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> The space metric fits very neatly into the Einstein field equations, and the expanding universe pops out of that directly. Is there a simple way to understan

by uh_uh 5y ago

> The space metric fits very neatly into the Einstein field equations, and the expanding universe pops out of that directly. Is there a simple way to understand why? I don't have an understanding of the relevant math. It's a bit hard for me to imagine how we get from the axiom of "speed of light is constant in every reference frame" to an expanding universe. Unless there are other axioms used for this.

adgjlsfhk1 5y ago
the other axiom you need is that gravity and acceleration are the same. the speed of light being constant only gets you special relativity.
- raattgift 5y ago
  The equivalence is between uniform acceleration and a uniform gravitational field. Breaking the uniformity, which the universe does for us whether we like it or not, has consequences. Real gravitational sources aren't uniform (they tend towards spherical) and come equipped with a tidal field with a potential and gradient. This is intrinsically gravitational, not accelerational. The non-uniform distribution of matter (including radiation) in the universe also matters. You can rest an accelerometer on the surface of the Earth and it will report ~ 1 g (upwards) for many -- even billions of -- years, with no ill effect. How long can you accelerate a rocket containing an identical accelerometer? Consider fuel, and crashing into matter (up to distant starlight and the cosmic microwave radiation) after a few months (of ship time) of the accelerometer indicating ~ 1 g (forwards). You don't get strong twin-paradox effects involving the Moon-walking astronauts, or long-mission robot probes on the Moon or Mars, even though the local equivalent of "g" is considerably lower than that here on Earth. By comparison, if you and and two roughly identical astronauts were to undergo hundreds of days (or Martian sols, or a few lunar days) ship's time in spacecraft doing a round-trip under constant accelerations of ~ 1g, 0.6g, and 0.17g respectively, the lesser-accelerated "twins" would be visibly older than you at the end of your respective round-trip journeys.
jfengel 5y ago
It comes out of extending that to an accelerating reference frame, which gives you a curved spacetime. That doesn't stay stable by itself. It has to either expand or contract, depending on how much energy is in it. (Mass is a form of energy, and so you get gravity.) It's a bit like noticing that objects can't float. They can either fly away or fall but they can't just sit there. It's not exactly the same thing, since we're talking about the spacetime itself rather than gravity as separate from the objects, but the analogy mostly works.

by uh_uh 5y ago

adgjlsfhk1 5y ago

the other axiom you need is that gravity and acceleration are the same. the speed of light being constant only gets you special relativity.

raattgift 5y ago
The equivalence is between uniform acceleration and a uniform gravitational field. Breaking the uniformity, which the universe does for us whether we like it or not, has consequences. Real gravitational sources aren't uniform (they tend towards spherical) and come equipped with a tidal field with a potential and gradient. This is intrinsically gravitational, not accelerational. The non-uniform distribution of matter (including radiation) in the universe also matters. You can rest an accelerometer on the surface of the Earth and it will report ~ 1 g (upwards) for many -- even billions of -- years, with no ill effect. How long can you accelerate a rocket containing an identical accelerometer? Consider fuel, and crashing into matter (up to distant starlight and the cosmic microwave radiation) after a few months (of ship time) of the accelerometer indicating ~ 1 g (forwards). You don't get strong twin-paradox effects involving the Moon-walking astronauts, or long-mission robot probes on the Moon or Mars, even though the local equivalent of "g" is considerably lower than that here on Earth. By comparison, if you and and two roughly identical astronauts were to undergo hundreds of days (or Martian sols, or a few lunar days) ship's time in spacecraft doing a round-trip under constant accelerations of ~ 1g, 0.6g, and 0.17g respectively, the lesser-accelerated "twins" would be visibly older than you at the end of your respective round-trip journeys.

jfengel 5y ago

It comes out of extending that to an accelerating reference frame, which gives you a curved spacetime. That doesn't stay stable by itself. It has to either expand or contract, depending on how much energy is in it. (Mass is a form of energy, and so you get gravity.) It's a bit like noticing that objects can't float. They can either fly away or fall but they can't just sit there. It's not exactly the same thing, since we're talking about the spacetime itself rather than gravity as separate from the objects, but the analogy mostly works.