Einstein, Symmetry and the Future of Physics
quantamagazine.org
quantamagazine.org
This isn't quite right. Energy isn't conserved in General Relativity. There is a conservation law involving the stress-energy tensor, but as the name implies, it's not energy alone that's being conserved.
But more generally, Noether's theorem, which leads to this conservation law, is probably the most beautiful theorem in physics: https://en.wikipedia.org/wiki/Noether%27s_theorem. Given that, what's amazing is that Emmy Noether only worked on physics for a relatively short time. She was asked by David Hilbert to work on the problem of invariants in General Relativity, came up with one of the most important theorems in physics, and then moved on to other (extremely important) mathematical work.
Correct, and the reason is that in GR there is (in general) no time translation invariance. The associated conserved quantity to time translation invariance is precisely what we call "energy". In our universe this manifests as the expansion of spacetime.
More on this: https://www.preposterousuniverse.com/blog/2010/02/22/energy-...
Interestingly I just read about this in a Lawrence M. Krauss book [0] where it was described that David Hilbert insisted on hiring Noether by the university but was overruled by the male majority that didn't like the idea that a female would teach male students. Hilbert commented that "this is university, not a bath-house!" [1].
[0]: I think it was "The Greatest Story Ever Told—So Far"
[1]: I'm writing that from memory so excuse some inaccuracies.
Is this right? I haven't studied physics formally since I was 16, but I thought that the extra gravitational force due to greater mass was effectively cancelled out by the extra inertia also due to the same greater mass: i.e., more massive bodies are indeed more strongly attracted by the Earth, but because they are more massive they are also harder to accelerate to the same degree, with the result that everything falls at the same rate, regardless of mass. And I also thought this was known long before Einstein: if I had to guess, I'd credit Newton.
Or am I fundamentally misunderstanding something?
In the paragraph after your quote is another point the author almost certainly gets wrong:
>When Einstein realized that a person falling freely would feel weightless, he described the discovery as the happiest thought of his life.
I have read elsewhere that this "happiest thought" was that there is no experiment that someone falling freely could do that would reliably distinguish between being stationary and falling freely, with an emphasis on measurements of the speed of light. I am pretty sure that it was common knowledge among physics PhDs back then that people falling freely feel weightless. It is not like physics PhD are incapable of jumping while noticing the sensations in their bodies when the sensations are a straightforward consequence of Newtonian mechanics.
Don't be so quick to make such judgments:
There is ample scientific interest in the differences between inertial and gravitational mass [1]. That they seem the same is a profound question known to Einstein. He explicitly assumed they were the same in his equivalence principle [2].
So their equivalence is a postulate, not derived from deeper theories. But one day we may find it is not consistent over time. It most certainly is a deep question in physics.
There are other theories of gravity, taken seriously, as possible future modifications to relativity, such as Brans-Dicke theory [3], that remove this equivalence principle, yet still agree with all observational evidence to date.
Current experimental evidence puts them equivalent to under 1 part in 10^-15 [2], with more experiments still being done.
[1] https://en.wikipedia.org/wiki/Mass#Inertial_vs._gravitationa...
[2] https://en.wikipedia.org/wiki/Equivalence_principle
[3] https://en.wikipedia.org/wiki/Brans%E2%80%93Dicke_theory
In Newtonian mechanics, there is no reason for m_i to equal m_g. It is simply a coincidence. If they were not always equal, then some objects would fall faster than others in a vacuum.
The interesting thing is that there exists a class of forces which are proportional to mass - so-called "fictitious forces." These are forces like centrifugal force, which only appear to exist if you are in an accelerating frame of reference. You only feel centrifugal forces if you're spinning, for example, and the "force" you feel is just your body trying to keep on going in a straight line. Fictitious forces always act on an object with a force proportional to its inertial mass.
Einstein's insight was essentially to view gravity as a fictitious force. The hint is that m_g = m_i. In General Relativity, gravity is not a "real" force. The effects of gravity are caused by geometry being non-Euclidean.
If you want to understand this better, you can start by reading about the "Equivalence Principle": https://en.wikipedia.org/wiki/Equivalence_principle
You won't if you keep reading them.