Physics and Miracles

In some of my previous posts, I have discussed quantum physics, and I wish to do so again today.  I will assume that readers have some rudimentary understanding of quantum physics or, if not, can carry out a little research on the Internet to improve their understanding. I can assure you that it is really quite interesting and that this post should also be interesting. What I wish to do is to explore some of the counter-intuitive implications of quantum physics and of thermodynamics, and then discuss probability again. If you have, as I do, some sense that science itself suggests that reality has some kind of mystical or supernatural component to it, you might find the ruminations in this post stimulating.

One of the most important rules of quantum physics is the Heisenberg Uncertainty Principle. This principle states that it is fundamentally impossible to measure with absolute precision the position and momentum of a particle along a given dimension; it is also fundamentally impossible to measure the energy and exact position in time of a particle. The uncertainty in one quantity multiplied by the uncertainty in the corresponding quantity can never be less than a given amount, specifically Planck's Constant divided by two. We can never know anything for sure. The classic example of how this principle affects experimental results is a diffraction experiment. Suppose we fire an electron horizontally at a narrow horizontal slit, that this electron passes through the slit and then, after a couple of meters, arrives at a detector. Because the slit is narrow, there is only a small uncertainty in its position on the y-axis, so there must be a large uncertainty its vertical momentum. Consequently, the wave associated with the particle spreads out a lot, diffracts, and there is a much larger vertical uncertainty in its arrival destination at the detector than the uncertainty in its vertical position when it passed through the slit. This simple experiment is the classic demonstration of the idea that light and matter exhibit both wave and particle characteristics.

However, when we think about this experiment, we can see it leads immediately to paradoxical results. Although there is a range of possible locations the electron can arrive at at the detector, in reality it is observed to arrive at only one place. This means that, if we know the distance between the slit and the detector, and if we know the time it took to travel from one to the other, we should be able to calculate its momentum when it hit the detector and, extrapolating backwards, work out its vertical momentum when it passed through the slit. This means that we can estimate both the vertical momentum of the electron and its approximate position when it passed through the slit with less uncertainty that that permitted by the Uncertainty Principle. The Uncertainty Principle specifies that the exact position and momentum of a particle cannot be known simultaneously but does not say that we cannot perform multiple experiments on a single particle at different times and combine the results. A related paradox is that for the particle to hit the slit it must be travelling dead horizontally and must have picked up the vertical momentum it possesses afterwards as a result of passing through the slit.

There are two solutions to this apparent paradox but before I get to them I wish to to discuss a second paradox. Suppose a particle is trapped in a box and is in the n=2 energy state. In this situation (a thought experiment often found in elementary introductions to quantum physics), there is a 50% chance the particle will be found in one half of the box and a 50% chance it will be found in the other half of the box. But the chance it will be found at the centre of the box, at what is known as the 'node', is zero. So, if the probability of the particle being found at the centre of the box is zero, how does it pass from one side to the other?

As I said, there are two solutions to these apparent paradoxes. The first involves looking at the quantum world from a Bohmian perspective. According to Bohm, both particles and waves exist objectively, with the wave acting as a pilot for the particle, guiding it. Furthermore, according to Bohm, particles do not have fixed velocities when not under the influence of a force; rather, their speeds and directions are continuously changing, although not so much as to deviate completely away from the pilot wave. As it were, they are always tending to jiggle about. The Bohmian theory enables us to dissolve the first paradox – even if we know the momentum of a particle when it hits a detector, this tells us nothing about its momentum when it passed through the slit. In this way, we can rescue the Uncertainty Principle from the paradox. The Bohmian picture resolves the second paradox because it enables us to suppose that when a particle is at the middle of the box, its velocity is momentarily infinite, and this is why we will never find one dead centre.

The second solution to these paradoxes is to suppose that an electron or a photon can sometimes be a wave and can sometimes be a particle but can never be both at the same time. It is senseless to speak of the particle's momentum when it passes through the slit because, at this moment, it is not a particle but rather a wave. Likewise, it is senseless to suppose that a particle in a box is literally a particle, bouncing backwards and forwards between the two walls – rather what we have is a wave in a box. It is a wave that collapses into a particle at the moment it is measured.

These two solutions represent two different interpretations of quantum physics, the de-Broglie Bohm interpretation, which asserts realism, determinism, and non-locality, and the Copenhagen interpretation which is unreal and indeterminate. According to the Copenhagen interpretation, reality consists of waves that are underdetermined, and which 'collapse', taking on properties such as position and momentum, when they are measured, observed. What I've read suggests that many physicists have disputed the idea, an idea that seems to me to follow logically from the Copenhagen interpretation, that consciousness causes the collapse, that consciousness in a sense creates the universe, but I don't see any alternative way to parse this particular interpretation. Given that the Copenhagen interpretation paves the way for such a flakey view of the universe, it may be surprising to remember that the Copenhagen interpretation was the orthodox position among most physicists for much of the twentieth century, although Einstein, among others, was uncomfortable with it and very much fiercely opposed to it.

These two interpretations are not the only two interpretations of quantum physics that can be found. Another is the many-worlds interpretation of quantum physics. This particular interpretation has no bearing on the two paradoxes I described above, but I mention it for the sake of completeness. The many-worlds interpretation has it that whenever more than one outcome is possible, different universes branch off, each instantiating one of the possibilities. A novel I didn't enjoy much but which nevertheless influenced me a great deal when young was The Schrodinger's Cat Trilogy by Robert Anton Wilson, a book that explores this interpretation through fiction. Interestingly, although the many-worlds interpretation of quantum physics was very much in vogue when I was a teenager, today hidden-variable theories such as the de Broglie-Bohm interpretation seem very much more in fashion, more so even than the Copenhagen Interpretation.

At this point in the essay, I wish to move a little away from interpretations of quantum physics to discuss some other unbelievable occurrences that physics permits. Suppose you were to lower your head and charge at a brick wall. A slim possibility exists that you would pass through the wall and find yourself, intact and uninjured, on the other side. This is known as 'quantum tunnelling'. Ordinarily, it is only subatomic particles that tunnel (it happens routinely during alpha-decay and thermonuclear reactions) but it is not entirely impossible for a grown person to 'tunnel' in such a way through a wall. It is so incredibly unlikely that we can call such an occurrence practically impossible, but it is not absolutely impossible. And this slim possibility exists regardless of the interpretation of quantum physics to which we subscribe. Suppose, now, that you drop an egg onto the floor and it breaks. There is nothing miraculous or unbelievable about such a happening. But it is also possible for a broken egg to gather energy from the ground, reform itself, and leap off the floor into your hand. It is incredibly unlikely but still possible: all the laws of physics are time-reversible. Readers who feel that I must be wrong about this might think to cite the Second Law of Thermodynamics to refute me, saying that "The entropy of an isolated system can never decrease". However, this 'law' is not really a law at all but more a general rule. Statistically speaking, entropy can decrease, although it is far more likely to increase than decrease, and the chance of it decreasing is much greater for smaller systems than larger ones.

This discussion is relevant to miracles. A traditional definition of a miracle is that it is an occurrence that violates the laws of physics. But it seems to me that a miraculous event could be one that is enormously improbable but still possible within the scope of natural laws. In the same way that it is possible for a grown human to 'tunnel' through a brick wall or for a broken egg to reform and jump into a person's hand, it may be possible for a person to walk on water. Extremely improbable, yes, but still possible. In the post "Evolution and Chance", I argued that the neo-Darwinian explanation for evolution fails because the evolution of a new species through chance mutation and natural selection alone is so incredibly unlikely as to be impossible, and it might seem that I am now contradicting myself. What I am rather saying is that the evolution of intelligent life is a kind of miracle or series of small miracles, and that such miracles may have occurred in more than one form more than once in human history. Whether we concern ourselves with the evolution of species or wonder if, if Christ existed, some of the stories surrounding him were true, we might want to consider the notion that human development has been steered by something supernatural. We might want to take 2001: A Space Odyssey seriously.

I have frequently discussed probability in this blog. Especially in the post entitled "Probability and Schrodinger's Cat" and its sequel, I argued that any estimate of probability is subjective rather than objective. I thought that this opinion was original at the time but have since discovered that the physicist and philosopher E.T. Jaynes put forward a similar view. What, to begin with, is probability? Everyone knows that the chance of rolling a six on a fair die is 1 in 6. How do we know this? Because we were told this at some point. How did the teacher or tutor who told us this know it? If we assume that an estimate of probability is objective, if we align ourselves with those statisticians who calls themselves objectivists, we might suppose that some time in the past, someone rolled a die many, many times and determined that, on average, a six popped up 1 time in 6. The problem with this account is that to be absolutely certain of a probability determined by counting how often a certain outcome occurs, we need to roll the die an infinite number of times. We might only roll a die sixty times, find that we roll a 6 fifteen times (this is possible) and then then erroneously conclude that the probability is 1 in 4. Obviously this is not how we work out probabilities in the real world. Instead we just look at a die and see that it has six sides of equal size and so know that the possibility of rolling a six is 1 in 6. Similarly all we have to do is look at a roulette wheel to see that the chance of winning is 1 in 37 (if we bet on a single number).

When making an adjudication as to the probability of an event occurring, one forms an abstract mental model of the situation of interest, an ideal representation or prototype, a model that is inevitably underdetermined, and applies certain rules of thumb to it. Suppose Bob is presented with a pack of cards and asked the probability of drawing a Queen of Hearts from the top. He will say the probability is 1 in 52. Dave, however, knows that the top 26 cards are all red and so estimates the probability as being 1 in 26. Jane knows that the top card is either the Queen of Hearts or the Ace of Spades and so estimates the probability as being 1 in 2, 50%. Eric knows for sure that the top card is the Queen of Hearts and so estimates the probability as being 100%. Any estimate of probability emerges from subjective uncertainty; in a deterministic universe, if an agent possesses all the relevant information, he or she will know with absolute certainty what will happen with respect to a particular situation in its future. To take an extreme example, if we know beforehand all the forces acting on a die when it leaves a person's hand, arcs through the air and rolls across the table, we would be able to predict with absolute certainty which number will be uppermost when it comes to a stop.

One of the major revolutions of quantum physics, a revolution which few people appreciate, is that it introduced a new concept, objective uncertainty. You don't need to be E.T. Jaynes to have worked out that this is a problem – that in a deterministic universe, estimates of probability arise from subjective uncertainty, from the uncertainty of individuals, and that the introduction of objective uncertainty involves a reconceptualisation of the concept of probability. The Heisenberg Uncertainty Principle, Schrodinger equation and Dirac equation all suggest that the universe itself is uncertain, indeterminate. This seems to me a mistake as it seemed to Jaynes – I think we should get rid of the idea of objective uncertainty altogether. We should say rather that these equations describe what we can know about the universe. The universe might be deterministic but the hidden variables at play are variables we can necessarily know nothing about. This means, among other things, that it may be impossible to know which of the interpretations of quantum physics I discussed above is true. It may also mean that if God does intervene in the world, He likes to keep His hand hidden.

I'll conclude by saying something about this blog. I have talked about my life in it in the past but have not done so for quite a while. This does not mean I have nothing more to say about it. I am still under a Compulsory Treatment Order, still cognitively enfeebled by medication, and am still banging my head against the brick wall which is the insane, evil, and idiotic Mental Health Service. A couple of days ago, my key worker said, "Would you rather be right or happy?" For me, it's not a choice. It has been living with lies for many years that made me 'ill'. All I want is for the sociopathic and mentally retarded psychiatrists who have been treating me to apologise and let me go. I don't know if this will ever happen.