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IN QUEST OF INFINITY – 25
By Prof. G. Venkataraman
Loving Sai Ram and greetings from Prashanti Nilayam. This is the 25th article in this series and all I can say is WOW! I am astonished that not only have I been able to come this far, but also retain so many of you dear readers! So let me start with a big thank you to all of you loyal readers out there.
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Artists conception of the dual nature of our sub-atomic material reality as both particles and wave-forms |
When we were together last, I was trying to tell you something about the complexity of the philosophy behind Quantum Mechanics [QM]. As a tool box, QM has become so common that students everywhere now routinely use it for solving all kinds of problems in widely different areas, ranging all the way from astro-physics to chemistry and bio-molecules.
However, when it comes to what the maths means, it still is a mystery, a mystery that has bugged even the pundits, then and also now it seems.
The Magical Cat who is Both Alive and Dead
Just to highlight this last point, let me start off this instalment with a brief reference to what is sometimes called Schroedinger’s cat paradox. The paradox, invented by Schroedinger himself, is a macabre gedanken [thought] experiment.
To perform the experiment, one first gets hold of a box. Into this is fitted a deadly contraption consisting of a bottle of hydrogen cyanide and a hammer held by a clip. The figure below gives you some idea of what I am talking about.
The clip is connected to a device that can detect radioactive emissions. In front of the detector is placed a radioactive source. The idea is that when the detector registers a particle emitted by the source, the clip holding the hammer is released. The hammer than falls on the bottle, breaks it, filling the chamber with cyanide vapour.
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FIGURE 1: Given here is a schematic of the gedanken experiment devised by Schroedinger to highlight the difficulties of interpreting QM. In this experiment, there is a lethal gadget that consists of, to start with, a weak radioactive source, that emits on the average, roughly one particle per hour. The emitted particle is detected by a particle detector [in those days, the most commonly used detector was the famous Geiger-Mueller counter].
Whenever a particle emitted by the source enters the GM counter, it gives out an electrical pulse, which can be made use of in many ways, depending upon the preference of the experimenter. In this case, the electrical pulse is supposed to release a clip holding a hammer. If the clip gets released, the hammer falls on a glass bottle, and breaks it, spilling its content. And what is in the bottle? Deadly hydro-cyanic acid! Why? All this is explained in the text!
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Now why all this deadly plotting? Ah, that is where the poor cat comes into the picture. When everything is almost set up, a cat is put into the box, the release clip put in place, and the lid of the box is quickly closed. By the way, the box is made of steel and so one cannot see inside.
OK, we have set up the gadget which clearly has some evil intention behind it, and in this environment, we have placed a poor cat! But what has all this got to do with QM? That is what Schroedinger explained. He said [in effect]: “Let us suppose the radioactive source is quite weak which means it would emit a particle only once in a while; say that on the average there is only a 50% chance of a particle being emitted during one hour – one can have sources that are as weak as that, in fact even much weaker. Anyway, let us assume that is how weak our source is.
We place the cat in the box immediately a particle has been emitted [taking care of course that the hammer is not allowed to be released at that time!]. We then quickly make the release clip on the hammer operational, close the lid and wait for one hour. Remember that during this period, there is a fifty percent chance for a radioactive particle to be emitted, and thus a fifty percent chance for the cyanide bottle to broken and the cat to die. However, we do not know that for sure; we just have a probability.
“Question: Without opening the box, what can we say about the fate of the cat” An average person would possibly say, “Well, there is a 50% chance the cat is alive.” Suppose you insist, “Give me a definite answer,” the person would respond, “That I cannot do.”
What about QM? It says, “The cat is in a state where it is both alive and dead.” To us that might seem absurd, but the strange thing about QM is that when no observation is made, it can talk only of potentialities. From the quantum mechanical point of view, the cat has the potentiality to be alive and also the potentiality to be dead. Hence, QM’s answer is that the state of the cat is one where it is alive as well as dead.
To us of course, this answer would be pure nonsense; either the cat is alive or it is dead. Thus, after a while during which all this big debate was gong on about the meaning of QM, some people said, “It seems from Schroedinger’s cat paradox that the way people are interpreting QM is wacky!”
An Unclear Picture
To be factually correct, this is not the way Schoredinger described it. His version of the description of the experiment is given in BOX 1 below. And about the meaning of QM he said that the physical interpretation of reality given by QM is actually a “blurred model” of reality. In other words, Schroedinger was cautious and essentially said, “The math is OK, but trying to interpret it the way it is being done now is not acceptable to me! We really cannot squeeze these equations to construct an intellectually acceptable picture of reality, at least not as things stand at present. ” That is the essence of what he said then, way back in the early thirties.
I hope I have not lost you! Basically what I have been trying to tell you is that while people quickly became skilled in using QM as a superb tool-box, very few understood what QM really implied, especially in terms of physical reality. And as the years went by, some of these issues became murkier and murkier, that is to all but a select few.
One reason for this apparent clouding of the issues was the enormous progress made in the physics of elementary particles. Basically, as one tried to study matter on a smaller and smaller scale, it also meant the study of phenomena on a smaller and smaller time scale. What made this combination of small length and time scales particularly interesting and exciting is that these are precisely the sort of conditions encountered in the Baby Universe, that is to say when the “age” of the Universe [age being reckoned of course from the “instant” of the so-called Big Bang] was about 10-30 seconds or even less!
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Einstein concedes to Bohr's QM theoretical position, but with strong reservations
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It emerged that on such small time scales [the length scales too were incredibly small], both Space and Time were quite possibly grainy! What kind of Physics Laws hold sway under such mysterious circumstances? To this day, no one knows for sure!
So you see, while the “technology” of QM has become very sophisticated, our understanding of its basics has also become more and more difficult. Nevertheless, it has become clear to the physics community as a whole, that there is a lot more than to QM than just the rule book and the tool box it provides. Why do I say that? For the following reason, and to explain it all, I must go back to about 1931 or so.
The first round of the great Einstein-Bohr debate, which took place largely during various conferences held in Europe, ended with Bohr being declared the “winner”. Einstein admitted he was not quite successful in rebutting QM, but continued to believe that all was not OK with QM, and that one day, QM would be replaced by some other new “super theory” where there would be no room for fuzzy interpretations and where Causality would once again reign supreme.
Meanwhile, Hitler had come to power in Germany and started his witch-hunting of Jews. It was time to worry about personal safety more than about what QM did or did not imply, and most Jews in Europe, particularly those in Germany did all they could to escape to safe havens. Einstein too joined in the exodus and having sold off his house in Berlin, left for America for good.
Having achieved world-wide fame already, it was no problem for Einstein to find a position, and soon he settled down in the small town of Princeton in the state of New Jersey, as a Professor in the Institute for Advanced Study, a position he held till his death in 1955.
Einstein, Podolsky and Rosen Enter the QM Debate
The issue of personal safety having been successfully solved, Einstein began to concentrate again on the one issue that was bothering him, namely, what did QM really mean? Working with two collaborators named Podolsky and Rosen, Einstein published in 1936, in the prestigious American journal the Physical Review, a paper entitled: Can Quantum Mechanical Description of Physical Reality be Considered Complete? By the way, this paper soon became famous and is generally referred to in the trade as the EPR (Einstein, Podolsky and Rosen) paper.
EPR began with the remark that for a theory of physics to be considered successful, it must be subjected to two tests:
- Is the theory correct?
- Is the description given by the theory complete?
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The very act of observation to measure a system in QM disturbs that system |
As far as the first question is concerned, EPR did not doubt the [mathematical] correctness of QM; in fact, Einstein had conceded this point as far back as 1930. The point at issue now was: “Could QM claim to be a complete theory?” This raises the question: “How to judge whether a theory is complete or not?” EPR themselves gave the answer. They said:
If without disturbing a system, we can predict with certainty [i.e., with probability equal to unity] the value of a physical quantity, there exists an element of physical reality corresponding to this physical quantity.
I should point out at this juncture, that basically EPR wanted to show that they did not quite subscribe to the Heisenberg Uncertainty Principle [which I have already discussed earlier]. If you recall, the crux of the principle is that if you want to know something about a system, you have to make an observation on the system; and when you do that, you are likely to disturb the system; the net result is that the value you measure for a property right now might not be quite be the same as the value that existed before the observation was made!
In other words, the very act of observation and measurement disturbs the system, which immediately raises all kinds of questions about physical reality. By the way, in Classical Physics, the assumption is always made that ideally, it IS possible to make measurements of the property of a system without disturbing it in the least. What EPR were now essentially saying was:
We would now describe a gedanken experiment where we make an observation and yet can make an exact determination of certain quantities; according to conventional wisdom this should not be possible, since the system would have been disturbed. Our analysis shows that conventional wisdom is in error; in turn this means, according to us, the notion that QM is a complete theory is wrong!
Let us briefly examine how EPR went about trying to knock out Bohr! Before I begin, I must caution you that the narrative that follows is very descriptive and qualitative and also full of hand-waving! But, as you would appreciate, that is inevitable at the level of presentation we are trying to maintain. I assure you, however, that despite these limitations, truth is not being sacrificed! With that caveat, let me proceed. Here is an extremely [over-simplified] account of the EPR gedanken experiment, the essential elements of which are sketched in Figure 2.
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FIGURE 2: This figure presents a schematic of the gedanken experiment invented by EPR to question the picture of reality that QM gives. (a) shows two particles held together by a spring in compression. When the spring is cut, the two particles would fly off in opposite directions as in (b). EPR argue how, by making observations on particle 1 alone, they can determine with infinite accuracy the position AND the momentum of particle 2.
This of course would violate the rules of QM. But EPR say: “We don’t care! Here is an experiment where your rules don’t work! What do you have to say about it?” That was the bombshell delivered from across the Atlantic that Bohr had to deal with. How he did that and what happened later is all described in the main text.
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There are two particles held in tension by a spring. The spring is cut, whereupon, the two particles fly away from each other in opposite directions, of course. Say the particles are 100 km apart; it does not really matter how far apart they are. EPR say:
Listen. According to QM, there are six quantities associated with these two particles. They are as follows:
- p1 and q1, which denote respectively the momentum and position of particle 1.
- p2 and q2, which denote respectively the momentum and position of particle 2.
- P which is the total momentum of the two-particle system, i.e., P = p1 + p2.
- Q which is the separation between the two particles, namely, Q = q1 – q2.
We also keep in mind the following facts:
- p1 and q1 cannot be simultaneously measured with infinite accuracy; that is what the Uncertainty Principle says, and we accept that.
- p2 and q2 cannot be measured simultaneously measured with infinite accuracy for the same reason.
- However, P and Q can be; QM allows that, thank God!
Let us now go to work.
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Nathan Rosen |
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Albert Einstein |
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Boris Podolsky |
EPR then go through careful arguments which are a bit too detailed for us and so I shall skip them. But one important aspect of their analysis is easy to understand; they simply avoid making any measurements on particle 2; all their observations are confined to a) particle 1 alone and b) the TOTAL properties of the system as enshrined in P and Q. From these observations, they then calculate the values of p2 and q2. They then say [effectively]:
At the end of it all, we have been able to determine accurately BOTH the position AS WELL AS the momentum of particle 2. Your way of describing QM says that is not possible. However, by using exactly the rules that YOU have laid down, we have been able to describe a situation where we can in fact beat the system and achieve what you claim is impossible! So, there you are!! Your QM does not appear to be a complete system.
I know I am taking many liberties in telling the story, but in essence that roughly was the argument made by EPR. Just to add a touch of contact with history, I would like to quote here the closing statement of EPR. They said:
The [Schroedinger] wave function does not provide a complete description of the physical reality, and we have left open the question of whether or not such a description exists.
The EPR paper was submitted to the Physical Review on 25th March 1936, and was published a few months later. As soon as it appeared in print, The New York Times carried a story under the heading: Einstein Attacks Quantum Theory. Einstein strongly condemned the article saying that it did not properly reflect his views. Be that as it may, Einstein had challenged QM, and back in Europe, Niels Bohr took due notice of it. Rosenfeld a close associate of Bohr later recalled:
This onslaught came as a bolt from the blue.....A new worry could not have come at a less propitious time. Yet, as soon as Bohr heard my report of Einstein’s arguments, everything else was abandoned!
Bohr Rebuts EPR
Bohr did not take the challenge to QM lying down. He replied with a paper of his own, in the Physical Review. Bohr’s arguments were long, complicated, and as always quite difficult to follow. He made two substantive points: 1) The first was technical and refuted the idea that when measurements are made of p1 and q1, they do not affect the value of P. Bohr said that is incorrect, and that is one weakness in the EPR argument. 2) Bohr’s second point was that EPR were quite ambiguous about what exactly they meant when they used the word “reality”.
So what did Einstein think of this rebuttal and what about the general public, meaning the physics community in this case? Einstein took one look at Bohr’s arguments and said, “Look, suppose the two particles are say, a trillion miles apart. How then would particle 2 know anything about measurements made on particle 1, until information of some kind travels from particle 1 to particle 2? That would take a huge amount of time since light travels at finite speed. The way Bohr is talking, it is as if information can travel from particle 1 to particle 2 with infinite speed; but that is against Relativity! So, I simply do not buy Bohr’s argument!”
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If two particles are separated by a great distance, how can the measurement of one effect a change in the other simultaneously? |
And so the difference remained, with each claiming flaws in the argument presented by the other. The question thus became: “OK, all this is fine; these two giants have very differing views, but what does Nature say?” That question was answered only after both Bohr and Einstein were gone, and the answer came from some very clever experiments performed in Europe during the seventies, using laser beams. The whole thing is quite complicated, and I am not too sure if I would be able to explain it in simple terms. But the essence of those experiments can certainly be stated in a simple manner.
The Web of Universal Relationship
The experiments showed that when particle 1 is observed, particle 2 does get disturbed and there is no question of calculating its properties the way EPR tried to. The question immediately arises: “But how on earth would that be possible? For particle 2 to know that a measurement has been made on particle 1, some signal/message has to come from that particle, and if the two particles are a trillion miles apart, it would be a long, long, time, before particle 2 even comes to know that its erstwhile partner has been disturbed. And, according to relativity, information cannot travel faster than light; so, something is surely wrong somewhere.” But then, Nature is full of surprises, and this was one time when it pulled off a huge one. Nature said, “Listen folks, you people are talking as if the two particles are separate. There is no two but only one!”
Now that sounds like a Swami Discourse, does it not? Indeed, and with good reason, which is that in the physical world too, there is actually only one entity! You don’t have to take my word for it and just hear what two experts say. First, we hear from Gary Zukov, who in his famous book Dancing Wu Li Masters says:
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Gary Zukov's book |
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The philosophical implication of quantum mechanics is that all things in our Universe [including us] that appear to exist independently are actually parts of one all-encompassing organic pattern and that no parts of that pattern are ever really separate from it, or from each other…. In short, the physical world, according to quantum mechanics is not a structure built out of independently existing unanalysable [indivisible] entities, but rather a web of relationships as a whole.
If you think that is weird, listen now to what Professor Geoffrey Chew of Berkeley says:
Your electrons and mine are only approximately distinguishable. In denying objective reality [that Einstein vehemently stood by], quantum mechanics denies absolute status to your individuality. The only individual is the entire Universe.
I hope you are able to appreciate what I am driving at; you had better, because the point is not only a subtle one but quite profound, at least in my opinion. And, as I shall point out [hopefully in the next instalment], this point of view is in fact shared by many leading physicists. Let me stop beating around the bush and come to the point itself.
It is that at its subtlest level, Modern Physics is in fact corroborating the Vedantic truth that underlying the seen and experienced world, there exists a mysterious substratum. Of course, Modern Physics does not talk about the Soul, good and evil, etc. But to say that the reality behind what is perceived as many is actually ONE, makes Physics appear just one step away from Vedanta. Where does that leave the scientists, a good number of whom are trying to debunk God?
Those are the interesting topics we shall begin to explore when we slowly make the transition from the Physical Universe and the realm of Modern Physics to the bridge of Meta Physics, before crossing over to the Infinite realm of Vedanta!
I shall stop right here, because that journey would require you to make a lot of preparations; and you have exactly one month to get ready!
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The Diabolical Cat Paradox Gedanken
Given below is how Schroedinger himself described his gedanken experiment relating to the cat, now famous as the Cat paradox.
A cat is penned up in a steel chamber with the following diabolical device [which must be secured against direct interference by the cat]: In a Geiger counter there is a tiny bit of radioactive substance, so small, that perhaps in the course of one hour one atom decays, but also with equal probability, perhaps none; if it happens, the counter discharges and through a relay releases a hammer which shatters a small flask of hydrocyanic acid. If one has left this entire system for an hour, one would say that the cat lives if meanwhile no atom has decayed. The first atomic decay would have poisoned it.
The above is the actual description of the cat experiment by Schroedinger himself. His discussion of the experiment is too technical to be included here! |
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To be continued...
Dear reader, how do you like this series? Please share your impressions about this article by writing to h2h@radiosai.org mentioning your name and country. Thank you for your time.
Previous Articles In The Same Series |
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