Certainly. One of the most fundamental philosophical questions is about the nature of time, precisely because all of our "laws" of physics are time reversible, so from the perspective of physics time doesn't really exist or is just a space-like dimension (no arrow). And so the Universe should be perfectly deterministic and with enough computing power and precise enough knowledge of the initial conditions everything should be perfectly predictable and the future should be "fixed". In some way or another probably most of philosophy is arguing about whether or not this is true and what it means.
This paper claims that 5% of 3-body systems in the Universe can't be predicted even in principle, because you would need to measure initial conditions to greater precision than the planck length, which is impossible. And of course N-body systems where N > 3 are even more unpredictable, and the whole of the Universe is an N-body system, so if correct it would mean the end of determinism.
For a good treatment of this topic for a lay audience see Lee Smolin's recent book "Time Reborn".
> And of course N-body systems are even more unpredictable, and the whole of the Universe is an N-body system, so if correct it would mean the end of determinism.
I read this as the systems are, for all intents and purposes, practically unpredictable, not fundamentally unpredictable.
Just because we can't measure beyond the plank length doesn't mean there aren't deterministic rules down there.
So my take is that the universe could still be deterministic, but that can't be knowable to us since we'd have to be able to peer below the plank length.
Just to go back to the philosophy thread, this is one of the things that made Kripke famous (relatively speaking, philosophically speaking): a priori "knowability" or predictability is not the same as determinism.
You can have a system that is perfectly deterministic, but with outcomes that are a priori unknowable, in the sense of being unpredictable. Kripke didn't use this language, but if the information required to compute the prediction becomes unattainable, either because of capacity or input requirements, you can't make the prediction.
I think there's some very abstract computability theorem in computer science that's more recent that came to a similar conclusion. I think that came at it more from the sense of the amount of change in inputs that would pass during the time it took to simulate a system makes it impossible to perfectly simulate things past some point.
These aren't examples in physics, but they speak to how determinism per se isn't necessarily the same thing as predictability.
Indeed. The evolution of the universal wave function as described by the Schrödinger equation is perfectly deterministic. If you believe in that as the fundamental description of reality (which also means not believing in wave-function collapse), the result is the many-worlds interpretation of QM. Similarly, hidden-variable theories are deterministic.
> It is arguably strongest in explanation, in the sense that it relies on the least amount of assumptions (just the Schrödinger equation).
It really seems like Physicists day this because they want it to be true, not because it's actually true.
I completely understand they don't like the idea of non-local hidden variables (I mean programmers don't love them much either) - but the idea that a non- local variable is somehow more complex than an infinitely dividing universe breaking into infinite copies and exploring all possible paths at all possible times relies on fewer assumptions or is simpler is just laughable to me. Maybe I'm just not getting it, but it really seems like a way of redefining the rules of a game until the preferred party wins.
"Hey we have this compression scheme that's incredibly fast. It's only a constant time lookup." "Really? How do you do that?" "Well we store and index all possible inputs." Won't some outputs be longer due to pigeonhole principle?" "Well actually in one single encoding it would, but we store an infinite number of different encodings of all possible inputs, meaning in at least one of the encodings it's smaller and just use that one." "So you store infinite variations of infinitely sized data and as a result claim your compression scheme is simpler?" "Yes because when we go to decompress we spawn an infinite number of threads and each thread decompresses by following one of the encodings, and in that thread's view it's just a constant time lookup to store the index which is clearly smaller (so compressed) and constant time to reverse and decompress." "And what about the complexity of the infinite threads with infinite copies of infinite storage?" "Ah we don't count that, we only count the world line of the successful thread."
I think you're confusing simplicity with computational cost.
Bubble sort is simpler than quicksort. It is also more computationally expensive.
Universal wave function theory is simple in this sense. (IMHO the term many-worlds is doing the theory a disservice because it's fundamentally misleading. There is only one world, we just can't perceive most of it. Which is as it has been for all of humanity's existence.)
The many-worlds interpretation isn't deducible from just the Schrödinger equation.
The Schrödinger equation roughly predicts that if you put two detectors at the two possible positions where a light beam can go after a beam splitter, and fire a single photon at the beam splitter, both detectors will detect some "amount" of the photon*. However, what you actually see in experiments is that one of the detectors detects a single photon, and the other detects 0. However, you also notice that if you repeat the experiment many times, the probability of detection is exactly equal to the square of the modulus of the amplitude of the Schrödinger function for that state.
To explain this observation, the MWI uses an extra assertion: that each "world" contains a single result, but that the number of "worlds" where the state is X corresponds to the square of the modulus of the amplitude of the Schrödinger function for that state. So, if doing simple frequentist probabilities over these "worlds", your chance as an observer to be in a "world" where the state is X is equal to that value, as the experiments observe.
Note that this assumption is exactly the same assumption as the wave function collapse, known as the Born rule.
* the Schrödinger equation actually predicts something more esoteric than even that: for any two complementary solutions X and Y, there is an infinity of additional solutions of the form aX + bY, with a and b real numbers with certain properties. So, in fact, it is actually impossible to use the Schrödinger equation to predict any particular state. You have to use the Schrödinger equation and a chosen basis of measurement, and only look at the solutions in that basis. The simple idea of "counting worlds" from above mostly breaks down at this stage - you need an additional third assumption of assuming a pre-existing "background" and using Decoherence to explain why only certain solutions normally manifest.
Consider a sealed room with an experimenter looking at a box with Schrödinger's famous cat in it. The question we usually ask is whether the cat is alive, dead, or in a superposition before the box is opened.
Schrödinger's famous equation predicts that if the cat itself can be described by quantum mechanics, then it must be in a superposition. If the experimenter can be described by quantum mechanics as well, then the experimenter must also go into a superposition upon opening the cat's box. And, thanks to thermodynamics, there is no experiment that is doable by the experimenter from which the existence of collapse can be demonstrated.
Therefore the claim that there is a collapse at all is an entirely unnecessary hypotheses. All other interpretations of QM have to invent explanations for an event (collapse) that no experimental evidence exists for.
That's all well and good, but it then predicts that all possible outcomes have equal probability, and this is measurably false.
Say you design the experiment such that the observer will see the cat is alive if 2 particles both have spin up, and dead if any particle has spin down. Say the Schrodinger equation will assign equal amplitudes to the 4 possible states (up-up, up-down, down-down, down-up), and let's ignore the composite states (e.g. 1/sqrt(2)up-up + 1/sqrt(2)up-down). So, the cat-alive (up-up) state has an amplitude which is 3* the amplitude of the cat-dead state (up-down + down-up + down-down).
In a naive interpretation of MWI that only used the Schrodinger equation, there are two versions of the observer, so the probability that the observer sees one outcome versus the other is obviously 1/2: you either happen to be the version that sees the cat alive, or you happen to be the one that sees it dead. This reasoning will work if we repeat the experiment many times: since the repetitions are independent, if I repeat it 10 times, I expect that I will happen to be one of the observers who sees the cat alive about 5 times, and dead about 5 times as well. In your interpretation, the amplitude of the Schrodinger equation is irrelevant, as long as it is greater than 0: all possible events happen.
If I actually do the experiment though, I will see the cat alive only about 2.5/10 times, since the total amplitude of the wavefunction for all states where the cat is alive is much lower than the total amplitude of all states where the cat is dead.
So, the actual MWI says that, while there are two kinds of worlds, they are not equally likely. In the multitude of all worlds, the prevalence of worlds where the cat is alive is proportional to the wavefunction amplitude of the cat-alive state (about 1/4) and the ones where the cat is dead follows the same logic (about 3/4). So, given that I am one observer in one of the many worlds, the chance I am the observer in a world where the cat is alive is only 1/4.
But this connection between the number of worlds and the amplitude of the wavefunction is an additional assumption atop the Schrodinger equation. Sure, the wavefunction doesn't collapse, but it splits according to the exact same formula as the collapse in the CI (Born's rule).
And I again want to mention that even this is not enough. If |cat-alive> and |cat-dead> are solutions to the Schrodinger equation, then so is x|cat-alive>+y|cat-dead>, for an infinite number of x and y real numbers. The MWI has to explain why no observer ever actually perceives such a state (how this state would look like to to an observer is not even definable). Decoherence solves this, and it was an extremely important contribution, but it also adds an additional assumption (that CI also needs): some pre-existing classical-like background.
Yes, you can construct a naive version of the MWI that produces answers in disagreement with experiment. But that naive version of the MWI also doesn't match the predictions of attempting to model both cat and experimenter with QM.
This is the essence of a straw man argument. OK, your ridiculous version of the theory doesn't work. Now what happens if you look at the actual theory under discussion?
My point is that the actual version of the MWI requires the Born rule (which can't be derived from the Schrodinger equation, and which is also known as the measurement postulate) just as much as any other interpretation.
I wasn't building a strawman, I was trying to explain why the simple explanation you had given in the previous post (which is the commonly presented explanation of the MWI in many popular channels) doesn't actually work. You were the one who was claiming that the MWI simply says that the observer is in a superposition itself, which is indeed what the Schrodinger equation predicts. But this entirely leaves out the other half (why does the observer in fact observe a single outcome , with some probability X) and I was explaining how the same maths as the oh-so-hated collapse sneak back in through there.
Basically, the MWI and the CI agree that from the point of view of the observer something happens when the observer opens the box which they can't predict deterministically. The collapse versions of the CI say that this event actually changes the wavefunction, it collapses it, and all other possible results don't happen. The MWI says that this is just how it looks like to one observer, and all other results happen to other observers, in a very precise proportion. The "shut up and calculate" version of CI says that it's unscientific to even discuss this distinction, since a single observer anyway observes a single thing, talking about observations that didn't happen and how real or false they are is unscientific speculation.
You've said nothing suggesting that the explanation doesn't work.
Whether you believe in collapse now, collapse later, or collapse never but the Born rule works, you get the same exact predictions. Therefore no experiment done to date represents evidence that there actually is a collapse. And evidence that the experimenter is modeled by QM is evidence against a collapse. This is all true, and is all verifiable from QM.
And whether collapse handles later or never, the math behind the MWI explains why we'd think we'd observed what we observed in the absence of a collapse.
"Fundamentally"as in "QM forbids this". If our universe were different, a simpler kind which Laplace dealt with, it could be completely predicable, as theories of 18th century stated.
>'One of the most fundamental philosophical questions is about the nature of time, precisely because all of our "laws" of physics are time reversible'
Many of our theories are, but the thing is we have several direct observations of time reversal symmetry violation (below), independent of the experimental demonstrations of CP violation which also imply T-Symmetry violation.
Yes! This is important. It's a finding from 1964, nearly 60 years ago, and it is included in the Standard Model of physics.
One interesting thing is that unlike the other discrete symmetries, we haven't found a system that has a large Time-reversal symmetry violation. Not having a large enough source of T-violation is actually one of the major problems with the SM!
The universe is not an N-body problem. Because we have things behaving like waves. Which are much harder to simulate. We can't even simulate a 2-electron collision precisely.
So this would be a totally separate source of indeterminism than quantum mechanics. So you could have a schrodinger's rocket fired at a indeterministic 3-body system which means multiple sources of indeterminism interact.
Entropy could be viewed as the simple addition of information due to indeterminism.
How can causality survive in a universe like that.
That only matters if you assume infinite measurement accuracy, and the scientific method has never assumed that.
Even if we assume the world is 100% fully deterministic, as long as our measurements are not 100% accurate we will have some amount of measurement noise which is completely indistinguishable, even in principle, from true fundamental randomness.
In fact, fundamental randomness is much easier to work around than measurement noise, since there is no risk of it being correlated with your experimental design. In contrast, measurement errors are often correlated to the measurement method, which makes them much harder to eliminate statistically.
Doesn't the Turing halting problem also imply that (some) things are not predictable (the halting of certain algorithms)? But I don't think that interferes with causality.
Causality in physics survived the discovery of quantum uncertainty, though it was changed by it. What parts of current physics would have to be abandoned if our current inability to predict outcomes with complete precision turned out to be fundamental?
A non-deterministic universe can have two kinds of events: caused events, and random events. That is, an event can simply happen, but it can also be caused by another event. For example, a ball could start moving on a pool table all on its own (random), but still any ball that is hit by another ball would start moving because of the impact (caused).
If the fully random events are rare enough, you can even still determine causality using statistical tests, just like we do today. Of course, you can never be 100% certain, but that is to be expected. This is anyway how experimental science worked even when the world was assumed to be 100% deterministic: true randomness is not really different to experimental science than measurement noise.
Note that this is not an actual physical experiment - it only works with an infinitely accurate and smooth shape of the dome, which contradicts all of the models of how matter exists at least since the ancient greeks. Any dome made up of atoms, even if arranged perfectly accurately up to the position of each individual atom, does not exhibit any kind of non-deterministic behavior in classical mechanics.
