© Chris Port, 2011
I was in a pub last night thinking about incomprehensibility (as you do). This was nothing to do with alcohol and the eternal mysteries of women. I was thinking about quantum mechanics. Stay with me now. This is only a three-pint epiphany, not a ten-pint skype from God…
I was reviewing a throwaway line in another post (see #264. A Classic Example Of How Empiricists Can Get Themselves Into Trouble... Which came first, maths or the universe?)
“The uncertainty principle, and the strange interference of measurement and even consciousness on quantum level 'events'/probability waveforms, are still profoundly incomprehensible to us.”
I was troubled by what I had actually meant by “incomprehensible”, and whether this was technically correct. Let’s shove quantum mechanics to one side for a moment and consider a car instead.
I don’t know much about car mechanics either, but I think it’s safe to say that I ‘comprehend’ what a car is. It’s a travel machine. I know roughly how it works. We extract a fossil fuel called oil (ancient mushed up plants and animals) from underground. We clean it up into petrol and put this into the machine. The engine burns the fuel to provide locomotive energy. An ingenious system of pistons and cranks uses this energy to turn the wheels. I don’t need to have a detailed knowledge of the intricacies of the internal combustion engine to comprehend a car.
Let’s return to quantum mechanics.
“Heisenberg was dismissive of attempts to understand what was ‘physically’ going on. As far as he was concerned, all that could be claimed about quantum mechanics was that the maths worked.”
If we take Heisenberg’s assertion at face value, then all we can ‘comprehend’ about quantum mechanics is the mathematics. In this instance, the mathematics is an analogy. The problem with analogies is that they can be misleading.
Let’s return to the car again. I don’t have a problem comprehending a car because it’s part of my everyday experience. But suppose we demonstrated it to a remote isolated tribe with no previous experience of technology.
Since the car has no visible means of propulsion, they would probably be perplexed. Their first attempt to comprehend a moving car might be to assume that it was ‘alive’ or animated by some invisible spirit.
Suppose an engineer tried to explain to them the basic mechanics of the car as mentioned earlier. Since they would have no everyday experience of concepts such as fuel and engines, he would have to use simple analogies by referring to more familiar concepts.
He could try something like this.
“When you eat and drink, that is fuel for your body. Your body turns food into energy. Your heart is like an engine. It pumps this energy around your body in the blood, and you can move. This liquid we call ‘petrol’ is food for the car. The engine is a bit like your heart. These mechanical parts are like your muscles. They turn the wheels and the car then moves.”
This analogy now starts to create a whole new set of problems…
“So, if the car is like our bodies, is it alive? Can it think and feel?”
“No. It has no mind of its own. It’s just a tool. We control where it goes and what it does.”
Now the analogy has moved into an even more perplexing concept: a mindless body… Something that behaves like us but is not like us….
Questions such as “What is the mind?” or “Am I just a car moved by the Gods?” might start to crop up. At this point, the frustrated engineer might start to get a bit irritated.
“Look. It’s just a comparison. Don’t get too hung up on it. All you need to know is… this is roughly how it works. Don’t worry about the mind. That’s got nothing to do with it. It just… works, ok?”
Some members of the tribe might be intrigued by this and want to find out more. They are starting to grasp that the analogy is flawed. They start to ask more questions: about the different engine parts, where the fuel comes from, how the machine ‘digests’ its food.
Other members of the tribe might huddle in frightened groups, speculating about supernatural explanations that are more familiar and comprehensible to them.
Whether the tribe decide to explore the 21st century, or sacrifice the engineer to the Car God, I leave to your imagination.
The underlying point is this: in quantum mechanics, is mathematics ultimately just a pedantic and misleading analogy?
Quantum mechanics accurately models the emergent behaviour of uncertainties in the quantum foam without semantic ambiguity. Advanced mathematicians profoundly comprehend the complex mathematics involved. Physicist pundits translate the maths back into physical analogies at a macroscopic scale to give them conceptual form (e.g. Schrödinger’s Cat, electrons ‘knowing’ where they’re meant to be, etc.)
Obviously, the more analogies we throw into the mix, the more scope for misunderstanding there is. (“Yes, it’s sort of like that. Only it’s nothing like that at all. If it helps to think of it that way, fine. But you really need to understand the maths to get it.”)
This, of course, brings us back full circle to Heisenberg’s interpretation. Quantum mechanics is the maths. It’s not anything else. So, was I wrong? Is quantum mechanics comprehensible (if only to mathematicians)?
The maths is incomprehensible to most laymen, but comprehensible to the initiated. However, the physical processes it notates are still just as profoundly incomprehensible to the advanced mathematician as they are to the casual dilettante.
The reason for this should now be clear. Car mechanics would be profoundly incomprehensible to a pre-technological tribe because it is outside all of their everyday experiences. If we try to explain the basic concepts using familiar references, our analogies just raise more questions than they answer.
If the car was to become part of their everyday experiences, it would become demystified through familiarity. They have comprehension ‘options’. They could leave their remote homeland and live in a technological civilization, or they could decide to allow technology to become part of their everyday existence.
But this familiarization option is not available to even the most brilliant mathematician or physicist. The quantum foam is profoundly imperceptible to us because it can never become part of our everyday experiences. For this reason, I think I was right. No matter how complex a mathematician’s understanding of the maths, he can never comprehend what the maths actually means.
Quantum mechanics is (and always will be) an analogy rather than an ontology. All we can truly understand about it is the analogy, not the ‘reality’. For this reason, it is correct to say that it is profoundly incomprehensible, because analogies will always raise more questions than they answer. Comprehending analogies (and the trouble they can get you in) is the task of philosophy, not maths or physics.
Consider the delightful philosophical paradoxes of the wonderful Richard Feynman…
"If you think you understand quantum mechanics, you don't understand quantum mechanics". ~ Richard Feynman
“To those who do not know mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty, of nature ... If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in.” ~ Richard Feynman
“If I could explain it to the average person, I wouldn't have been worth the Nobel Prize.” ~ Richard Feynman
“We can't define anything precisely. If we attempt to, we get into that paralysis of thought that comes to philosophers… one saying to the other: "you don't know what you are talking about!". The second one says: "what do you mean by talking? What do you mean by you? What do you mean by know?" ~ Richard Feynman
“So, ultimately, in order to understand nature it may be necessary to have a deeper understanding of mathematical relationships. But the real reason is that the subject is enjoyable, and although we humans cut nature up in different ways, and we have different courses in different departments, such compartmentalization is really artificial, and we should take our intellectual pleasures where we find them.”
“...the "paradox" is only a conflict between reality and your feeling of what reality "ought to be.” ~ Richard Feynman