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In absence of the observer any system undergoes unitary evolution, that is reversible evolution without entropy change.

It is believed that the initial state of the universe had very low entropy, possibly, zero.

So the entropy of the universe grows only in interaction with the observer, i.e. in the process of wave function collapse.

But the total amount of entropy in the universe characterizes the amount of information stored there (and needed to describe the state).

As such it turns out that the wole information stored in the universe comes from the interaction with the observer. The observer serves as the channel which swells the universe with its content from outside.

Am I correct?

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    $\begingroup$ @Ján Lalinský no, the entropy of the universe increases because the observer becomes entangled with the observable. $\endgroup$ – Anixx Apr 19 '14 at 11:14
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    $\begingroup$ Can you please provide some reference to this? $\endgroup$ – Ján Lalinský Apr 19 '14 at 19:48
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    $\begingroup$ In absence of the observer any system undergoes unitary evolution, that is reversible evolution without entropy change. Not true. $\endgroup$ – user4552 Aug 19 '14 at 0:43
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    $\begingroup$ @Ben Crowell Why is it not true? $\endgroup$ – David Herrero Martí Oct 19 '16 at 9:19
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    $\begingroup$ @BenCrowell, isn't your assertion "Not true" in conflict with the no-hiding theorem? [arxiv.org/pdf/1004.5073.pdf] and [arxiv.org/pdf/gr-qc/0603046.pdf]? $\endgroup$ – S. McGrew Jun 20 '18 at 13:00
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When people say that "unitary time evolution does not change the total entropy" and "entropy increases over time", they're talking about two different kinds of entropy in the two sentences. If the entire universe is in state $\rho$ and its time evolution is given by the Schrodinger equation, then its "total entropy" $S = -\mathrm{Tr }(\rho \ln \rho)$ is constant over time. But when people talk about entropy increasing over time in a closed system, they mean the internal entropy of its spatial subsystems. That is, if you take a spatially contiguous subsystem $A$ of the entire universe and form its reduced density matrix $\rho_A$, which acts on a smaller Hilbert space than $\rho$ does, then its entanglement entropy $S_A = -\mathrm{Tr }(\rho_A \ln \rho_A)$ will generically increase in time, even as the total entropy remains constant.

More roughly, the different spatial pieces of the universe get more and more entangled with each other, increasing the "internal, relational" entropy, even as the universe as a whole does not grow any more entropic. A strange fact of quantum mechanics, which does not occur in classical physics, is that the entropy of a subsystem can be much greater than the entropy of the entire system, so this process can continue indefinitely.

All this can be done entirely through Schrodinger time evolution, with no need for collapse to be invoked at all. Depending on your interpretation of quantum mechanics, collapse may cause an increase in entropy, it may result from an increase in (entanglement) entropy, or it may not occur at all. But it isn't logically necessary to explain (internal) entropy increase.

I personally like to think of all entropies as being "relational" entanglement entropies between subsystems. In this interpretation, the "internal" entropy is the entropy between two different spatial pieces that partition the entire universe. The "total" entropy can formally be thought of as the entropy between the universe and "everything else", although obviously if the "thing" is the universe then there are some obvious conceptual difficulties with exactly what we mean by "everything else". But the point is that entanglement builds up between the different pieces of the universe, but no entanglement ever "leaks out" to connect anything inside the universe with anything outside. (How could it? There's nothing outside the universe to get entangled with.)

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    $\begingroup$ By talking about "different spatial pieces of the universe" and "subsystems", aren't you implicitely introducing observers? Else, who decides what a subsystem is? $\endgroup$ – Stéphane Rollandin Jun 20 '18 at 19:46
  • $\begingroup$ I second the previous comment. This answer is technically correct but trivial. If we take an observer, from his point of view entropy of the (observable to him) universe increases as he gets entangled with matter (and does not encrease when he is isolated from other matter), is not it? $\endgroup$ – Anixx Jun 21 '18 at 1:15
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    $\begingroup$ @StéphaneRollandin I don't really understand your objection. A "subsystem" is simply any spatially connected patch of space. To define notions of connected, all you need is for your spacetime to have a point-set topologically, which is observer-independent and automatically implied by the spacetime's manifold structure. There's nothing subjective about what counts as a subsystem. $\endgroup$ – tparker Jun 21 '18 at 2:55
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Many of these particles do not have/exhibit any of these characteristics except during the act of observation therefore there is little or no entropy except during the measurement of position, spin, velocity etc....in other words position, spin, velocity ...these properties are not present except when measured.

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Observer, if you assume as someone watching the experiment or activity, is plainly wrong. Anything that can be detected and measured and thus, in principle, from infinitely hard calculation can tell us about the past or previous states, can be said to be information, and thus, entropy increased while the process was being carried out. Take for example, a box with 10^23 atoms. We can't know exactly the current state of the box and retrace it's pretty bcoz of our humanly limitations, but we can randomly guess some things about its past. So nature did take all the things into account to take the system towards its future, increasing entropy at the same time. Our actions themselves are physical actions and increase entropy. Your initial statements are incorrect. Entropy must increase, I guess, even when the system does not collapse. If quantum theory is a complete theory, even our decoherence process (measurement) can be explained quantum mechanically. How does the entropy increase in that case?

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No.

Decoherence. No observer necessary.

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  • $\begingroup$ Decoherence without observers is impossible. Even if possible somerthing resembling decoherence, it will not make the evolution non-unitary. $\endgroup$ – Anixx Apr 19 '14 at 1:40
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    $\begingroup$ But what comprises an "observation"? Clearly, the quantum world doesn't sit around and wait for some sufficiently highly conscious being to perform a measurement before decoherence ensues. It would have to be some sort of interaction that doesn't care about the "observer"'s mind state. $\endgroup$ – Thriveth Apr 19 '14 at 12:00

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