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The way things are traditionally presented about time, there is the present, the past is fixed, and the future is open. The second law of thermodynamics is invoked. But how can we be so sure the past is fixed?

Some musings on this topic can be found on this blog post. The past is fixed because there are memories and records of the past. Memories and records are macroscopic averages over microstates. A generic typical state of the universe constrained only by the macroscopic records and memories with the unconstrained microstates varying randomly will increase in entropy in both directions toward the future and past. This is none other than the Boltzmann brain hypothesis. The universe starts off with a random high entropy configuration, accumulates miraculous random fluctuations over time to become more and more ordered, and conspires to a marcostate which apparently tell the story of a past which never happened. How can we know the past is what it is without making the further assumption that the entropy in the past was far lower than what it is now?

An alternative coherent hypothesis is there is a malicious demon who deliberately planted fake memories and records to make it seem as if the past were something it was not. Is there any convincing way of ruling out this hypothesis?

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  • thermodynamically, it is most likely we are Boltzmann brains, by far much more likely than a universe with lots of mass and energy spread over many light years... – Bak1139 Mar 19 '16 at 20:37
  • There are several ways to achieve a specific pattern on a chess board. You can't know which of them was true if you are constrained in your knowledge by only seeing what is the present pattern. But there still is only finite amount of possibilities. And you can know if given solution is wrong. – rus9384 Sep 27 '18 at 14:06
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As Richard Feynman and undoubtedly many others independently realized, as long as one insists on the scientific method, it is very easy to falsify the hypothesis that we are a Boltzmann Brain that just randomly fluctuated into the existence in a very infrequent random event occurring in a high-entropy environment.

The reason is that such a hypothesis predicts many things. For example, it predicts that if we look just a little bit further than the volume where our brain emerged, we find a complete disorder that maximizes the entropy. If we try to investigate where we came from, we find chaos and no order. It's because in a random high-entropy environment that the hypothesis assumes, chaotically looking configurations of the matter outside the brain are vastly more likely than the organized, low-entropy ones.

However, if we actually make another observation and ask whether we had parents and grandparents, instead of the chaotic soup where we emerged etc., and whether there is some order beyond the volume where our brain lives, we always find out that there is order; parents and grandparents are real; memories fit together; the broader cosmic environment seems to have the same non-maximal entropy as the very vicinity of our brain.

All these observations disfavor the Boltzmann Brain hypothesis because this hypothesis predicts that any of these observations only occurs with the tiny probability of order $\exp(-S)$ where $S$ is some huge entropy of order $10^{26}-10^{120}$. The double exponential is obviously zero for all practical purposes: the Boltzmann Brain hypothesis predicts that things we observe can't happen in practice, so it is falsified by the evidence.

The evidence clearly shows that our past did occur within a spacetime where the second law of thermodynamics was obeyed. The reasoning paying any attention to the Boltzmann Brain hypothesis is simply fallacious, incompatible with the logical proofs of the second law that show that such events are ludicrously unlikely – which means that such events may be forgotten when we're scientifically explaining anything. For the same reason, the Boltzmann Brain scenario can never be used to exclude a dynamical model of physics because all dynamical models of physics respect the second law of thermodynamics.

P.S.: Feynman's disproof of the Boltzmann Brain scenario starts with "We would like to argue that this is not the case" in the page linked above.

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    Of course, we are not a Boltzmann Brain, but I still claim you cannot prove it. Because we have seen stars that are billions of light years away doesn't prove anything since that fact could just be a false memory implanted in my brain by the fluctuation that assembled my Boltzmann Brain. And now my brain has the false memory that I just wrote that previous sentence. My point is that it is no different than proving that we are in some giant simulation of our universe in a different universe - it is a philosophical question which, like all philosophical questions, cannot be falsifiable. – FrankH Nov 9 '11 at 17:31
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    In which case it should be migrated to the philosophy stack exchange. :) – AdamRedwine Nov 9 '11 at 22:37
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    @FrankH "I still claim you cannot prove it". What Lubos says is that the hypothesis is disfavored by every moment in which you go on existing or see something other than randomness. The idea that you were created a moment ago by a thermodynamic fluctuation is a physical hypothesis, and one can make a judgment about its likelihood (ultra-super-exponentially unlikely) by quite conventional physical reasoning. The idea that we are in a simulation is qualitatively different, and harder to reason about, because we then know nothing about the true physics underlying the simulation. – Mitchell Porter Nov 10 '11 at 3:50
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    @Mitchell, I agree that the entire universe cannot be a Boltzmann fluctuation - our real bodies can do experiments over a period of time that will reduce the chance that the entire universe is random to as small a value as you want. But in terms of a single Boltzmann brain that can only experience the current moment - there is no way in that single moment that it can determine that it is not a Boltzmann brain with fake memories of previous experiences before the current moment in time. Once that moment has passed, in the next moment (NOW) the previous moment memory could still be a fake. – FrankH Nov 10 '11 at 4:03
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We can't be sure. Just as we can't be sure that we aren't living in some giant computer simulation of our universe. Each of these cases would feel exactly as real as if the universe was real and as if it has existed for at least 13.7 billion years.

Physics and science discovers truth by testing falsifiable hypothesis. So a hypothesis that is not falsifiable cannot be said to be true (or false). The only possible way to falsify the claim that I am a Boltzmann Brain is to wait and see if I disintegrate. And that is not a falsifiable test because I won't remember that I disintegrated.

By the way, if we are a Boltzmann Brain, it is "I" who is the brain and "you" who is just a figment of my imagination...

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As Luboš Motl and others have argued, we are almost certainly not Boltzmann brains in the obvious sense: a thinking object produced by a random fluctuation within the universe as we know it. But perhaps you ask whether the universe as "we" know it—that is, as a given observer knows it—might "be" the imagination of a randomly created, thinking object in some outer world—that is, whether said observer might reasonably consider the world to be such an object's dream. This, I argue, can not be disproved.

As observers, we collect observations and form hypotheses. Collected observations are essentially just data. Hypotheses are essentially observations of our own thoughts. So as scientists, we are essentially just observation databases, or if you prefer, just one database.

All that which we know about the universe, including the fact of its existence, consists of our observations. Much confusion stems from the assumption that the universe first exists, and that we observers arise within it. But such an assumption is unwarranted. We must acknowledge the primacy of observations, given that these are necessary to establish the very existence of the universe. When we speak of our universe, we mean a certain mental model with which each of us seeks to explain and predict his or her observations.

In this context, let us consider Sean Carroll's statement: In the set of all such fluctuations, some brains would be embedded in universes like ours, but an enormously larger number would be all by themselves.

On first reading this, I imagine a real, human brain floating in a huge vacuum of space, thinking along until it freezes or otherwise dies, eventually to vanish by proton decay or quantum tunneling. But then I realise how I arrived at that image of a Boltzmann brain and how much further I have to go. Yes, an enormously larger number of lone, human-like brains would arise, but so would an even larger number of exotic, thinking objects unlike anything on earth.

When Dyson, Kleban, and Susskind touched on the problem, they didn't even go as far as the lone human brain. They gave the example of a universe like ours but with a 10 Kelvin background radiation instead of 2.7 K, and they pointed out the trouble that such a change would cause for cosmology (as if cosmology didn't have enough trouble already).

So yes, a real universe as modeled by scientists runs into trouble, and so do a slightly warmer universe and a freezing brain in space. But what would a Boltzmann brain really be like? Well, it would have to satisfy some criterion of capacity for thought, but that's it: anything more would be unlikely. Probability would far outshine both evolution and human technology in the design of such a minimal brain/computer. It would not react to the vacuum like an earthly organism suddenly cast into space. It would contain essentially no feature extraneous to the thought requirement, such as redundancy or component isolation.

Boltzmann's brain would have neither sensory input nor motor output, and anyway, there would be nothing around for it to perceive or to move. A human lacking those things would, I think, sleep very deeply. It is hard to extrapolate from humans to the class of typical Boltzmann brains, but given the requirement for thinking, we can assume that nothing would disturb its thought, nor would it feel any urge to affect its environs.

What I describe strikes me as similar to a dream. Perhaps our universe—which is to say, my observations—are part of such a dream. (Before I am accused of solipsism, note that in this supposed dream, I—the human author of this post—seem to have roughly the same kind of brain and mind as other humans, so there is no contradiction in their reaching a similar hypothesis with themselves at the centre.) Like a human dream, our world seems internally consistent—at least, mostly so—but never completely fathomable.

If the dream-universe analogy holds, what can we say about the dreaming Brain? Almost nothing. Nothing constrains it to be made of atoms or subject to our physical laws, since it exists in a meta-world. Perhaps, as in a human dream, our world somewhat resembles the Dreamer's world with a few subconscious elements thrown in, or perhaps not.

Perhaps, also as in a human dream, the Dreamer makes this world up as it goes along, in which case I see no problem with your point about unconstrained microstates of the past. Occam's razor suffices to discard the hypothesis about a malicious demon.

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One problem with this idea of 'the universe being just a dream in Boltzmann brain' is this;

should we include the laws of thermodynamics amongst the concept 'universe'? Of course yes! So the very same argument, which rely on thermodynamics, would be false by its own standard as it demands that all the memory be false, which must include the memory of thermodynamics itself!!

  • It does not require all known facts to be false, only or memory of how we acquired them. – user9166 Aug 9 '15 at 0:39
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You can be a Boltzmann brain, but there are other theories that greatly reduce their number; and if these theories are true, then the likelihood of being a Boltzmann brain is similar to the idea that billions of humans will have their flesh burn for eternity.

If you read this answer, then know that I never actually wrote it because you never actually asked the question- this is just your randomly conscious brain giving you a message about your existence. You may have began existing when you woke up this morning, or you might have popped into existence at this very moment. When you wake up tomorrow to think about these things, there’s really nothing to think about because you never actually read this answer.

Bohemian Mechanics

There is a physics theory that greatly reduces the number of Boltzmann brains called the pilot-wave interpretation or Bohmian mechanics. It’s recieved some praise in recent years because it gets rid of all the “quantum weirdness”, but it’s deterministic and “normal brains” don’t like that.

According to a paper called The Bohmian approach to the problems of cosmological quantum fluctuations there are two possible outcomes of Bohmian mechanics that the authors categorize as optimistic and pessimistic.

The first, “optimistic” view insists that a Boltzmann brain will be problematical only if it is a functioning brain, at least for a short time. In a frozen universe, even if a Boltzmann brain configuration existed, it would not be functioning, exactly because it is frozen. A functioning brain requires in Bohmian mechanics the right kind of configuration and the right kind of wave function (just as it would require in classical mechanics the right kind of configuration and the right kind of momenta), and while the right kind of configuration may occur, the wave function ψ is not of the right kind.

The second, “pessimistic” view retains the worry that a mere brain configuration may be problematical as it may encode all memories of the brain and perhaps the present thoughts. If that is so, then it becomes important that in a frozen universe, Boltzmann brain configurations cannot occur over and over (unlike in a classical gas in a box which, due to the eternal irregular motion, repeatedly assumes every configuration over time). To be sure, if a Boltzmann brain configuration occurs once, then it stays forever and has the majority of observer-time since the normal brains are finite in number and lifetime. Thus, in the pessimistic view, this configuration poses a threat to the theory. However, if 3-space is not extremely large, then the |ψ|2 probability that a Boltzmann brain configuration occurs anywhere in space is tiny. Thus, with overwhelming probability, the problem is absent if 3-space is not extremely large.

This is basically explaining how it’s possible for a single Boltzmann brain to form- with all sorts of memories, which would possibly contain a vast amount of knowledge. This Boltzmann brain will remain forever and has the majority of observer-time because “normal brains”- like the brains we have- eventually die.

So now we’re back to where we started, but with a different presupposition. Is there no God, one randomly generated God, or are you God?

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