If one takes this problem seriously, perhaps one could conclude that the dark energy will never decay. But even then, this second type of Boltzmann brain still exists. The low-temperature Bunch-Davies vacuum of de Sitter space is locally very similar to the zero-temperature vacuum of Minkowski space, and the amplitude to have a Boltzmann brain in each space-time volume is essentially the same.
We can compare the probability i. The probability to nucleate a compact object 3 3 3 Here we neglect the entropy of the object, i. The nucleation rate should be multiplied by the number of such possibilities, but the correction to the huge exponent would be relatively tiny.
Considering the uncertainty about the exponent, there is no point in calculating the prefactor. Thus p vac is enormously larger than p dS. An explanation of the Boltzmann brain paradox in terms of the measure on the multiverse will have a harder time solving the problem if a Boltzmann brain production rate proportional to p vac must be overcome than if we need overcome only an infinitesimally smaller rate depending on p dS.
Thus it seems important to determine which kinds of Boltzmann brains should be considered as part of the reference class. One might try to argue that no Boltzmann brain should be considered, for example because in either case the objects are sectors of a pure-state wave function.
But this does not seem feasible. Assuming the usual scenario of inflation is correct, our galaxy condensed from an early quantum fluctuation in the field driving inflation.
Thus we ourselves are a sector of a pure-state wave function describing the inflating universe. Since we put ourselves in the reference class, it appears that arising from a quantum fluctuation is not a disqualification. If eternal inflation is correct, our whole universe was nucleated as a bubble in de Sitter space, and there is an even closer analogy to the nucleation of Boltzmann brains.
Vacuum fluctuations, however, are somewhat different. While nucleating objects can last forever, vacuum fluctuations in Minkowski space have a finite lifetime and can never decohere, since the vacuum wave function must remain pure.
We shall discuss these issues below. Thus if we are Boltzmann brains, all our past experiences are just an elaborate illusion with no connection to the external world. Thus our observations of the universe and our knowledge of physical laws are just delusions, and we have no real knowledge of anything outside ourselves.
But it is just such knowledge of the supposed external world which has led us to formulate the Boltzmann brain paradox in the first place. If we abandon it, we will have no understanding of the real world and thus no possibility to understand the likelihood that we are Boltzmann brains. So let us state the problem more carefully. We want to know whether theory X is correct, so we compare our observations with what it predicts.
If theory X has a Boltzmann brain problem, then it predicts usually with probability 1 that we are Boltzmann brains. The vast majority of Boltzmann brains do not have correct observations of the external world, so their observations would not be in accord with theory X, as ours are.
Furthermore the great majority of Boltzmann brains would vanish immediately, as discussed above. Thus theory X leads to high-confidence predictions at odds with observation. We do not in this analysis consider Boltzmann brains arising under some other theory Y but falsely believing they exist under theory X. Of course such Boltzmann brains could exist, but we have no way of meaningfully discussing them, because we have no way of knowing all possible theories Y that might have Boltzmann brains.
Minkowski-space vacuum fluctuations are local, in the sense that, while consideration of the state restricted to a local region gives a nonzero amplitude for a Boltzmann brain, the state of the entire space is just the unchanging, pure vacuum.
Thus it is not possible for a brain arising as a vacuum fluctuation to send out any durable signal of its existence. If it could, the global state would now consist at least of the vacuum plus the outgoing signal. Vacuum fluctuations in de Sitter space are very similar, except if the fluctuation or its effects extend across the de Sitter horizon. In that case, we have not the vacuum-fluctuation case that is analogous to Minkowski but the different case of nucleation, as discussed above.
According to Turing Turing , to determine whether something has human intelligence we should allow a human interrogator to ask it questions and see if its answers are indistinguishable from those of a real human. But the vacuum Boltzmann brain can never communicate with any external entity, so the test cannot be done Gott More generally, the thoughts of a vacuum-fluctuation brain can never have any impact on anything.
These arguments appear to motivate the exclusion of vacuum-fluctuation brains from the reference class. On the other hand, the same argument would apply to an ordinary observer enclosed in a perfectly sealed box which we imagine here to be sealed even against gravitational waves.
His thoughts could never affect anything outside the box. If we were sealed in such a box, especially without our knowledge, it seems very strange to declare that we should no longer be members of the reference class. In fact, if we deny the reality of the vacuum-fluctuation brain, it appears that we are denying the famous argument of Descartes. This seems a powerful argument in favor of including vacuum-fluctuation brains in anthropic reasoning.
It is often argued that quantum mechanical decoherence produces the distinction between quantum and classical behavior. Decoherence means irreversible coupling to the environment. For example, if the electron in a two-slit experiment is permitted to interact with a bath of background photons, there will be no interference pattern.
The quantum state of the electron necessary to produce interference is entangled with the photons and transported away from the apparatus.
In principle one could track down these photons and recover the coherence and thus the interference pattern, but in practice that would not be possible. Since a Minkowski vacuum fluctuation can never send out any durable signal, it can never be decoherent. This is different from the situation in de Sitter space. A nucleating brain in de Sitter space can send out signals which travel outward forever, and can thus decohere in the usual way. Even though the entire de Sitter space might be in a pure quantum state, the existence of horizons allows for decoherence.
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Publication Type. More Filters. Why Boltzmann Brains Are Bad. Some modern cosmological models predict the appearance of Boltzmann Brains: observers who randomly fluctuate out of a thermal bath rather than naturally evolving from a low-entropy Big Bang. A … Expand. A note on Boltzmann brains. Understanding the observed arrow of time is equivalent, under general assumptions, to explaining why Boltzmann brains do not overwhelm ordinary observers.
It is usually thought … Expand. The measure problem of cosmology is how to obtain normalized probabilities of observations from the quantum state of the universe. The framework discussed here also addresses the question of whether a Minkowski vacuum may produce Boltzmann brains.
Many UC-authored scholarly publications are freely available on this site because of the UC's open access policies. Let us know how this access is important for you. Skip to main content. Email Facebook Twitter. Abstract Understanding the observed arrow of time is equivalent, under general assumptions, to explaining why Boltzmann brains do not overwhelm ordinary observers. For improved accessibility of PDF content, download the file to your device. Thumbnails Document Outline Attachments.
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