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It is implied, per QM, that the behavior of subatomic particles cannot be precisely predicted. However, these indeterministic effects do have defined probabilities. By the law of large numbers, they can “average” out and result in approximately deterministic laws.

For this reason, I presume, we can predict with pinpoint accuracy whether or not atleast some kinds of events will happen in the macro scale even if we can’t know their minute details on a subatomic level.

The question then is how fine or loose grained of an event is predictable given all knowledge about antecedent conditions. And how antecedent must these conditions be?

Suppose I woke up today at 9 AM and ate toast for breakfast. If I were to know everything that could be possibly known about the configuration of the universe right after the Big Bang, is this event predictable? Can one say, given that knowledge, with assuredness whether or not this will happen?

  • "By the law of large numbers, they can “average” out and result in approximately deterministic laws." This doesnt really make sense. The law of large numbers tells us, that if we repeat an experiment over and over again, then the average value of the outcome will converge to the expectation value. In this case, repeating the experiment would mean to restart the universe in the same configuration right after the big bang wait for a fixed time and then check if you ate toast for breakfast and then restart. But that wouldnt make it deterministic. – jd27 Sep 15 '23 at 11:47
  • Well how else do deterministic laws come about? There is still some sort of averaging or percolating factor, no? –  Sep 15 '23 at 11:49
  • Which deterministc laws are you talking about? – jd27 Sep 15 '23 at 11:55
  • Laws like F = m*a –  Sep 15 '23 at 11:57
  • But such laws are not strictly valid (this is why QM exists) in all cases. And quantum effects do have macroscopic results. For example the stability of matter. – jd27 Sep 15 '23 at 11:59
  • IDK whether the universe is deterministic or not, but if it is, then all you would have to do is build a perfect simulation of it, and let that run for 13.8 billion simulated years, and sure enough, you would be in there eating your toast. I don't have any reason to think that there could be any simpler way to "predict" your toast eating episode though. – Solomon Slow Sep 15 '23 at 12:07
  • We do not have a physical model for the whole universe, at all scales, for its whole history. So the answer, practically speaking, is clearly "no". Now, having followed your current stream of questions, I guess you mean this in principle. Then the question amounts to "is physics intrinsically determinist?", which makes it a duplicate of https://physics.stackexchange.com/q/63811/109928 – Stéphane Rollandin Sep 15 '23 at 12:46
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    Does this answer your question? Is the universe fundamentally deterministic? – Stéphane Rollandin Sep 15 '23 at 12:46
  • Consider that once you build your simulator, you'd expect it to not only predict your toast-eating habits, but also predict your building the simulator, and the outputs of the simulation, and that the simulated simulator would also be expected to predict the building of the simulator and its outputs, and so on... – The Photon Sep 15 '23 at 12:52
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    Does this answer your question? Is the universe fundamentally deterministic? – anna v Sep 15 '23 at 13:15

2 Answers2

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When thinking about the entirety of the Universe in terms of QM you will very quickly run into paradoxes. That's why I don't think we are at a point when your question can be meaningfully answered. For instance, the Universe is by definition a closed system (there is nothing else but it). So it must be in a pure state. Therefore its entropy must be zero ${\it always}$. How does this agree with the Second Law, the most obvious physical law out there?

John
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  • "For instance, the Universe is by definition a closed system (there is nothing else but it). So it must be in a pure state. Therefore its entropy must be zero always ." By your theory any (perfectly isolated) gas (closed system) has zero entropy too (which does not conform to mainstream physics). Entropy measures our lack of knowledge of a systems current state, not the systems state itself. And so if we have perfect knowledge of a systems state, then the entropy will always be zero, but there is no contradiction. But this does not have anything to do with the system being isolated. – jd27 Sep 15 '23 at 12:15
  • The (von Neumann) definition of entropy in QM is $S=-Tr{ \rho \ln \rho}$. You can check it is zero for any density matrix that corresponds to a pure state. This is as mainstream as it gets. – John Sep 15 '23 at 12:18
  • the density operator $\rho$ is an encapsulation of our knowledge of the system. We asign probabilities to different quantum states based on our beliefs. – jd27 Sep 15 '23 at 12:19
  • In a pure state $| \psi \rangle$ the probability of that state is 1 by definition. – John Sep 15 '23 at 12:20
  • Indeed. But how is that related to anything i have written? Next you gonna write that being in a pure state implies that $S=0$? I am aware. If you knew with certainty that the universe is in the state $|\psi \rangle $, then the universes entropy would be $0$ and there would be nothing wrong with that. The same thing is true for an isolated gas as well. There is no contradiction. – jd27 Sep 15 '23 at 12:29
  • The Universe could be in a mixed state, at the Big Bang, such that the density matrix isn't pure. How do you know that it's a pure state? What physics imply it must be? A closed system could be in a mixed quantum state. And why is the Universe a closed system? If it's infinite in size, you could also consider it to be "open" by definition. You don't know the state of the universe at the boundaries. – Cham Sep 15 '23 at 12:35
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    @Cham Any system is in a (pure) state at any time (by definition). A mixed state is just one where we do not know the state of the system and therefore asign probabilities to different states, that we think are likely for the system to be in. Clearly OP is assuming that we have knowledge of the state of the system at (or shortly after) the big bang. Obviously how usual QM applies to the whole universe is another question. – jd27 Sep 15 '23 at 12:47
  • @jd27, this is false. Any system could be in a mixed state because of interaction with another part (if the system is "open", and the universe could be open if it's infinite in size). It could also be in an initial thermal state at some time, and stays mixed after evolution. The evolution could also renders a pure state to become mixed, if the hamiltonian contains some unknown parameters. There are many ways a system could be in a mixed state and the probabilities of the pure state could be unavoidable. There are tons of papers about this, especially in quantum computing. – Cham Sep 15 '23 at 12:59
  • @jd27 But you cannot really isolate any part of our world from the rest completely, down to the exponentially small factors. So you can always say that some ignorance "creeps into" your gas vessel from outside, thus erasing some phase information. Over time this arbitrarily small perturbation will grow exponentially and voila you have finite entropy. But this trick would not work for the Universe in total, as there is nothing external to the Universe, whose degrees of freedom could be traced-out to give a mixed-state-density-matrix. – John Sep 15 '23 at 13:02
  • @jd27, mixed states are more fundamental than you think. Pure states aren't sacro-saint in Quantum Mechanics, and the "classical" probabilities that are assigned to the pure states could also be of quantum origin. So it's not just about mixed state is just one where we do not know the state of the system and therefore asign probabilities to different states. These probabilities are more fundamental than what you think. – Cham Sep 15 '23 at 13:04
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I can't help but think of such things as the weather and the large amounts of money spent on hardware and software. In the UK the BBC spent £1.1 Billion on a supercomputer project. This is, of course only one project.

Wikipedia (Numerical weather prediction) says “Manipulating the vast datasets and performing the complex calculations necessary to modern numerical weather prediction requires some of the most powerful supercomputers in the world.”

It is difficult to predict short-range forecasts though it is easier than looking at the longer range which gets so much harder. We are only talking of days and weeks.

Your question spans approximately 14 billion years. Thinking about this on a QM scale would involve an inordinate amount of variables and calculations. Our present skills and understanding of maths and physics (QM) seem to fall far short of being able to compute such a problem.

DrJay
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