Wednesday, May 13, 2015

No particle upon a quantum field means no information

Backreation promotes a paper,
Information transmission without energy exchange
by Jonsson, Martin-Martinez, and Kempf, which claims that in 1+1 (exception), 2+1, 4+1, and other odd dimensions, and in curved spaces, the information may be transmitted by a massless quantum field without any exchange of energy. Moreover, the signals move much slower than the speed of light and the communication involves production of no quanta in the field.

The authors play with some subtle "defect" of the Hyugens principle in odd dimensions (and other spaces) and they try to convert this "strange thing" into "other strange things". A problem is that their claims are not right.

First, the communication always involves heat generation. The most beautiful original piece of work about this very principle was written by Rolf Landauer in 1961,
Irreversibility and heat generation in the computing process
He worked in IBM and the brilliant article was actually published in the IBM journal. If you're told that big corporations can't fund beautiful pure science, think about this work at IBM – and many other great advances done by IBM, Bell Labs, and others.

I think it is refreshing to read the abstract of Landauer's paper because it sounds rather clear. Operations of a computer inevitably involve some logical irreversibility. The logical irreversibility must translate into the physical irreversibility of the system that does the computing. And physical irreversibility really means "heat generation". If you need to erase one bit of memory, for example, you have to produce at least \(E\geq kT\cdot\ln 2\) of energy.

The argument of the logarithm is \(2\) because I discussed "bits" which have two possible values. You may imagine that the information is expressed in a more natural way – in \(e\)-digits, if you wish – and \(\ln 2\) is then replaced by one. And the energy is proportional to \(kT\) for dimensional reasons. The energy has units while the information in bits doesn't, so there has to be a conversion factor. If you cool your computer down, you may limit the heat generated by the erasure of one bit.

Landauer's principle is a bit controversial. Most of the opposition is just silly. But there's some freedom about "how you exactly add or subtract the useful information to/from the entropy". Depending on the choices, the "heat generation" occurs at different stages of the computation process. But "something like this principle" simply has to be right. Jonsson et al. don't discuss these matters – insights by Landauer, or those by Leo Szilárd and others – at all even though it is clearly important to understand the heat generation in any manipulation with information.

Instead, they focus on the properties of the classical massless fields. They try to reformulate these properties in the language of quantum field theory but what they end up is weird. Their strategy for the sender is to entangle the state of the field with the transmitted information. And they say that in this way, there will be no quanta going in between A and B.

However, in weakly coupled quantum field theory, all asymptotically vacuum states may be written as linear combinations of states with different quanta or particles. And the state without any quanta or particles is unique, the vacuum itself, which means that it can carry no information.

Like most other people who "misinterpret" quantum mechanics, they seem to be confused by Bohr's complementarity. Indeed, one may measure different observables \(L\) than the "number of particles in particular one-particle states", such as the fields at given points, \(L=\phi(x,y,z,t)\). However, if \(L\) was measured and it doesn't commute with \(N_a\), then one mustn't make claims about \(N_a\) at the same moment. However, the claim that "there are no quanta involved" is a claim about \(N_a\) – namely \(N_a=0\). Such a claim can't be made simultaneously with the claims about the measured information about \(L\) because of Bohr's complementarity or Heisenberg's uncertainty principle.

It's pretty much the same mistake that all the "realists" are doing all the time. They are imagining that they can assign truth values to all questions that could be in principle answered by experiments. (In some way, they give answers "No" or "zero" to all the other questions that were actually not addressed by the measurement.) But quantum mechanics prohibits that. If one assigns classical truth values (or real values) to some operators, one can no longer assign truth values (or real values) to "complementary" (not mutually commuting) operators and questions they represent. Instead of the correct statement that "the value of \(N_a\) isn't determined if one measures \(L\) instead", they say that it is zero which is just wrong.

Even though the Hilbert space of the (free massless) quantum field theory may be described in terms of many other bases, not necessarily just in terms of the occupation number eigenstates basis, it is still 100% correct to say that if there are no excitations anywhere, we deal with the vacuum state which is always exactly the same and cannot transmit any information.

Whether the "irregular" behavior of Hyugens' principle in odd spacetime dimensions leads to important conclusions is debatable. The commutator of the massless field with itself is only nonzero on the light-cone separation in 3+1 dimensions (and other flat, even-dimensional spacetimes). However, in odd spacetime dimensions, the commutator is nonzero everywhere inside (in the timelike-separated part of) the light cone. Note that for spacelike separations, the commutator always has to vanish by causality. This obviously means that in 2+1 dimensions etc., some "responses" may occur at a later time than when the light (moving by the speed of light) gets from A to B.

But those things are well-known, intrinsically classical facts about the propagation of waves in different spaces. They don't change the fact that when a quantum field is used to transmit the information, one must allow states of the quantum field with nonzero occupation numbers. Even slowly changing "classical" waves are coherent states i.e. superpositions of states with different quanta (excitations), although possibly ones with very low energies/frequencies. And they don't change the fact that the heat \(kT\ln 2\) will have to be emitted per each bit at some point of the "learning and forgetting cycle", as Landauer taught us. One may reduce the heat generation by reducing the frequency and/or the temperature of the gadgets but one can't make it fundamentally zero.

What I wanted to complain in the previous paragraph is the authors' suggestion that quantum fields may go "beyond" quantum mechanics and circumvent some general laws, e.g. Landauer's principle. But a quantum field is just another quantum mechanical system – one obeying all postulates of quantum mechanics ("Copenhagen school" postulates, if you wish). Quantum field theories form a subclass of quantum mechanical theories but they can't get any exemptions from the laws – like the statistical physical ones or thermodynamic ones – that are valid in all quantum mechanical theories. After all, you may always "emulate" a quantum field by a collection of particles or springs with some appropriate interactions included in the springs etc. The whole idea that quantum field theories (or quantum gravity) provide us with exceptions to general laws of physics is misguided.

So the whole combination of topics and ideas outlined by Jonsson et al. is just one big confusion composed of several smaller random confusions which neglects the actual physical laws that govern such processes.

Another insane paper on the Boltzmann Brains

This paper by Jonsson et al. is still excellent if compared to a new preprint about the Boltzmann Brains that was allowed to be posted to hep-th. Sorry, Paul Ginsparg et al., but you are failing as moderators of the archive. The preprint offers a solution to a non-existent problem of the Boltzmann Brains by making vague claims about some ill-defined would-be interpretation of quantum mechanics (many worlds) combined with some assertions about the de Sitter space that are wrong in any interpretation.

The Boltzmann Brain problem is non-existent (in any classical or quantum model) because there is no reason to think that "the infinitely many thermal fluctuations that locally look like our brain" are equally likely to be "us" as the "proper brains that have evolved from a legitimate Big Bang via evolution and natural selection". We are simply the latter, not the former. The cosmology and biology shows that and the cosmology and biology really follow from the fundamental laws of physics when done correctly. I've written numerous clear posts showing the spectacular logical defects that lead people to talk about this nonsense of "Boltzmann Brains" as if they were a real issue.

Similarly, ideas that "the many worlds interpretation" saves us from some "paradoxes" is absurd as well. It is a source of paradoxes, not a positive contribution to physics. Morever, the key claims in this paper that the Many Worlds Interpretation produces a perfect equilibrium are the opposite of the truth, too. If this interpretation adds something, it's the idea that there is never a "full-fledged equilibrium state" because "new worlds" still have to branch and be created.

Finally, all of their claims about the de Sitter space are completely wrong. It can't be given by a unique pure state. De Sitter space carries the huge entropy \(S=A/4G\) derived from its cosmic horizon of area \(A\), much like a black hole. So the empty de Sitter is analogous to a black hole – an object with a huge degeneracy of exponentially many microstates that are macroscopically indistinguishable.

You may feel some deja vu.

So the preprint a "solution" to a non-existent problem based on a random combination of claims from about 5 different fringes of theoretical physics, claims that are demonstrably pushing the "problem", whatever it is, almost exactly in the opposite direction than what is advertised. The arrogance allowing someone to send this stuff to leaves me speechless.

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