Quantum Physics and Perception
By Kenneth H. Norwich
Work in progress
To introduce the mysterious quantum physical experiment with which this project deals, in elegant but simple cartoon form, please view and enjoy the following You Tube video, which spans only 5 minutes and 12 seconds:
Dr. Quantum, Double-Slit
In summary, a diffraction pattern, which is a curve on a screen produced when waves pass through two slits, changes from one form to another when the observer, or “perceiver”, simply knows something about the waves – does not change anything in the apparatus – just knows something. Knowledge alone changes the pattern.
We replace the word knowledge with the word information, and we regard the gain of information as the loss in uncertainty. For example, if you are uncertain about the time (Is it 9 or 10 o’clock?), and I relieve your uncertainty, (It is 9) then you have gained information about the time. Let’s carry this idea a little further.
If you toss a fair coin, it may land heads or tails. Two possibilities. Uncertainty is 2 (actually the logarithm of 2, but that doesn’t matter). If you roll a fair die, it may land 1 or 2 or 3 or 4 or 5 or 6. Six possibilities. Uncertainty is 6. Uncertainty is not always that easy to calculate, but it can often be done.
The double-slit experiment is about the uncertainty of where a small particle may strike a screen. Instead of an electron, we can talk about a particle of light, called at photon. Same idea. It may pass through either slit (slit uncertainty) and may land on various places on the screen (screen uncertainty). Under very special conditions, the total photon uncertainty is preserved: that is, the sum of slit uncertainty plus screen uncertainty does not change. Now, if in some way you decrease the slit uncertainty (remember, that means gaining information about events at the slits), then the screen uncertainty will increase (loss in screen information) so that the sum of the two uncertainties remains unchanged. That is essentially the gist of this little paper. So you now understand it. However, let’s go back and add some of the details that were omitted.
Recall from Dr. Quantum that when you fire a particle (say a photon) at two slits, and the photon can pass through either (or both!!) slits and you don’t know which, then you get an interference pattern on the screen (Figure 1 below). Call this Case 1. However, if you repeat the experiment, but now you determine (i.e. you know) which slit the photon passes through, then you get a different pattern on the screen (Figure 2 below). Call this Case 2.
Figure 1 is an interference pattern, a curve showing where photons strike the screen. The taller the curve, the more probable it is that the photon will strike the screen at that point. We see that the photon will strike the screen largely in only 5 places (the 5 peaks in the screen pattern). However, in Figure 2, the photon may strike the screen anywhere from the left-hand side of the “bow” to the right-hand side. Figure 1 has a very small uncertainty in photon position; Figure 2 has a very large uncertainty. We can now understand why this occurs.
In Case 1 there was a larger slit uncertainty. The photon could pass through either of the two slits. So there is a smaller screen uncertainty (Fig. 1). In Case 2 there was a smaller slit uncertainty. The photon was known to pass through only one of the slits. So there is a larger screen uncertainty (Fig 2).
The sum of the slit uncertainty PLUS the screen uncertainty remained unchanged.
In reality, the argument is not quite this simple. Mathematically, we are restricted to measuring differences in uncertainties rather than absolute uncertainties. However, I think the above discussion does introduce the idea.
Figure 1. Double slit
Position on Screen
Figure 2 Single slit
This pattern is somewhat wider than the one shown by Dr. Quantum, a consequence of using very narrow slits.
Position on Screen
So, we now have a glimmer of understanding of the double-slit paradox, so beautifully illustrated by Dr. Quantum. When the experimenter, whom I call the perceiver, does not know through which slit the particle will pass (maximum screen uncertainty) he or she perceives the interference pattern of Fig.1. When the perceiver knows that the particle passes through only one slit, (reduced screen uncertainty; information passes to the perceiver) she or he perceives the pattern of Fig. 2. The perceiver emerges as an integral part of the experiment.
The foregoing is a simplification of a mathematical paper that I published recently*. The mathematical demonstration embraced only the case where there were very narrow slits. The grant generously awarded by Senior College has supported me in the endeavor to express the ideas more simply and perhaps more generally.
The mathematical details for some of the above material can be found in the journal paper:
*Kenneth H. Norwich, “Boltzmann-Shannon entropy and the double-slit experiment”, Physica A 462, 141-149, 2016.