I have a question about interpreting (explaining, even) the general theory of relativity.
A common interpretation of GR, as I understand it, is to imagine two-dimensional space represented by flatlanders (ants) living on the surface of a trampoline (or stretched elastic sheet). The third ‘hyper-dimension’ from the point of view of the ants is time.
If a heavy object is placed in the middle of the trampoline, it distorts the surface in space-time, so that ‘straight lines’ of motion become geodesics, which are actually curved. A marble rolled across the trampoline curves around the object, because it’s following the shortest path in space-time. So far so good.
A reader here a while back (Why would spacetime curvature cause gravity?) posted the question: so why do two stationery objects move towards each other, and the answer was that in space-time, they are not stationery - they are moving through time. And it’s their space-time lines which still try to take the shortest/straightest route, as illustrated very nicely in a YouTube video linked in one of the answers.
Now I’m interested in getting back to a more intuitive understanding of why an attractive force seems to be exerted on the second object by the first, without getting tied up in the rather complex tensor representations of geodesics etc. At the same time, I want to know WHY a massive object distorts space-time.
Most texts take the curvature of space-time as an axiom (postulate), without pretending to offer any explanation. Note that (as I understand it) the heavy object on the trampoline is only intended to represent or visualise the curvature - there is no suggestion that it’s a simple matter of heavy objects ‘weighing down’ space time.
But I’m thinking, why not take the analogy literally, and follow through on this idea of weighing down?
In the analogy, it seems obvious that a heavy object distorts the surface downwards - it’s a result of the external, real gravity in the analogy (acting in a hyper dimension from the ants’ perspective). And the marble, of course, is simply rolling downhill.
Now as we know from Einstein’s principle of equivalence, gravity equals acceleration. The third dimension in ant-world is time - so, what if we suppose that time is accelerating and hence generating that hyperdimensional force?
For me, the surface of the trampoline is not simply a snapshot, or slice, of space-time, but far more significant - it is the present universe. (As an aside, because of its distortion, the relative ‘hight’ of points in space time (above ground level) varies. Furthermore different observers (ants on the trampoline) project different tangential planes from their standpoints. Do these two effects explain all the results of special relativity?)
Now assume that time moves inexorably forwards, and the surface of the trampoline is moving upwards, indeed accelerating. As we know, acceleration and force are the same thing: so the surface of the trampoline is pushing up against all objects in the universe.
Suppose also that all massive objects have a type of inertia which resists time - then the trampoline surface is retarded, or flexed backwards! That is what causes the distortion.
Now looking at a stationery marble sitting off to the side of the heavy object in the middle, it too is being pushed forwards (upwards) by time (the surface of the trampoline). Only the surface is now inclined - so there is a sideways component of the force, which pushes the marble towards the heavy object.
Simple, obvious, and indeed an inevitable consequence of the assumptions that a) time is accelerating forwards, and b) heavy objects have an inertia which resists the passage of time.
Is this idea complete nonsense, or is it a valid way of interpreting how space-time is bent (and how that generates the appearance of gravity)?
Is this how some physicists already interpret general relativity - am I wrong to suppose that the analogy is not usually intended to provide a reason for the curvature?
It’s really a question for someone very familiar with the mathematical underpinnings of GR - can the curvature of space-time be successfully modelled by an accelerating timeframe and massive objects having an inertia which resists it?