Should General Relativity Still Exist, Given the Rise of Quantum Theory?

On the 100th anniversary of Einstein's Theory of General Relativity, James Stuart-James asks whether it should still exist.

General relativity has grown into becoming the standardised formulation of gravitational theory since its inception 100 years ago by Albert Einstein. Nowadays, it finds itself unquestioned in its several applications in astronomy and physics due to having won progressive dominance over the course of its existence despite it  being fiercely contested when first published. I wish to invite you to examine this status and question whether such uncontested standing can truly be justified after all this time or whether more progressive theories should be given their time in the spotlight instead.

 
However, I should first offer some background information on the events that preceded General Relativity’s existence. Newtonian gravitational theory had been unsuccessful in monitoring various effects such as the re-fraction of light at the limb of the sun, the gravitational lensing of distant galaxies, what would come to be known as gravitational redshift and the radiation emitted by gravitationally accelerated bodies. Consequently, it was seen that Newtonian theory would not last and needed to inevitably be replaced by a more all-encompassing theory.

The Rise of General Relativity

Then in 1905 Einstein published ‘The Special Theory of Relativity’, which covered electromagnetism and the mechanics of inertial systems but it still seemed to be incapable of treating gravitation. With this background, General Relativity’s successes (since its publication in 1915) have given it a monopoly on all matters concerning gravitation. As a result, the act of questioning general relativity nears insanity, and those who raise doubts concerning it often reap indifference (if not scorn) from the intellectual community that would usually be reserved for heretics and cranks. Nevertheless, every theory, including General Relativity, should be open to critical analysis. Without further apology, I shall discuss some shortcomings or outright failures of the theory and from there suggest why its opposition to other theories should not discredit them on an inherent basis.

Criticisms

Equation for
Gravitational Redshift

The last major implication of General Relativity was the prediction of “black holes”. These are suggested by the Schwarzschild metric which has a singular surface known as the event horizon at a specified distance about a compact mass. Point singularities abound in physics, but a black hole is unique. This uniqueness should be an area of caution as we still (probably) lack knowledge on the majority of the universe. Furthermore, there is no method of observable identification relating to a black hole that doesn’t remain highly ambiguous. It cannot be discriminated from a possible “non-black hole” of equal mass and radius. One may therefore in my opinion be forgiven for developing a healthy scepticism in the confident identification of a multitude of these objects and may even take the stance that the implied existence of said black holes could be a possible failure of the theory.

Furthermore, it is stated that photons cannot escape from a black hole. As such I would like to postulate a scenario in which a photon is emitted radially within the black hole. What happens then? It cannot decelerate and reverse itself, as a mass particle would, so perhaps it may be ‘redshifted’ into extinction. However, surely this would oppose the equation for gravitational redshift? It seems to me this may be an interesting topic of debate to propose one day.

Furthermore, I wish to examine the models in which the theory was applied. Some of the earliest applications of general relativity were to models of the universe. Therefore, it is characteristic of all such models that they are finite in mass, volume and age. However, the British astrophysicist, Edward Arthur Milne, found a hole in such a model back in the thirties. He inferred from the conditions already stated that if one were to view the model correctly, one should also view the model universe must therefore have unique mass and velocity centroids, which are features that relativity was apparently intended to avoid as one of its purposes, thus suggesting that it may have failed in one of its primary aims in existence. 

Milne then followed this up by suggesting that expanding models necessitate that matter be created at the boundary during expansion and that oscillating models require the destruction of matter during the contracting phase. As a result, one could argue nowadays that these models lack cosmic background radiation, though this was not remarked upon at the time since the cosmic background radiation would not be discovered until several decades later.

Another criticism of these general relativistic models could be the very fact that they are ultimately hydrodynamic, meaning that they run along the assumption that the matter in the universe is spread continuously throughout existence. This may become an issue because the real existing universe is atomistic and granular as it consists of objects such as electrons, protons, molecules, planets, stars, galaxies and even clusters of galaxies. At its core, general relativity is a field theory and does not account for the granular nature of the cosmic background radiation’s appearance or the vast seemingly empty spaces between galaxies. 

However, the theory may also be denounced as being ambiguous. It relies on observation which is not inherently problematic as appeals upon observation should always be applied to a theory but the ambiguity comes in the sense of the subjective manner in which observers are to carry out this observation as the theory does not outright state whether its model universes are oscillating, static or forever expanding. Thus this decision is left to the observing parties rather than the theory itself.

Can General Relativity and Quantum Theory Work Together?

The title suggests that I do not intend to simply rant on about relativity, as that is not my aim here. Instead, I would now like to ponder whether it is justifiable that theories like Quantum Theory are often stripped back in order to substantiate relativity’s involvement.

Quantum Physics and General Relativity tend to function on differing scales. Quantum Theory, as a result, was completely unknown to science for so long because it normally becomes important only on the scales of atoms. There have been grandiose versions of this theory in the sense of Quantum Theory governing the density of a cat but at heart, that still tends to be a bit of a stretch to many as it currently only relates to said particles; therefore, to apply it to larger concepts can be seen as metaphysical or even fantastical to many.

General Relativity, on the other hand, is most often applied to strong gravitational fields. It suggests that concepts like time slow down when close to the surface of the Earth compared to far away; thus light bends itself around clusters of galaxies. These effects may sometimes even be ignored unless you're talking about the surfaces of neutron stars or similar objects; i.e. General Relativity usually functions on large(-ish) scales, such as stars all the way up to the entire universe.

To be fair, there are some aspects of space-time where General Relativity and Quantum Mechanics do share common interest. Black holes may be one of these aspects (for a while, at least) as they usually are both small and have extremely strong gravitational fields. In fact, the first attempts to successfully combine both gravitational and quantum effects occur on the edges of black holes due to the discovery of the now (largely) famous Hawking Radiation (I wonder who discovered it…), which will eventually (on a scale of several quadrillion years) cause even the biggest black holes to evaporate and supposedly lead to the heat death of the universe. When we discuss the outsides of black holes, we find that due to this radiation we have been able to attribute some understanding. However, as we move further in to the centres of black holes, we find that we have far less of an idea how physics really does function.

Singularities

When something ‘drops’ into the event horizon of a black hole, not only can it never escape, but it will be drawn inexorably inward. The result of this is that in a world where gravity is the most important force around (not the strongest), everything that enters a black hole will ultimately be confined to one literal point, the so-called "singularity." The instant of the Big Bang has the same sort of problem: incredibly high density and thus strong gravity confined to a very small space; due to it being in the first instant, this space is presumably infinitesimally small.

We never have and probably will never see a so-called "naked singularity" directly, which is unfortunate from the perspective of understanding them (though we can also say we are rather fortunate from the stance that we will not be ripped apart by the gravitational tidal forces). The illustrated result of General Relativity is that the cores of black holes have zero radius but Quantum Mechanics says something entirely different. In Quantum Mechanics, there is an ‘uncertainty principle’ which says that you cannot ever determine the exact position of anything. In practical situations this implies that even things that we call ‘particles’ cannot truly be arbitrarily small. Consequently, Quantum Mechanics dictates that no matter how hard you try, a mass as large as our sun cannot ever be confined to a region smaller than about 10^-73 m. This is indeed ridiculously tiny but it is still not zero.

If I found this to be the only manifested area of disagreement between Quantum Mechanics and Gravity, I could forgive you for being underwhelmed by the magnitude of the problem. However, the real conflicts between Quantum Mechanics and General Relativity are made manifest on scales that are far more important than a space of 10^-73m.

Personally, I do not believe we even need to think in terms of a black hole to see the conflict between Relativity and Quantum Theory. I invite you to consider the famous ‘double slit experiment’ (you knew this was coming the moment I mentioned Quantum Theory). This involves implementing a beam of particles (usually electrons due to their miniscule size) through a screen with two small slits cut out. Due to the previously stated uncertainty principle of Quantum Mechanics, there is no way to figure out which slit a particular electron travels through and as a result, the electron travels through both slits at once. This, according to many intellectuals, is rather absurd. That being said, in the context of gravity, it becomes even stranger. If the electron goes through one slit it presumably creates a very slightly different gravitational field than if it goes through the other. So how does it know which gravitational interference is made?

This becomes even stranger when you realize that, according to Wheeler's delayed choice experiment, it is possible to set up the experiment so that, after you have already run the experiment, you can then retroactively observe the system and force the electron to travel through one slit or another by observing it closely (though you cannot choose which). Surely, this is crazy. Putting it this way, the world of gravity is supposed to be entirely deterministic, but Quantum Mechanics is completely different in that sense, deterministic causality collapses among such unpredictability. (Personally, I find this to be very beautiful due to its later connections to string theory/ inter-dimensional theory and the results they bring but I am probably alone in that sense). 

As I was stating earlier, in electromagnetism and other quantum interactions, calculations become severely confusing at a very small scale known as the “Planck Length” (around 10^-35 m – much smaller than an atom). At this point, I feel obliged by long tradition to point out that we have no idea how physics is supposed to work on scales smaller than the Planck Length as continuous reality collapses. On those scales, Quantum Mechanics says that miniscule black holes can pop into and out of existence due to complete randomness, which suggests space-time itself destroys itself as a concept, if you observe it too closely.

We try to avoid these collisions of theories through a process known as "Renormalization" (thrown in as fan service for the experts - you are most welcome). Renormalization is essentially a fancy way of saying that we only do the calculation down to a certain scale and then stop. It abolishes the infinities in most theories, and allows us to carry on with our lives. Since most forces only involve taking differences between two energies, it doesn't really matter, if you add or subtract a constant to all of your numbers (even if the constant you are adding is infinity). The differences work out fine.

However, my point is that there are some who are not so happy about this limit that has been set upon Theoretical Physics. The great Richard Feynman once stated:

"The shell game that we play . . . is technically called “renormalisation”. But no matter how clever the word, it is still what I would call a dippy process! Having to resort to such hocus-pocus has prevented us from proving that the theory of quantum electrodynamics is mathematically self-consistent. It’s surprising that the theory still hasn’t been proved self-consistent one way or the other by now; I suspect that renormalisation is not mathematically legitimate.”

These objections aside, this worsens when we talk about gravity. Ultimately, gravity affects all particles (unlike electromagnetism despite it being much stronger as a force) and these infinite energies mean that we shall encounter different curvature. Renormalization (American, hence the ‘z’) doesn't even seem to be a real option for gravity after giving it some research. We cannot make the infinities go away.

So what can we actually know beyond these limits?

By now, we know that we don't have a theory of quantum gravity, but we have some idea of what a successful theory must be like, after giving it some thought. For instance, there obviously needs to be a graviton due to the presence of gravity and because gravity seems to be able to extend over all space, the graviton (like the photon) needs to be massless so it can handle the infinite range. Massive mediators (like the W and Z bosons) can only operate over a very short range.

But there is more to say about this theory (although it's a little more technical so, to be honest, my understanding begins to falter at this level). It seems there is a unique relationship between more classical theories i.e. relativity and quantum theories. For example, electromagnetism is generated by electric charges and currents. The sources are described mathematically by a vector, and it turns out that vectors produce spin of -1 mediator particles. It also turns out that mediators with odd spin produce forces in which particles tend to repel each other. And, indeed, two electrons will repel one another (fine, so far).

General relativity, on the other hand, is known as a "tensor theory" due to there being a variety of sources related to pressure, flow and density of an energy distribution. The quantum versions of tensor theories have a spin of -2 mediator particles. So, whatever else, the graviton will be at spin -2. And, you guessed it, even spin mediators attract like particles. So this should demonstrate that particles do indeed attract gravitationally!

So, we can now feel a sense of accomplishment in knowing a little something about what gravitons must be like. As for all of those infinities, I shall let far greater minds handle those postulations.

My point in writing what has become a rather lengthy piece by now is that both General Relativity and Quantum Theory have and can offer much to our process of understanding the universe/multiverse (Quantum Theory). However, I and others have taken umbrage at the domineering effects of General Relativity in the modern age and, as such, I hope I have been able to demonstrate, at least partly, why I do not agree with this renormalization process and would instead like to see both theories scrutinised on an equal playing field. If one is ultimately disproven as a result, that would be a shame - but at least we would be able to gain a more accurate understanding of the universe as a result.

Images of Quantum Theory’s multi-dimensional theory: