The Limits of Science to know Reality without a Thing-in-Itself

Definitions
scientific reductivism: (aka, material reductivism, scientism) the belief science reveals total reality. The belief total reality is phenomenological in nature and consequently discoverable by scientific methodology and describable by scientific law.

transcendental idealism: the belief that we apprehend reality through ideation, as with concepts like space, time, and causation. Reality, however, as it exists in itself, transcends ideation, as well as the very notion of relational objects that arises from ideation.

Space and Time

Einstein and Philosophy
“A human being is a part of a whole, called by us 'universe', a part limited in time and space. He experiences himself, his thoughts and feelings as something separated from the rest... a kind of optical delusion of his consciousness. This delusion is a kind of prison for us, restricting us to our personal desires and to affection for a few persons nearest to us. Our task must be to free ourselves from this prison by widening our circle of compassion to embrace all living creatures and the whole of nature in its beauty.” ~Albert Einstein

Though Kant is little regarded in today’s physics, his philosophical legacy would have preceded and influenced Einstein’s revolutionary thinking. It was Kant who first made space and time contingent on an observer through perception, and it was Kant who first conceived the idea that knowledge of experience proceeds from frameworks formed in the mind.

“Einstein therefore confirms Kant’s basic insight, that insofar as science is to be necessary and universal, it must be grounded in transcendental principles, whereas once it becomes genuinely empirical, it loses this quality and becomes tentative and ever-changing.”~Stephen Palmquist, The Kantian Grounding of Einstein’s Worldview

Though Einstein questioned the existence of Kant’s a priori ideas, he nonetheless grasped their essential feature in being transcendental, especially where descriptions of scientific principles in pure geometry diverge from real world preceptual experience. Whereas an abstract idea is forever pure and absolute in the mind, once it takes on applied form in the world, it becomes subject to endless re-visitation.

From Schopenhauer, Einstein learned the deeper meaning behind perception:

“I believe with Schopenhauer that one of the strongest motives that leads men to art and science is escape from everyday life with its painful crudity and hopeless dreariness, from the fetters of one's own ever shifting desires. A finely tempered nature longs to escape from personal life into the world of objective perception and thought; this desire may be compared with the townsman's irresistible longing to escape from his noisy, cramped surroundings into the silence of high mountains, where the eye ranges freely through the still, pure air and fondly traces out the restful contours apparently built for eternity .” ~Albert Einstein, Address before The Physical Society in Berlin

Note Einstein’s use of the phrase “objective perception”. For those unacquainted with Schopenhauer, the tendency here is to assume Einstein speaks only of a scientific approach to Nature, but clearly from the artfulness of his address he means precisely what Schopenhauer intended: namely, an irreducible oneness behind reality that makes every thing, at face value, ephemeral illusion. Pure perception is the true beginning of all understanding, and not merely knowledge.

The Bait-and-Switch of Space/Time
“There is no dynamics within space-time itself: nothing ever moves therein; nothing happens; nothing changes.” ~Robert Geroch

In classical relativity, space and time appear uniform when velocities are calculated for moving objects. When velocities approach the speed of light, a new physics is required, one where, owing to the vantage point of the observer, space and time give way to respect the speed of light.* Whereas Einstein’s Theory of Special Relativity makes space and time relative to the observer, his Theory of General Relativity combines space and time into a single idea, space/time, and it is made interchangeable with the concept of gravity.

Einstein argued space and time could not be regarded as objective outside their subject-dependent experience. That is, there can be no objective present, past, or future in time, and no privileged location in space. In his mathematical formulation, space/time, though finite, is not absolute in the Newtonian sense. In considering the hole paradox generated by his General Relativity Theory, he concluded that points in space and time were meaningless in absence of matter, saying, “People before me believed that if all the matter in the universe were removed, only space and time would exist. My theory proves that space and time would disappear along with matter.”

The question is: In absence of space, time, and matter, what exists?*

It is proposed that the Universe, whether we are discussing the observable Universe or the Universe proper, has a point beyond which it does not extend. Yet how is this boundary (dare we call it an edge) demarcated in either substantialist or non-substantialist terms? This “boundary” is not simply a question of space/time being counter-intuitive as an idea, but also counter-intuitive to experience.* As a space/time Universe involves math—and requires matter—, we have no way of contrasting it with nothingness as a concept. Nothingness is only the point (if not the place) where mathematics cease to describe anything recognizable. We are led to believe more is being explained by space/time than is actually being demonstrated.

We reach an impasse where Einstein cannot help us.

In the transcendental idealist view, space and time are neither finite nor infinite because, outside the theatre of the observer’s mind, they do not exist. When physicists speak of space and time in phenomenal terms, this is usually in reference to either an observer (stationary or in motion) or a set of relational geometric coordinates. Yet these are formal consideration that, in themselves, allude to nothing physical.

“My ideas about time all developed from the realization that if nothing were to change we could not say that times passes. Change is primary, time, if it exists at all, is something we deduce from it.” ~Julian Barbour

With time dilation, where, as measured by one stationary atomic clock, a contraction of time is detected in a second clock that either resides closer to a larger-bodied object with gravitational pull, or is in motion. Yet what exactly is being measured? It is clear in both cases we are comparing process speeds, where one is slower than the other. But is a different process speed due entirely to a “contraction of time”? As Barbour’s quote alludes, change is essential to our notion of time. We deduce its presence, and elasticity, by comparing differing interactions of particles. Yet if both sets of measurements could be taken simultaneously, and observed simultaneously, then in what regard would time fracture for the third observer? He would see, from his timeframe, two clocks running at different speeds, and nothing more. Similarly, when we say gravity “warps space” when it “bends light” around a larger-bodied object, is this really what we are observing? How do warped space and bent light differ as distinct phenomenal concepts? In Einstein’s physics, they are one in the same. However, the physical effects needed to assert the physical existence of space/time (namely, atomic structure) are only seen in the behavior of bending light, even as this is inferred to constitute warped space.

Relativity tells us, the faster we move the more slowly times flows. And yet, what space signifies in this situation is not an actual volume of something. It is not that a given amount of space is literally equal to a given amount of time, but that a distance of space covered at a given speed is equal to a given measurement of time. In other words, the relationship between space and time is interdependent based on other inputs. It is a subtle distinction, for both space and time yield to momentum, and an observer moving at the speed of light (as opposed to one not moving at the speed of light) perceive time and space differently when measurements are compared. Therefore, the contention that space and time are things that magically grow or shrink in themselves comes only by way of a comparison. Observation of phenomena—not space and time—is what leads us to conclude space and time are elastic concepts, which we take to mean elastic “things”. This does not undercut the mathematics of space/time, but it does cast doubt on the assertion that what is being captured in a proof is true ontology.*

(*The anchor of relativity theory and causality is the absolute speed of light. However, recent research at CERN has clocked neutrinos travelling faster than light, which, if confirmed by other sources, turns Einstein’s Relativity on its head.)

(*Interestingly, as we plumb the depths of atomic structure [more with theory than seeing], we encounter mostly space; and the further we unravel subatomic bits, the more space we find.)

(*When we think about space and time willed through the mind as extension and duration of our being, we realize we are not talking about the same thing as geometry. Definitions fundamentally change the character of what is being discussed.)

Intuitive Space versus Constructed Space
“We can know a priori of things only what we ourselves put into them.” ~Immanuel Kant

Analytic a priori knowledge, such as found in definitions and logic, share an intuitive template with synthetic a priori knowledge according to Kant. Moreover, he claimed that synthetic a priori knowledge, which is not formal truth in the manner of a priori logic, nevertheless prefigure all logic and experience. Where Kant blundered was, in wanting to give objectivity to scientific truths of his day, he linked this non-logical (but necessary) intuition too necessarily to specific formal content, that somehow the latter, as dogma, could be derived from the former. Einstein, along with the invention of non-Euclidean geometry before him, made scientific and mathematical knowledge far from matters of simple revelation. Consequently, one of Kant’s central goals in devising his philosophy was undermined.* Non-Euclidean geometry created counter-intuitive space, and its discovery challenged Kant’s claim that all geometry is a formal extension of inner intuition. Einstein’s space is non-Euclidean and empirically testable, and nothing about it is intuitive on first pass.

By way of illustration: We are told curved lines making up hyperbolic and elliptical shapes only appear to be straight and Euclidean when viewed as shorter line segments. Nothing in sense intuition anticipates this idea, and this can be appreciated if you think about an airplane flying from Russia to the United States, where flying over Greenland makes for a shorter trip than flying in a straight line. Sense, where we are not careful in our observations, tells us the Earth is flat, but non-Euclidean geometry proves otherwise. This is a crucial oversight on Kant’s part.*

If we are to accept Non-Euclidean geometry as a description of actual space, then it makes Euclidean geometry, which Kant suggested is synthetic a priori, only analytic a priori.* In other words, Euclidean geometry is not the deep grammar of the mind as it pertains to space, which Kant supposed, but only one tautological possibility for understanding space where other possibilities for understanding can also be constructed. Had Kant been more critical in his thinking, he would have been happy with the informal nature of synthetic a priori knowledge, and left science to work out its “truths” for itself. His contributions are to epistemology, not to physics and mathematics.

As to non-Euclidean geometry, it is still an open question as to whether it strikes closer as an explanation of actual space than previous formulations. Still, in a sense its counter-intuitive principles can be made intuitive according to Mathematician Reichenbach. He argued that, with practice, one can visualize non-Euclidean structures as easily as Euclidean structures. In his paper, Kant and Mathematical Knowledge, Thomas McFarlane concluded: “On this interpretation, a priori space itself is more primitive than any formal intuition of it, Euclidean or non-Euclidean.”

Scientific and mathematical knowledge are therefore capable of generating axiomatic systems that can become acquired forms of self-evident intuition. Though a priori space and time prefigure all such intuition, in themselves they are transcendentally aesthetic, not logical or empirical. Yet if all our “formal” understandings of space are to be analytic and self-naming by tautological axiom, then as Poincaré puzzled, what is being indirectly named? Our in-born understanding of space, given to us first by informal intuition, remains hidden from us as an object of sense,* even as we use geometry to describe its relationships. What Kant regarded as synthetic a priori knowledge can only be, above its transcendental essentialness, tentative as both formal and informal truth. Synthesis becomes analysis in time, until more insight is required than analysis can produce on its own.

What I have outlined here is functionalist’s critique of Kant’s synthetic/analytic distinction, where the answer you get depends upon the question you ask. Though Kant was mostly interested in the phenomenal applications of his philosophy, functionalism, ironically, in undercutting his claims about the linkage between formal intuition and geometry, lends substance to the noumenal side of his argument: that reality, outside formal criteria, is, for all intents and purposes, unknowable as a thing-in-itself.

(*Philosopher of science Karl Popper agreed with Kant on essentials: We impose laws on Nature, although as demonstrated by Einstein’s game-changing Theory of Relativity over the Newtonian model of gravity Kant thought unassailable, it is more truthful to say we attempt to impose laws on Nature. Kant’s philosophy anticipated this, and yet his goal to rescue classical science from the ravages of Hume’s destructive empiricism led him into error by insisting intuition reveals the Laws of Nature. What is imposed on Nature is a structure hatched first in the mind and corroborated later by evidence.

With the emergence of multiverses and the anthropic view, John Barrow launched a related attack against Kant over the inverse square law of universal gravitation, which Kant saw as a necessary consequence of our three-dimensional universe. Barrow believes the reverse is true, and principally because less-stable universes, where there is a different mix of space and time dimensions, would yield a different law. Our Universe is seen as “privileged”, not necessary. The difference here is that multiverses, which trade in unwieldy and superfluous dimensions, are complete speculation and run afoul of Occam’s razor. Kant is perhaps closer to the truth in assuming something classical and orderly about the nature of reality and our resulting Universe, and that three dimensions of space and one of time, far from being a haphazard arrangement, are necessary conditions of all reality and not its cause.)

(*In Kant’s defense, though space can be constructed outside sensibility, boring a straight line through the mantle of the Earth would still get you to the United States from Russia faster by way of a straight line: i.e., an actual curvature of space is not proven by mapping the surface of solid spheres.)

(*Nowhere did Kant overtly call Euclidean geometry synthetic a priori truth, but the impression was left.)

(*We can think about geometry in reference to nothing as easily as we can suppose it to be filled with energy; and conversely we can talk about the structure of energy with little reference to the metric space we suppose it to occupy. Moreover, if you accept the notion of a singularity, where energy becomes infinitely dense, then space, geometrically speaking, is a nonessential feature where energy’s ontology is concerned.

And as we are calling space “energy”, can we do the same for time? Given we impose a “time flow” onto molecular structure by way of The Second Law of Thermodynamics, time no more appears to be an inherent characteristic of energy at the subatomic level than does space. Naturally, science does not necessarily look for symmetry between space and time. They must be regarded as different questions whose answers may not be related or simple. Intuition told Kant that, because space and time presented the same difficulty to our understanding, they were fundamentally connected in framing the understanding.)

The Value in Constructed Space
“We can no more say that Einstein's geometry is 'truer' than Euclidean geometry, than we can say that the meter is a 'truer' unit of length than a yard.” ~Hans Reichenbach, The Philosophy of Space and Time

“So the truth of the geometrical axioms does not rest in self-evidence or a priori intuition, nor does it rest exclusively in empirical verification. We are left with various axiomatic systems, and the only question is, Which definition of space is most valuable?” ~Thomas McFarlane, Kant and Mathematical Knowledge

The relationship between atomic space and geometry is emergent. The two are not synonymous. We must keep this in mind when we employ non-Euclidean geometry, which, where paired with speculative physics, does not limit itself to three dimensions of space.

In the case of the hypersphere, a model for the Universe is advanced where an end-run is made around the problem of infinity by placing the contents of the Universe on a ball-like model. With this analogy, the surface area is finite while possessing no edge, and in theory if you travel in a straight line you will wind up where you started. Two problems arise with this: Because the Universe is expanding, one would never complete the trip all the way around the curved space since the starting point would continually get further away. Secondly, if space is finite, then what is this finite spherical space expanding into if not more space? We are not here dividing the Universe into infinitely smaller bits, or making galaxies smaller to enlarge the space between them. In other words, though infinity never changes in relation to the size of the finite, here it is claimed the finite is expanding, that space is creating itself.

For something to be created, it must have being-in-itself, but beyond geometry, what are we saying space is? And as dimensions of space are added, and the number of Universes mushroom, what are we adding up?

Space/Time versus Substantialism
“I consider it quite possible that physics cannot be based on the field concept, i.e. on continuous structures. In that case, nothing remains of my entire castle in the air, gravitation theory included, and of the rest of modern physics.” ~Albert Einstein in a letter to Michel Besso

Within speculative physics, most notably among superstring and multiverse supporters, we see space/time becoming “substance” in its own right. A space/time manifold is not merely a mathematical model but something that has distinct objective reality. As such, matter/energy-driven events that occur within the manifold are dependent on the manifold as a background: i.e., matter does not simply create space and time as it flies apart but space and time expand to fill a membrane that operates independently of what comes to occupy it. This independent yet inaccessible background resolves (it is argued) a host of issues, because the enigmatic nature of both gravity and virtual particles are explained: they pass in and out of our universe through a permeable membrane. This model also allows for the quantization of gravity so it may be joined to the known forces of the Universe, as well as to substantive boundaries in order to conjoin other universes to our own.

However, nothing of substance is demonstrated by this claim beyond an appeal to simplicity by paradoxically creating more moving parts.* A proliferation of universes via branes does not put all-possible branes containing all-possible universes in a jar with a neat label. We do not escape Russell’s nesting paradox so easily. We only add another layer of contents to the list of things we want to put in a container.

(*Superstring skeptics [among them, Lee Smolin and Peter Woit] have argued that multiversers are working from a perturbative theory that cannot show universes other than our own exist; therefore, the central contention, even if true, is untestable, and consequently unfalsifiable as science.)

Space/Time and Picture-Thinking
Space/time came to be represented as a two-dimensional geometry in the form of fabric or grid, which served to illustrate the warping effect on space/time by large masses such as stars. Real space, however, is three-dimensional, not two-dimensional, so the idea of a flat, bendable substrate does not translate easily to a three-dimensional visual aid. What would the empty space over our heads look like if we were to curve it? It has no visual bottom, top, or thickness like the fabric depicted in the two-dimensional space/time model. More to the point, what would its boundary look like? In the two-dimensional model, the geometry simply stops like a table ledge.

Einstein’s emphasis was—again—on the non-objectivity of space and time, whereas with Minkowski and others we begin to think about space/time as something that can be described geometrically, which naturally leads us to assume it is something physical. As this visual presentation has evolved, we now have things like the Möbius strip being used to illustrate how space/time manifolds can have a continuous surface with only one edge. Still, it is telling how a Möbius strip can only demonstrate these “features” as a ribbon (object) described against a three-dimensional backdrop that in itself has no boundaries.

In other words, where substantialists attempt to represent space as an object, they do not account for the space needed to present the object. Again, a set cannot be a member of itself; hence, space cannot be a subset of itself. You cannot treat the space outside the Möbius strip’s defining boundary as differentiated from the space used to define it in actuality. This feat is only accomplished through an idea.

Science tells us that even if such visual aids as tabletops and Möbius strips are faulty, the mathematics is not, even if intuition and sense cannot make sense of the mathematics. Infinity, we are told, can shrink or expand mathematically without affecting the boundaries of finitude. But what are the “boundaries” of finitude where space and time are concerned? Though only the finite can be made sensible, we regularly revert to analogy where we make it related to non-sensible infinity. This bait-and-switch is far from satisfying, for it is infinity that we want to see and touch, because we understand that its mystical ontology is related to our own.*

(*Einstein was clearly an idealist when it came to space and time, if not in the same sense as Kant. Space/time can only be understood as an idea via geometry, yet, again, where is ontology in geometry?)

The Hypersurface of The Present
By converting a theoretical fourth dimension of space into the dimension of time, Minkowski was able to represent the whole Universe—past, present, and future—in a two-dimensional diagram. This hypersurface of the present is where the observer resides as a point, and he can only be considered in reference to a past light cone that intersects him on this grid, for everywhere he looks he is bombarded by light from the past, and to which he must consider even his body as being something lapsed. The future light cone can only be a projection, which like the past light cone, is visualized in widening concentric circles out from the observer. Whatever lies beyond these circles, in the past or future, is not causally connected to the observer and must be unknowable.

Though this mathematical model is useful in mapping past and future coordinates, as well as useful in determining the perimeter of a causally connected Universe via the speed of light, a fourth dimension of space is not physically interchangeable with time. Science has neither established the existence of a fourth dimension of space nor a “substance” for time. Regardless, this model is a testimony to the ingenuity of science. The danger, again, is confusing such description for the thing-in-itself. The most we do here is impose formal order on something that is first understood (and perhaps best understood) informally, even while our evolving symbolism bares less and less likeness to the actual content of our experience.

Space/Time as Factor X
So where is there physical reality in the symbolism of mathematics?

For example, the recent Fermi probe set out to understand one descriptive aspect of space/time by testing whether it was “frothy” or “smooth” by comparing the arrival times of two different photons to a detector: one with a short gamma wavelength, and another with a longer wavelength. According to the frothy view, the shorter wavelength should snag up on the textured surface of space/time, and thus be recorded as traveling at a slightly slower speed than the longer wavelength. What was observed was no difference in the speed of either photon, so the frothy model of space/time was “ruled out”. This result is in keeping with Einstein’s model of a smooth space/time, though one can just as easily argue the result works equally well for space and time having no substance at all.

These piecemeal experiments, where one “closes in” on a better understanding of space/time by eliminating what it is not, amounts to the feeblest form of scientific proof: that of using negative evidence to assert the existence of positive proof elsewhere.* Claiming this process vindicates the certainty of space/time’s physical substance is like saying that by devising tests to show Factor X is more like cauliflower than broccoli one vindicates the view Factor X is a vegetable. (There is nothing in the experiment to disprove Factor X is fruit.)

(*We see this in science journalism where it is reported, for example, that “CERN is closer to finding the Higgs Boson” when it is only compiling a list of places where it is not. A physicist in a recent NPR interview characterized this “closing in” on the Higgs Boson to having a hundred drawers to search through in hope of locating a favorite pair of socks. Having gone through ninety-nine drawers, what are the chances one has “closed in” on the pair in the last drawer? Only the unlikeliest fluke would put them there, and only hopeful human nature would expect to find them in the last place one would look.)

Psychological Time versus Einsteinian Time
Though relativistic time is compelling as physics, it remains counter-intuitive and disconcerting as psychological experience, so much so physicist Arthur Eddington maintained that time had a “back door” into the mind, irrespective of its treatment in the laboratory.

When molecules collide, there is no past-future asymmetry. Such encounters at this scale are easily reversible. However, at the macrocosmic scale, fluids disperse and gases escape—and there is no putting the genie back in the bottle. The Second Law of Thermodynamics makes events of this kind irreversible through the asymmetry of entropy. Physicist Paul Davies argues our concept of time having a direction is due entirely to The Second Law of Thermodynamic. He goes so far as to suggest “that time doesn’t really ‘flow’ at all; it’s all in the mind.” (Here he walks right up to Kant and does everything but shake his hand!)