Postulates of General Relativity

[Jimmy87]

Hi guys,

A real easy one. Are the following postulates completely true about general relativity as they are pretty amazing to me.

1) Black holes are a solution to his field equations for GR (or are predicted by the theory)
2) His field equations also suggested the universe was expanding
3) Gravitational waves come out of his field equations

This seems ridiculous to me. So his equations suggested black holes, gravitational waves and that the universe was expanding. These three things have huge evidence now for their existence. It seems completely crazy that a scientist can come up with a theory so good that it predicts three extreme postulates which all turned out to be true. I know the man was a genius but this is crazy! Is that correct or is it not as good as websites describe his theory?

 

[Dale]

None of those are postulates. Those are all solutions to the Einstein Field Equations.

The postulates of GR are basically that spacetime is a 4D pseudo Riemannian manifold of signature (-+++) and that the curvature of the manifold is determined by the matter content via the EFE

 

[Mister T]

1) Black holes are a solution to his field equations for GR (or are predicted by the theory)
2) His field equations also suggested the universe was expanding
3) Gravitational waves come out of his field equations

As far as I know all three were predicted by the theory before they were ever observed.

 

[sandy stone]

I could be wrong (often am) but I'm not so sure about #2. Seems to me the theory initially predicted the universe would inevitably contract due to gravity, so he added the 'cosmological constant' by hand, so to speak, to allow for a static (there's that word again) universe. Or, choosing a different value for the constant, an expanding one, but I don't think that was the original intent. I stand ready to be corrected.

 

[PeterDonis]

Seems to me the theory initially predicted the universe would inevitably contract due to gravity, so he added the 'cosmological constant' by hand, so to speak, to allow for a static (there's that word again) universe. Or, choosing a different value for the constant, an expanding one, but I don't think that was the original intent.

You are misunderstanding both the history and the implications of the theory. The original EFE, without the cosmological constant, allowed both expanding and contracting solutions for the universe, but not a static one. In the expanding solutions, the expansion would be decelerating; and in the contracting solutions, the contraction would be accelerating. (This is what you would intuitively expect from "attractive gravity".) However, in the first few years after the EFE was published (1915 to roughly the early 1920s), nobody was considering either expanding or contracting solutions for the universe; there was no evidence either way, and most people (as far as I can tell) expected the universe to be static, at least on large enough scales.

Einstein originally proposed the cosmological constant in order to make a static solution possible for the universe; however, he failed to realize that such a solution would be unstable, like a pencil balanced on its point--any small perturbation would cause it to either contract or expand, and it would not return to a static state. Plus, in the 1920s, when evidence began to mount that the universe was in fact expanding, the cosmological constant no longer seemed to be necessary, and Einstein ended up calling it "the greatest blunder of my life".

However, that too proved to be mistaken. In the 1990s, evidence began to mount that, for the past few billion years or so, the expansion of the universe had been accelerating, which is not possible without a cosmological constant (or something equivalent to it--we don't actually know where the effective cosmological constant we observe, aka "dark energy", comes from). So our current best fit model has a cosmological constant in it, whose magnitude is based on the best fit to available data.

 

[sandy stone]

I seem to be learning quite a lot today. Thanks for the correction.

 

[PeterDonis]

Thanks for the correction.

You're welcome! Glad I could help.

 

[Jimmy87]

You are misunderstanding both the history and the implications of the theory. The original EFE, without the cosmological constant, allowed both expanding and contracting solutions for the universe, but not a static one. In the expanding solutions, the expansion would be decelerating; and in the contracting solutions, the contraction would be accelerating. (This is what you would intuitively expect from "attractive gravity".) However, in the first few years after the EFE was published (1915 to roughly the early 1920s), nobody was considering either expanding or contracting solutions for the universe; there was no evidence either way, and most people (as far as I can tell) expected the universe to be static, at least on large enough scales.

Einstein originally proposed the cosmological constant in order to make a static solution possible for the universe; however, he failed to realize that such a solution would be unstable, like a pencil balanced on its point--any small perturbation would cause it to either contract or expand, and it would not return to a static state. Plus, in the 1920s, when evidence began to mount that the universe was in fact expanding, the cosmological constant no longer seemed to be necessary, and Einstein ended up calling it "the greatest blunder of my life".

However, that too proved to be mistaken. In the 1990s, evidence began to mount that, for the past few billion years or so, the expansion of the universe had been accelerating, which is not possible without a cosmological constant (or something equivalent to it--we don't actually know where the effective cosmological constant we observe, aka "dark energy", comes from). So our current best fit model has a cosmological constant in it, whose magnitude is based on the best fit to available data.

Thanks. So what his field equations showed wasn't quite as amazing as some people seem to sell it by saying his theory was ahead of his time by predicting an expanding universe at a time when all scientists thought it was static?

 

[PeterDonis]

So what his field equations showed wasn't quite as amazing as some people seem to sell it by saying his theory was ahead of his time by predicting an expanding universe at a time when all scientists thought it was static?

The field equations IMO are quite amazing enough without having to make claims about what they predicted for the universe. However, if people are claiming that the original field equation (without the cosmological constant) predicted an expanding universe, that's not strictly correct. It predicted that the universe should be either expanding or contracting, but by itself it could not tell which; both are valid solutions. (Adding the cosmological constant doesn't really change that, because as I noted, the static solution allowed by the cosmological constant is unstable against small perturbations, so we would not expect to see the actual universe realizing such a solution.)

 

[Ibix]

Thanks. So what his field equations showed wasn't quite as amazing as some people seem to sell it by saying his theory was ahead of his time by predicting an expanding universe at a time when all scientists thought it was static?

You have that backwards. Friedmann, Lemaitre, Robertson and Walker came up with a solution to Einstein's equations that implied that the universe was expanding (edit: or at least, as Peter says, that it wasn't static). But our observations at the time did not match that. Einstein tweaked the theory to fit, but then Hubble's (the man, not the telescope) observations showed that the universe was expanding after all. And Einstein's tweaks didn't really work very well anyway, and he eventually described them as his biggest mistake.

Modern observation, however, shows that FLRW's work isn't quite right, and a very very small tweak of the kind Einstein introduced rather heavy-handedly turns out to be necessary. This is the modern concept of "dark energy".

 

[Jimmy87]

You have that backwards. Friedmann, Lemaitre, Robertson and Walker came up with a solution to Einstein's equations that implied that the universe was expanding (edit: or at least, as Peter says, that it wasn't static). But our observations at the time did not match that. Einstein tweaked the theory to fit, but then Hubble's (the man, not the telescope) observations showed that the universe was expanding after all. And Einstein's tweaks didn't really work very well anyway, and he eventually described them as his biggest mistake.

Modern observation, however, shows that FLRW's work isn't quite right, and a very very small tweak of the kind Einstein introduced rather heavy-handedly turns out to be necessary. This is the modern concept of "dark energy".

What do you mean by backwards? Do you mean Einstein wasn't the one who saw his equations were predicting an expanding universe? i.e. FLRW did?

 

[PeterDonis]

Friedmann, Lemaitre, Robertson and Walker came up with a solution to Einstein's equations that implied that the universe was expanding. But our observations at the time did not match that. Einstein tweaked the theory to fit

I don't think the timing you are describing is quite correct. The FLRW models weren't developed until the 1920s (Friedmann IIRC was first in 1922). Einstein proposed adding the cosmological constant to allow a static universe in 1917. Einstein was aware that the field equation without a cosmological constant did not allow a static universe solution, but I don't think he had developed a model like the FLRW model in any detail; he had just made some very general deductions about what a static solution to the original field equation would require.

 

[Jimmy87]

When he first put forward his theory is it right that his equations predicted gravitational waves and black holes? Is this why people went looking for black holes? Because they were a solution to his equations.

 

[Ibix]

What do you mean by backwards? Do you mean Einstein wasn't the one who saw his equations were predicting an expanding universe? i.e. FLRW did?

I mean Einstein's theory predicted an expanding universe at a time when observation implied it was static. Einstein just didn't believe it so "fixed" his theory. Peter says I have the sequence of theoretical discoveries in the wrong order and he's probably right, but it doesn't change that point. My reading of your post #8 that I quoted is that you thought Einstein had not predicted an expanding universe. He had, and his "fix" to try to make it match then-current observational evidence never worked right.

Einstein was correct to doubt his theory when it disagreed with observation. But in this case it turned out to be the observations that weren't sufficiently developed and the theory that was right.

 

[PeterDonis]

When he first put forward his theory is it right that his equations predicted gravitational waves and black holes?

Since the field equation he proposed in 1915 is the one we still use today (except for the cosmological constant, which doesn't affect gravitational waves or black holes), then the answer to this question as you state it is yes. However--

Is this why people went looking for black holes? Because they were a solution to his equations.

Not the way you mean, because even though Einstein published his field equation in 1915, it wasn't until the 1960s that it was understood that black holes (and gravitational waves, for that matter) were actually solutions that were worth looking for actual realizations of in our universe.

Here is a quick summary of the history with regard to black holes: Schwarzschild found his solution, the one that we now know describes a static, non-rotating black hole, in 1916 (and sent it to Einstein, who had it published, not long before Schwarzschild himself died on the Russian front in WW I), but nobody understood then what it implied; it was thought to simply be a description of the vacuum region of spacetime around a static star or planet (which it is, if we only consider the portion well outside the horizon). In 1939, Oppenheimer and Snyder published a paper describing a model of the collapse of a non-rotating, pressureless star to a black hole, but WW II and the Manhattan Project soon occupied the attention of anyone who might have picked up on it. One of the key limitations in everyone's thinking then was the use of what we now call Schwarzschild coordinates, which are singular at the horizon and don't give a good intuitive picture of what is going on there.

In 1958, Finkelstein discovered a new coordinate chart for describing Schwarzschild's solution, and soon after other charts were discovered (the Kruskal-Szekeres chart, for example), and physicists finally began to realize what was actually going on at and below the horizon. Only after that did black holes start to seem like a realistic possibility that could be searched for in our actual universe.

 

[Jimmy87]

I mean Einstein's theory predicted an expanding universe at a time when observation implied it was static. Einstein just didn't believe it so "fixed" his theory. Peter says I have the sequence of theoretical discoveries in the wrong order and he's probably right, but it doesn't change that point. My reading of your post #8 that I quoted is that you thought Einstein had not predicted an expanding universe. He had, and his "fix" to try to make it match then-current observational evidence never worked right.

Einstein was correct to doubt his theory when it disagreed with observation. But in this case it turned out to be the observations that weren't sufficiently developed and the theory that was right.

Ah I see. No in post 8 I actually meant what you just said in post 14. Maybe I didn't word it well - sorry. I meant 'ahead of his time' in that it predicted the correct concept of an expanding universe in a time when a static universe was the mainstream (yet incorrect) concept. It just seems quite amazing that all the things that come out of his theory like black holes were not even in scientists minds when his theory came about. This is what is so incredible and that's what I mean by his theory being so far ahead of his time.

 

[Jimmy87]

Since the field equation he proposed in 1915 is the one we still use today (except for the cosmological constant, which doesn't affect gravitational waves or black holes), then the answer to this question as you state it is yes. However--
Not the way you mean, because even though Einstein published his field equation in 1915, it wasn't until the 1960s that it was understood that black holes (and gravitational waves, for that matter) were actually solutions that were worth looking for actual realizations of in our universe.

Here is a quick summary of the history with regard to black holes: Schwarzschild found his solution, the one that we now know describes a static, non-rotating black hole, in 1916 (and sent it to Einstein, who had it published, not long before Schwarzschild himself died on the Russian front in WW I), but nobody understood then what it implied; it was thought to simply be a description of the vacuum region of spacetime around a static star or planet (which it is, if we only consider the portion well outside the horizon). In 1939, Oppenheimer and Snyder published a paper describing a model of the collapse of a non-rotating, pressureless star to a black hole, but WW II and the Manhattan Project soon occupied the attention of anyone who might have picked up on it. One of the key limitations in everyone's thinking then was the use of what we now call Schwarzschild coordinates, which are singular at the horizon and don't give a good intuitive picture of what is going on there.

In 1958, Finkelstein discovered a new coordinate chart for describing Schwarzschild's solution, and soon after other charts were discovered (the Kruskal-Szekeres chart, for example), and physicists finally began to realize what was actually going on at and below the horizon. Only after that did black holes start to seem like a realistic possibility that could be searched for in our actual universe.

Excellent, thanks for taking the time to write this.

 

[Ibix]

Ah I see. No in post 8 I actually meant what you just said in post 14.

Fair enough - at least we understand each other now.

I meant 'ahead of his time' in that it predicted the correct concept of an expanding universe in a time when a static universe was the mainstream (yet incorrect) concept.

This is generally how science progresses. We develop a theory that explains some existing observations that previous theory couldn't (the anomalous precession of Mercury's orbit, in this case). People explore the implications of the theory, and find new things that we haven't seen and then we go looking for them.

Relativity is quite dramatic in its predictions, but not fundamentally unusual.