Re: [math-fun] Stupid GR question
Henry Baker <hbaker1@pipeline.com> wrote:
Physicists talk about the expansion of the universe.
Wouldn't it be equivalent to talk about the compression of time?
No. Distances in space are increasing, but the sizes of objects are not. The original definition of the meter was pegged to the size of the Earth. Later it was defined as the length of a specific metal ruler. Still later, in terms of a wavelength. And today, in terms of the speed of light. Under all those definitions, the size of the Earth and of the things on it are not changing. Similarly with other planets and other solid objects in space. It's possible that the expansion exerts a force on solid objects to make them get larger. But if so, their internal cohesion easily resists this force. (Any such force is much too weak to directly detect or rule out with today's technology.) You could devise a system of measurement such that the size of the universe is constant, but the speed of light is slowing down and the sizes of atoms are shrinking. But most people would find that less intuitive and less useful. Anyhow, to make it work I think you'd also have to have some or all of the charge of the electron, the permittivity of space, Planck's constant, and the gravitational constant changing in sync, but I haven't worked out the details. If you're willing to have the sizes of atoms and the speed of light vary, not with time, but with location, you can devise a system in which the Earth is inside out. In that system, most of empty space seems distant only because as objects get closer to the center they shrink and slow down, Earth's surface seems to curve the "wrong" way only because light curves due to its varying speed with altitude, the cosmological horizon is located at the center and is smaller than an Earth-surface-atom, and the infinite volume of rock that fills almost all of space has a finite mass because it gets less dense as it gets more distant.
Hmmm... The fundamental data that tell us about the expansion of the universe is the "red shift" of atomic spectral lines. These spectral lines are a *quantum* effect, and so we have an interaction of "GR time" with "quantum time". So we have arbitrarily decided that quantum time is constant and the speed of light is constant -- both by axiom. Yes, quantum times are slowed down by GR -- e.g., the decay rate of unstable particles -- but from a "constant" base. Everything else seems to fall out from these 2 axioms. About the only "pure" apple-to-apples effect would be the comparison of gravitational orbit velocities in the vicinity of large red shifts with orbit velocities close by. We're not having a great deal of success with that comparison just now -- see the evidence for "dark matter". At 03:27 PM 5/22/2016, Keith F. Lynch wrote:
Henry Baker <hbaker1@pipeline.com> wrote:
Physicists talk about the expansion of the universe.
Wouldn't it be equivalent to talk about the compression of time?
No. Distances in space are increasing, but the sizes of objects are not. The original definition of the meter was pegged to the size of the Earth. Later it was defined as the length of a specific metal ruler. Still later, in terms of a wavelength. And today, in terms of the speed of light. Under all those definitions, the size of the Earth and of the things on it are not changing. Similarly with other planets and other solid objects in space.
It's possible that the expansion exerts a force on solid objects to make them get larger. But if so, their internal cohesion easily resists this force. (Any such force is much too weak to directly detect or rule out with today's technology.)
You could devise a system of measurement such that the size of the universe is constant, but the speed of light is slowing down and the sizes of atoms are shrinking. But most people would find that less intuitive and less useful. Anyhow, to make it work I think you'd also have to have some or all of the charge of the electron, the permittivity of space, Planck's constant, and the gravitational constant changing in sync, but I haven't worked out the details.
If you're willing to have the sizes of atoms and the speed of light vary, not with time, but with location, you can devise a system in which the Earth is inside out. In that system, most of empty space seems distant only because as objects get closer to the center they shrink and slow down, Earth's surface seems to curve the "wrong" way only because light curves due to its varying speed with altitude, the cosmological horizon is located at the center and is smaller than an Earth-surface-atom, and the infinite volume of rock that fills almost all of space has a finite mass because it gets less dense as it gets more distant.
On 5/23/2016 8:35 AM, Henry Baker wrote:
Yes, quantum times are slowed down by GR -- e.g., the decay rate of unstable particles -- but from a "constant" base.
"Quantum times" are just proper time measured along world lines. GR allows that the spacetime is curved so locally parallel world lines don't remain parallel, but there is no other effect on the rate of atomic phenomena. Along it's own world line every cesium atom keeps the same time (i.e. is an ideal clock). Brent
Yes, but there's still an assumption that 'quantum time', as measured by your cesium atoms -- when moving along world lines -- remains constant. I.e., axiom: world-line time = quantum time. What if this weren't so ? What if the time measured by gravitational orbits *didn't match* quantum time -- i.e., it changed ever so slightly over billions of years ? Could such a difference look like "expansion" ? At 11:27 AM 5/23/2016, Brent Meeker wrote:
"Quantum times" are just proper time measured along world lines. GR allows that the spacetime is curved so locally parallel world lines don't remain parallel, but there is no other effect on the rate of atomic phenomena. Along it's own world line every cesium atom keeps the same time (i.e. is an ideal clock).
participants (3)
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Brent Meeker -
Henry Baker -
Keith F. Lynch