"Space and time may be illusions" - By Avik Dubey
One of the deepest philosophical questions is: why is there something rather than nothing? A more tractable question is: why is there space and time even when there is no matter?
Most things in physics are represented as fields, continuous functions defined over space and time. There are electromagnetic fields, matter fields, strong and weak fields. All of these fields have what is called a “ground state”, a state in which they exist at their lowest energy level. In classical physics, the physics of Newton, Lagrange, Hamilton, and even Einstein’s relativity, fields tend to have zero ground states. For example, if I do not have anything charged around, I can expect that there will be no electric field around either. The electric field is in its ground state where there is nothing there to disturb it and make it active.
The one fundamental theory in classical physics that I know of that has a non-zero ground state is Einstein’s general relativity. It predicts that you can have something when there is nothing.
General relativity is, of course, the theory of gravity and how curvature in space and time create the illusion of a gravitational force, but when you have no masses, no planets, stars, galaxies, or anything to curve space and time, you still have space and time. They are just flat.
Many theories of gravity, therefore, actually represent the gravitational force as not space time itself but deviations from flat spacetime. That creates something of a conundrum for us. Electromagnetism certainly does not appear to work that way. Neither do any other forces or matter.
That raises the question: what is space and time? Where does it come from? And is it really fundamental? That is, does it exist of its own accord or is it really the product of some microscopic quantum phenomenon which is more fundamental?
String theorists, despite claims of having a theory of everything, do not have a theory of space and time. They depend, rather, on knotted up spacetimes (so-called micro spacetimes) in which their strings vibrate. And one of the functions of strings is actually to create gravity and some how self-generate those curved spacetimes. Yet, flat spacetime in string theory is always a backdrop — a given.
Other theories, such as loop quantum gravity, propose that spacetime is not fundamental. Rather, events and the connections between events is. Space and time is ultimately the product of interconnected things happening and causing one another. Causal set theory is similar in this way.
Then again, why are events fundamental? How does all this stuff get there and connected up in the first place?
A Brief History of Space and Time
Before the development of modern physics, the dominant philosophy of physics was mechanistic. Mechanistic philosophy assumed the universe consisted of a fixed set of basic quantities and that the goal of physics was to determined a limited framework of rules that govern those quantities. Particles were points that were mediated by forces, electromagnetic and gravitational. These were all assumed to exist independently and have a discrete set of properties. For example, an electron had charge and rest mass.
Coming out of this philosophy was the idea that space and time were an arena where physical processes take place. Thus, particles and forces were assumed to obey certain principles of space and time:
- Continuity: particles followed continuous trajectories through space and time.
- Locality: Interactions are always local with entities separated in space not able to interact.
The development of General Relativity modified but did not destroy the notion of an arena. Rather than being a fixed arena, space and time were able to change based on the matter in them. Continuity and locality are maintained but independence of arena from players is not.
Einstein’s goal was to eradicate the idea of space and time as fundamental at all. In his own words,
There is no such thing as empty space, i.e. a space without field. Space-time does not claim existence on its own, but only as a structural quality of the field
As I mentioned above, his theory admits a space and time with no matter at all, so despite his claims, his theory never achieved this.
Quantum Theory destroys Locality Assumption
The debate over the meaning of quantum theory rages on, yet, one thing is clear about quantum systems and how they differ from classical. Quantum phenomena such as describe particles are not always separable. What this means is that you can have two particles A and B that have interacted at some point in the past, and no matter how far apart they become, they share a single state. Because they are not separable, their locations are also not separable.
Despite his desire to destroy space and time as independent entities, Einstein believed in locality and that the nonlocality of quantum theory indicated something was wrong with it.
Because of Heisenberg’s uncertainty principle, however, you cannot even attribute properties to arbitrarily small regions of space and time. Properties must always be assigned to probability fields that exist over regions of space and time. Locations in space and time, hence, have no identity and can be said to exist only as mathematical conveniences.
Quantum theory suggests that locality is an illusion, a byproduct of the decoherence that occurs between quantum waves so that nonlocal effects are damped while local effects are reinforced. When you make predictions about what happens inside a particle accelerator, for example, you are looking at how everything across all space and time affects what happens in the accelerator. While many of those contributions will ultimately cancel one another out, they are still there. That is how nonlocal quantum theory is.
Despite the loss of locality, space and time are still fundamentally there in quantum theory. Continuity also remains.
Black holes and Quantum Gravity Challenge Continuity
One of the problems with Einstein’s theory is that it implies that space time will from time to time develop singularities. These are points of infinite curvature and density of matter where the laws of physics lose meaning. This may be a problem with continuity for, in a universe that is defined purely in discrete chunks, singularities are no longer possible.
The earliest challenge to the continuity of space and time came from the work of John Wheeler who showed in this theory of quantum geometrodynamics (the quantum dynamics of spacetime geometry) that at small scales space and time will form little wormholes connecting previously unconnected points. This spacetime quantum foam makes it impossible to measure distances smaller than the Planck length or synchronize clocks closer than the Planck time because the continuity that would be required to do so no longer exists. You cannot say how far apart two times or points in space really are since they could be multiply connected by arbitrary routes.
Given the nonsense that appears at the smallest scales, where locality vanishes, it may mean that the continuity of spacetime is only an approximation. Therefore, any approach to construct a quantum theory of spacetime geometry in which the assumption of a continuous manifold is fundamental is doomed to failure.
Indeed, since both general relativity and quantum theory suggest that there are problems with continuity at extreme scales either in matter density as with black holes or in terms of locality and separability, and their combination only makes it worse, it seems that the continuous manifold of Einstein and Newton may be the problem.
The idea of spacetime being discrete rather than continuous is not new. It goes back at least to the Greeks. Yet, in the modern sense of curved geometry it was recognized even before Einstein by the 19th century mathematician Riemann to whom General Relativity owes much of its mathematical underpinnings. Riemann questioned the validity of defining geometries on very small spaces suggesting in 1854 that
[T]he reality which underlies space must form a discrete manifoldness, or we must seek the ground of its metric relations outside it, in binding forces which act upon it.
In other words, a continuous manifold cannot exist of its own accord. It must be made continuous through some outside force. The reason is because in a discrete geometry the components of that geometry do not have that geometry applied to themselves. Thus, the geometry does not have to be defined recursively ad infinitum. In a continuous geometry, on the other hand, you cannot define a “ground” of the metric (i.e., measure or definition of the geometry). Instead, you have to impose it externally like God handing down the metric from on high and saying that all points have this given relation.
The great Mathematician W. K. Clifford expounded on Riemann in 1876, long before Einstein, suggesting a scheme of discrete “hills” in an otherwise flat geometry that communicate via waves to generate that geometry. He further suggested that this communication was responsible for the motion of matter itself! This was 45 years before General Relativity!
Thus, experiment appears to have ruled out all the assumptions of Newton but this last one: continuity. Reason suggests that it too must fall.
Alternatives to Continuous Spacetime
The most obvious way to get rid of continuity is to assume that space and time are some kind of lattice. Many early lattice models of general relativity did away with continuous space time but kept the real numbers as quantities on the lattice points. These seemed to suffer from the same problems as relativity since they retained continuity on the lattice. Many of these models have gone on to become computational models of general relativity.
To get away from the real numbers entirely, a lattice approach can be made that indicates that, for example, quantum fields generate measurements which are all rational numbers (ratios of whole numbers). If only the rational numbers are real and the real numbers are not, then continuity is a byproduct of the density of the rational numbers. (The term density here refers to the fact that there are no measureable holes in the rational numbers versus the reals. Essentially, the distance between a real number and the nearest rational number is always zero.) Such an approach retains the symmetries of General Relativity such as Lorentz invariance despite lacking the reals.
In these discrete lattice approaches all the differential equations of relativity are usually replaced with finite difference equations. These equations contain the ratio of a function at two points divided by the distance in the two points, approximating a derivative. Yet, this is not really appropriate because finite difference equations are simply approximations to differential equations. Not to mention they retain the idea of “distance” in the equation. They usually violate the symmetries that the continuous differential equations satisfy. This is why in developing his lattice gauge theory for the strong force, Kenneth Wilson defined his lattice equations in terms of what are called gauge operators which retained the symmetry of the continuous equations. In this case finite difference equations were only an approximation to both the discrete gauge invariant lattice equations and the continuous differential equations.
This leads to another approach: the Ashtekar programme which is the basis for Loop Quantum Gravity. In this program, the continuous manifold of general relativity is replaced with loops instead of finite differences. These loops resemble those of Wilson’s strong force loops but they no longer have an existence on a spacetime manifold. Rather, the loop itself is fundamental and the positions in space and time of its points are meaningless.
A more exotic approach is non-commutative geometry which arise more from the mathematics of quantum theory than any genuine physical motivation. It is unclear that its results have any applicability to the physical world, but it represents a powerful mathematical program to relating algebras and geometries that may be important to process-based approaches I’ll mention later.
Many of these approaches assume that the discrete spacetime only appears at the smallest scales and spacetime emerges with scale. In his theory of spin-networks and twistors, however, Penrose attempted to build up a theory of spacetime and quantum theory together using combinatorics rules that apply to all scales. This approach in which rules cause the emergence of physical reality is also popular with mathematica mogul Stephen Wolfram.
Other approaches to emerging spacetime from quantum theory apply some sort of integer value “order parameter” to quantum systems and then show how spacetime emerges, e.g., from the Dirac fields that govern matter, with the correct number of dimensions. These also get around the problem of “empty” space having a geometry since quantum spacetime is never really empty. These still regard quantum fields as independent and fundamental.
Beyond Mechanism to Process
Most of the approaches above are still mechanistic in philosophy. They assume finite sets of parameters or properties and independently existing fields as a given.
An alternative is a process based philosophy.
In a process based philosophy, physical properties, particles , and fields do not have intrinsic being. Rather, they are a process becoming.
Hence, motion, not property, is fundamental. There is no “thing” moving. There is simply moving.
David Bohm was perhaps the greatest champion of this approach to physics in the 1950s on with his theories of implicate and explicate orders. Moreover, quantum physics contrasts to classical in just this way because nothing is truly separable into distinct entities. Particles are only relatively stable aspects of the underlying structure. Thus, there is no such thing as an external cause to an event. Rather, all events are simply modes of a single structure dynamically reconfiguring itself.
Despite this reality, quantum physics has, since its birth, artificially been placed in a mechanistic structure in which operators evolve wavefunctions (the state of any quantum system) in a linear way. This is a classical interpretation, however. The dynamics of the system (given by some quantum algebra) rather than the state should be regarded as more fundamental. Such an approach was championed by none other than one of the fathers of quantum field theory: Paul Dirac.
The key here to transitioning quantum mechanics and therefore all of physics into a process oriented structure is to remove the emergent wavefunctions (state vectors) and fields (such as spinor fields) from the quantum algebra so that only the process or motion of quantum systems remains. Thus, there are no particles or fields, simply motion. The fields and state vectors then are emergent from the dynamics.
Implications of Process Philosophy to Spacetime
Quantum algebras that create both matter and spacetime geometry at once may be the solution to the illusion of spacetime and quantum gravity. Problems like nonlocality, continuity, and independence of physical entities and properties all emerge from the process described by quantum algebras. In a sense, this is similar to the rule based spin-network approach of Penrose but rests of the idea of an algebra which naturally connects to geometry in the same way that high school algebra connects to Euclidean geometry.
While this approach to quantum gravity and ultimately solving the problem of where space and time come from is still in work, it offers a powerful alternative to theories in which space time is either fundamental or some underlying intrinsic and independent mechanism is fundamental. Rather all emerges as the result of process. It is the nature of that flux that determines what emerges.
Reference :- Monk, Nicholas AM. “Conceptions of space-time: Problems and possible solutions.” Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 28.1 (1997): 1–34.
Kaplunovsky, Vadim, and Marvin Weinstein. “Space-time: Arena or illusion?.” Physical Review D 31.8 (1985): 1879.
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