The nine billion names of God

English: A GIF animation about the summary of ...
English: A GIF animation about the summary of quantum mechanics. Schrödinger equation, the potential of a “particle in a box”, uncertainty principle and double slit experiment. (Photo credit: Wikipedia)

If you are an easily offended religious fundamentalist you should probably stop reading this now.

The nine billion names of God” is a famous science fiction short story by Arthur C. Clarke. In essence the plot is that some researchers complete a piece of work and suddenly notice that the world is being switched off.

A piece of whimsy, obviously. But what if it were something that could really happen (I am now risking a listing under “questions to which the answer is no” by John Rentoul)? If your scientific experiment reached a conclusion would you just let it run on, or switch it off (or maybe wait till your paper was accepted and then switch it off!)

The issue here is the question of whether or not the universe, as we see it, is in fact all just a gigantic computer simulation. As I have written before, if we accept that computing power will continue to grow without limit we are almost bound to accept it is much more likely we are inside a simulated than a real universe. Of course, if the universe was confirmed as a simulation it would make no physical difference to us (though I suspect the psychological blow to humanity would be profound), so long as nobody turned the simulation off.

Testing whether it is true that the universe is simulated requires finding a fundamental minimal size beyond which we cannot further explore the universe: this is because computing a simulation relies on the fundamental digital nature of a computer – you cannot get below one bit, however you have scaled the bits. Now, chance, God, the simulators (take your pick) have made this quite difficult via the Heisenberg Uncertainty Principle:

\sigma_x\sigma_p \geq \frac{\hbar}{2}

Where \sigma_x is the uncertainty in a particle’s position, \sigma_p uncertainty in momentum and \hbar a very small number – 1.055 x 10^{-34} Joule seconds. In most situations the very smallness of \hbar means the uncertainty principle is of no concern but once we start to reduce \sigma_x (ie look at extremely small parts of space) then \sigma_p starts to soar and the amount of energy needed to conduct experiments also flies through the roof.

But nature also gives us extreme energies for free in the form of cosmic rays and these could hold the clue as to whether the universe is grainy (hence a simulation) or smooth (at least at currently detectable sizes).

Footnote: the fundamental weakness in the argument seems to me to be the fact that computing is increasingly showing that an unlimited increase in computing power is unlikely. But if you want to know more about this I really do recommend Brian Greene’s The Hidden Reality.

Magnetic fields, again

English: The magnetic field of a bar magnet re...
Image via Wikipedia

I asked a couple of questions about magnetism before and I have to say I was not fully convinced by the answers – so here is another way of stating what puzzles me.

Imagine a static magnet. Now magnetism cannot propagate instantaneous as if it did the magnet would surely immediately cease to be magnetic – even though we know, via Oblers’s Paradox if nothing else, that the universe is finite, we must surely also assume it is very large and contains a very large number of magnetic objects.

So magnetism is propagated at some finite speed. Naturally we will assume that speed is c , the speed of light and the propagation is via photons. But what are these photons?

If they are real, physical particles, then they must carry energy and so the magnet should ‘run down’ – otherwise it would be a perpetual motion machine. But static magnets apparently run down very slowly – so slow I have never been aware of it really happening, though I have no doubt it does.

So what else might they be? Presumably a function of quantum electrodynamics (QED) as formulated by Feynman? In this case then the energy of these “virtual” photons is a function of the uncertainty principle.

This would essentially mean that the strength of these magnetic photons would be limited by \delta E \delta t \leq h where E is the energy of the QED photon, t time and h the familiar Planck constant – a very small number indeed.

Here the particles can come and go in an instance or presumably, live mysteriously for a very long time at very low energies. But no actual energy is expended unless this virtual photon is “observed”.

So, is this right? And if it is, how did anyone explain magnetism before QED? And if it is wrong how do magnetic fields propagate.

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