dougal wrote:It's this: Science has determined there are 4 fundamental forces in the Universe, one of which is Gravity. The other three forces are fairly well-understood and the bosons that carry them have been identified. But Einstein theorized that gravity is not really a force per se, but the apparent effect on the inertial properties of a mass that is travelling through a region of spacetime that has been "curved" by another mass.

Right?

That's correct. In Einstein's schema, gravity isn't actually a force, but a consequence of the geometry of spacetime.

So why are TOE guys trying to incorporate gravity into their theories in terms of being either a wave (gravity waves) or particle (the graviton)? Is this simply a contrivance made for mathematical purposes, for convenience and simplicity's sake? What I mean is, is the force of gravity expressed mathematically in terms of a particle (or wave) so that the issue can be approached mathematically within the context of both GR and QM, within which particles and wave behavior is already mathematically robust and well-understood?

Am I way off on this?

Well, we know we need a quantum theory of gravity for several reasons. The first is that we know that QM and GR are both incomplete. Neither tells the complete story but, more importantly, there are real situations in which they seem to contradict each other.

The first and most obvious scenario to deal with is a black hole. According to a purely relativistic treatment of black holes, any entity whose mass is contained entirely within its Schwarzschild radius will necessarily end in a singularity. Let's first deal with what a singularity actually is, from the perspective of physics, because we are working between two very distinct definitions here, and it is apposite to expose just what those definitions are:

The first definition of a singularity is a region of infinite density and infinite curvature. This is what we have as the classical picture of a black hole singularity (and indeed the big bang singularity). It is important to note that this type of singularity, i.e. a physical singularity, is far from having been established, and when we deal with the second definition of 'singularity' we will actually be a lot closer to understanding why this is.

The second definition of a singularity is an event at which our theories break, usually by yielding solutions that amount to nonsense. Infinities are generally taken to be a sign that there is something wrong with our theories, not because there is any barrier to an infinite actually existing, but just because we expect the universe to be quantifiable, and infinity is, by definition, something that cannot be quantified. This is the erroneous basis of arguments such as Kalamity Kraig's that something must halt the regress of causes, which he calls god. Of course, this is an error, because there is no barrier, physical or theoretical, to infinities actually existing in nature. Having said that, infinities are extremely unhelpful to theories, because they mean that the results of theories cannot be quantified, which means that our understanding is not progressed by them. For this reason, when we reach a singularity, or a solution of infinity, we usually take it to mean that we're on the wrong track.

More importantly, in this context, those infinities arise when we try to marry the equations of general relativity with those of quantum mechanics. Quantum theory renders outputs that are necessarily probabilistic in nature. Now, probabilities can only fall within a certain narrow range of values, namely 0 and 1. A probability of 0 means that something is impossible (although some caveats are appropriate here, because events with a 0 probability do occur), while a probability of 1 means that an event is inevitable. Most often, we see probabilities rendered as a fraction, a ratio or a percentage, but it must always fall between 0 and 1. Since we encounter solutions to the marriage of the equations of GR and QM that tell us that probabilities are infinite, we know the solutions are nonsense.

In the case of black hole singularities (and it is this second definition that is the reason that we call it a singularity, regardless of what the singularity actually comprises), General Relativity, from which the black hole singularity arises, tells us that the singularity should be a singularity under the first definition, which means that it is a quantum event with relativistic mass. Unfortunately, every attempt thus far presented to marry the equations of Quantum Mechanics and General Relativity yield solutions that equate to infinity, which we take to mean that our theories aren't working properly together. More importantly, the details of the physical singularity are such that QM tells us that the singularity is an asymptote, which means that it can be approached but never reached.

It's fairly certain that, in order to fit gravity into a quantum framework, it will have to be a dual theory (wave and particle)*, because that's what quantum theory deals with.

*Actually, this is a bit misleading. What QFT (quantum field theory) actually tells us is that neither particle nor wave are real, nor any combination thereof. Both particle and wave are simply the behaviours of fields that result from the way we interact with the field during observation. So, we interact with the field one way (watch the particle go through one slit in the double-slit experiment, for example) and we see particle. Interact with the field another way (don't watch it go through the slit) and we see wave. Neither are real, it's just a field.