If you believe there are laws of physics, they connect the moment of now to the past. At least if you believe either classical mechanics, which you shouldnt, or the many worlds interpretation of quantum mechanics, which at least has a chance of being right, if you knew everything about the present state of the universe, you could predict the past and future with perfect accuracy. And in any version of quantum mechanics, if you knew the present state of the universe exactly, you could at least predict the future in explicit probabilities, you would know a lot about what could possibly happen. However, we dont know everything, we dont have perfect information about the present micro-state of the universe. Thats what we imagine LaPlauss demon might have, but we certainly dont think that we have it, and we will never have it. So, in the real world, when we talk about the future, when we talk about trying to predict what will happen in the future, we need to work in a world of incomplete information. And now that we have understood Boltzmanns ideas about entropy and macro states constructed from micro states that look macroscopically the same, we can be very very explicit about what it is we do know and what it is we dont know. What we talk about as if we know is the current macro state of the universe, we have some incomplete information about the present state. If we modeled the universe as a box of gas, or glass of water, we know things like the temperature and the density, some course grain features of reality at the present time, we also know the past hypothesis. The only sensible way to precede in life is to go under the assumption that the past hypothesis is true. So we assume both, that we have current information about the macroscopic configuration of stuff in the universe, and we also know that in the past, about 13.7 billion years ago, the entropy was much much lower. The imbalance gives us the extra information about the past than the future which of course gives us the arrow of time. So in other words, the past hypothesis modifies LaPlauss principle of indifference. The principle of indifference said that if you were in some macro-state, you assume that were equally likely to be in any of the micro states contained within that macro state. Given the macroscopic information, we could be in any of the micro states compatible with that macroscopic information. The past hypothesis says that is not quite right. Within our macro-state, we are not equally likely to be in any of the micro-states, we happen to be in one of the very specific micro-states which if you evolved it into the past, the entropy would decrease. Thats a very tiny fraction of all the micro-states within our macro-state, most of them would have the property that entropy would increase if you followed them to the past. So we dont know which micro state that is, but it is one that had a much lower entropy in the past. That is the modification of LaPlauss principle of indifference that has been given to us by the past hypothesis, it picks out a tiny fraction of the micro-states among those within our macro-states. This information is incredibly useful to us as we go through out lives, even if its so ingrained in how we think, we dont actually access it consciously. So let me give you a specific example of how we use the past hypothesis every day even tho we dont put it in those terms. Imagine youre walking down the street and you see a broken egg lying on the sidewalk. What your observing is the macro-state, not the micro-state. Current information about the universe right now, not complete information, some macroscopic course grained information, a broken shell and splattered egg in a configuration. What you want to know is, what will happen in the future and what did happen in the past. You want to make predictions and retrodictions based on the information you have. So what you can you say about the future of this broken egg on the sidewalk? The answer is you cant say the one true thing that will happen, you dont have enough information. Even if you have other macroscopic information about the world around you, its still not enough information to say with 100% certainty what will happen to the egg. A dog could lick it up, it could sit there for days and cook on the sidewalk, it even could probabilistically form back together and put humpty dumpty back together again. The future of the egg is pretty wide open, anything could happen to it. Now lets ask, what is the past of the egg. What was that egg doing 24 hours ago? Right now we see it is broken on the sidewalk, it looks to us as what we would call fairly fresh. So we say, we dont know where the egg was 24 hours ago, but we are essentially certain that it was an unbroken egg. There is a huge imbalance between how we talk about the future of the egg and how we talk about the past of the egg. In the future, many things are possible, in the past, we think there was an unbroken egg, the egg did not begin life messily scattered around the ground. Why is it that we can be so much more specific about the past of the egg rather than the future? The answer is the past hypothesis. We dont look at the egg and think there is some micro state we just dont know, we imagine that the egg was one that came from a lower entropy past. And we know that the way the real world creates broken eggs is first by making unbroken eggs. That is the likely conclusion, if you want to connect the past hypothesis, the low entropy past of the big bang, to the current situation where there is an egg lying on the sidewalk. That is where our asymmetry of epistemic access comes from. We are able to say more about the likely past given our current information than about the likely future because we know more about the past, we have a boundary condition in the past, one of lower entropy. There is no boundary condition of the future, because higher entropy makes it more disorganized. There is a direction of time we follow in the universe with our thought. This is why there is a directionality to our knowledge of the universe. If we didnt know about that, we wouldnt be able to remember the past any more than we could remember the future. We tend to think that the past is fixed. The past is real, the past happened, it is not something we can alter by our current actions. But there is a tension with that way of thinking, and our belief that the underlying laws of physics are reversible. If you believe that the underlying laws of physics are reversible. If you believe that the underlying laws of physics are Newtonian mechanics or quantum mechanics, they treat the past and future the same. So at the deep level at our best understanding of the laws of nature, there is no more reality or fixedness to the past as there is to the future. The real difference between the past and the future is not how real it is, not how settled it is, but how much more we know about it. The difference about the past and the future is that we can infer much more accurately about the past because we not only know the current macro state, but bc we know the past hypothesis. The past hypothesis illuminates the actual past. There is on particular past and one particular future because of how well we know it. In cause and effect, the cause is the lower entropy, and the effect is always the higher entropy. When I look at the broken window lying on the floor, we dont just think about every possible way for the molecules of glass to arrange themselves in the form of a broken way on the floor. We also imagine that there was a past low entropy condition. And given that past hypothesis, then the most likely way to get the broken window on the floor is to have an unbroken window that something broke. What we call the cause on the broken window of the floor is the event that connects the past event of lower entropy to the future event of higher entropy, that tells us the cause must have happened before the effect. But the same logic applies to your choices. What we call free will. We think that you have the ability to decide where to go to have dinner tonight or tomorrow night. We dont think you have the ability to decide what to have had for dinner last night. The laws of physics treat the two events the same, if you knew the micro-states, there would be no difference in predicting the future and retrodicting the past. But we dont know that, we have less information. The reason why we think we have free will about the future and not the past is because of the past hypothesis. The past hypothesis fixes enough about what happens in the past that we dont think we can affect it. Because there is no future hypothesis, the set of things that are open to us in the future is very very large. We conceptualize that large set of possibilities in terms of choices, in terms of free will. Philosophers up to this day try to argue that free will is real, thats not what im trying to adjudicate right now. There are compatibilists who think that the laws of physics do govern everything and never the less, we should talk in the language of free will because we dont know what will happen next, even though the laws of physics tells us what will happen next if we have enough information about the micro state, which we dont know, so we talk about the real world as if we are making choices. There are also libertarians in the philosophical sense, which believes that our human choices overcome the laws of physics. That you are not determined by the laws of physics. This is not a view point of most physicists, but free will is the correct way to talk. The third group just says that there is no free will, bc the laws of physics predict the future. Even though I believe in the laws of physics and that the future is determined at least probabilistically, if we know the micro state of the universe, I dont mind talking about free will. I believe it is okay to say we have free will, bc we dont know what the micro state is. When we use the language of free will, were not describing the individual micro states of the universe, were not talking about atoms and molecules. .Just like when were talking about the melting of ice in a glass of water, we can talk about that in the language of molecules in the water, or we can talk about it in the thermodynamic language, of fluids and temperatures, and densities. We dont talk about it in both languages at once. We dont talk about the temperature in water and the density and velocity of every molecule. You use one vocabulary or the other. Likewise, you can use atoms and micro-states to describe what you as a human might do, and in that language there is no free will. But when we dont talk that language, which makes sense bc we dont have all of that information, we talk about human beings in a different vocabulary, and that vocabulary includes the possibility of making choices. Which of course follow the laws of physics in a macro-state.
Posted on: Thu, 11 Sep 2014 15:21:59 +0000
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