Resists spacetime when it is curved

Does the acceleration of time explain gravity (and not the other way around)? [closed]

John Duffield

Does the acceleration of time explain gravity (and not the other way around)?

Note, however, that gravity does not slow optical clocks when they are lower. Gravity is there because optical clocks run slower when they are lower. Since a concentration of energy in the form of a massive star "conditions" the surrounding space and changes its metric properties, this effect decreases with distance. Further information can be found in the Einstein Digital Papers.

If a heavy object is in the middle of the trampoline, it distorts the surface in space-time, so that "straight lines of motion" become geodesics that are actually curved. A marble that has rolled over the trampoline curves around the object because it follows the shortest path in space-time. So far, so good.

The rubber sheet analogy can be misleading, but it is not entirely wrong. It shows a curved spacetime, or "curved metric," and a metric has to do with measurement. For example, suppose you place optical clocks in an equatorial section through the earth and surrounding space, and then record the clock rates. They show lower slower clock rates than lower at the bottom in a 3D image and higher faster clock rates higher at the top. So your plot looks like this:

CCASA image of Johnstone, see Wikipedia

This is a picture from the Wikipedia Riemann curvature tensor page. It is the rubber sheet of curved spacetime. And because it's derived from optical clock rates, it's a graph of the "coordinated" speed of light. It could also be said that it is a representation of the time rates, but note that there is no actual time ticking through an optical clock. A clock is not a type of gas meter. It doesn't literally measure "the flow of time", that's just a phrase. Note that the curvature you can see on your graph affects the tidal force during the Tilt relatesrefers to gravity. But also note that you need this curvature to take the plot off the plane and make it flat in the middle. So if you don't have it, you don't have a gravitational field. For this reason the space-time curvature is called the "determining feature" of a gravitational field.

A reader here a while ago (Why should the curvature of spacetime cause gravity?) Asked the question, why are two stationery objects moving towards each other and the answer was that in spacetime they are not stationery - they move through time .

That's wrong, I'm afraid. There is no actual "movement through time". There is also no movement through space-time, see Ben Crowell's answer here. And the curvature of spacetime doesn't actually cause gravity. Your optical clock won't slow down when it's lower because your chart of clock rates is curved. It goes slower because a concentration of energy in the form of a massive star "conditions" the surrounding space and changes its metric properties, this effect decreasing with distance.

And it is their space-time lines that are still trying to take the shortest / straightest path, as shown very well in a YouTube video linked in one of the answers.

Light doesn't bend because it tries to take the shortest path through spacetime. You won't find Einstein saying that. You can find what he said in the digital Einstein papers.

Now I am interested in returning to a more intuitive understanding of why an attractive force appears to be exerted on the second object

IMHO it's easier than you think. Think of pair production and electron diffraction, and think of the wave nature of matter. Think of matter as light rotating over and over, and then simplify it into a square path. What happens to the horizontals? You bend down a little. Draw it.

I want to know WHY a massive object distorts space-time.

The clue lies in the stress-energy-momentum tensor, the Describes "the density and flow of energy and momentum in space-time" . Note the energy pressure diagonal and the shear stress and google about elastic spacetime. As you add energy, you add more space at this point so that you create a similar "pressure gradient" in the surrounding space. Like this picture, but push out instead of pulling in. Note that a massless photon creates gravity. A Energy concentration causes gravity, not mass itself.

Most texts take the curvature of space as an axiom

Take note of this article from Baez which states: "Similarly, relativity in general is not really a 'force', just a manifestation of the curvature of space-time. Note: Not the curvature of space, but space-time. The distinction is crucial." . One can say that a gravitational field is curved spacetime, but not curved space.

But I guess why not take the analogy literally?

Because that's not how gravity works.

What if we assume that time is accelerating and thus creating this hyperdimensional force?

Then you leave Einstein and general relativity for no good reason. I urge you to read the Einstein digital papers instead of being "my theory".

Is this idea utter nonsense?

Sorry i'm afraid it is. But it is good that you think for yourself.