Parashat Pekudei 5782 — 03/05/2022
Beginning with Bereishit 5781 (17 October 2020) we embarked on a new format. We will be considering Rambam’s (Maimonides’) great philosophical work Moreh Nevukim (Guide for the Perplexed) in the light of the knowledge of Vedic Science as expounded by Maharishi Mahesh Yogi. The individual essays will therefore not necessarily have anything to do with the weekly Torah portion, although certainly there will be plenty of references to the Torah, the rest of the Bible, and to the Rabbinic literature. For Bereishit we described the project. The next four parshiyyot, Noach through Chayei Sarah, laid out a foundational understanding of Vedic Science, to the degree I am capable of doing so. Beginning with Toledot we started examining Moreh Nevukim.
Shemot 38:21-40:38
Our discussion of causality, occasioned by Rambam’s discussion of the root Y-L-D, to give birth to, has taken us far afield. Up till now we have been discussing Relativity theory, which is most pertinent in discussions about cosmic structures and events. Today I want to start a discussion of quantum mechanics, which is on the other end of the size spectrum, being pertinent at atomic scales and below. Trying to integrate quantum mechanics and Relativity theory is one of the most intractable problems in physics today.
There are many fine, non-technical works that describe the early development of quantum theory, and for our purposes we don’t need to recapitulate that story in its entirety. Quantum theory began when it was discovered that light, which was known to be a wave of the electromagnetic field, was discovered to have particle-like qualities. Planck was the first to propose that radiant energy came in packets in order to explain the spectral distribution of black body radiation (1900). Shortly thereafter, Einstein used this idea to explain details of the photoelectric effect, Shortly thereafter, Einstein used this idea to explain details of the photoelectric effect, where light hitting a metal surface causes electrons to be ejected from that surface (1905 – this is the work that earned Einstein the Nobel Prize). The “packets” of light energy were called photons, and it appeared that at times light acted like a wave, and at other times like a particle.
This dual nature becomes more pronounced when light is passed through a diffraction grating. If you send a beam of monochromatic light through a diffraction grating, you get a series of darker and lighter bands on whatever screen we use to view it on. This is all very well-understood based on the wave nature of light. However, if we now reduce the intensity of the light we find a strange phenomenon – where the light hits the screen, there are individual dots of light (or exposures on a photographic plate). Eventually, if we leave the photographic plate in place long enough, the dots will merge into the familiar light and dark bands, but each band is made of individual dots. After pondering these kinds of experiments for a while, physicists worked out that light is a wave, except when we go to measure it, at which point it “collapses” to a particle which can be detected.
The experiment was repeated with electron beams, instead of light beams, and the results were the same. A strong beam passing through a diffraction grating produced the characteristic light and dark bands, but when the beam was reduced to one electron at a time, the electrons could land anywhere. All that could be said about the position of any individual electron was that it was more likely to wind up where the bands were dark and less likely where the bands were light. It was recognized that despite their important differences, both electrons and light acted like waves when they were free, but appeared to “collapse” when they were measured. The probability of any particular outcome is given by the square of the amplitude of the wave at that particular place.
This of course really messes with our ideas of causality! It would seem that if a particle is really a particle, we should be able to measure where it is and how it is moving, and from this predict its future motion – like a billiard ball. But now we see that a “particle” is also a wave, and the wave has very different behavior from a particle. Defining the wave as a probability amplitude for finding the particle at a particular position is a way of joining the two interpretations together, but at the expense of removing exact measurement from physics and replacing it with probability. This caused profound unease among physicists. Einstein famously remarked, “Gd does not play dice with the universe.”
This change from a wave to a measurable particle is sometimes called the “collapse of the wave function.” The collapse of the wave function is random, and it occurs during the process of measurement. Various attempts were made to get around the collapse of the wave function, but they all failed. Any fully local attempt to add variables (“hidden variables”) that we cannot measure, but which provide at least a theoretical foundation to restore causality, were found to be impossible in principle – they lead to results which contradict what we measure (Bell’s Theorem). In fact, there has been a lot of excitement recently about quantum entanglement,which is the very phenomenon that Bell analyzed to demonstrate that if quantum mechanics is true, the very idea of localized particles must be false.
I want to back up a bit and return to the statement that the collapse of the wave function takes place during the process of measurement. If we consider the process of measurement, we realize that it is the process that connects the subject, the consciousness of the observer, to the object of observation, whatever that object may be. In other words, measurement, which is just a more precise form of perception, links the consciousness of the observer to the physical phenomenon that is being measured. In other words, it is precisely when consciousness interacts with the physical world that we get this kind of “collapse.”
Now the nature of a wave is that it is inherently non-local. Go to any body of water and look at the waves, and it’s easy to see that they’re spread out over the surface of the water, and they’re moving in time as well. When we measure the position of the particle, we’re asking a wave to behave in a way that’s totally foreign to the nature of the wave. Nature does respond, but not in a deterministic manner. Instead, we get only probabilistic results. I want to point out that the equations describing the evolution of the wave function (Schrödinger’s equation in the simple cases we have been discussing) are completely deterministic. That is, there is no randomness in the wave function itself; it is only when we try to interpret phenomena as localized particles that we run into trouble.
In essence, what we are doing when we try to measure the position (or other characteristics) of particles, we are trying to force nature to fit our paradigm. The resulting misfit shows up as uncertainty, but that uncertainty is in our consciousness, not in nature. We, of course, can’t force nature to do anything. What we are doing is applying our limited consciousness to unbounded nature, and of course our evaluation of it is wrong! We are asking nature stupid questions, and like any good mother, she tries to give us the best answer she can, while gently nudging us to open our eyes and see reality as it is, not as we think it must be.
Next week I will, Gd willing, continue looking at quantum entanglement and causality, and look at the idea of locality from a different angle.
Chazak, Chazak v’Nitchazeik!
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Commentary by Steve Sufian
Parashat Pekudei
“Pekudei” means “amounts of.” Aaron’s son, Ithamar, kept track of the half-shekels that were donated and those who Gd has filled with wisdom use them to create the parts of the Mishkan, the Tabernacle; they bring them to Moses who assembles them into a Whole: Gd’s Presence fills the Tabernacle.
We may have a vision of the Whole that allows us to create each part according to the plan, human or divine. But to assemble the parts into a whole, a Whole, we must have harmony with ourselves and our Self, with our surroundings, with Gd, so that we assemble from a level of Wholeness.
“Moses” is a quality of Wholeness, connectedness, that is within each of us, within everybody.
Through our innocence, our faith, our service this level of Wholeness becomes more and more functional in our lives; we gain the Support of Nature, of Gd, to complete our tasks in a way that is lasting. Our personalities, bodies, homes become Tabernacles, Temples within which Gd’s Presence is experienced as the Eternal Reality.
How fortunate we are, to be innocent, to trust, to serve and to be Blessed and Blessed so that Gd’s Presence becomes more and more visible and soon! fully visible to all of us, to everyone!
How fortunate we are!
Baruch HaShem