A critique of Adrian Kent's "One world versus many: the inadequacy of Everettian..."

A funny coincidence: many-worlds interpretations are the cover story of New Scientist this week
http://www.newscientist.com/article/dn26267-four-ways-you-can-see-the-multiverse.html#.VCVPb3YcR2E

Adrian Kent tries to refute many-worlds interpretations of quantum mechanics:
http://arxiv.org/pdf/0905.0624v3.pdf
In his paper "One world versus many: the inadequacy of Everettian accounts of evolution,
probability, and scientific confirmation", Adrian Kent aims to show that the many-worlds interpretation of quantum mechanics, first proposed by Hugh Everett, leads to absurdities when one tries to define a "rational" betting strategy for an inhabitant of the multiverse.

Toy multiverses and betting strategies of an inhabitant

In section III of the paper, Kent defines some toy multiverses and discusses possible betting strategies for an inhabitant.

In my opinion, the inhabitants of a multiverse are "robots" created by evolution. They do not have "free will". We have to study them like laboratory mice in a labyrinth. It does not make sense to think about their betting strategies from the viewpoint of an outside observer who sees the whole branching universe of the many-worlds interpretation.

One specific question is if it makes sense for an inhabitant to take a maximum risk in betting, because then he maximizes the win in ONE branch of the multiverse. Again, I do not see this as a relevant question at all. Rather, we should study what kind of players thrive in a "typical" branch of the multiverse. Obviously, in most branches, evolution favors players who take only moderate risks. An animal species which would always take huge risks to maximize the return in ONE branch of the universe, would quickly become extinct in most branches of the multiverse.

Probabilities in tossing of a coin

In section IV A, Kent worries about a coin toss experiment in a toy multiverse. Kent describes an experiment where a quantum process prints either 0 or 1 to a tape. The inhabitants of the toy multiverse should determine the relative frequency of 0s and 1s experimentally. Kent is worried that in some branches of the multiverse, the inhabitants will see a wildly biased distribution of the binary numbers.

I do not see any problem in this. Even in the one-world case, we can run a similar experiment where we have a big number of participants tossing a coin. If we have 1 000 000 participants in the experiment, then one will probably see a string of 20 tosses that are all heads. What is the problem then? Most of the participants will get roughly 50 % heads and 50 % tails. The ones who get a very biased distribution may deduce from the physics of the coin toss experiment that they have been incredibly "lucky" to get a very biased distribution. There is no philosophical problem in this, whether the experiment happens in one world or in a multiverse.

Multiplication of species in a multiverse

In Appendix C, Kent describes a thought experiment. There are two species, A and B. B takes huge risks and tries to increase its population wildly, while running also a big risk of extinction. Then, there is one branch in the multiverse where B's population grows exponentially. And the sum of populations of B in all the branches quickly dominates the sum of A populations when time increases. If we live in a multiverse, does it mean that it pays to take huge risks for huge returns? If we get a huge population of our species in one branch of the multiverse, do we need to care if our species becomes extinct in almost all other branches?

The flaw in the thought experiment is that the resources of the visible universe are not infinite. The population of species B cannot grow exponentially for very long. In the long run, the risk-avoiding species A will dominate the total population of A + B in the multiverse because B becomes extinct in almost all branches.

De Broglie - Bohm interpretation is very close to many-worlds interpretations

Adrian Kent seems to sympathize with de Broglie - Bohm interpretation of quantum mechanics because that interpretation is "one-world".

http://en.wikipedia.org/wiki/De_Broglie%E2%80%93Bohm_theory#Occam.27s_razor_criticism
But David Deutsch has said: "pilot-wave theories are parallel-universe theories in a state of chronic denial.^"

Since de Broglie - Bohm interpretation does not involve a collapse of the wave function, and since it evolves the wave function using the exact same equations as many-worlds interpretations, that means that de Broglie - Bohm interpretation is almost equivalent to many-worlds interpretations. The difference is that hidden variables in de Broglie - Bohm pick one branch of the multiverse as "more real" than other branches. De Broglie and Bohm believe that "conscious" observers only exist in this one branch.

But since the other branches may still interfere with the "real" branch of the universe in de Broglie - Bohm interpretation, we may conclude that the other branches also "exist" in some sense. Furthermore, physical phenomena in the other branches are similar to the "real" branch. There are humans living in the other branches, doing physics, and thinking about quantum mechanics. That raises the question: in what sense is the "real" branch more real than the other branches? This question makes de Broglie - Bohm interpretation look awkward.

In many-worlds interpretations, we might define that the branch where I am currently living as an observing "subject", is more "real" than other branches. But it is not mandatory to claim it is more real. Rather, we may say that I as a subject have landed through some random process in one branch, but that one branch is not more "real" than other branches.

I as a living subject was born in Finland. Does that mean that the UK is less "real" than Finland? I do not think so. Similarly, I think all the branches of the multiverse may be as real as the one where I am living.

The problem in one-world interpretations

We saw in the preceding section that de Broglie - Bohm interpretation is essentially a many-worlds interpretation of quantum mechanics though it pretends to be a one-world interpretation.

What is the problem in genuine one-world interpretations, like the Copenhagen interpretation where there is a "collapse" of the wave function when a quantum system is measured?

The problem is that there is no natural way to decide what kind of interactions with a quantum system constitute a measurement that collapses the wave function. In the traditional Copenhagen interpretation, a "conscious being" does the measurement and causes the wave function to collapse.

The paradox of the Schrödinger cat raises the question whether a cat is a "conscious observer", or if it is just humans that are "conscious observers". This all looks very ugly, and in recent years experiments in quantum mechanics have shown that almost macroscopic lumps of matter can be in a superposition of quantum states, that is, such a lump of matter cannot be a "conscious observer". Maybe in the future we are able to show that even humans can be in a superposition of quantum states.

True one-world interpretations need some way to prune the branches of the multiverse in a many-worlds interpretation. Such pruning involves a "collapse" of the wave function of a kind. I do not believe such collapse exists, and that is why I have long been a supporter of many-worlds interpretations.

Many-worlds interpretations can explain some miracles in the origin of life

How the first living cell was formed is a mystery. No pathway from simple molecules to a complex cell that contains, say, a billion atoms is known. Many-worlds interpretations can explain such miraculous happenings. However improbable it is that simple organic molecules spontaneously react and form a living cell of one billion atoms, that DOES happen in some branches of a multiverse.

Using a similar "anthropic" reasoning we could also explain the origin of intelligent life, if the evolutionary pathway to intelligent beings is extremely improbable.

But evolution in general cannot be explained using an anthropic argument in a many-worlds interpretation, because evolution has created many wonderful creatures that are not necessary in the pathway to intelligent life.

Black hole firewalls - real or not?

I have been combing through the web about arguments for and against so-called black hole firewalls. I will present some of my thoughts.

http://en.wikipedia.org/wiki/Firewall_(physics)
Joe Polchinski et al. caused commotion in the theoretical physics world in 2012 when they published their paper that seems to imply there is an infinitely hot "firewall" just behind the event horizon of an old black hole.

That is, assuming that black holes do not lose information, and that they radiate their information away in Hawking radiation, and assuming that the no-cloning theorem of quantum mechanics is true, then there MUST be an infinitely hot firewall just under the event horizon. The firewall prevents any observer from entering the black hole alive.

Their observation is in a stark contrast to Einstein's equivalence principle which states that a freely falling observer should not observe anything special as he falls through the event horizon (this is called the "no drama" hypothesis).

The Black Hole Information Loss Problem

http://en.wikipedia.org/wiki/Thorne%E2%80%93Hawking%E2%80%93Preskill_bet
Stephen Hawking initially claimed that black holes DO destroy information. The information would be forever lost in the singularity of the black hole. The Hawking radiation would be totally random black body radiation and would not carry away the lost information. In 2004, Hawking famously reversed his opinion and conceded that black holes do not destroy information, after all.

Information loss in a black hole is mathematically an ugly phenomenon, as it breaks the "unitarity" of quantum mechanics. That is, in quantum mechanics, time is reversible in the CPT symmetry, and the earlier state of a system is uniquely determined by a later state of the wave function. But if a black hole would destroy information, then there would be no way to deduce the early state - before the formation of the black hole - from the later state - where the black hole has already formed.

2004: Hawking Claims Black Holes Preserve Information, After All

http://arxiv.org/pdf/hepth/0507171.pdf
In 2004, Hawking presented his argument that black holes do preserve information, after all. His idea is to consider the formation and the radiating away of a black hole as a scattering experiment from the point of view of a very faraway observer. Particles are sent into the system. If the particles at some point in time become dense enough, a black hole forms. But the black hole is later radiated away in Hawking radiation.

Hawking seemed to claim that since there is a possible history where the black hole does not form at all, that is, the particles involved never condense enough to collapse into a black hole, then the information of the initial state is preserved in the wave function of that history.

Hawking's argument seemed flawed to me, and it looks like no eminent physicist has endorsed Hawking's idea. In quantum mechanics, we have to consider ALL possible histories. We cannot discard any. We cannot omit the case where a black hole forms and radiates away. The probability of black hole formation might be, say, 99.999 %. It does not help if the information is preserved in the remaining 0.001 % of cases. Unitarity must hold for all histories. It is not enough that it holds for 0.001 % of histories.

Quantum Mechanics Seems to Imply a Firewall in a Black Hole

http://arxiv.org/abs/1207.3123
In their paper, Polchinski et al. show quite convincingly that we have to give up one of the basic principles of quantum mechanics, the no-cloning theorem, or we must give up Einstein's equivalence principle that states there is "no drama" for an observer that falls freely inside a black hole.

I personally now favor the quantum mechanical point of view. Unitarity is a beautiful mathematical property. Giving up unitarity would be a much greater loss than giving up Einstein's equivalence principle.

Einstein's Solution is Mathematically Ugly

The black hole model of general relativity contains a singularity at the center of the black hole. Needless to say that a singularity is an ugly phenomenon from the mathematical point of view. As is laws of nature would break down at a point of space.

To do away with the singularity, people have suggested that some theory of quantum gravity prevents the singlularity from forming. Let us assume that there are some unknown laws of nature that stop the collapse of a black hole into a singularity. If there are some unknown laws that cause nature from differ from general relativity, it might be natural that the differing happens already at the event horizon of a black hole?

Decay of Protons in a Black hole

http://en.wikipedia.org/wiki/Virtual_black_hole
http://en.wikipedia.org/wiki/Proton_decay
As a sidenote, let us bring up the question about the decay of protons. If Hawking radiation really makes a black hole to evaporate, and the radiation is mostly photons, then we have a mechanism to turn a hydrogen atom, a proton plus an electron, into photons. That would imply proton decay. Proton decay is predicted also by some grand unified theories in physics.

Does a Black Hole Have an Interior at All?

http://en.wikipedia.org/wiki/Holographic_principle
If there is searing hot firewall just behind the horizon of a black hole, we can ask if the black hole has an interior at all. According to Bekenstein and Hawking, a black hole is the structure which has the maximal possible entropy in a given area of space. The entropy is NOT proportional to the volume of the enclosed space, but proportional to the area of the black hole. This has been taken as evidence for the holographic principle that the universe really has only two large spatial dimensions and a 3D universe is an illusion.

Since the black hole, in a way, reveals the holographic nature of the universe, it does not sound too far-fetched to speculate that a black hole does not have an interior at all in the sense of our 3D universe. Maybe material falling in a black hole gets distributed in some exotic form on the horizon of the black hole, and the "inside" of the black hole does not exist at all.

Is a Black Hole Analogous to an Atom for Quantum Mechanics?

The hydrogen atom is an example of an object which can superficially be viewed as a classical ball from a long distance. For example, if hydrogen atoms form ideal gas, the atoms in the gas seem to behave like in classical mechanics. But when we go close to the atom and start to study its internal structure, we notice that classical mechanics does not work at all. We have to study the structure of a hydrogen atom in quantum mechanics to get right results.

Maybe a black hole is an "atom" of universe in the way that its internal structure can only be understood through quantum mechanics? That is, we have to forget about the theory of general relativity when we study the internal structure of a black hole. In the previous section, we argued that since black holes reveal the holographic nature of our universe, it might be that they have to be treated in a quantum mechanical way and we must forget about general relativity in their internal structure.

Attempts to Reconcile Quantum Mechanics and the Equivalence Principle

After Polchinski et al. published their seminal paper about firewalls, there has been a flurry of papers where different authors try to get rid of firewalls by reconciling quantum mechanics and Einstein's equivalence principle in some way.

http://arxiv.org/abs/1306.0533
Juan Maldacena and Leonard Susskind suggest that entangled systems in quantum mechanics are not separate entities after all, but are connected through a wormhole in general relativity. Then the interior of a black hole would NOT be separate from the exterior, and the no-cloning theorem for an infalling observer is not violated. That is, we do not need any firewall behind the event horizon. The observer falls with no drama inside the black hole. The authors coin a slogan "ER = EPR".

http://arxiv.org/abs/1402.5674
In another paper, Leonard Susskind suggests that the no-cloning principle is preserved in the way that it is exceedingly hard to compute the state of the interior of a black hole from the Hawking radiation. That is, though the no-cloning principle is violated, it is impossible for anyone to see the violation because the calculation to show the violation would require too big computing resources.

To my mind, the two above suggestions to do away with firewalls sound as complicated and far-fetched as hidden variable theories that try to revert quantum mechanics back to classical physics.

http://arxiv.org/abs/1401.5761
Trying to solve the firewall problem, Stephen Hawking himself suggests that a black hole does not contain an event horizon at all, but just an "apparent horizon". Then there would be no need for a firewall, as there does not exist a true black hole in the classical sense. If Hawking is able to form a mathematical theory from his ideas, it would be a nice solution to the problem. If I understand correctly, the "firewall" in Hawking's solution is the matter that is densely packed very close to the apparent horizon of his quasi black hole.

Fuzzballs

http://en.wikipedia.org/wiki/Fuzzball_(string_theory)
A fuzzball is an attempt to explain a black hole as a string theoretic object. A fuzzball does away with the singularity in the black hole, and it predicts that information is not lost in a black hole. Maybe a fuzzball is the right description of a black hole, if we abolish Einstein's equivalence principle and use quantum mechanics as our guide?

Conclusion

I have been browsing the World Wide Web for a few days now, and it is obvious that there is no consensus among physicists whether black hole firewalls exist or not. A large number of papers have been published in the past two years, and many of them try to do away with firewalls. But none of these papers seems convincing enough. My guess at the moment is that we really have to give up the equivalence principle and treat black holes as purely quantum mechanical objects. Maybe that involves a firewall or maybe we have to assume that a black hole has no interior at all.