Hal Finney wrote:
Symmetry in the fundamental equations of physics doesn't imply that the solutions of those equations have the same symmetry. Lee Smolin has made some very cogent criticisms of the idea that we can dispense with time as a fundamental variable. SeeSometimes we consider here the nature of consciousness, whether observer moments need to be linked to one another, the role of causality in consciousness, etc. I thought of an interesting puzzle about Boltzmann Brains which offers a new twist to these questions.As most readers are aware, Boltzmann Brains relate to an idea of Boltzmann on how to explain the arrow of time. The laws of physics seem to be time symmetric, yet the universe is grossly asymmetric in time. Boltzmann proposed that if you had a universe in a maximum entropy state, say a uniform gas, then given enough time, the gas would undergo fluctuations to regions of lower entropy. Sometimes, purely at random, clumps of molecules would happen to form. Even more rarely, these clumps might be large and ordered. Given infinite time, one could even have an entire visible-universe worth of matter clump together in an ordered fashion, from which state it would then decay into higher entropy conditions. Life could evolve during this decay, observe the universe around it, and find itself in conditions much like our own. The Boltzmann Brain is a counter-argument, suggesting that the universe and everything else is redundant; all you need is a brain to form via a spontaneous random fluctuation, and to hold together long enough to engage in a few moments of conscious thought. Such a Boltzmann Brain is far more likely to form than an entire universe, hence the vast majority of conscious thoughts in such a model will be in Boltzmann Brains and not in brains in large universes. If we were tempted to explain the arrow of time in this way, we must accept that the universe is an illusion and that we are actually Boltzmann Brains, a conclusion which most people don't like. Now this scenario can be criticized in many ways, but I want to emphasize a couple of points which aren't always appreciated. The first is that the Boltzmann scenario, whether a whole universe or just a Brain is forming, is basically time symmetric. That means that if you saw a movie of a Boltzmann universe forming and then decaying back to random entropy, you would not be able to tell which way the movie was running, if it were to be reversed. (This is an unavoidable consequence of the time symmetry of the underlying physics.) It follows that while the universe is moving into the low-entropy state, it must be evolving backwards. That is, an observer from outside would see time appearing to run backwards. Eggs would un-scramble themselves, objects would fall upwards from the ground, ripples would converge on spots in lakes from which rocks would then leap from the water, and so on. At some point this time reversal effect would stop, and the universe would then proceed to evolve back into a high entropy state, now with time going "forwards". Now, the forward phase will not in general be an exact mirror image of the reverse, because of slight random fluctuations and the like, but it will be an alternate path that essentially starts with the same initial conditions. So we will see one path backwards into the minimum-entropy state, and another path forwards from that state. Both paths are fully plausible histories and neither is distinguishable from the other as far as which was reversed and which was forward, if you ran a recording of the whole process backwards. One might ask, what causes time to run backwards during the first half of the Boltzmann scenario? The answer is, nothing but very, very odd luck. Time is no more likely to continue to run backwards, or to run backwards the same everywhere in the local fluctuation-area, than it is to start running backwards right now in the universe around you. Nothing stops eggs from unscrambling themselves except the unlikelihood, and the same principle is at work during the Boltzmann time-reversal phase. It is merely that we select, out of the infinity of time, those rare occasions where time does in fact "happen to happen" like this, that allows us to discuss it. I want to emphasize that this picture of how Boltzmann fluctuations would work is a consquence of the laws of thermodynamics, and time symmetry. Sometimes people imagine that the fluctuation into the Boltzmann low-entropy state is fundamentally different from the fluctuation out of it. They accept that the fluctuation out will be similar to our own existence, with complex events happening. But they imagine that the fluctuation into low entropy might be much simpler, molecules simply aggregating together into some convenient state from which the complex fluctuation out and back to chaos can begin. While this is not impossible and hence will happen occasionally among the infinity of fluctuations in the Boltzmann universe, it will be rare. It will be no more common for a "simple" fluctation-in process to occur than for a simple fluctuation-out process. In our universe, knowing it will evolve to a chaotic heat death, we might imagine that molecules would just fly apart into chaos, but we know that is highly unlikely. Instead, by far the most likely path is a complex one, full of turbulence and reactions and similar activity. By time symmetry, exactly the same arguments apply during the fluctation-in phase. The vast majority of Boltzmann fluctuations that achieve a particular degree of low entropy will do so via complex, turbulent paths which if viewed in reverse will appear to be perfectly plausible sequences of events for a universe which is decaying from order to disorder, like our own. Following on to this, let us consider the nature of consciousness during these Boltzmann excursions. Again let us focus on larger scale ones than just Boltzmann Brains, although the same principles apply there. During the time reversal phase, if conscious entities are present, their brains are running backwards. They are talking backwards, walking backwards, doing everything in reverse. They remember things that are coming in the future, and forget everything as soon as it has happened. The question is, is there any difference in consciousness during the reverse and forward phases? Consider that during the forward phase, we started with a low entropy state, and now the laws of physics are playing out just as they do in our own universe. Everything is happening for a reason, depending on what has happened before. Events cause memories to appear in brains by virtue of the same causal effects which give rise to our own memories. Hence I imagine that most would agree that brains during the forward phase are conscious. However, during the reverse phase, things are quite different. Brains have memories of things that haven't happened yet. Again, one might ask how this can be. The reason is because we stop paying attention to fluctuations where this doesn't happen. We only focus on Boltzmann fluctuations which take the universe into a plausible and consistent low-entropy state, one from which things can evolve in a way that is similar to what we see. When a brain remembers something, if that doesn't happen, the fluctuation is inconsistent. We skip over that one and look for one that is consistent. In the consistent fluctuations, brain memories turn out to be correct, purely by luck. Similarly, every internal function of the brain which we might attribute to macroscopic-type causality, like neuron A firing because neuron B fired, will happen instead by luck, with neuron A firing as though neuron B is going to fire, and then neuron B just happening to fire in precisely the anticipated way. The point is that during the time-reversal phase, causality as we normally think of it is absent. Subjectively-past events do not cause subjectively-future ones; rather, subjectively-future events take place before subjectively-past events, and it is merely through luck that things happen in a consistent pattern. Again, if we hadn't gotten lucky so that things work out, we wouldn't have called this a Boltzmann fluctuation of the kind we are interested in (Boltzmann Brain or Boltzmann Universe). By paying selective attention to only those fluctuations where things work, we will only observe cases where luck, rather than causality, makes things happen. But things do happen, in the same pattern they would if causality were active. So the question is, are brains conscious during this time? Do the thoughts that occur during the time reversal (which recall is not exactly the same as what happens during the forward-time phase) have the same level of subjective reality as thoughts which occur when time runs forward? We can argue it either way. In favor of consciousness, the main argument is that time is fundamentally symmetric (we assume). Hence there is no fundamental or inherent difference between the forward and reverse phases. The only differences are relative, with the arrow of time pointing in opposite directions in the two phases. But within each phase, we see events which can both be equally well described as leading to consciousness, and therefore conscious experiences will occur in both phases. On the other side, many people see a role for causality in the creation or manifestation of consciousness. And arguably, causality is different in the two phases. In the forward phase (the part where we are returning from a low-entropy excursion to the high-entropy static state), events follow one another for the usual reasons, and it is correct to attribute a role for causality just as we do in our own experience. But in the reverse phase, it is purely by luck that things happen in a consistent way, and only because we have an infinity of time to work with that we are able to find sequences of events that look consistent even they arose by simple happenstance. There is no true causality in this phase, just a random sequence of events where we have selected a sequence that mimics causality. And to the extent that consciousness depends on causality, we should not say that brains during this reverse phase are conscious. I lean towards the first interpretation, for the following reason. If consciousness really was able to somehow distinguish the forward from reverse phases in a Boltzmann fluctuation, it would be quite remarkable. Given that the fundamental laws of physics are time symmetric, nothing should be able to do that, to deduce a true "implicit" arrow of time that goes beyond the superficial arrow of time caused by entropy differences.
The present moment in quantum cosmology: challenges to the arguments for the elimination of time
(Submitted on 29 Apr 2001)
Abstract: Barbour, Hawking, Misner and others have argued that time cannot play an essential role in the formulation of a quantum theory of cosmology. Here we present three challenges to their arguments, taken from works and remarks by Kauffman, Markopoulou and Newman. These can be seen to be based on two principles: that every observable in a theory of cosmology should be measurable by some observer inside the universe, and all mathematical constructions necessary to the formulation of the theory should be realizable in a finite time by a computer that fits inside the universe. We also briefly discuss how a cosmological theory could be formulated so it is in agreement with these principles.
The whole point of time symmetry, the very definition, is that there should be no such implicit arrow of time. This suggestion would seem to give consciousness a power that it should not have, allow it to do something that is impossible. And if the first interpretation is correct, it seems to call into question the very nature of causality, and its posible role in consciousness. If we are forced to attribute consciousness to sequences of events which occur purely by luck, then causality can't play a significant role. This is the rather surprising conclusion which I reached from these musings on Boltzmann Brains. Hal Finney
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- Boltzmann Brains, consciousness and the arrow of ti... "Hal Finney"
- Re: Boltzmann Brains, consciousness and the ar... Brent Meeker
- Re: Boltzmann Brains, consciousness and th... Bruno Marchal
- Re: Boltzmann Brains, consciousness and the ar... Stathis Papaioannou
- Re: Boltzmann Brains, consciousness and the ar... Bruno Marchal
- Re: Boltzmann Brains, consciousness and th... Brent Meeker