Beginning the search for the theory of everything

Prologue

I suppose “everything” has to begin somewhere – for me, it was Mother Cabrini Hospital in upper Manhattan, but physicists keep insisting it was the Big Bang. They are now hypothesizing a ToE (theory of everything) that would snugly explain both the origin and fabric of the universe and how it all behaves. Well I was born with a big ToE too (in fact, two of them) – so you might say I got a head start on the hypothesis.

In physics, a ToE is typically a theory which unifies the four fundamental forces of nature – gravity, the strong nuclear force, the weak nuclear force, and electromagnetism in an attempt to fully explain and link together all known physical phenomena. Though there have been numerous hypothetical ToE’s proposed by physicists, popular candidates for a functional ToE at the moment include string theory and M-theory (which some say is yet to be defined).

Some spin-offs on the basic ToE include:

GUTs (grand unified theories), which attempt to unite all the fundamental forces EXCEPT “gravity”. Basically, GUTs attempt to unify the strong nuclear and “electroweak” forces. You might say “gravity gets gutted out of the hypothesis,” but that’s another story.

The Kaluza-Klein theory,- an early attempt to unify electromagnetism with gravity; the Grand Theory of Everything (tGToE); even an Exceptionally Simple Theory of Everything, and M-Theory – a FINAL theory of everything?

There’s also my take on all this: tRUTH – The REALLY Unified Theory Hopefully!

Some theorists seek to neatly lace up their ToE with String Theory, while others have wrapped up their scheme in fundamental quantum foam. Many seekers have discovered that for all their efforts, the shoe simply doesn’t fit and their ToE is a big source of embarrassment amongst academic peers. Personally, I’m convinced that there is no one-size-fits-all solution to the Theory of Everything unless you create an “open ToE” option, lopping off the oppression of excessive complexity with Occam’s Trusty Razor.

My personal ToE goes as follows:

Before getting all tangled up in String Theory and synchronistically bumping your hypothesis with an unprecedented Big Bang while attempting to put your best ToE forward, remember Werner Heisenberg’s assurance that nothing determinant ever happens without an “observer” – you! You’re it, the grand ToE, assuming you’ve been watching your step!

When in the dark of the hypothetical shoe box, Schrodinger’s cat pitifully wails and you begin to identify with his plight, maybe you’ll sneak a peek outside your own box! If you’ve read this, you must have been peeking after all.

Beginnings of the Search for the Theory of Everything

The ancient Greeks had “theories of everything” – ancient philosophers considered that there is an underlying unity concealed by the apparent diversity of appearances.

The “mechanical philosophy” of the 17th century theorized that all forces could ultimately be reduced to forces of contact between tiny solid particles.

This mechanical philosophy was outmoded by the acceptance of Newton’s long-distance force of gravity. Newton’s Principia also introduced dramatic empirical evidence for the unification of seemingly distinct forces.

Other players in the upstart to the search for a ToE include:

* Galileo – work on terrestrial gravity.

* Kepler – laws of planetary motion and the phenomonenon of tides were quantitatively explained by a single law of universal gravitation.

* Hans Christian Oersted – in 1820, discovered a connection between electricity and magnetism which triggered decades of work culminating in James Clerk Maxwell’s theory of electromagnetism.

* Michael Faraday – in 1849-50, experiments attempting to unify gravity with electromagnetism.

* Einstein – in 1915 his theory of gravity (general relativity) was published spurring on the search for a unified field theory that would combine gravity with electromagnetism, when it was assumed that no other fundamental forces existed.

– Searching for a Unified Field Theory

Contributors to this search included Arthur Eddington, Gunnar Nordstrom, Hermann Weyl, Oskar Klein, and notably Einstein – none of their proposals were ultimately successful.

The search for a unified field theory was interrupted by the discovery of the strong and weak nuclear forces, which couldn’t be accounted for by either gravity or electromagnetism.

During the 19th and 20th centuries, it became apparent that many common forces – elasticity, contact forces, viscosity, friction and pressure resulted from electrical interactions between the most minute particles of matter.

– Quantum Mechanics

In the 1920s, the newly conceptualized quantum mechanics revealed that chemical bonds between atoms were examples of (quantum) electrical forces.

It was surmised that gravity and electromagnetism could peacefully coexist amongst other Newtonian forces – but for years it seemed that gravity could not be incorporated into the quantum framework and was not unifiable with other fundamental forces. For this reason, work on unification (for much of the 20th century) was focused on understanding the three “quantum” forces – electromagnetism and the weak and strong forces.

In 19678 Sheldon Glashow, Steven Weinberg and Abdus Salam unified electromagnetism and the weak nuclear force (electroweak force) and conceded that the strong nuclear and the electroweak forces peacefully coexist but remain distinct in the standard model of particle physics.

– Grand Unified Theories

Several Grand Unified Theories (GUTs) have been proposed to unify the strong and electroweak forces, although the simplest GUTs have been experimentally ruled out – nonetheless, the general concept, especially when linked with supersymmetry remains favored by many theoretical physicists.

Where the ToE Stands Today

In contemporary mainstream physics, a Theory of Everything would typically need to unify all four fundamental interactions of nature: gravity, the strong nuclear force, the weak nuclear force, and the electromagnetic force.

Since the weak force notably can transform elementary particles from one kind into another, a ToE should comprehensively take into account the various different kinds of particles as well as the different forces.

In addition to the fundamental forces of nature, modern cosmology may require a ToE to take into account an inflationary force, dark energy, and dark matter composed of fundamental particles outside the “standard model.” The existence of these new entities has not been proven and there are alternative theories including that of modified Newtonian dynamics.

Electroweak Unification and Symmetry

The unification of electromagnetic and weak forces amounts to a broken symmetry: the particles carrying the weak force (W and Z bosons) have mass, whereas the photon – which carries the electromagnetic force – has no mass. At high enough energies Ws and Zs can be easily be created and the unified nature of the electroweak force becomes apparent.

Grand unification (GUT) is expected to work similarly, but at energies far greater than could be reached by any Earth-based particle accelerator. Conceptually, the unification of the GUT force with gravity would be expected at the Planck energy – roughly 1019 GeV (gigaelectron volts).

There is as yet no direct evidence for an electronuclear force, therefore the search for a ToE may seem premature; nonetheless, most physicists believe the necessary unification is possible.

Supersymmetric GUTs seem plausible – not only for their theoretical “beauty” – they inherently produce large quantities of dark matter and the inflationary force may possibly be related to GUT physics. GUTs however are not the final answer.

Unsolved Problems and the “Cat’s Cradle”

Inconsistencies between quantum mechanics and general relativity imply that one or both of these must be replaced by a theory that incorporates quantum gravity.

The only current mainstream candidate for a theory of everything is superstring theory or M-theory (a new limit of string theory in which 11 dimensions of spacetime may be identified) – current research on loop quantum gravity may also come to play a fundamental role in a ToE.

String theories and “supergravity” suppose that the universe has more dimensions than the three of space and one of time. Behind this approach is the Kaluza-Klein theory in which it’s noted that applying general relativity to a five-dimensional universe yields the equivalent of general relativity in four dimensions together with Maxwell’s equations (which describe the properties of the electric and magnetic fields).

This outlook motivated efforts to work with theories containing larger numbers of dimensions in the hope of yielding equations similar to those of known laws of physics. Extra dimensions would also help resolve the “hierarchy problem”: the question of why gravity is so much weaker than any other force. The practical answer would involve gravity leaking into extra dimensions in ways that the other forces don’t.

– The String Theory Landscape and Anthropic Approach

In the late 1990s, it was noted that a problem with several of the proposed theories of everything (especially string theory) was that they didn’t constrain the characteristics of the universe each them predicted. Example – various theories of quantum gravity can create universes that have arbitrary numbers of dimensions or arbitrary cosmological constants. Even “standard” ten-dimensional string theory allows that the “curled up” dimensions can be compactified in an enormous number of different ways, each of which corresponds to a different set of low-energy forces and fundamental particles. This array of theories is called the “string theory landscape.”

One proposed solution is that any of these theoretical models are realised in any of a huge number of universes, of which only a small number are habitable – hence the fundamental constants ultimately result from the “anthropic principle” rather than as a consequence of the theory of everything. This anthropic approach is frequently criticised because of its being flexible enough to encompass practically any observation, and it can’t make useful scientific predictions. From this perspective, string theory would be considered a pseudoscience – where an unfalsifiable theory is adapted to fit experimental results.

The problem here may be – does “string theory landscape” afford us the road to a successful theory of everything, or is it just a blind alley – or the ultimate game of cat’s cradle?

– Godel’s Incompleteness Theorem

According to Godel’s theorem, pure mathematics are indicated as inexhaustible – no matter how many problems are solved, there will always be other problems that can’t be solved within the existing rules – according to this theorem, physics is inexhaustible too, since the laws of physics, though a finite set, include the rules for doing mathematics; Godel’s theorem therefore also applies to physics.

There are some scientists who call upon Godel’s incompleteness theorem as proof that any attempt at constructing a ToE is destined to fail.

Stephen Hawking originally believed in the Theory of Everything but concluded that a ToE was uobtainable after considering Godel’s Theorem: “Some people will be very disappointed if there is not an ultimate theory that can be formulated as a finite number of principles. I used to belong to that camp, but I have changed my mind.” Stephen Hawking; Godel and the end of physics; July 20, 2002

This view has been argued against by others including Solomon Feferman and Douglas S. Robertson who asserts that the underlying rules are simple and complete – but that there are formally undecidable questions regarding the game’s behaviors.

Assuming it’s possible to completely state the underlying rules of physics with a finite number of well-defined laws, there’s little doubt that there are questions about the behavior of physical systems which can’t be formally decided on the basis of those same underlying laws.

Many physicists consider the underlying rules alone as sufficient to define a “theory of everything” – these theorists assert that Godel’s Theorem does not prove that a ToE cannot exist.

There is no ToE to date that is believed to be completely accurate – physics has proceeded by a series of successive approximations that allow increasingly more accurate predictions over a progressively wider range of phenomena. Some physicists even hold that this series of approximations will never culminate in the “truth” (Einstein occasionally expressed this view).

It is often claimed however, that the theories of everything are becoming progressively simpler. It would be reasonable to assume that the process of simplification can’t continue indefinitely – it would terminate somewhere.

One hard reductionist view in the ongoing debate is that the ToE is “the” fundamental law and that all other theories applicable within the universe are a consequence of the ToE.

– Free Floating Laws

Another view is that emergent laws – called “free floating laws” by Steven Weinberg – which govern the behavior of complex systems, ought to be seen as equally fundamental. The second law of thermodynamics and the theory of natural selection are examples of these emergent laws.

The premise is – that although in our universe these “low-level” laws describe systems whose behaviour could (in principle) be predicted from a ToE – they’d also hold in universes with different emergent laws, subject to only some very general conditions. It’s of no help then, even in principle, to invoke such low-level laws when discussing the behavior of complex systems.

Others argue that this attitude would violate Occam’s Razor if a totally valid ToE were formulated. Perhaps the only point of these debates is that of vying for the right to apply such a high-status word as “fundamental” to respective subjects of interest.

The Merits of Seeking a ToE

Perhaps the main (if not most noble) motive for seeking a ToE, besides pure intellectual satisfaction, is that all previously successful unifications have predicted new phenomena – some of which have proved to have practical technological application, as in electrical generators.

The ToE, as in other cases of theory reduction, would also allow us the security of defining the domain of validity and of residual error of low-energy approximations to the complete theory – this could later be applied to important practical calculations.