Gravity Is Not Weak

The dinosaurs didn't worry about extrasolar impacts because gravity is weak and wasn't worth worrying about.

Einstein’s theory of general relativity still stands apart from the other known forces by its refusal to be quantized. Progress in finding a theory of quantum gravity has stalled because of the complete lack of data – a challenging situation that physicists have never encountered before.

The main problem in measuring quantum gravitational effects is the weakness of gravity. Estimates show that testing its quantum effects would require detectors the size of planet Jupiter or particle accelerators the size of the Milky-way. Thus, experiments to guide theory development are unfeasible. Or so we’ve been told.

But gravity is not a weak force – its strength depends on the masses between which it acts. (Indeed, that is the very reason gravity is so difficult to quantize.) Saying that gravity is weak makes sense only when referring to a specific mass, like that of the proton for example. We can then compare the strength of gravity to the strength of the other interactions, demonstrating its relative weakness – a puzzling fact known as the “strong hierarchy problem.” But that the strength of gravity depends on the particles’ masses also means that quantum gravitational effects are not generally weak: their magnitude too depends on the gravitating masses.

To be more precise one should thus say that quantum gravity is hard to detect because if an object is massive enough to have large gravitational effects then its quantum properties are negligible and don’t cause quantum behavior of space-time. General relativity however acts in two ways: Matter affects space-time and space-time affects matter. And so the reverse is also true: If the dynamical background of general relativity for some reason has an intrinsic quantum uncertainty, then this will affect the matter moving in this space-time – in a potentially observable way.

- Sabine Hossenfelder at Backreaction (emphasis added).

The unqualified statement that "gravity is weak" has been a pet peeve of mine since I first heard it, probably sometime around the time that I was in middle school.

This makes an assumption that the only relevant comparison is of the action of the fundamental forces of the Standard Model and gravity on fundamental particles or simple composite particles of the Standard Model at atomic distances, where it is true that gravity is weaker than the other forces.

Indeed, even in the limit as distance goes to zero, the electromagnetic force, weak force and gravity all get stronger, so at very short distances in gravity remains weak compared to the electroweak force.

But, the strong force, once it crosses the distance at which it peaks, actually gets weaker.  An important unsolved question in physics is whether the strong force is zero in the limit of zero distance (i.e. is trivial), or is non-zero.  If the strong force is trivial in the limit of zero distance (probably the more likely possibility), then, for example, there is both a long distance regime and a short distance regime in which gravity is stronger than the strong force between two quarks.

The weak force has a limited range because its massive carrier boson has a short mean lifetime which means that even if that carrier boson is traveling at speeds approaching the speed of light that it will almost always decay before traveling for more than an atomic scale distance.  Thus, is rapidly starts to approach zero at even microscopic distances, while gravity and the electromagnetic forces do not decay nearly so rapidly.

(And, in modified gravity theories, such as MOND and its more sophisticated and relativistic cousins, many of which assume that gravity has an additional Yukawa potential term, the electromagnetic falls off with distance squared, while gravity does not abate quite so quickly, making gravity grow stronger relative to an equivalent electromagnetic force at a given distance at much greater distances in the gravitational weak field.)

In sum, the standard assumptions are very context specific without appropriate justification.  When substantial masses are involved and macroscopic distances are involved, gravity is frequently dominant, while the other forces are frequently negligible.  The assumption that gravity is weak, for example, is often unwarranted in the context of astronomy, which is an equally valid frame of reference.

The Rainbow gravity theory discussed in the same post is not ready for prime time and doesn't warrant a discussion here, but the distinction that Hossenfelder makes in her post does merit repeating, because the echo chamber has propounded an inaccurate statement one time too many and deserves some counterpoint.