Which is too bad since the math has been shown to be an accurate model for our solar system, better than what existed before.
Can you show me the evidence of this? I have seen no such theory.
just because he leveraged Riemann's equations to help him with his own, it doesn't necessarily mean that spacetime is curved or anything (even though he concluded it did), but instead it shows that Riemann's equations, which were developed for measuring distances in a manifold of any dimensions, works for spacetime
Enough with the really good responses. You're making me dig deep here. (Not really, its great!)
I agree that "Curvature" (and Riemann's extension of the concept) is purely a mathematical construct. It doesn't have any real physical meaning. We give meaning to these concepts through the filter of how we define what it means to be physical (to have a "physical distance" or a "movement in time"). Our ideas of physicality may be deeply flawed.
Einstein's GR equation says that the mathematical construct of curvature (and measurements of distance in the 4 dimensional spacetime) IS energy density distribution. They are the same thing. But its really only saying that changes in energy density distribution, between two measurement points, which is something we can measure, can change 3 velocity measurements and time measurements (another thing we can measure) based on your observer point. It also says the 4 velocity (and 4 momentum) measurements will always be the same for all observers.
The point is, you can think of a deformation (and its resulting curvature) of spacetime as an energy density distribution (like a gradient), or a change in the mathematical construct of curvature, and you will arrive at the same answer either way.
The idea of a 4 vector gives meaning to spacetime as a physical entity. But our measurements do coincide with the physical meaning we give (arbitrarily) to curvature, and thus the problem is, this confirmation bias reinforces our marriage to the physical concept overlays we attribute to it.
To effectively divorce these concepts we would have to be motivated to do so (which many are), but we would also have to come up with completely new ideas of what it means to be "real".
All measurements in physics, or any other physical science are ultimately measurements of two things; spatial and temporal distance. When you measure temperature, or power output, or any other measurement, when you break it down to brass tacks, you are really measuring a movement through space and time. That is why the physical universe as we have defined it (and the concept of curvature that we overlay on it) are so powerful. Those concepts help us measure everything that isn't spiritual or psychological (if those two concepts even have different meanings).
Until we can find another thought paradigm than physical reality as having "distance" in time and space, we are ultimately also married to curvature of space and time, because it works out so well in measurement. Even if we use the other side of the equation (energy density distribution), ignoring the curvature part (which allows us to accurately measure distances in space and time) is disingenuous without that paradigm shift in our concept of reality.
Can you show me the evidence of this? I have seen no such theory.
The best evidence is the application of the GR field equations to predict the orbit of the planet Mercury, which before GR had an unexplained anomaly with it's perihelion precession. Any good book on GR will walk you through it. It's probably the strongest test of GR and considered a hallmark proof that the equations do accurately predict planetary orbits around our Sun.
My understanding is that Tesla didn't refute Einstein because his theory didn't marry E&M with gravity, but because he couldn't comprehend the math behind it. Which is too bad since the math has been shown to be an accurate model for our solar system, better than what existed before.
I think we might have gotten signals crossed here. I thought you meant Tesla had a theory of E&M gravity that gave a better prediction of planetary motion than GR. That was what I was asking evidence for. I am aware of the predictions and measurements that asserted GR.
Can you show me the evidence of this? I have seen no such theory.
Enough with the really good responses. You're making me dig deep here. (Not really, its great!)
I agree that "Curvature" (and Riemann's extension of the concept) is purely a mathematical construct. It doesn't have any real physical meaning. We give meaning to these concepts through the filter of how we define what it means to be physical (to have a "physical distance" or a "movement in time"). Our ideas of physicality may be deeply flawed.
Einstein's GR equation says that the mathematical construct of curvature (and measurements of distance in the 4 dimensional spacetime) IS energy density distribution. They are the same thing. But its really only saying that changes in energy density distribution, between two measurement points, which is something we can measure, can change 3 velocity measurements and time measurements (another thing we can measure) based on your observer point. It also says the 4 velocity (and 4 momentum) measurements will always be the same for all observers.
The point is, you can think of a deformation (and its resulting curvature) of spacetime as an energy density distribution (like a gradient), or a change in the mathematical construct of curvature, and you will arrive at the same answer either way.
The idea of a 4 vector gives meaning to spacetime as a physical entity. But our measurements do coincide with the physical meaning we give (arbitrarily) to curvature, and thus the problem is, this confirmation bias reinforces our marriage to the physical concept overlays we attribute to it.
To effectively divorce these concepts we would have to be motivated to do so (which many are), but we would also have to come up with completely new ideas of what it means to be "real".
All measurements in physics, or any other physical science are ultimately measurements of two things; spatial and temporal distance. When you measure temperature, or power output, or any other measurement, when you break it down to brass tacks, you are really measuring a movement through space and time. That is why the physical universe as we have defined it (and the concept of curvature that we overlay on it) are so powerful. Those concepts help us measure everything that isn't spiritual or psychological (if those two concepts even have different meanings).
Until we can find another thought paradigm than physical reality as having "distance" in time and space, we are ultimately also married to curvature of space and time, because it works out so well in measurement. Even if we use the other side of the equation (energy density distribution), ignoring the curvature part (which allows us to accurately measure distances in space and time) is disingenuous without that paradigm shift in our concept of reality.
The best evidence is the application of the GR field equations to predict the orbit of the planet Mercury, which before GR had an unexplained anomaly with it's perihelion precession. Any good book on GR will walk you through it. It's probably the strongest test of GR and considered a hallmark proof that the equations do accurately predict planetary orbits around our Sun.
I think we might have gotten signals crossed here. I thought you meant Tesla had a theory of E&M gravity that gave a better prediction of planetary motion than GR. That was what I was asking evidence for. I am aware of the predictions and measurements that asserted GR.
It would seem so.
Great exchange though, thank you.