January 2, 2009
Recently I came across an argument about 'reversal of time' and our conscious experience (I am sure this type of argument must be at least hundred years old) and I thought I should mix it with an old idea of mine. I am curious what others think about it; So here it goes:
Imagine that we can describe the world as a Newtonian universe of classical particles so that xi(t) , where x is the position(vector) of the i-th particle and t is the classical time parameter, determines the configuration of our world for each moment of time. I am pretty sure that the following argument can be generalized to a quantum mechanical description, but it is much easier to stick to Newton for now.
We assume that the world evolves according to the laws of Newtonian physics up until the time t0. At this moment an omnipotent demon reverses all velocities: vi(t0) = x'i(t0) -> - x'i(t0), where ' is the time derivative, and the Newtonian evolution continues afterwards.
Obviously, for t > t0 everything moves 'backwards'; If a glass fell on the floor and shattered into many pieces for t < t0, it will now assemble and bounce back up from the floor etc.; If the entropy S(t) increased with t for t < t0, it now decreases for t > t0.
One can also check that xi(t0+T) = xi(t0-T) and x'i(t0+T) = -x'i(t0-T) for every T (as long as we rule out non-conservative forces).
The interesting question in this thought experiment is "what would an observer experience for t > t0 ?".
If we assume that the conscious experience E(t) of an observer is a function of xb(t), where b enumerates the particles which constitute her brain, then we would have to conclude that the observer does not recognize anything strange for t > t0, since xb(t0+T) = xb(t0-T) and it follows immediately that E(t0+T) = E(t0-T). So if all the experiences E(t0-T) contained only 'normal' impressions then the same is true for E(t0+T). In other words, while the sequence of experiences is 'backwards' no single experience contains the thought "everything is backwards" and nobody feels anything strange.
But this would mean that no observer is able to recognize 'backward evolution' with entropy decreasing and distinguish it from normal evolution!
One way to avoid this strange conclusion is to assume that E(t) is a function of xb(t) and vb(t). Of course, we do not have a physical description of conscious experiences and how they follow from the configurations of our brain (yet). It is reasonable that our conscious experience depends not only on the position of all molecules in our brain but also their velocities.
Unfortunately, this leads us into another problem. If we rescale the time parameter t as t* = s*t, this would rescale all velocities so that v(t*) = s*v(t) and thus E(t) = E[x(t),v(t)] -> E(t*) = E[x(t*),s*v(t*)]; But if the function E is sensitive to vb then it would be sensitive to the scale s too. I find this to be quite absurd, our experiences should not depend on an unphysical parameter.
The summary of my argument is the following:
i) If the world evolves 'twice as fast' we should not notice a difference (the molecules in our brains would move twice as fast as well).
ii) However, if the world suddenly evolves 'backwards' we would like to be able to recognize this (otherwise how would we know if the 2nd law is correct).
iii) But it seems that one cannot have both i) and ii) if one assumes that our conscious experience is a 'natural' function of the material configuration of our brain, e.g. if we follow Daniel Dennett and assume that consciousness simply is the material configuration of our brain: E(t) = [xb(t)] or E(t) = [xb(t),vb(t)] (*).
Perhaps one can solve this puzzle by assuming E depends on higher derivatives x'' and/or perhaps one can find some clever non-linear function. But I think this would introduce other problems (at least for the few I tried ) and I don't find this very convincing [x].
Of course one can challenge other assumptions too. I already mentioned quantum mechanics instead of Newton or perhaps we have to assume that our conscious experience is not a function of the particle positions in our brain. But still, none of these solutions are very convincing in my opinion.
What do you think?
(*) Dennett is never that explicit about his explanation of consciousness.
In general, one could imagine that E is some sort of vector in the 'space of all possible conscious experience' - whatever that means.
[x] e.g. E could depend on vb/N with N = sqrt(sumb v2b) instead of vb. But where would the non-local N come from and also there would be a singularity at N=0, i.e. when all velocities are zero. One would not expect a singularity of E for a dead brain (with all molecules at rest) but rather zero experience.