3

I've just watched Sabine Hossenfelder's Gravity video on YouTube.

A couple of things in this have got my head spinning, but I think they basically come down to the definition of "accelerating". SH points out that an accelerometer placed on the earth's surface shows +1G, so it must be accelerating upwards, supporting the Einsteinian rather than Newtonian view of gravity. There's also a sequence where an astronaut jumps off a tower, and she points out that the astronaut doesn't accelerate. This isn't explained, but is presumably deduced from the fact that an accelerometer placed on the astronaut would read zero.

Ok, here's my problem. There's no magic in an accelerometer. It doesn't measure 'acceleration', whatever that is. It's (presumably) a piezoelectric device that produces a measurable charge depending on the dimensions of the crystal lattice. When it's at rest in the lab, the electronics for the vertical axis are set to show '+1G', because we all 'know' that there's +1G at the Earth's surface. When it's in free fall, the electronics are set to show 0G. Or maybe some measurements are taken in the horizontal plane and are used to offset 'at rest' vertically, but all we actually know for sure is that there's some minor compression in the vertical axis.

Question: given this, how can an accelerometer be at all relevant in any discussion of whether or not gravity is actually a force? Surely it would show exactly the same thing in:

  • Case (a), where gravity is a real force, pulling down the atoms in the crystal lattice, which are supported/pushed up by the EM force of the atoms on the surface of the lab bench, and
  • Case (b), where gravity is a geodesic pseudo-force, and the atoms on the bench surface are pushing away the crystal lattice (I'm a bit hazy here on what produces the lattice compression)?

My other question was how an astronaut falling into a black hole could feel nothing, rather than some pain while being shredded, but I guess that can wait.

Qmechanic
  • 220,844
EML
  • 161

1 Answers1

16

There's no magic in an accelerometer. It doesn't measure 'acceleration', whatever that is.

In physics there are two distinct concepts of acceleration.

Proper acceleration is what is measured by an accelerometer. It is the physical acceleration that can be felt and produces physical effects.

Coordinate acceleration is the second time derivative of the position in some coordinate system. It is mathematical and produces no physical effects. It can only be inferred from motion.

all we actually know for sure is that there's some minor compression in the vertical axis

Sure. One common type of accelerometer works in that fashion. There are also devices that use compression to measure weight or mass. The fact that a measurement device uses piezoelectrics or electronics hardly disqualifies the resulting measurement.

how can an accelerometer be at all relevant in any discussion of whether or not gravity is actually a force?

Indeed, as you mention the case A and case B are not physically different. It is entirely a semantic or philosophical choice.

If you choose to define gravity as a real force then proper acceleration is proportional to the sum of the non-gravitational real forces. If you choose not to define gravity as a real force then proper acceleration is proportional to the sum of real forces. In either case neither inertial forces nor gravitational forces contribute to proper acceleration.

So the question is just a matter of preference and definition. Many scientists prefer to consider gravity to be an inertial force because of the similarities and the resulting mathematical simplicity. Like inertial forces gravity is proportional to mass, cannot be detected by an accelerometer, and can be made to vanish by choosing appropriate coordinates. So many feel that is a better definition.

So an accelerometer is relevant in a discussion of whether or not gravity is a force because it motivates the choice. Physics is an experimental science and so many physicists like definitions that are closely tied to experimental measurements

Dale
  • 117,350