Part V (Appendix)

Is Quantum Theory True?*

Professor Smith subscribed to the theory that the harder something is to digest the more nourishing it will be so he tended to be pithy and somewhat abstract. He intentionally omitted details to force the audience to figure out how to fill in the gaps without his help. But he possessed a unique viewpoint on most matters and always provided a fresh perspective replete with many unanticipated twists and turns, so that sitting through his mind stretching but frequently long-winded lectures was always worth the effort. Ben served up his direct question, “Is quantum theory, as bizarre as it is, really true?”

The professor volleyed in his usual roundabout manner. “What is truth? Sir Francis Bacon²⁹ reminds us Pontius Pilate asked that of Jesus but, alas, would not stay for an answer. We must explore this question first before trying to answer yours. There can be no such thing as indisputable universal truth unless one believes in solipsism.”

“What's solipsism?”

“Bishop Berkeley's ingenious proposition³⁰ that God created only you, and all reality is no more than His Ideas operating on your imagination. I have restated this in verse form:

It seems as if I've always known

From somewhere deep within,

That all the schemes and all the dreams

Myself, alone, have ever been.”

“Not bad. You possess latent poetical talent. Still, the idea is a bit too intangible for my liking.”

“In that case universal truth doesn't exist in our world, which is why Plato refrained from positing an ideal ‘Truth’. But there are near truths that can be approached, as Peirce, William James and the other Pragmatic philosophers asserted.”

“Can this be expressed mathematically?”

“Zorn's lemma asserts that in any lattice of infinitely long chains there exists a unique maximal chain to which they all converge. In plain English, for our purposes a chain is merely a set of progressively more intricate, yet successful, tests where each one simultaneously reconfirms and extends the same initial theory in a consistent manner, and a lattice is a collection of such chains all pertaining to the same starting theory and each moving in a different direction than its rivals. The unique maximal chain they all approach is the one complete ‘true’ theory extended to all circumstances that could possibly fall within its scope. As of now Zorn's lemma is and will probably always remain a mere lemma. But if it could be proved it would support the assertion that all approximate partial truths approach the same unique ‘Absolute Truth’, which might be called ‘God’ or Aristotle's ‘Prime Mover’ or a Platonic ideal ‘Truth’ or some other such thing. The main contenders for universal truth are physical laws, historical events and non-tautological definitions, but all fall short of the goal.

“A reputed event requires a mere consensus of agreement among all firsthand observers to qualify as a probable truth, and the closer to unanimity the stronger the likelihood it will be dubbed indisputable. But humans are notoriously prone to err. Furthermore, even were all spectators to assent, there is always the chance that had one more been present at the scene he would have demurred.

“A non-tautological definition of either a real thing or a concept is not ‘true’ per se. At best it is only an asymptotic approximation to ‘truth’. No two trees are identical in every respect so there exists no unique ‘perfect’ tree, no ideal Platonic form of a tree, except in an approximate sense; at least not in our world. A ‘true’ ideal form of a tree or anything else would necessarily possess infinite attributes and we could never know them all at once so there is always a chance of discovering a new one. If one crops up we must either redefine or enlarge the class to include it. Thus no definition can be indisputably permanent or ‘absolute’ for us.

“Conversely, although reputed ‘facts’ and non-tautological definitions aren't absolute, neither are they purely arbitrary. ‘Facts’ are either false or mythic if they conflict with science. Definitions of things are amended if they are incomplete. Definitions of concepts are discarded as meaningless if they are internally inconsistent or if they conflict with human aims. Society is always negotiating the meaning of human truths.”

“How do we test a definition of a concept? We can't use either direct observation or scientific experiments.”

“One way is dialectically, in other words with a series of yes or no questions that narrow the definition's scope so as to determine its applicability and consistency. This was the method Socrates used to rigorously define justice.³¹ Another way is empirically. Nazism was repugnant to most Germans and odious to other powerful antagonists to the point of overt counter-reaction; thankfully it was overthrown. A few delusional bigots tried to resurrect it in the late 20th century but the pestilence has now been wholly eradicated due to its futility as a viable type of government. It is now obsolete as a human concept although it still has a definition for purposes of discourse.

“Now to get back to your original question about quantum theory, let's consider physical laws. Although they are the most reliable form of earthly truth, Hume pointed out an insurmountable hurdle³² — even if a series of natural events has always followed the same course of action throughout human existence, such as if you let go of a heavy object and there is nothing to hold it up it will fall, that's no guarantee the same thing will occur the very next time, let alone forever. If it has never yet failed to happen it is extremely likely to continue, but that's not the same as saying it must happen as does every physical law, not just Newton's law of gravity. But we must put aside this irrefutable argument if science is to remain useful.

“Science does the best it can by demanding conformance to the correspondence principle: before any new theory can attain the status of a ‘law’ it must absorb and amplify all old ones that haven't yet failed any experimental test. But this falls far short of absolute certainty. Infinitely many possible scientific experiments can be contrived and the next test might disprove the ‘law’, in which case it will fall by the wayside and be replaced by a new one.

“Furthermore, all increases in knowledge have arisen from either the discovery of new methods of testing and/or new ‘facts’. These discoveries and methods are not without limit; they are inherently restricted by our inability to conceive all attributes of reality. The aspect of quantum theory most likely to withstand all efforts at disproof is the assertion that we create our own reality since it dodges the question of whether or not some form of concrete truth can exist even if it were impossible to be observed by us. As we are currently constituted there will always be a part of reality that is inaccessible. Bees can apparently see ultraviolet light but we can't even imagine, let alone see, a new color. This provides evidence that our sets of senses and modes of imagination are incomplete. The best we can do is hope to augment our senses by discovering new methods of detection, such as ultraviolet or infrared photography.”

“This is all very interesting but also very confusing. Can we ever be certain of anything?”

“Not unless we acquire, perhaps through mutation or invention, a sufficient set of sensory receptors and modes of thought. At any given time there may be many hypotheses or theories that have thus far passed every test but they are and will always be only provisionally true.”

“Even quantum theory? It's so weird and distasteful to physicists that hundreds have designed experiments to discredit it. Consequently it has been exposed to far more trials than any other theory yet has passed them all with flying colors.”

“Nevertheless, there's still a chance it too will be proven wrong in some respect. Even Newton's aforementioned law of gravity, although seemingly infallible, had to be augmented by Einstein's general relativity before it could account for the perihelion of Mercury's orbit. Furthermore, although quantum theory passes all current tests, we may come up with a different theory tomorrow that also passes the same tests. Then we would have two concurrently ‘true’ theories, only one of which will prevail as more tests are performed.”

“Using Ockham's razor wouldn't we go with the simplest, the one requiring the fewest assumptions, until one or the other eventually wins out?”

“Yes but simplicity doesn't make a scientific theory any truer. Our minds can only comprehend phenomena by lumping them under as few categories as possible, so we are all reductionists by nature. We seek one inclusive label like ‘dog’ or ‘cat’ or ‘tree’ or ‘triangle’ or ‘chair’ with which to name many similar individuals, none of which are identical. Without the label we could not make sense of the boundary-less sensory input that inundates us every moment of our waking lives; everything would appear as one big blur of sensation.

“The natural tendency to simplify also applies to causes and theories but to a lesser extent. Science's search for a ‘complete unified theory of everything’ and religion's positing of one ‘ultimate cause’ i.e. God, are motivated by this same human impulse. So, as you surmise, the simplest or most convenient theory would be psychologically preferred, or in the last analysis naturally selected, since a predilection for reductionism is necessary for our survival.

“The more complex of the two will be shelved for the time being and ultimately rejected altogether. Only the favored one will persevere. This will be unfortunate if the simpler one is subsequently found wanting since the other will have probably been forgotten and may not resurface even though never having been disproved. We will then have to start over from scratch rather than have available a perfectly sound alternative that was rejected merely because of its relative complexity.”

“So there are no true theories?”

“Only in a limited sense. All ‘true’ theories have this in common — they pass all currently existing tests. But we would have to run all the tests simultaneously to provide a common set of starting circumstances, so they are still merely partial truths. Furthermore we can never be sure our test or tests have covered everything. Even were we to possess more than our meager set of sense receptors our ‘truth’ would still be ascertained by what we choose to measure, but these choices are restricted to the relatively small number of practical tests our limited minds can contrive.

“Before we can perform any experiment we must first decide which set of predictions we want to test. In this sense the ancient Greek sophist Protagoras was on firm ground when he said, ‘Man is the measure of all things.’ To top things off, we would be incapable of arbitrarily choosing what to experimentally measure without bias even if we did have the requisite inventiveness, senses and precise instrumentation.”

“How so?”

“We would still be limited by our innate inflexibility. Mankind has always studied the same basic attributes of reality using the same modes of imagination as evidenced by the congruous approaches taken in widely divergent fields of study. Compare the subject matter of various disciplines: infinite Being in philosophy, infinite spacetime in physics and Cantor's various degrees of infinity in mathematics. All of these concepts have a similar structure, which indicates we virtually pre-select reality.”

“Isn't it possible we are merely persuaded by tradition and education to follow the same path rather than being compelled by our basic nature? After all, Aristotle's influence over his European successors limited the range of fields of study and severely retarded any improvement in methods of investigation for over a millennium.”

“Yes it's possible but it's much more likely we are constrained by an inherent human trait. The Renaissance geniuses after Aristotle didn't produce new theories ‘out of the blue’. They merely furthered investigations he had already begun. ‘Truth’ tends to evolve slowly rather than arise spontaneously. I conjecture this is so because we have only a small number of modes of conceptualization, imagination and perception with which to make sense of the parts of reality we can comprehend.”

“What are they?”

“I don't recall Kant's entire list³³, but it includes hierarchy (or inclusion), inversion, series (or limit), divisibility, dualism, contradiction, unity, multiplicity, eternity, causality, comparison and necessity. Compounding these with each other enables us to derive other concepts such as: freedom and will; desire, attraction and force; change, motion, quantity, number, space and time; perfection, God, goodness, virtue and purpose; similarity, commonality and difference; paradox, error, knowledge and truth; repetition, custom and habit; order, symmetry and regularity; progress, growth and evolution; and nothingness, vacuum, emptiness and death.”

“Many of these have a mathematical flavor.”

“Einstein's proclamation that ‘God must be a mathematician’ is an eloquent expression of the fact that we, but not God, can only conceive things in certain fixed ways and mathematics is the most precise language in which we do so. All of physics and probably all of philosophy can be described more concisely and accurately in mathematical symbolism than ordinary language.”

“How do you explain that Riemann ‘constructed’ differential geometry as a purely mental exercise yet Einstein later showed it perfectly described spacetime? Wouldn't this prove Riemann's work was absolutely true even though it was a product of human imagination? Perhaps reality is finite and, even though our senses are incomplete, our modes of thought alone suffice to comprehend it.”

“Like all of us, Riemann was born and raised in our world so his insights could not have been mere mental constructs; they were based on a synthesis of his earthly experience of space and time.³⁴ Moreover, Einstein's theories don't attempt to explain how the universe works: this is beyond our grasp. They only construct models enabling us to predict future events. We analyze all new facts through the same old modal techniques. Even our analyses of the modes themselves are constrained by the selfsame modes, so we can't get outside of them through philosophical thought experiments unless we mutate new modes or senses. Without a mathematical model or an analogical pictorial representation any posited part of reality, for instance a fourth dimension, that doesn't conform to one of our inherent modes or senses is incomprehensible to us.”

“Such as ESP?”

“No. It can be easily imagined as can ghosts, déjà vu, time travel and many others. But beyond these there are attributes of and relations among space, time and causality that we can't even begin to visualize, yet whose existence lends credence to strange but imaginable old notions that haven't been disproved, like ESP. Quantum theory is an example of an inscrutable concept.”

“Are there others?”

“Several. Superstring theory is one. It may simplify and/or expand existing models for perceiving reality but won't add new modes of perception to the current collection of substance, space, time, change and a few others. New facts can expand the applicability of a given mode but can't create a new mode.”

“Didn't the concept of energy require a new mode?”

“No. We can't sense energy per se, only manifestations of it. It is merely a particularly useful and economical quantification of kinds of motion and force, and these concepts are themselves derived from the old modes of substance, space, time and change.

“Without new modes we can neither envision nor create new aspects of reality. The best we can do is to apply old modes of conception to new facts, which is all we have ever done. This is why true paradigm shifts in knowledge aren't yet possible. Copernican theory merely shifted the center of the solar system's circular motion from the earth to the sun. Non-Euclidian geometry didn't create new modes for imagining shapes and distances; it merely applied the old ones differently. Even quantum theory doesn't create a new mode. It's merely an ingenious attempt to ‘explain’, using only existing modes, unperceivable phenomena such as discrete chunks of time.”

“I thought mathematics gives us a complete understanding of quantum theory.”

“Mathematics gives us a complete description of quantum theory but this isn't the same as comprehension. Mathematics is a concise symbolic language that must resort to the use of ‘mega-symbols’ to represent things like infinity (denoted by ‘∞’) or the square root of –1 (denoted by ‘i’) that we can't begin to imagine. Physics has its own special set of mega-symbols, for instance the one denoting the wavelength of ultraviolet light that represents its ‘color’. The more of these a theory requires the more incomprehensible it will be and quantum theory is necessarily suffused with them. That's why we'll never be able to intuit it at a fundamental level until we evolve new modes of conception, and no theory would be so bold as to propose it introduces us to new modes.”

“Do other philosophers share your views?”

“Many, but not all. Any philosophy of truth must also be tested. Mine is bolstered by science since it echoes the correspondence principle's criteria for arriving at truth, namely that a competing theory can survive only if it correctly expands other theories that haven't been dialectically disproved. I've given you a lot to chew on. Feel free to stop by anytime if you have questions or refutations.”

* See footnote 4

____________________

²⁹ In his Essays

³⁰ In The Principles of Human Knowledge

³¹ As related in Plato's Republic

³² In An Enquiry Concerning Human Understanding

³³ In Critique of Pure Reason

³⁴ As Dewey generally remarks in Human Nature and Conduct