I ended my short piece "Science and Me" (NQ160) by alluding to the search for a "Theory of Everything" (TOE). Stephen Hawking, the well known cosmologist of Black Hole fame, has joked that he receives claims to several TOEs in his mail every week. Lots of contenders, but no winners in these high sweepstakes. But to mark the centenary of Einstein's classic papers of 1905, and the fiftieth anniversary of his death, some thoughts regarding this TOE are in order.

To reiterate, a TOE aims to unify all the basic forces that govern the natural world. More specifically, it is a theory that would unite General Relativity, a theory of gravity, with the quantum world — hence the TOE is often called a theory of 'quantum gravity', in which the equations that describe physical behavior would apply to very large bodies as well as to subatomic particles.

One of the protagonists in this search is Michio Kaku. He believes that the new discipline of String Theory is promising, and may realize Einstein's dream of a unified field theory, a series of numbers and symbols, perhaps less than an inch long, that would constitute a pure, simple 'Theory of Everything'. It would be appealing, even ideal, to have a single innocent-looking equation to express something so profound, yet 'not-so-innocent'.

The mathematician, Roger Penrose, however, does not believe that string theory can or will provide an answer, and thinks that a TOE is centuries away from being realized in the strictest sense. He has wrestled with many problems in physical theory, including that of consciousness.

But I'd like to reflect on the main ideas that issue from this Trinity: relativity (Einstein), uncertainty (Heisenberg) and incompleteness (Gödel). Just as Darwin, Marx and Freud were revolutionary thinkers in the 19th century (with Freud spilling over into the 20th), it's fair to say that Einstein, Heisenberg and Gödel were originals who changed the course of thought in the 20th century, at least in the realm of science and mathematics.

Relativity theory offers a reasonably accurate picture of behavior on a very large scale, but Quantum Mechanics (QM) emphasizes the uncertainty of behavior on the subatomic scale. Heisenberg's Uncertainty Principle pointed out that in the quantum world we cannot precisely determine the behavior of very small particles —  the very act of measurement alters the physical reality. In his own words, "The idea of an objective real world whose smallest parts exist objectively is impossible." Our role as observers decides the 'objective' picture; there is no independent reality.

Tying these two pictures together with a single explanation is the challenge. QM seems to share the subjective character of our perceptions, hazy as they mostly are. The illusion of the passage or flow of time is a good example. Physics does not deal with illusions or perceptions. It deals with the measurable or quantifiable. Yet QM appears to be in sync with our perceptions because of the choices and possibilities it suggests with regard to different worlds, other outcomes. Penrose believes that consciousness is hard to explain in purely physical terms, but an explanation may lie somewhere between QM and the 'classical' theory of relativity because QM allows the possibility of multiple states that may be analogous to the nature of awareness.

Gödel's Incompleteness Theorem must be invoked when we speak of limits, conclusions, finalities, infinities. Our idea of ‘complete’ was forever put to rest when Gödel proved his startling—and disorienting—theorem in 1931. Here's the Incompleteness Theorem in a nutshell, though couched in mathematical terms: Any set of axioms contains within it undecidable propositions. It brings closure to Russell's paradox: 'the set of all sets that are not sets of themselves', which leads to contradictions if one tries to make sense of it. In short, in layman's language, there can be no last word on anything —  the very attempt is doomed from the start.

Playing with these ideas suggests more that is intriguing. Incompleteness — which Gödel proved beyond a doubt — has affinities with the uncertainty of the quantum world, as Heisenberg conceived it: the idea of free will that QM supports implies that an action or event can take any direction, with unpredictable outcomes. You may know one thing for certain, like the velocity of a particle, but always at the expense of something else, like the position of that particle. And incompleteness closes in to stifle any notion that we will know everything about that one thing, or anything for that matter. A TOE aims to discover laws that are immutable, that can explain any phenomena; it's not aimed at describing every instance or result of those laws. It is only a theory of everything, not everything one can think of. So it's reasonable to say that it would be consistent with incompleteness.

Descartes, the great skeptic, posed a deceptively simple question in his Meditations: Is there anything of which I can be certain? This question continues to haunt us. QM amplifies its concern at the level of the infinitesimal.

The structure of Space-Time in relativity supports determinism, positing that all outcomes have already taken place. QM supports free will — we can alter our destiny. Relativity offers an accurate picture on the large scale, QM deals with the microcosmic.

In talking about the insights of relativity, Brian Greene — author of The Elegant Universe — gives an example from life: Someone writes you a letter from New York, saying it's snowing "now". Two days later, you receive the letter. Is it snowing "now"? When is "now," anyway? And where? You don't have to decide because each moment exists for always somewhere in space-time. Wherever you go, it's here. Whenever it is, it's now. Between relativity and quantum mechanics, there's no where to stand; no when to stand, either.

Einstein and Gödel were at the Institute for Advanced Study in Princeton at the same time, and became friends. Both shared a belief that the truth about physics and mathematics was objective; it was there to be discovered. As he faced death, Einstein made a rather sad remark: "the distinction between the past, the present, and the future is only an illusion." It flowed from his special theory of relativity, which claims that there is no universal 'now' — one man's now might be another man's past or future, since time passes at a different rate depending on how fast a person is moving. Gödel also believed that the passage of time is an illusion, and explained why:

The illusion of the passage of time arises from confusing the given with the real. Passage of time arises because we think of occupying different realities. In fact, we occupy only different givens. There is only one reality.

Hence, we suffer from the illusion of feeling like prisoners of time. We often speak of being in a ‘time-warp’, of occupying a world that is out of tune with a supposed ‘present’. In a sense, that is the ‘given’ in Gödel’s interpretation. Gödel applied his mathematical mind to Einstein's physics and, as David Berlinski — writing in Discover (Mar 2002) — elucidates, "vindicated the deepest insight of Einstein's theory, namely that time is relative. But Einstein's theory of relativity suggests only that time does not exist in the conventional sense, not that time exists in no sense whatsoever. Einstein's claim is more subtle. He suggests that change is an illusion. Things do not become, they have not been, and they will not be: They simply are. Time is like space; it is precisely like space. In traveling to Singapore, I do not bring Singapore into existence. I reach Singapore, but the city has been there all along. So, too, I reach events in the future by displacing myself in time. I do not bring them into being. And if nothing is brought into being, there is no change."

In this age of the Internet, we have a kind of analogy of this notion of where and when. In the virtual universe of the World Wide Web everything seems to be instantly available everywhere, all the time. This shows how the extraordinary ideas of relativity are manifested in the realm of ordinary life through digital technology. Not surprising, since the practically 'instant' nature of the wired world depends on electrical signals traveling at the speed of light. Indeed, teleportation — in which, say, a human being could in theory be fully documented, disassembled, transmitted electronically over vast distances, and reassembled at the other end, offering an exact replica of the original, as though it were cloned at a moment in time — is like instant travel: being anywhere, everywhere at the same time.

In his original paper, Space and Time, the physicist-mathematician, Hermann Minkowski began by saying "Henceforth, space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality." He put it in simpler words, "Nobody has ever noticed a place except at a time, or a time except at a place." Do we not say, for instance, 'That town is two hours away'? Upon reflection one becomes aware that where and when are always fused. Thus was born the 4-dimensional space-time continuum of General Relativity — and the curvature of space-time in a gravitational field. The gravitational force exerted by a star or planet deforms the geometry of space-time. Einstein showed, for example, that light bends in a gravitational field, and rejected the very notion of absolute space and time. To elaborate, I quote from Lee Smolin's account of Einstein's legacy (Logosjournal, Summer 2005):

General relativity rejects the whole idea that space and time are fixed at all — the properties of space and time evolve dynamically in interaction with everything they contain. Furthermore, the essence of space and time is just a set of relationships between events that take place in the history of the world…Thus, there is no fixed framework, no stage on which the world plays itself out. There is only an evolving network of relationships, making up the history of space, time, and matter. All previous theories described space and time as fixed backgrounds against which things happen. The point of general relativity is that there is no background.

Coming back to the incongruity of Relativity and QM: Relativity deals with phenomena on a very large scale, which can be studied with certainty, or predictability (observations bear this out) — it is deterministic. But QM deals with the very small scale of the subatomic, where there is uncertainty, or unpredictability with regard to physical behavior — QM allows free will, as it were. Yet we all perceive that the small makes up the large, and is an integral part of the whole; so how indeed can the two views, dealing with the same reality, be at odds with each other? How can they be reconciled; how can they satisfy the same equation? How can one theory account for both — obviously conflicting — phenomena? That is what puzzled Einstein, and egged him on to try and produce a consistent TOE that unifies these two and all other phenomena. QM predicts that two particles having no contact whatsoever can somehow be in touch over arbitrarily large regions of space — an  absurdity. Yet experiments show that particles do just that. And what is "space" if it doesn't separate one thing from another? Einstein was obsessed with a theory of 'principle' that connects everything, not just an operational theory, like QM, that agrees with a host of observations and has proved to be useful in the practical world.

Einstein must have had a kinship with Erwin Schrödinger, who formulated the wave function that described the probability of an event at the quantum level. In his book What is Life, Schrödinger tried to reconcile physics and biology, drawing on the Upanishads for deeper spiritual insights. He was convinced of a certain beauty in the observable physical world, and had strong aesthetic intimations of an equation to transcend all equations, that would characterize the workings of the universe in all its complexity, large or small, as an integrated whole accurately described by a collection of symbols related to each other in a precise way — this equation would demystify the cosmos. Such an equation, a unified theory, remains elusive as ever. But interestingly, as Smolin maintains, it is as unclear now as it was for Einstein whether pursuing a unified field theory will lead to real progress in understanding nature.

And consider the human angle: if we were to somehow destroy a major part of the human race, and most other forms of life on earth, with atomic power, either through carelessness, war or terrorism, then E=mc² (which was derived in Einstein's second paper on relativity in 1905) will come to symbolize a "Theory of the End". We won't need an equation that represents a TOE to augment our intellectual legacy. 

So I share the astronomer, Martin Rees' view that "our everyday world presents intellectual challenges just as daunting as those of the cosmos and the quantum. We need the kind of perspective that Einstein himself espoused — global, humanistic and long term."

Arguably, the last true frontier is the human mind, not the observable universe 'out there' which we perceive and make sense of with that mind. We are for the most part where our minds are. To that extent we live in a symbolic universe, in a time and space of our own choosing. Time and space are constantly being distorted to fit our perceptions. We think back, we think ahead, forever avoiding the present, which is too real, too close for comfort. All our records and chronicles (mixed with memory) are tinged with the virtual — that's how we represent the supposedly real. Our concern, first and foremost, is how we think and feel, what we imagine. As Gödel might have said, the real is confused with the given, and so illusion reigns. The challenge posed by a "Theory of Everything" is one aspect of that last frontier: Mind.