Showing posts with label quantum mechanics. Show all posts
Showing posts with label quantum mechanics. Show all posts

Thursday, November 19, 2020

The magic is back!

Existential Comics had a funny and funnily true Facebook post a couple years ago that's worth remembering:

Science has been the slow process of showing that the exciting magical world we believed in doesn't exist, and there is nothing but boring reality. Well, except for quantum mechanics, which showed boring reality doesn't exist, and everything is basically magic. (December 13, 2018)

That's actually a strong theme among Thomistic-Aristotelian philosophers these days: the vindication of Aristotle's natural philosophy in quantum mechanics. The world needn't be the disenchanted drudge modernity has made it. Instead we have back the world of possibility and meaning.

Some references:

Edward Feser, Aristotle’s Revenge: The Metaphysical Foundations of Physical and Biological Science (Editiones Scholasticae, 2019).

Robert C. Koons, “Hylomorphic Escalation: An Aristotelian Interpretation of Quantum Thermodynamics and Chemistry,” American Catholic Philosophical Quarterly (2018) 92:159-78.

Adam Schulman, Quantum and Aristotelian Physics (Harvard University dissertation, 1989).

Tuesday, January 04, 2011

Heisenberg on Nature and Science

Last post, I mentioned how I have been reading Werner Heisenberg's Gifford Lectures (1955-56), and I related an incisive insight of his on peace declarations to Christmas.

Of course, Heisenberg has written much more of interest on science than on peace. His philosophical observations are surprisingly well informed—or at least seem so these days in which prominent scientists seem to have taken it upon themselves to prove the depth of their education in philosophy is inversely proportional to expertise in their own field.

This is not to say that everything Heisenberg says is flawless, but simply that his remarks are surprising in their philosophical sanity. Below I've excerpted several of the better passages.

To begin with, it is important to remember that in natural science we are not interested in the universe as a whole, including ourselves, but we direct our attention to some part of the universe and make that the object of our studies. (52)

In classical physics science started from the belief—or should one say from the illusion?—that we could describe the world or at least parts of the world without any reference to ourselves. This is actually possible to a large extent.... Certainly quantum theory does not contain genuine subjective features, it does not introduce the mind of the physicist as a part of the atomic event. But it starts from the division of the world into the "object" and the rest of the world, and from the fact that at least for the rest of the world we use the classical concepts in our description. This division is arbitrary and historically a direct consequence of our scientific method... (55)

The concept of atom does ... has its origin in ancient Greek philosophy and was in that early period the central concept of materialism taught by Leucippus and Democritus. On the other hand, the modern interpretation of atomic events has very little resemblance to genuine materialistic philosophy; in fact, one may say that atomic physics has turned science away from the materialistic trend it had during the nineteenth century. (59)

In the theory of general relativity the answer is given that geometry is produced by matter or matter by geometry. The answer corresponds more closely to the view held by many philosophers that space is defined by the extension of matter. (66)

It has been pointed our before that in the Copenhagen interpretation of quantum theory we can indeed proceed without mentioning ourselves as individuals, but we cannot disregard the fact that natural science is formed by men. Natural science does not simply describe and explain nature; it is a part of the interplay between nature and ourselves; it describes nature as exposed to our method of questioning. This was a possibility of which Descartes could not have thought, but it makes the sharp separation between the world and the I impossible. (81)

Our perceptions are not primarily bundles of colors or sounds; what we perceive is already perceived as something, the accent here being on the word "thing," and therefore it is doubtful whether we gain anything by taking the perceptions instead of the things as the ultimate elements of reality. (84)

The limitations of the field [of physics] can generally not be derived from the concepts. The concepts are not sharply defined in their relation to nature, in spite of the sharp definition of their possible connects. The limitations will therefore be found from experience, from the fact that the concepts do not allow a complete description of the observed phenomena. (101)

In order to give a quantitative description of the laws of chemistry one had to formulate a much wider system of concepts for atomic physics. This was finally done in quantum theory, which has its roots just as much in chemistry as in atomic physics. Then it was easy to see that the laws of chemistry could not be reduced to Newtonian mechanics of atomic particles, since the chemical elements displayed in their behavior a degree of stability completely lacking in mechanical systems. But it was not until Bohr's theory of the atom in 1913 that this point has been clearly understood. In the final result, one may say, the concepts of chemistry are in part complementary to the mechanical concepts. If we know that an atom is in its lowest stationary state that determines its chemical properties we cannot at the same time speak about the motion of the electrons in the atom. (101-2)

Just as in the case of chemistry, one learns from simple biological experience that the living organisms display a degree of stability which general complicated structures consisting of many different types of molecules could certainly not have on the basis of the physical and chemical laws alone. Therefore, something has to be added to the laws of physics and chemistry before the biological phenomena can be completely understood. (102-3)

It is very difficult to see how concepts like perception, function of an organ, affection could be a part of the coherent set of the concepts of quantum theory combined with the concept of history. On the other hand, these concepts are necessary for a complete description of life, even if for the moment we exclude mankind as presenting new problems beyond biology. (104)

We would never doubt that the brain acts as a physico-chemical mechanism if treated as such; but for an understanding of psychic phenomena we would start from the fact that the human mind enters as object and subject into the scientific process of psychology. (106)

But the kind of stability that is displayed by the living organism is of a nature somewhat different from the stability of atoms or crystals. It is a stability of process or function rather than a stability of form. (154)

As Bohr has pointed out, it may well be that a description of the living organism that could be called complete from the standpoint of the physicist cannot be given, since it would require experiments that interfere too strongly with the biological functions. (155)

Therefore, we have here actually the final proof for the unity of matter. All the elementary particles are made of the same substance, which we may call energy or universal matter; they are just different forms in which matter can appear. ¶ If we compare this situation with the Aristotelian concepts of matter and form, we can say that the matter of Aristotle, which is mere "potentia," should be compared to our concept of energy, which gets into "actuality" by means of the form, when the elementary particle is created. (160)

The physicist may be satisfied when he has a mathematical scheme and knows how to use it for the interpretation of experiments. But he has to speak about his results also to nonphysicists who will not be satisfied unless some explanation is given in plain language, understandable to everybody. Even for the physicist the description in plain language will be a criterion of the degree of understanding that has been reached. To what extent is such a description at all possible? This is a problem of language as much as of physics.... (168)

Furthermore, one of the most important features of the development and the analysis of modern physics is the experience that the concepts of natural language, vaguely defined as they are, seem to be more stable in the expansion of knowledge than the precise terms of scientific language, derived as an idealization from only limited groups of phenomena. This is in fact not surprising since the concepts of natural language are formed by the immediate connection with reality; they represent reality. It is true that they are not very well defined and may therefore also undergo changes in the course of centuries, just as reality itself did, but they never lose the immediate connection with reality. On the other hand, the scientific concepts are idealizations; they are derived from experience obtained by refined experimental tools and are precisely defined through axioms and definitions. Only through these precise definitions is it possible to connect the concepts with a mathematical scheme and to derive mathematically the infinite variety of possible phenomena in this field. But through this process of idealization and precise definition the immediate connection with reality is lost.(200)

We know that any understanding must be based finally upon the natural language because it is only there that we can be certain to touch reality, and hence we must be skeptical about any skepticism with regard to this natural language and its essential concepts. (201-2)


Werner Heisenberg, Physics and Philosophy: The Revolution in Modern Science (New York: Harper & Row Publishers, 1958).

Monday, August 02, 2010

Fallacious Application of "non-Euclidean" to Physical Space

Physicists sometimes talk about space—by which they of course mean physical space—as Euclidean or non-Euclidean. The problem with this way of speaking is that geometry is timeless. It cannot really apply to physical space.

Notice that if there's one lesson that Einstein's relativity has taught us, it is that space is intrinsically temporal: you can't have one without the other, which is why the combination in the relativistic context is usually called spacetime. Our measurements of length are always in time.

To see this point more clearly (more clearly at least if you are a physicist; I make no guarantees for others), think of the the Minkowski diagram, which plots time on the vertical axis and position on the horizontal (looking at a diagram may be helpful). (It also applies to general relativity with flat spacetimes, that is, regions far from masses.) Light rays are marked at 45-degree angles that divide the plane into four quadrants; the "light cone" consists of the north and south quadrants. There are time-like intervals (points that that lie within the "light cone," that is, that are separated enough in time that they can connect causally) and space-like intervals (points outside the light-cone, that is separated so far in space that they cannot connect causally).

To test whether space is Euclidean, one would have to set out measuring rods in the present, in other words, along the space-like interval parallel to the position (horizontal) axis. (And then test whether parallel lines remain parallel, or else either converge or diverge....)

But relativity has shown us that what one considers the present depends on one's state of motion: the ordering of events is not absolute, there is no unambiguous or absolute "present". On the Minkowski diagram in the frame of a primary, stationary observer, the "present" of a second, moving observer appears as an x' axis tilted obliquely to the x axis.

The assumption of what we usually mean by "length measurement" is that one measures both ends at once (as de Koninck points out, in contradistinction from Maritain, there is no absolute notion of length apart from an observer situated in space and time). Length measurements that are simultaneous in one frame are not simultaneous in another. Because of the relativity of simultaneity, "at once," and thus length measurement, becomes tied to the relative states of motion of the measurer and the object measured.

As we have seen, there is no unambiguous "now"; so the application or denial of the qualifier "Euclidean" to physical space confuses physics for pure mathematics (the error of Descartes). It presumes some sort of a timeless frame for making length measurements and it is precisely the existence of such an absolute frame that relativity denies.


This argument occurred to me when reading Vincent Smith, and was corroborated by de Koninck writing about Eddington.

Vincent Edward Smith, Philosophical Physics (New York: Harper & Brothers, 1950), 355.

Charles de Koninck, The writings of Charles de Koninck, vol 1, ed. & trans. Ralph McInerny (Notre Dame, Ind. : University of Notre Dame Press, 2008), 147-158.

Thursday, March 15, 2007

Interesting Items

Personal Note: Just got back from a trip. My travel preparations kept me from posting beforehand, and then for some reason Blogger wouldn't work on the computer where I was staying.

Steve Barr has a provocative piece "Faith and Quantum Theory" in the March First Things (subscription required for access). I was hoping to have something substantive to post on it, but then realized I'm still struggling with Steve's explanation of quantum weirdness: I have not come to a coherent understanding of his notion of decoherence (transition from quantum wave-like behavior to particulate classical behavior). Perhaps I'll put together something later.

Cardinal Schönborn has a well-considered piece, "Reasonable Science, Reasonable Faith," in the April First Things. Apparently, it is a condensed version of a talk he gave last month in New York ("Fides, Ratio, Scientia: On the debate over Evolution"). It will be interesting to see if Barr publishes a response, in light of his previous exchanges with the Cardinal!

Monday, May 30, 2005

Smith's Alloyed Wisdom

A friend lent me an interesting book called The Wisdom of Ancient Cosmology: Contemporary Science in Light of Tradition by Wolfgang Smith. The book is difficult to summarize: while it contains many startlingly significant insights, it also contains an embarrassing admixture of error. These errors may in fact be relatively minor (and they are compared to what "Enlightened" people spout these days), but they seem so sophomoric as to impair the objectivity of my review. But if you, dear reader, keep this caveat in mind, I will give my best shot at objectivity. (Some of these ideas are rather complicated and I'm not sure I've explained them adequately; please let me know if anything is unclear.)

The great aim of the book is return to the titled "wisdom of ancient cosmology." Smith sees the entire science-inspired contemporary worldview as radically hostile to ancient wisdom. He defends the perennial (Thomistic-Aristotelian) philosophy, and furthermore the traditional cosmology in which it grew.

Part of Smith's self-appointed task is to refute the error in modern thinking that he calls "bifurcationism"—what is generally called dualism (mind/body or subject/object)—that has plagued human thinking explicitly since Descartes. The quality of his thought on this subject is wildly uneven; containing much truth, the book is unable to fully exorcise the Cartesian-Kantian demons in the end.

Intelligent Design

The best part of the book is chapter X's explanation of intelligent design (ID). The subject of evolution is one on which the author has written before in Teilhardism and the New Religion. Here he likewise rejects Darwinism, and more generally, the theory of common descent.

I can't claim to have more than general notions of ID, but Smith's prose made a lot of sense to me. He distinguishes complex information (e.g., the positions of all the rocks that make up a mountain) from complex specified information or CSI (e.g., the arrangement of rocks in the form of the words "Welcome to Boulder"). CSI, as William Dembski has shown, cannot come about randomly, at least not fast enough to generate in the lifetime of the universe even the simplest creature's DNA.

Smith's idea of "vertical causality" is an interesting (and I think helpful) reconception of intelligent causation. The terminology highlights the fact that, unlike purely material causes that are unable to create CSI, intelligence acts "above time," i.e., outside the stream of deterministic, temporal causality. (I would add that intelligence acts with a telos or end in mind, and I wonder how this fits into the scheme. Does purpose transcend material time?)

Quantum Mechanics

Smith does not fare so well in his treatment of physics and modern scientific cosmology. I suspect his training in mathematics1 is the main hindrance.

The treatment of quantum mechanics is well intentioned, but naive. He fails to grasp the point of the famous Schoedinger's cat paradox. Recall that the cat paradox goes something like this: imagine a box containing a live cat along with a poison-releasing mechanism. The mechanism is connected to a radioactive particle whose half-life is one hour, which means it has a 50% chance of decaying in an hour. Should the particle decay, the mechanism will release the poison, killing the cat.

According to the standard Copenhagen interpretation of quantum mechanics, at the end of an hour, the cat will be both half-dead and half-alive until someone opens the box and observes the cat, at which time the "wavefunction" of the cat "collapses" from 50-50 dead-alive to 100% either dead or alive. (Physics terminology: the Schroedinger equation of quantum dynamics gives a "wavefunction," i.e., a range of possible values each with a probability of occuring. According to the Copenhagen interpretation, on measurement the range of possibilities coalesces or "collapses" to the actual measured value, which then has a probability of one. This coalescence is known as "wavefunction collapse.") Common sense tells us that a cat can only be dead or alive: there is no half-and-half.

Schroedinger devised the paradox to show the absurdity of the Copenhagen idea that a particle has no definite position, for example, until it is measured. (In a nutshell, the Copenhagen school mistakes epistemology for ontology.)

On top of this problem, Copenhagen also creates an arbitrary boundary between observer and observed (subject/object dualism). Think about the cat paradox: why should the wavefunction collapse when a scientist opens the box? What's so special about observation by a person? Would the scientist need to be observed by another scientist before his wavefunction collapses (and this process could be carried ad infinitum)? Or perhaps the cat's "observation" of itself causes the collapse?

The underlying problem is the arbitrary distinction of physical interactions that are part of a measurement from "ordinary" interactions. If one assumes such a dualist distinction, it is no surprise that one gets dualism in the result.

Smith follows Eddington's distinction of the "corporeal" realm in which we live from the "physical" world that is the subject of mathematical physics. "The credo of bifurcation thus entails a reduction of the corporeal to the physical," Smith observes rightly. Unfortunately the writing in this section is somewhat unclear about the actual relationship between the two, so that the reader can easily misunderstand Smith to solve the confusion of the two by imposing an absolute distinction between them. For example, Smith writes,

...the Schrodinger evolution operates within the physical domain, whereas the projection has to do with a transit out of the physical and into the corporeal.
Statements like this seem to imply that the physical and corporeal are exclusive of each other. Such a division merely substitutes one form of dualism for another. In actuality, the quantitative, physical world, must be an intrinsic subset of the real, corporeal world. (For more on the relationship between form and matter, see Schindler's "The Problem of Mechanism," about which I've written here.) Later in the book Smith's belief in this truth does come out (e.g., 222), but the initial lack of clarity is confusing, especially for beginners.

Modern Cosmology

Oskar Milosz's observed: "Unless a man's concept of the physical universe accords with reality, his spiritual life will be crippled at its roots" (170). Smith tries to remedy this spiritual void by justifying ancient cosmology, specifically by addressing two of its inadequacies: (1) the distinction between terrestrial and celestial matter, and (2) geocentrism.

In chapter VII, Smith attempts to revive the ancient idea that celestial matter, unlike matter on earth, is incorruptible. To do so, he has to ignore the expansion of human knowledge since the middle ages, such as the observed changeability of the heavens (e.g., supernovae, movement of stars, comets) and human space exploration. He does in fact allude to the moon-landings, but he explains the apparent mundaness of lunar matter by waiving away the ability of our senses to properly perceive them as anything but terrestrial (143)—an argument that undercuts his defence of the perennial philosophy's insistence on the primacy of sense knowledge. (Pierre Duhem and Stanley Jaki maintain the scientific "democratization" of matter that Smith abhors is the product of the Christian belief that Jesus Christ, instead of the universe, is the Only-begotten of God.)

In chapter VIII, Smith charges at the windmill of heliocentrism. This is Tychonian, not Ptolemaic geocentrism he defends. Tycho Brahe's model is simply the Copernican system, but with a stationary Earth: the planets orbit the Sun, and the Sun and Moon orbit the Earth. He tries to show that this view is compatible with Newtonian physics via Einstein: "Relativity implies that the hypothesis of a static Earth is not incompatible with the laws of physics and cannot be experimentally disproved" (159). There is some truth in this claim: Einstein's theory tells us that we can't distinguish free-fall (as the Earth does as it orbits the Sun) from uniform motion or even from rest. But to claim the Earth is motionless necessarily negates its daily rotation in favor of the Sun's movement, and this motion can be measured. In fact, if you've ever seen a Foucault pendulum in a science museum, you've seen the empirical evidence: a motionless Earth cannot explain the strange precession of the pendulum; if Newtonian physics is at all applicable to terrestrial matter (and it certainly is as a limit to Einstein's theory), the Earth rotates and the stars are fixed. It's not a big jump to "discover" that the Sun is (relatively) stationary in the center of the solar system.

Smith also rejects stellar parallax as evidence of the Earth's motion: "The logic here is once again of the ponendo ponens variety, which is to say that the hypotheses in question are judged or validated by their success in 'explaining' observable phenomenon" (159, cf. 118). Could anyone but a mathematician mistake reasoning by observation and induction for begging the question?

(Such mathematical apriorism is, I believe, also behind Smith's advocacy of "Fisher information" theory (50): that laws of physics can be deduced from the process of measurement—as if our intellects aren't primarily recipients and not creators of sensory information; this is a basic tenet of the perennial philosophy that Smith is ostensibly defending.)

Other notable ideas

A interesting insight in the quantum mechanics section. After observing that transcendence is the mark of objectivity, he writes,

How can somthing that is defined mathematically exhibit such a mark [of transcendence]? Here again Nature contrives to outwit our simple logic: the probabilities of physics manifest transcendence precisely when they "collapse" into objective fact; it is at that moment that they suddenly and unexpectedly, as it were, reveal their objective side by violating the Schrodinger wave equation, which up to that point they had strictly obeyed. (66)

I'm not sure of the value of this statement Smith quotes from Eddington (p. 53), but it is thought-provoking nonetheless:

The new conception is not merely that the whole is analysable into a complete set of parts, but that it is analysable into parts which resemble one another... I will go farther, and say that the aim of the analysis employed in physics is to resolve the universe into structural units which are precisely like one another.

From chapter IV on "Bell's Theorem and the Perennial Ontology":

The astrounding fact is that in the form of Bell's theorem physics has declared its own boundedness, its own incapacity to deal with the deeper strata of cosmic reality....

What physics can prove, and what it has indeed established beyond a reasonable doubt, is that external reality, and thus the cosmos as such, cannot be confined within the bounds of Einsteinian space-time: for if it could thus be confined, it would satisfy the Einsteinian condition of locality, which in fact it does not obey. (74, 77)

In discussing anthropic "coincidences":

If you break a clay pot, you will find that the resultant shards fit together perfectly so as to consitute the pot in question; and obviously this 'fine tuning'—which seems quote miraculous so long as one does not know the true provenance of the shards—is the result neither of chance nor of design. In short, the physical universe is fine tuned because the corporeal world demands as much. (222)
I would add that the wholeness of the universe is summed up in man (cf. St. Maximus the Confessor).
What both the Darwinians and most creationists have failed to grasp is that the corporeal universe in its entirety constitutes no more than the outer shell of the integral cosmos.... So long as one thinks tha the origin of a plant or an animal can be conceived as a spatio-temporal event, one has entirely missed the point. (80)

Summary

The friend who lent me the book called it "eclectic." This description is apt on multiple levels. No only does he mix Eastern philosophical terms into his Western traditional philosophy, but also Kantian and Cartesian dualism.

Smith's aims are noble, his methods unorthodox. I certainly sympathize with his abhorrence of modern errors, but a blanket rejection that excludes even genuine developments in human knowledge is not just scandalous, but foolish. The book contains unique insights, but unfortunately the mutiplicity of mistakes compromises its value. The tragedy is compounded by the fact that many of these mistakes could have been easily avoided by allowing a working physicist1 to review the book, or even by simply taking to heart the perennial philosophy's foundation in the reliability of the senses. Smith's attempt to forge a unified view of the world is so reactionary that it ironically ends up incorporating the modern ambiance that it set out to exclude.


1. Though Dr. Smith received one of his undergraduate degrees in physics and a masters in theoretical (a.k.a., mathematical) physics, his doctorate is in mathematics, as was another of his (three) bachelors degrees, it seems fair to say that he is more of a mathematician than a physicist.

Wolfgang Smith, The Wisdom of Ancient Cosmology: Contemporary Science in Light of Tradition, (Oakton, VA: Foundation for Traditional Studies, 2002).

David L. Schindler, "The Problem of Mechanism," Beyond Mechanism: The Universe in Recent Physics and Catholic Thought (Lanham, New York: University Press of America, 1986).

Stanley L. Jaki, Science and Creation (Lanham, New York: University Press of America, 1990).