Things Unfolding as They Did II

I didn’t mean to sound so oracular last post. Let me expiate by filling in a little. The claim is that things unfolding as they did from the big bang, including such things as an ordinary trip to the store as ordinarily described, had a probability either of 1 or something exquisitely close to 0. In light of quantum theory, it is almost certainly the latter.

The physics of reality is either deterministic or not. If everything was deterministic all along, then from any state of the universe, however early, the laws of nature are going to lead to your buying exactly those five items at the store. Probability 1. I am here talking about “objective probability,” probability built into the physics of the world. This probability could be 1 even if we (wrongly) believed on very good evidence that determinism was false.

Our best current science, however, has it that determinism is massively false. Quantum mechanics is very well confirmed, and its standard interpretation, now also well confirmed, has it that probability is woven into the fabric of the world, and it is woven in everywhere and everywhen at the level of the basic constituents of reality.

 

Consider the past light cone of that last trip of yours to the store – all the events in the universe from which light could have gotten to you entering the store. Cut up that light cone into slices, one second apart, starting with your putting the last item in your cart and then working back in time. Quantum theory would seem to tell us that there was some non-1, non-0 probability of getting to each of those states from the prior state. In each case there were possible, but unrealized next states.

So if we were going to calculate the probability from the beginning of things transpiring exactly as they did right down to you in the store, using the assumption of a quantum indeterminacy from each second to the next, we would get a very low probability indeed. Making the unmotivated assumption that the probability p was the same for the transition from each time slice to the next, the total probability of things working out exactly as they have would be p raised  to the power of 4 x 10¹⁷ . Anything less than 1 raised to a power with 17 zeros after the significant digit is a very small number  – unless p is very, very close to 1. Moreover, quantum indeterminacy appears more frequently than second to second, presumably it affects things right down to the shortest unit of time, if such there be. This pretty well guarantees us that the probability of a state from one a whole second before is going to start out, not close to 1, but pretty close to 0.  So we have something close to 0 multiplied by itself 10¹⁷ times. Small!

This, I think, gives us very good reason for believing that the probability of things unfolding exactly as they have is an exquisitely small number. However, it is entertaining to think not about the probability of absolutely everything turning out exactly as it did, down to the state of each electron, but instead about the probability of an ordinary life event as we would ordinarily describe it. We would count you as having bought those five items at the store, even if some electrons were in different states. I am willing to count it as the same five items even if you had grabbed the bottle of oregano next to the one you did grab, both being the same brand, size, and all.

This latitude is obviously going to boost your probability of buying those items well above the probability of everything, down to quantum detail, being exactly identical to what it was in reality. I am going to contend, however, that, though higher, the probability will remain almost inconceivably low.

It might seem initially that the probability of your buying just those items might well be respectably high. It could be argued that the quantum indeterminacy, which looms so large when the target is the exact states of an event down to the micro level, becomes completely irrelevant once we raise our focus to the macro level. Classical physics generally works perfectly well at the macro level. Thermal noise normally washes out quantum effects, leaving us for most practical purposes with classical macro level physics and classical physics is deterministic.

So can we forget about that very long chain multiplication of terms close to 0? Could it be that even from the big bang the probability that you would buy those five items at the store was 1, or something respectably close to 1, or at least not something with lots of zeroes after the decimal point?

Apparently not. The quantum level cannot be entirely ignored. It does have effects that break through into the everyday macro world. One kind of possible breakthrough, however, I am going to ignore. As you were reaching for that oregano jar, there is a very small probability that one of the electrons in the jar would turn up in the ice cream freezer. That the electron and a proton from the same atom would do so simultaneously brings the probability down to a level that we do not have ordinary language to express. It is, indeed possible, that this should happen to every particle in the whole jar, resulting in its disappearing as your hand approached, and materializing in that freezer next to the rocky road. This is a probability so small, however, that I am happy entirely to leave it out of consideration. I will just assume that the oregano jar does not deviate from classical physics for purposes of estimating the probability that you would buy the five items you did.

If we ignore these sorts of hyper-improbable incursions of quantum indeterminacy into the macro world, however, there remain to be considered other ways that the quantum level can affect life among ordinary sized objects. 

Science and engineering have developed some devices for magnifying quantum events so that they can affect the decisions that people make. The Geiger counter is an early example. The liberation of an alpha particle from a piece of uranium is a non-determined event, but you could award a grocery coupon to the customer who happened to walk through the door on the 5^th Geiger counter click.  Other devices, mostly confined to labs, can perform the same trick.

There was no Geiger-counter equipped coupon awarder at the door to your store, as it happened, and it is unlikely that any such device had any direct effect on your trip to the store. (Probabilities go up a little if you are an experimental particle physicist.)  Indirect effects from the use of such instruments would have a better chance of getting involved. Although much less unlikely than quantum oregano transposition, still be low enough to ignore. In addition to the fact that they now have only a pretty small effect in changing macro events, these scientific devices for bringing the micro macro have only been around for about a hundred years. So they had no effect on macro level probabilities for those billions of years between the bang and now.

There are, however, a couple of other ways quantum indeterminacy, even in pre-Geiger years, might be relevant to your shopping probabilities. Neither at this point benefits from overwhelming evidence, but there is enough support to make them worth considering.

One is the conjecture that indeterminate quantum events involving the hydrogen bond in DNA could cause mutations. It is clear that this can happen, and I think there is now little doubt that it does happen. Still unknown is how significant it is in terms of the percentage of mutations so caused. There is the possibility, however, that there was a quantum indeterminacy based probability, perhaps a significant one, that life not have arisen, or that primates not have evolved, or that you might not have existed to go shopping. This means that there was some objective probability other than 0 for you-incompatible events stretching back 4.3 billion years or so. These events were doubtless far less frequent than every second, but there would have been a lot of them. There were both the probabilities of the right mutations not occurring and of wrong mutations occurring. In addition to affecting your genealogy, these quantum-initiated mutations may cause cancers with their far reaching awful consequences for our macro level lives.

Another conjectured bridge between the quantum and the everyday world brings probability right down to your decisions at the store. There has been controversy as to whether quantum indeterminate events can affect human decisions. The neurophysiology in question involves the synapse, and in particular the (very thin) presynaptic membrane and the role of microtubules.  

Neuro-quantum effects have largely been discussed by philosophers and philosophically inclined neuroscientists in terms of free will and of the formation of consciousness. I am confident that the possibility of non-determined synaptic events is not significant for the free will issue, and doubtful that any quantum phenomenon is central to the explanation of consciousness. However, to dismiss quantum effects in the brain for these purposes is not to say that don’t affect the probability that you would select just those five items at the store. 

If truly random events sometimes affect human decisions, then there is some probability of such an effect upon each of your five choices (especially the closest buy-don’t-buy decision). It also might have affected your choice to go to the store at all, the manager’s choice to restock the oregano, the corporate decision to produce that size bottle, and on back and back. Had Genghis Khan been influenced by a quantum event going the “wrong” direction, then one of your great-times-fortieth grandparents might not have been born. Good luck for you that this didn’t happen. 

Such potential interferences with your coming into existence to make that store trip will stretch back well before Genghis. A quantum randomness that affected a decision of any of your ancestors might have meant no you, and the set of ancestors in question would include any that had neurons anything like ours. In addition, a decision so affected by a non-ancestor, say a saber tooth cat, could have resulted in one of your ancestors not reproducing. It was, again, only good luck that this didn’t happen. The temporal reach of this synaptic bridge between the quantum level and the macro world will not go quite as far into the past as the DNA mutation effect, but it will cover quite a large chunk of time, perhaps half a billion years. 

Before leaving these two “recent” factors lowering the probability of your making the trip to the store and buying those items, and particularly this last one involving brain physiology, let me concede that a careful consideration of this neighborhood turns up some probability increasers. You do not only buy those items in the actual world, but also in some reasonable number of possible worlds. In the actual world you intended to buy almond milk all along.  In a slightly non-actual world, reached through different outcomes of a few quantum influenced decisions, you were planning to buy soy milk, but the shopper ahead of you, on a (quantum?) whim, grabbed the last soy, and you decided to try almond milk. Maybe this would boost the probability of your 5 item selection by a couple of orders of magnitude, but I hope you already suspect that we are now so far down in orders of magnitude that a few here or there make not much of a difference. Moreover, the big probability reducer is still to come.

The heavy weight factor in your probability of buying just those items at the store is way back in the big bang itself. In the post bang world most of macro physics is classical – with quantum effects leaking out to have discrete macro effects only in special cases: Geiger counters, some mutations, possibly certain decisions. On the currently most widely accepted version of inflation in the big bang, however, there was a time (very short and very early) in which the universe was so small that quantum physics affected everything. The universe inflated so fast that the quantum effects were not entirely washed out. The randomness introduced into the proto-stuff of that early universe results in the slight inhomogeneity that led to galaxy clusters and galaxies. 

The probability that we should have just these clusters, these galaxies, this star is going to be no greater than the reciprocal of the number of different ways you could take the stuff we have in the observable universe and rearrange with different clusters, galaxies, and stars with spacings not significantly different from the sorts of spacings we observe. (That is, the galaxies are not all huddled together or spaced uniformly about, do not all have the same number of stars.  Astronomers getting a look at one of these possible worlds would say, “That looks pretty much like our universe.”)  Each of these possible universes could, then, have been a quantum effect outcome of the big bang, and we only need to count them.  The probability of our exact universe is no greater than 1 divided by that extraordinary number. (It might be a good deal worse than this if, as some believe, early bang quantum effects had gone another way so that e.g. hydrogen would never have formed.)

When we are concerned, not with reality unfolding exactly as it did in full detail, but with your trip to the store as ordinarily described, we, again, have to adjust upward. There will be non-actual universes that differ from ours only in ways that don’t affect your existence or your trip to the store.  A likely candidate would be a universe with a slightly different arrangement of a cluster of galaxies barely within our light cone.  So for this question it isn’t 1 divided by the number of all possible universes. The numerator embraces all those possible universes with differences from ours so far away as not to make a difference, and doubtless some possible universes with differences from ours much closer that wouldn’t happen to be different for your descent chain -- even broadly conceived to include the long dead stars that produced the carbon in the molecules of your biological forebears. Lumping all these “wouldn’t make a difference” possible configurations of the universe into the numerator, will make it quite a large number. It will, however, still be much, much smaller than the denominator, there being so very many ways that early quantum effects could have arranged the universe that would have been uncongenial to producing you, and conceivably a few more you-congenial but not Oreo-congenial.

So it seems to follow from quantum theory together with the inflationary theory of the big bang that the objective probability as of the start of things that things should develop just as they did, and even the larger probability that you should buy what you did on your last trip to the store, are both small in a way that makes other smalls look large.