| 1Lurçat,
2006, p. 61
2See Newell, 2004 |
I read with some disappointment François Lurçat's paper on Phenomenology and Quantum Physics in The St. John's Review. Yet, as he stated "Today mimetism and unanimity are harmful to science,"1 so perhaps he will pardon me if I attempt to serve science and differ with the views that he expressed. I do not, of course, wish to differ with everything that he said. I strongly agree that the metaphysical foundations of science need to be reassessed and revised,2 and that, when science itself veers off toward the irrational, it is fair to regard that as a pressing crisis. |
| _________________ | Yet, while desperate times may call for desperate measures, it is always better to keep your head while those around you are losing theirs. I think all persons with a scientific approach to things would be happier with an explanation that pointed to a continuity between the world of quanta and the everyday world of common experience. Lurçat urges us to take a different route: |
| 3 p. 60-61. The whole passage is worth reviewing. I hope I have not distorted the meaning by lifting out what I see as the central statement. |
…for [the phenomenologist] the essential difference between the modes of givenness of atoms on the one hand, and of stones and stars on the other hand, points out that they belong to different regions of reality. The misunderstandings between Bohr and most physicists stem from his claim of an essential difference between quantum phenomena and the world of classical physics. The drama of physics, and more particularly of quantum physics, is that it never admitted the notion of regions of reality or, equivalently, the notion of essential differences. |
| As Lurçat notes, the adoption of this notion of regions of reality has met with some resistance. Why should that be? There may be a number of reasons (though not all of them reasonable). We may review a few here. One is that the notion of regions of reality is one that is rather difficult to come to grips with. If we recall the opening section of Plato's Parmenides where Parmenides interrogates the young Socrates on the connection between the Forms and the world about us, the establishment of such a dichotomy is one thing, but getting the separated entities to interact once you make the dichotomy is quite another problem. And this interaction is necessary in the case of quanta, because we want to say that the objects of the phenomenal world are made up of them. There is already reluctance to say that all the parts act in accordance with one set of rules, while the wholes they compose act in accordance with a completely different set of rules, how can we go further to say that the parts belong to one 'realm of reality' and the wholes to another? | |
| As the quotes about the phrase 'realm of reality' indicate, the concept itself is something that needs clarification, but we can set this aside as a minor quibble. A second objection to taking this route is that it is contrary to the entire enterprise of science. What we are looking for in the course of our many scientific investigations is a single, coherent account of how everything in the universe works. Dividing the universe into different realms of reality, each with its own sets of rules, does not further this goal. As an example, we can recall that the ancients successfully divided the sensible world into sub-lunar and super-lunar realms. There was one set of rules for things down here (straight line motions of earth, air, fire, and water) and another set for things out there (eternal circular motion of aetheral objects). Newton's grand achievement (or one of his grand achievements) was figuring out how to unify those two realms. This was what was regarded as scientific progress. Einstein, too, was motivated to find unified theories (first special relativity and then general relativity) to account for a weird 'two worlds' approach to things in a stationary inertial frame versus those in a moving inertial frame. Historical examples like this suggest strongly to those with a scientific mindset that Lurçat's solution comes awfully close to giving up. | |
| Lurçat, however, has his reasons. There is a small thing, called Bell's Theorem, which has convinced nearly everyone that there really is an insurmountable dichotomy between the behaviors of quanta and the behaviors of 'classical' objects. If we want to strive for unity (and not be regarded as madmen in the process), Bell's Theorem has to be shown to either be faulty or to be misapplied to the situation at hand. The mathematics of Bell's Theorem are as simple as the definition of 'radius' for a circle and the Pythagorean theorem, so the odds of finding a mathematical flaw in it are quite slim. | |
| It is possible, however, for a theorem to be mathematically perfect, and for it to produce solutions that map onto experimental outcomes, and yet have nothing to do with what is actually happening in the world. We can look to Ptolemy's mathematical model for the movements of the planets for an example. The mathematics are rock solid. The positions of planets can be nicely predicted using the model. Yet there is nothing in the world that corresponds to the deferents, epicycles and equants that the Ptolemaic system hypothesizes. The Copernican system provides another example of the same sort of thing, and helps us to realize something rather odd: for any given problem, there can be multiple mathematically sound systems that provide reliable results and yet which have no connection to reality. In other words, having a mathematical solution does not mean that you have the solution. | |
| How can this be possible? It is possible as a simple function of probability that becomes obvious when we recognize that the scope of mathematics is infinitely more vast than that of physics. As an example, we can recall that the law of gravitation is an inverse square law (the force diminishes as the square of the distance between the attracting objects increases). Physics allows for only this formulation: other formulas do not fit the facts. Mathematics, however, can supply inverse cubed laws, or inverse to the fourth power laws, or inverse to the 6.89734th power, and so on; or the law does not have to be an inverse proportion, but a direct one. From this single example we could generate several distinct infinite families of mathematically sound laws, but only one of them would fit the facts. If we created a computer to generate mathematical equations, and another to compare the results such equations gave with the outcomes of physical experiments, we would, from time to time, come across equations which, by coincidence, provide outcomes that match experimental results. | |
| 4We can agree with Lurçat and Husserl that this mathematization of nature can go too far and lose track of its origins (as it has in the case of twentieth century physics), but it is easy enough to learn that lesson, and to correct the course we are on without having to resort to a whole new approach. | We might be tempted to regard such equations as freak items,
but there are probably far too many of them for the term to bear real meaning.
The freaky ones are the ones that actually make physical sense. It would
be more meaningful, then, for us to regard equations as being either grounded
or ungrounded with--or by--physical meaning. The task of the modern theoretical
physicist who adopts Galileo's notion that nature is mathematical4
is to find or develop such grounded equations.
This is important for us to bear in mind, for Quantum Mechanics is a mathematical apparatus that can supply solutions that map onto experimental results, but, as Lurçat points out with some remarkable quotes at the start of his paper, nobody really understands it (we might go so far as to say that it does not make sense). We may, then, comfort ourselves with the idea that we have stumbled onto one of these odd, ungrounded mathematical systems that provide good results but have no relation to reality. If that is the case, then Theoretical physicists need to move on and find the grounded theory that we are looking for. Practical physicists, on the other hand, can, in the meantime, continue to reap the benefits that Quantum Mechanics provides. |
| 5 The notion of degrees of truth is a hard one to fully explicate, but most of us take advantage of it in our daily lives. | As an aside, we can say, on a philosophical front, that the ungrounded equations of Quantum Mechanics do not supply us with an explanation, though they do provide a method for predicting results. This is a slightly different thing than what, say, Ptolemaic astronomy provided. There we had an explanation coupled with a fruitful mathematical method, but we had the wrong explanation. In the case of Quantum Mechanics, we have fruitful math, but no explanation at all. This points out an interesting thing about equations: equations per se can not be true or false (where truth and falsity are gauged by a correspondence between thought and reality), they can only be well-formed or not, and their solutions can be correct or incorrect. Grounded equations, on the other hand, can be true or false, and, though some Socrates may take us to the cleaners for saying so,5 most of us would admit to thinking that certain grounded equations (like Newton's) take us closer to the truth than others (like Ptolemy's). |
| 6
They simply have the mindset of a practical physicist, but, in that case,
they should not dabble in theoretical physics. I have, for example, been
in discussions with physicists who have pounded the table, asserting, "It's
the equations! It's the equations!" But how can this be? The act of simply
referring to equations does not qualify as 'making sense of the findings,'
because the equations in question are simply a codification (and perhaps
a mystical one at that) of the outcomes. Grounded equations take their
meaning from 'common language' theories that make some kind of sense. In
such cases, the equations can be used as shorthand for the explanation.
So, for example, Newton had some ideas about inertial motion in a straight
line and gravitational attraction. He worked these ideas into a coherent
theory and provided some equations. Now we can teach Newton's theory primarily
through work with the equations, but there is always meaning behind the
symbols. Un grounded equations, on the other hand, lack this foundation
in theory and so, ultimately, lack meaning. This lack of meaning persists
no matter how successful the equations may be at predicting or affirming
results. Ungrounded equations cannot serve as a substitute for an explanation
because there is no theory for which they serve as the shorthand. Equations
are not explanations. They are tools. In doing physics, these tools are
designed to help us work with nature. When we have equations that
wondrously map onto real events, but no further connection, we do not have
an explanation; we have a coincidence. We do not have something
that assists us to understand nature; we have, instead, a second mystery.
When the tools one is using only serve to complicate the task one is attempting
to accomplish, it is time to reassess their usefulness, and it may be time
to reach for a new tool.
7 Lurçat p. 56 8 Aristotle, Politics 5.4 9 We might broaden this statement to include the likelihood that multiple models can yield identical results, and so say that just because certain kinds of classical approaches fail does not mean that every kind will fail. 10 Incidentally, to my mind, Bohr's approach does not seem to go much beyond giving a report about such reports. So, for example, he will say, "When I do this with the machine, it does that." There is a great deal of honesty in this approach, but I do not think it qualifies as an explanation. 11 This is not the same as assuming that we have the answer, but just that we are not wasting our time by looking for it: it is out there, somewhere. In other words, we wouldn't bother hunting for a Snark if we didn't believe that one existed. |
There will not be a few readers who will view the preceding
paragraphs as idealistic or naïve, and it will not be easy to impress
upon them the magnitude of their error. Among physicists, there will be
those who have been thoroughly convinced that no grounded explanation
is possible for the phenomena exhibited by quanta. They are content
with the useful results provided by the ungrounded equations of Quantum
Mechanics.6 Among philosophers, there will
be those who have been convinced that no grounded explanation is possible
at all because they have firmly decided that all metaphysics is a delusion.
We could spend ten thousand years discussing these matters with them and
probably get nowhere, so, instead, we shall simply proceed to doing it,
and then see how they manage to deny a reality that stares them in the
face. What is repugnant about their position is that it is indistinguishable
from the positions of those who are mindless, those who are lazy, those
who are in a state of despair, and those who selfishly desire to foster
ignorance. This is not company that any reasonable person should desire
to keep.
To his credit, Lurçat also shuns this route. What he proposes, 'biphotons' in the case of polarization measurements carried out on calcium atoms,7 is, in some sense, a grounded theory. The problem is that, at first glance, the object doing the grounding (the biphoton) appears to be an imaginary object of the order of the Questing Beast of Arthurian legend. That is to say, it appears not only to be a fiction, but also one that houses internal contradictions. The problem really comes into focus when we couple the notion of a biphoton with the experimentally verifiable fact that the testing apparatus can be placed miles apart. The result is an object of subatomic scale that somehow extends for miles! If we couple this with the wave-particle duality that photons already house, this 'scientific' object blows every mythical creature right out of contention for the prize of the most impossible thing to imagine. The fact that we have reached the point where all attempts to make sense out of the information that we have on hand leads to conjectures about wildly impossible or totally unobservable entities suggests that we are fairly far along the wrong track. As Aristotle observed: For a mistake that happens in the beginning is said to be--as is said of old--half of the whole, so that even a small error at this [point] is proportionate [in this way] to [all] those in the other parts.8The result is that a small error gets magnified as we build conclusions upon it, and we end up very far from the truth. It is like a small error in the firing angle of a missile: by the time it lands, it is miles off course. Still, there is Bell's Theorem standing in the way. This theorem, or 'inequality' as it is often termed, makes the case that we have not merely made an error, but that we have encountered an impossibility. Yet let us remember the immortal words of Captain James Lawrence, and not give up the ship. Sometimes the answers appear after all hope is gone. So let us look more closely at this theorem. With Bell's Theorem, we do not have a single equation that maps onto real results, but two different mathematical models. One is that of Quantum Mechanics, the other represents a classical understanding. The classical model predicts one outcome for a particular kind of experiment; the quantum model predicts a measurably different outcome. When the experiment is conducted, the results line up with the quantum model, not the classical model. The conclusion that is drawn from this is that the quantum model is the correct model, and that there is no classical model that can provide the kind of result that we get when we conduct an experiment. The paragraphs above, however, show that this conclusion is likely to have been drawn too hastily. There is an error--not a mathematical error, but a theoretical error--in making the assumption that the Quantum Mechanical approach is the only approach that can supply the answers that we are looking for. There is a further error in leaping to the conclusion that, just because one classical approach fails, all classical approaches will fail.9 Compounding these errors is the fact--readily admitted as we have seen--that nobody really knows what is going on. How can we make such blanket statements about what is or is not possible when we have not even managed to come to grips, intellectually, with the raw data? Bell's Theorem tells us that the classical approach that we have tried does not work. Let us take that result and move forward. Let us propose another classical model, one that avoids the problems that the last approach encountered. As we noted above, the problem we are encountering is probably the result of a small error that crept in unnoticed when we first began to develop a theoretical approach to explain the phenomena. As Lurçat has pointed out, quanta are given to us in a peculiar, mediated way. We deal, not so much with the things themselves, but with 'reports' we get about them from various detection devices.10 We cannot see what electrons do. We cannot pick up a handful of photons and put them on a scale. Consequently, when we try to talk about quanta, we tend to use analogies. We strive to find objects in the world around us that act like quanta, and then say, "It's like this" or "It's like that." The problem with analogies is that it can be quite tricky to find a good one, and finding good analogies is more like the work of a poet, writer, or philosopher than that of a physicist. Let us, then, make two useful assumptions: one is that there is a classical model that will provide the kind of explanation we are looking for (we just have to find it);11 the other is that, to date, we have been working with lousy analogies. To these assumptions, let us add another element: a suitable attitude towards the entire problem. We can all safely admit that this has been, in the technical sense of the term, a hell of difficult thing. No one is to be blamed or shamed for trying to scale this mountain and failing to reach the peak. If we find we have made a silly error, we must be willing to own up to it with good humor, and be consoled with the thought that we did our part: we gave it a good try. To this point we have been able to get away with talking about the problem in the sense of talking around it, now we must start to enter into it. We shall not, however, dive directly into the deep end, but wade in by, first, dealing with some of the analogies that have been offered, and then by coming to terms with the experiments themselves. At this point we can bid farewell to Lurçat and move on to a more generalized treatment of the subject. |
| Bibliography | |
| Aristotle, Politics http://www.perseus.tufts.edu/cgi-bin/ptext?
doc=Perseus%3Atext%3A1999.01.0057;query=toc;layout=;loc=5.1303b
Bell, J. "On the Einstein-Podolsky-Rosen Paradox" Physics 1 (1964) 195-200. Carrol, Lewis The Hunting of the Snark, http://www.literature.org/authors/carroll-lewis/ the-hunting-of-the-snark/ Copernicus De Revolutionibus http://webexhibits.org/calendars/year-text-Copernicus.html Einstein, A. Podolsky, B. and Rosen, N., "Can Quantum Mechanical Description of Reality Be Considered Complete?" Physical Review 47 (1935) 777-780. Lurçat, Francois, "Understanding Quantum Mechanics with Bohr and Husserl" The St. John's Review, XLIX.1 (2006), 33-70. Mallory L'Morte d'Arthur http://www.malory.net/frame3.htm Newton Principia http://burndy.mit.edu/Collections/Babson/Online/Principia/ Newell, John, "Education: The End of Faith?" http://www.hellos.com/books/faith.html Plato, Parmenides http://burndy.mit.edu/Collections/Babson/Online/Principia/ Ptolemy, Almagest (G. J. Toomer, Ptolemy's Almagest, Duckworth, 1984) |