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I'm reading Sabine Hossenfelder's new book Existential Physics, where she explains that because fundamental laws are time-reversible, we need an explanation for the arrow of time. Why is that exactly? Why can't we just say that fundamental laws are time-reversible, and there exist an arrow of time, where's the contradiction here?

EDIT: I'm wondering if this is not backwards reasoning. Physics is about explaining natural observations, so any theory would have to be compatible with the natural observation that time flows towards the future. But there's no condition that it shouldn't explain more than the observed or that it shouldn't explain things in regimes that hasn't been observed in the natural world. Time reversibility of physics equations could just be a feature of the mathematics, while it's a necessary condition that the maths accounts for the flow of time in the direction we observe, we don't know if it makes sense to take seriously the case where time flows backwards. Sure the fundamental laws work the same if we invert the flow of time, and it's very useful, but why should it be considered real? It almost sounds like a mathematical-realist view, which I know Sabine doesn't subscribe to.

qleguennec
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  • @user330563 the answer of your question might be, "because there is an arrow of time" – qleguennec Aug 11 '22 at 10:16
  • It's a good question, but I think it has already been raised + answered in https://physics.stackexchange.com/questions/285307/is-this-an-adequate-resolution-of-the-paradox-of-the-arrow-of-time – Ruben Verresen Aug 11 '22 at 10:16
  • OK, but let me rephrase. Lets imagine that the fundamental laws were not time - reversible. Then, plausibly, we could explain irreversibility of macroscopic processes by reduction to irreversible microscopic processes. The arrow of time would come ready with a neat explanation. That is what I take her to mean. – user330563 Aug 11 '22 at 13:10
  • (global) Entropy defines time: dS/dt > 0 – planetmaker Aug 11 '22 at 17:31

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We would like to understand whether or not the time arrow is consequence of fundamental laws or, better, of the initial conditions of the evolution of a single system or the entire universe.

It is quite weird that some phenomena, in principle permitted by the fundamental laws, do not take place in practice in our world. Or maybe they take place but with a negligible probability. Why?

Ok, we may assume that there is an arrow of time in addition to time-symmetric fundamental laws. But this is just a philosophical statement. How does it really act? What the selection process of phenomena is?

Valter Moretti
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  • But Quantum Mechanics laws already include collapse of probabilities. This means that knowledge about the universe can only be gained in one direction of time. – Ryder Rude Aug 11 '22 at 10:20
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    Yes, in the Copenhagen intepretation. However there are reasons to believe that we would have an arrow ot time at macroscopic level even if classical mechanics were true at microscopic level. – Valter Moretti Aug 11 '22 at 10:31
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    Isn't statistical mechanics enough to show why some events are much more likely to happen in one direction? – Juan Perez Aug 11 '22 at 11:35
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    Indeed...Boltzmann's H theorem is completely based on classical physics. – Valter Moretti Aug 11 '22 at 11:37
  • @ValterMoretti Except Boltzmann's H "theorem" isn't an actual mathematical theorem. It's an illuminating model, but it's not rigorous. https://en.wikipedia.org/wiki/H-theorem#Criticism_and_exceptions – John Doty Aug 11 '22 at 20:17
  • Yes I know, the point I wanted to stress is that it is a remarkable attempt to prove the existence of an arrow of time using only classical physics and relying to the relevance of initial conditions. The issue is however still open. I do not think that irreversibility is a consequence of the collapse postulate by Luders and von Neumann – Valter Moretti Aug 11 '22 at 20:21
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Personally, I do not think the "arrow of time problem" is an independent problem on its own, and is just a rephrasing of the measurement problem. (Although it's a reasonable rephrasing of the measurement problem, which might make it more clear what the problem is.)

From a quantum mechanical perspective, my opinion is that this "arrow of time" connumdrum is just asking "why does wavefunction collapse occur when the equations of QM (without measurement) are unitary?"

Putting it another way: if wavefunction collapse occurs in our perspective then it means that things are moving from being superpositions to collapsing to a specific state. This, in an observer's perspective, happens forward in time and there is no way to undo the measurement or "rewind time" to observe a different collapse possibility. This is basically the "arrow of time problem." Seems like time has a preferred direction, yet Schrodinger's equation is unitary?

But if you are OKAY with the fact that superposition exists and collapse occurs when measurements are made, then there is no "problem of the arrow of time." This "problem" is just asking why there is a perferred direction to the arrow of time, but we've already answered this if we accept that wavefunction collapse occurs.

This is the same problem as the measurement problem: Schrodinger's equation is unitary but when we make measurements it becomes nonunitary, why does this happen?

My somewhat-unnecessary opinion about the measurement problem: My opinion is that these problems are gone if you believe in the many-worlds interpretation. Measurement is just you experiencing yourself in a branch in this multiverse, and there are no longer issues with unitary equations suddenly becoming nonunitary when observers make measurments (only in their perspective does this happen). There are some arguements that the many-worlds interpretation doesn't solve the measurement problem, but I think that is more related to the lack of ability to specify why you end up in what universe (not a problem if you accept it) -- and a tangential problem related to measuring in a particular basis.

Steven Sagona
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    I don't agree with your premise that the arrow of time is a consequence of the measurement problem. If time could be reversed then the effects of measurements would be reversed. The MWI has no bearing on the issue. – Marco Ocram Aug 11 '22 at 14:59
  • @marco, only if MWI exists could time reversing cause the state to become the same, otherwise reversing time would produce a different outcome because of the change due to the collapse due to measurement. – Steven Sagona Aug 11 '22 at 21:17
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Indeed, laws aren't fundamental: experiments and observations are. Physics is not math. We devise models to capture the phenomena. So, we observe that past and future are different, in specific ways. That constrains the models we devise. But, then, to say that those models explain the phenomena is, indeed, circular reasoning.

We need to stop pretending that theories are fundamental. We need stop calling models explanations. Instead of talking about how models explain phenomena, we should talk about how models capture what we see.

John Doty
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