Most will know the "Space-time tells matter how to move; matter tells space-time how to curve" So I was wondering, did anyone ever figure out which (if any) goes first?
Does matter first curve space-time and then space-time tells it how to move or is it the other way around?
Just curious if it was ever scientifically tested.
Posted Sep 8, 2021, 5:49 AM UTC
Neither “goes first”. They are tied together by an equals sign in Einstein’s equations, which relate spacetime curvature and the stress energy tensor. They are always in this relation, at every moment and position.
Is there any info on how this works?
I find it very odd that there is a loop, my movement effects the curvature and the curvature effects my movement. How can this relation exist if one is dependant on the other?
Lot's of phenomena work this way in physics. The wave equation for instance is a 2nd order partial differential equation in which the curvature in space depends on the curvature in time and is ubiquitous in pretty much all of physics (note, I'm using "curvature" here to refer to the 2nd derivative of a function). This is why things oscillate. In fact, any physics equation which involves derivatives is going to simultaneously depend on the instantaneous rate of change of another variable. In electromagnetics, the changing E field creates a B field, and the changing B field creates the E field (but this is just another example of the wave equation).
Theres a couple of things going on here with your intuition I think. But this situation is hardly unusual. Imagine a cold table with a heat source we apply to the center. At any given moment and location, the rate of heatflow depends on the temperature gradient, but the temperature depends on the amount of heat which has flowed in and out of that location. Does that seem weird to you?
The second thing going on is that GR is frankly a little weird... Mass determines the stress energy tensor, which determines the curvature of spaceTIME. Much of our intuition is built upon situations where time is independent. The idea that it too is subject to curvature is a bit hard to fully fathom. In fact, in extreme situations, the geometry admits Closed Time-like Curves (CTC's) for which problems with causality can exist. (Mostly these are considered unphysical situations, but there's some debate about that.)
Yeah it's the same thing, I get it but it just feels off.
I don't know what to make of it yet as all the answers are quite hard to understand. But I appreciate the effort and will try dig in a bit more to see if I can nudge my intuition the right way ;)
Neither affects the other at the moment, they affect the rate of change of the other. So basically they tell the other how to well act in next instant.
There's no "loop" the causality is just going in both directions of the equals sign. For analogy consider something much more mundane: when two billiard balls hit each other, which one changes its motion first?
The answer to which came "first" is relative. I know, I know, but I'm just typing what you all were thinking.
Other commenters answers are correct.
😂
Other commenters have provided great answers! I wanted to comment on the semantics of the question. “First” implies some kind of variable (usually time) that we can order events with respect to. Since the Einstein equations are generally covariant (true regardless of coordinate choice), the concept of first is only sensible once you’ve chosen a “direction” (vector field) on space time. As other commenters note, equality is reflexive so both “sides” of the Einstein equation happen together. When you pick a direction on space time you’ll see that the components of both the curvature and energy tensors evolve together (simultaneously)
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Just my counter question in a similar style.
Which comes first, the force or the acceleration?
We know they are explicitly linked in newtonian physics by F = ma
There is no preference to an order of this. If you have a (resultant) force you will have an acceleration and the exact same instant and vice versa
They happen concurrently and simultaneously, there is no “first”.