The Role of Gravity among the Fundamental Forces of Nature

Question

If we look at the standard model, we have 4 fundamental forces which include

1. Gravity,

2. Electromagnetism,

3. Nuclear weak force,

4. Nuclear strong force.

I would like to look at Gravity for a minute. Scientists are still searching for what causes gravity. But is it possible that gravity is only a property of the space-time fabric?

For example take a blanket that is stretched tight and put different weight balls on the blanket. As one would see, the balls sink into the blanket differently. If you look at the space-time fabric as the blanket and the different balls as objects in the space-time fabric when it comes to planets and more on the macro scale, thinking gravity as a property of space-time fabric seems to work.

Since the standard model deals more at the quantum level though and we are looking at it here on earth where gravity is $9.8\,m/s^2$, it seems to me that the standard model would also need to stand up to say if we had gravity that was $11.4\, m/s^2$ or something more absurd like $20.6\,m/s^2$ . Also could we not say that gravity is really just a property of space-time fabric?

Answer 1

This is the grand story of physics since the time of Maxwell up to today. Maxwell found ways to think of electric fields and magnetic fields as being aspects of one thing - the electromagnetic field. He had it easy because the characteristic energy relevant to unifying these is zero - the mass of the photon.

When physicists found that neutrons could change into protons, and protons into neutrons, measurements of energies and momenta of the particles involved indicated a characteristic mass of somewhere around 100GeV. The early theories using a "Fermi constant" fell apart, but Weingberg, Glashow and Salam, using an idea from Peter Higgs, came up with a good theory having W and Z bosons. These and the photon are aspect of one multidimensional field. EM + weak were then unified - after sufficient experimental verification, of course.

The strong force came to be seen as a matter of gluons. No one has yet unified the strong force with the electroweak. The energy range involved in this unification many times higher. Despite much research effort since the 1970s, and quarks and gluons commonly accepted as real, there's too little we know about how these unify with the leptons and electroweak interactions.

The key idea is that when something sufficiently complex vibrates, classical or quantum, the different modes of vibrations might start off seeming all the same, but they usually pair up or combine in ways leading to qualitatively different phenomena. Those are vague, mushy words. An example to illustrate: imagine two identical pendulums side by side, with a wimpy rubber band or spring connecting them. The pendulums could start off swinging with any different amplitudes or any relative phase, but wimpy spring will cause them to eventually swing together with identical amplitudes. This is the lowest energy state. Another state is for them to swing exactly opposite, same amplitudes. This state oscillates faster, and is easily perturbed into its lowest energy state + waste heat, sound, photons or however the system gets rid of excess energy.

With photons, W and Z - what is it that's doing the waving? No one knows. At some fundamental level, something in the "fabric" of spacetime is shaking about. In some way it has a zero-mass mode where it all swings together, with frequency time wavelength equal to the fundamental speed constant c. It has also higher energy modes where this is not so, but instead with waves characterized by masses of about 80 or 90 GeV. Something about these vibrations involves opposite motion, analogous to the pendulums swinging oppositely.

The old rubber sheet illustration of gravity is bogus. Spacetime does not have longitudinal vibrations (movement along the surface) at least it doesn't match up well with any theory. Vibrations and bending perpendicular to the surface (meaning along 4th or more dimensions outside our 3D) correspond to gravitational waves and gravitational fields, although missed the point. Gravity, outside of crazy places like black holes, is mostly a matter of rate-of-time. This is a hard concept to explain without getting into General Relativity and differential geometry. If someone has a stopwatch they'll find it takes one minute for a minute to pass by, no matter where they are. It's all about comparing nearby points of space - things seem to happen a bit faster for you as seen by me. Read about "gravitational redshift".

To write $\psi=A sin(2\pi f t)$ is to describe an oscillation. This tells us frequency and amplitude, but does not tell us if it's a steel bolt hanging on a string, a buoy floating in the see, or an avionics control system that's gone unstable.

To try to understand what it is that's doing the vibrating, you might as well pick up a book on new-age metaphysics. Even charge, plain old + and - of electrons and quarks, is a mystery what it really is. Some kind of pucker or topological twist of the fundamental substance? Electromagnetic fields are some kind of strain in that stuff? We can only write the equations describing overall behavior as waves.

Whatever space-time-energy-matter is made of fundamentally, little overlapping patches of space-thought-goop, quivering liquidy 3D membranes in higher dimensional space, strings or M-branes, who knows, all that physicists can do (for now) is mathematically describe the symmetries and energies and coupling constants of the vibrations.

Answer 2

On a large (i.e. non-quantum) scale describing gravity as a property of spacetime works well, and in fact it's exactly what General Relativity does. The problem is that the equation that describes the curvature of space-time is:

$$ G_{ab} = 8\pi T_{ab} $$

where the quantity on the left, $G_{ab}$, describes the curvature and the quantity on the right, $T_{ab}$, describes the matter that is present.

The problem is that the matter, i.e. $T_{ab}$, is described by the Standard Model and we know it is quantised. So the equation has a non-quantised $G_{ab}$ on the left and a quantised $T_{ab}$ on the right, and equating a non-quantised to a quantised quantity doesn't make mathematical sense.

So while the GR description of gravity works well at large scales it must break down at scales where quantum effects become important. At these scales gravity has to be quantised and described by some theory that includes the Standard Model and General Relativity as low energy approximations.

Answer 3

First the standard model does not include gravity, but only the other interactions. Precisely the search of a unified theory of interactions is the search of a theory that joins the standard model with gravitation.

The cause of gravity is the stress-energy-momentum $\Theta_{ab}$. Anything with stress-energy-momentum generates gravity and feels gravity.

General relativity, which is a metric theory, describes gravitation as spacetime curvature via the Hilbert Einstein equations $G_{ab} = 8 \pi G T_{ab}$, where $T_{ab}$ is the stress-energy-momentum for matter and radiation alone. Gravitation can be described in alternative non-geometrical forms. In the field approach to gravitation (pioneered by Feynman and Weinberg among others), gravitation is related to a gravitational field associated to quanta of gravity that we call gravitons.

At the macroscopic level and for the usual applications both approaches, the geometrical and the non-geometrical, give the same answers and can be somewhat considered equivalent. The differences appear at the quantum level where general relativity breaks down.

I would finally add that although gravitation is widely considered a fundamental interaction, some authors speculate that it is not fundamental but derived from the other interactions. Such approaches to gravity are usually named "emergent gravity" approaches, and are under active research today.