Where does the energy to erase information from the universe come from?

Question

Landauer's principle states that erasing information costs energy, and only a reversible system can keep processing information without external energy input.

Consider the whole universe as an information processing system. The universe doesn't seem to be reversible - quantum physics is irreversible (= erases information) in principle and classical (non-quantum) physics is irreversible in practice (and perhaps in principle as well).

Where does the energy to erase information from the universe come from?

Comments

I am bumping this up because I would like to hear an answer from someone who agrees with "quantum physics is irreversible in-principle" (because of the collapse of the wavefunction upon measurement).

Answer 1

Quantum physics is not irreversible in principle; it exists in both a conservative form (Schroedinger, Heisenberg, or von Neumann equation) and in a dissipative form (Lindblad equation). Usually, the latter is considered to be a coarse-grained limit case of the former; only a minority of physicists holds the view that irreversibility is intrinsic.

Irreversibility in the universe as a whole is most likely a property for the universe's view of each particular observer only. Information does not disappear on a fundamental level, but moves to less and less accessible degrees of freedom - either at very short distance (responsible for the fact that locally, it can be described well by hydromechanics) or at very large distance from the observer (receding beyond its light cone). 

Thus all theoretical and experimental facts known are consistent with the view of a conservative dynamics of the universe as a whole.

added Nov.1:

Note that collapse and the irreversibility associated with it is not part of the rules of quantum mechanics itself but only of its interpretation in terms of measurements. It is not needed to model or explain the dynamics of a quantum system. Collapse solely happens upon measurement - since measurement is done by an observer roughly localized in space It is this localization that,through scattering to far away places, results in a loss of both information and energy.

But the universe as a whole cannot lose anything through scattering, since it is a closed system. (Indeed, it is the only closed system containing us.)

Comments

@ArnoldNeumaier re "Quantum physics is not irreversible in principle." - Thanks, this assumption does answer the question (I am unable to upvote your answer at the moment, probably because I joined recently and don't have enough karma). If information does not disappear at a fundamental level, then there is no need to ask where the energy to erase information comes from.

However, I question your assumption. My understanding is that 1) collapse erases information, and 2) this is actually the consensus view at the moment. Please correct me if I am wrong. We can't rule out existing collapse-less interpretations of quantum physics, and I guess new collapse-less interpretations will emerge, but my understanding is that the current majority view of quantum physics includes collapse and fundamental irreversibility.

By the way, this wasn't the question about fundamental randomness that we anticipated in the other thread. I will formulate that question today.

---

@ArnoldNeumaier - see related question: http://www.physicsoverflow.org/33923/is-quantum-randomness-fundamental

---

@GiulioPrisco: I augmented my answer to meet your objections.

---

@ArnoldNeumaier, thanks for the update. Re "collapse and the irreversibility associated with it is not part of the rules of quantum mechanics itself but only of its interpretation in terms of measurements."

But it is, because you need it to predict experimental results. If, according to the equations of quantum physics, a spin can be up with probability a and down with probability 1-a, you will measure it up or down with frequencies a and 1-a. That is a fact.

Yes, collapse seems an ad-hoc trick, "something else" that must be added to the "real" rules of quantum physics to make sense of observations, but quantum physics doesn't seem to work without collapse.

"Regarding Ψ as describing the 'reality' of the world, we have none of this indeterminism that is supposed to be a feature inherent in quantum theory'-so long as Ψ is governed by the deterministic Schrodinger evolution. Let us call this the evolution process U. However, whenever we 'make a measurement', magnifying quantum effects to the classical level, we change the rules. Now we do not use U, but instead adopt the completely different procedure, which I refer to as R, of forming the squared moduli of quantum amplitudes to obtain classical probabilities! It is the procedure R, and only R, that introduces uncertainties and probabilities into quantum theory. The deterministic process U seems to be the part of quantum theory of main concern to working physicists; yet philosophers are more intrigued by the non-deterministic state-vector reduction R (or, as it is sometimes graphically described: collapse of the wave/unction)."
(Roger Penrose, The Emperor's New Mind)