities computed according to the Born rule).
Edit: I should also mention that without the Born rule, if Det1 and Det2 were both going to launch a satellite if they detected P1, then both satellites would have some amplitude in orbit; and you would start expecting to see the gravity of both satellites, which breaks off with experimental observations even more sharply.
That's also part of quantum mechanics. At least if you are trying to do physics.
https://www.math.columbia.edu/~woit/wordpress/?p=10533&cpage...
You may have missed the subtle but important aspect of the uncertainty principle. It is not the case that there is a true underlying value of position and momentum for which the error bars are limited by quirk of theory. It is more like you expect to be able to observe 2 bytes of position information and 2 bytes of momentum information but the underlying quantum state is defined by 2 bytes in total. The full 4 bytes cannot fit inside 2 bytes. You can have a state which encodes the 2 bytes of position information but no momentum information, a state which encodes 1 byte of each, a state which encodes 2 bytes of momentum information but no position information, and everything in between. The uncertainty principle is actually a non-existence principle. When the position information exists the momentum information isn't uncertain, it just outright doesn't exist.