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How Einstein arrived at his theory of general relativity

179 points by 8ytecoder 5y ago

Waterluvian 5y ago
I feel like “does it reduce to Newton’s Laws under non-extreme conditions” is basically “is it compatible with everyday observations?” Or to invert it: “is it trivially disprovable?” This is probably a meaningless distinction but I find it cutely fascinating.
- derbOac 5y ago
 Interesting to think about what's really extreme in the universe, versus what was meant in that passage.
- unlaxedneurotic 5y ago
 >>“does it reduce to Newton’s Laws under non-extreme conditions” Thomas Kuhn said something about this in his Structures of Scientific Revolutions. Imagine a set of statements, E1, E2, . . . En , which together embody the laws of relativity theory., ..... This enlarged set of statements is then manipulated to yield a new set, N1 , N2 , . . . , Nm , which is identical in form with Newton’s laws of motion, the law of gravity, and so on. Yet the derivation is spurious, at least to this point. Though the N1’s are a special case of the laws of relativistic mechanics, they are not Newton’s Laws. Or at least they are not unless those laws are reinterpreted in a way that would have been impossible until after Einstein’s work. The variables and parameters that in the Einsteinian E1’s represented spatial position, time, mass, etc., still occur in the N1’s; and they there still represent Einsteinian space, time, and mass. But the physical referents of these Einsteinian concepts are by no means identical with those of the Newtonian concepts that bear the same name.
leephillips 5y ago
Always a pleasure to read an appreciation of this turning point in human thought. But, like most accounts, this book excerpt gives the impression that Einstein worked alone to develop his theory. In fact, it was more of a collaboration: https://arstechnica.com/science/2015/12/general-relativity-100-years-of-the-most-beautiful-theory-ever-created/ https://arstechnica.com/science/2015/12/general-relativity-1...
- purple5 5y ago
- pvarangot 5y ago
  Even that article doesn't mention Minkowski. Journalists and writers have such huge egos that can never see past the man in Einstein no matter how hard he tried to explain he was also standing on the shoulders of giants.
  - leephillips 5y ago
    Do you think that Minkowski was important in the development of GR? Why, specifically? (I mean in its creation, not in the evolution of its interpretation after 1915.) EDIT: I don’t understand the relationship between the egos of writers and their estimation of Einstein’s role. “Shoulders of giants:” in fact, it was Einstein who jealously guarded his credit for GR and never seemed to mention, in public, the contributions of others, although he did in his private letters.
    - pvarangot 5y ago
      Doesn't Minkowski's work with hyperbolic space predate GR? I thought it was like a stepping stone between Special and General Relativity. I don't understand GR, I'm not even close and I tried for years twice or thrice to teach myself GR and I find it pretty impenetrable. Maybe I see Minkowski's work as a stepping stone because that's one of the paths that I was put into to understand it.
      - leephillips 5y ago
        In my article I talk about the people that Einstein collaborated with in his struggle to arrive at the field equations. Minkowski was not one of those people (although he was one of Einstein’s math teachers in school). I don’t think this work of Minkowski’s that you mention is directly relevant, but, even if it’s part of the mathematical background, Minkowski is not part of that particular story. Now we talk about "four dimensional" spacetime, and that point of view is largely due to Minkowski. But it wasn’t Einstein’s point of view, and for years Einstein remarked that he didn’t see the point—it seemed needlessly formal and academic to him. But he sort of came around later.
jdrc 5y ago
One day we will be able to link Einstein's worldview with the intricacies of human brain. His theory probably aligns with something fundamental about the way we perceive space and time that nobody had tapped into before him. I wonder if there are other such alignments that will ever happen again, before we collectively step back and allow machines to take over the rest of this timeline
- bpodgursky 5y ago
  I suspect Von Neumann pointed a slightly different direction would have had a pretty good shot at it.
- pvarangot 5y ago
  Regarding GR I don't think he really perceived or saw time and space much more differently, as much as was well equipped to discuss it with the likes of Minkowski and Poincare and teach himself the tensor calculus. I would really enjoy a discussion with someone versed on the history of GR about this because it's something I've been thinking for a while. How he "saw" special relativity is I think related to riding a bicycle and the Michelson–Morley experiment.
  - jdrc 5y ago
    we don't really know either do we? The idea of equivalence is not an intuitive path in the universe of possibilities. We don't know if him or others tried other equally singular paths. And do we know to what extent the MM experiment inspired the constancy of speed of light?
    - pvarangot 5y ago
      Really don't know what? How Einstein experienced time? I think that a sensible man like Einstein that was also very well versed in physics and the social sciences would have extensively written if he really "experienced" time and space differently. But he didn't, he just wrote about physics and formulas and their manipulation to describe a collectively experience reality. I don't know how to attribute an "extent" to how the Michelson-Morley experiment influenced Einstein but Einstein himself quotes Maxwell-Lorentz theory of electromagnetism as heavy inspiration in his papers and books and mentions the Michelson-Morley experiment directly many times. "Relativity: The Special and General Theory" is really approachable and even though I can't find a searchable version right now I am pretty sure grepping for Michelson-Morley and Maxwell there will find references. Einstein was inspired by studying movement of particles like electrons in a CRT to come up with ideas for both Special and General Relativity. He was much more of a working physicist than what popular media tends to portray, it's not that he was some kind of alien magician that had an answer for everything because of his alien magic. He was just super up to date on a lot of things electromagnetism and light, remember he also discovered the photoelectric effect before relativity.
bronlund 5y ago
nmaleki 5y ago
"In 1915, Albert Einstein wrote a letter to the philosopher and physicist Moritz Schlick, who had recently composed an article on the theory of relativity. Einstein praised it: ‘From the philosophical perspective, nothing nearly as clear seems to have been written on the topic.’ Then he went on to express his intellectual debt to ‘David Hume, whose Treatise of Human Nature I had studied avidly and with admiration shortly before discovering the theory of relativity. It is very possible that without these philosophical studies I would not have arrived at the solution.’" https://aeon.co/essays/what-albert-einstein-owes-to-david-humes-notion-of-time https://aeon.co/essays/what-albert-einstein-owes-to-david-hu...
kleton 5y ago
Seems incomplete without at least some token mention of Lorentz and Poincare.
- lisper 5y ago
  And Minkowski.
- not2b 5y ago
  Lorentz and Poincare were very important in the development of special relativity. This article is about general relativity. For general relativity there's a good argument that David Hilbert deserves more credit.
  - LudwigNagasena 5y ago
    Are Newton, Galileo, Coulomb and Archimedes more important to general relativity?
    - not2b 5y ago
      Than Hilbert? No. Riemann, perhaps. Making it work was all about the proper non-Euclidean geometry. Einstein needed to learn the right mathematics.
    - avmich 5y ago
      > Archimedes, the ancient Greek philosopher, had asserted that heavy objects fall faster than lighter ones. Wasn't that Aristotle?
phkahler 5y ago
Wait, light doesnt bend as an equivalent mass? It behaves that way in other cases like calculating radiation pressure.
sakesun 5y ago
I've read from a cartoon that it started from his curious question of what would happen if a person looking at a mirror in a lightspeed spaceship.
Zamicol 5y ago
The question I've always ask is how did Einstein miss black holes? Schwarzschild immediately saw the obvious and checked the limits of Einstein's work. This is similar to Minkowski seeing the obvious with spacetime, once finally bothering to look at Einstein's work, whom he had taught, years after the 1905 publication.
- mrjangles 5y ago
  Einstein and all the great scientists from that era didn't miss black holes, they thought the idea of black holes were stupid and looked down on people doing that kind of research. Freeman Dyson talks about this in a few interviews - though he doesn't seem to understand why they thought that as he personally loved black hole research. A singularity is, afterall, a mathematical effect that occurs everywhere in science when the mathematics used to describe the system in one region is no longer valid in another. Only in modern, government funded 'science' do we start to find people taking mathematical errors seriously. Also, to preempt any responses I might get, no, massive dark objects at the center of our galaxy are not even close to being evidence that space-time singularities are real.
  - lupire 5y ago
    If you don't believe black holes exist, you need to believe in a theory of physics that explains why they won't form. What is that theory?
    - mrjangles 5y ago
      This makes no sense. When you apply the mathematics of fluid dynamics to the problem of water leaking through a dam wall, you get singularities. It makes no sense to say "you either believe the amount of water in a dam wall becomes infinite and the universe collapses in on itself inside a dam, or you have a better theory, what is that theory?" (you would become a famous mathematician if you had that theory by the way).
      - deleted 5y ago
        [deleted]
paulpauper 5y ago
> No experiment can distinguish free fall in a gravitational field from motion with uniform acceleration (as in the elevator). This has been tested so many times and still holds. Amazing he thought of it.
- deleted 5y ago
  [deleted]
paulpauper 5y ago
Interesting article. But it's not obvious how you go from principle of equivalence to the equations that describe general relativity, specifically curved space-time. That is a huge leap. Obviously, the author cannot cover all of the inbetween steps. But you don't need special relativity to get to general relativity, nor do you even need equivalence principle. GR is more geometry than anything else.
deleted 5y ago
[deleted]
pmontra 5y ago
One of the commenters in the post wrote this > Einstein didn't use Maxwell's original quaternion equations. He used the dumbed down vectors of Lorentz, Heaviside, Gibbs, Hertz, etc. Make no mistake—this is the reason why Relativity doesn't play well with quantum mechanics. > Maxwell's original equations are scalar in nature. The reduction of these equations by Lorentz, et al. in the early 20th century removed the scalar (time) component entirely, and theoretical physics, whether it knows it or not, has been reeling ever since. [...] Can anybody here explain why this is so important?
- gmt2027 5y ago
  Maxwell's original paper presented 20 equations. Heaviside's elegant formulation simplified these into the 4 familiar vector calculus equations. I doubt that this has been the obstacle to a unified field theory.
  - Qem 5y ago
    Geometric algebra boils them down to a single equation. See https://www.researchgate.net/publication/340037736_CHAPTER_FIVE_Maxwell_Equations_in_Geometric_Algebra https://www.researchgate.net/publication/340037736_CHAPTER_F...
- CamperBob2 5y ago
  It's important because it suggests that GPT3 or a similar model can now synthesize scientific-sounding gibberish.
- blendergeek 5y ago
  I am not a theoretical physicist. I have only done first semester college physics and I have read hacker news comments (and physics related articles) for years. However, I can assure you that if it was a simple as using the proper Maxwellian quaternions instead of the dumbed down Lorentz vectors to get a unified theory, this would have been done a long time ago. The comment you ask about seems to make no sense whatsoever. That is why you are having trouble parsing the comment and figuring out what its significance is.
- 5y ago
29athrowaway 5y ago
Einstein worked at a patent office in Bern, Switzerland and many of the patents at that time had to do with synchronizing clocks.
- blendergeek 5y ago
  The article being discussed relates to the development of the theory of general relativity. You are thinking of when Einstein developed the theory of special relativity. Special Relativity relates to time dilation where as General Relativity relates to gravity.
Waterluvian 5y ago
An unrelated note: In this article there are these red text excerpts. Sometimes immediately before the location of the text. I get that these probably make more sense in desktop or magazine format, compared to phone. But I find them amusing nonetheless: it’s an ad break where the article advertises itself.
bmitc 5y ago
For some context surrounding the mathematical difficulties of general relativity at the time, I recommend the book Einstein's Italian Mathematicians: Ricci, Levi-Civita, and the Birth of General Relativity. https://www.amazon.com/Einsteins-Italian-Mathematicians-Levi-civita-Relativity/dp/1470428466/ https://www.amazon.com/Einsteins-Italian-Mathematicians-Levi...
Loic 5y ago
How? Thanks to his wife Mileva Marić[0]. [0]: https://en.wikipedia.org/wiki/Mileva_Mari%C4%87 https://en.wikipedia.org/wiki/Mileva_Mari%C4%87
mrtri 5y ago
EMM_386 5y ago
> The effects of free fall can also be achieved with aircraft by shutting off the engines for a period. This is not how this is accomplished. They fly a parabolic trajectory.
- dreamcompiler 5y ago
  More generally, the plane flies along a spacetime geodesic, the most convenient of which is a ballistic parabola. This does require cutting the engines. Cutting the engines is necessary but not sufficient. In level flight, air still supports the plane even without engine thrust, so the passengers would still feel "weight." The "vomit comet" could achieve the same weightless effect without climbing by cutting the engines and pointing the plane toward the ground. That's effectively the second half of the ballistic parabola. But it would only provide about 12 seconds of weightlessness instead of 25.
rurban 5y ago
Huge cliff hanger. Not a note about the EPR paradoxon and his fights with the standard model of quantum mechanics.

179 points by 8ytecoder 5y ago

I feel like “does it reduce to Newton’s Laws under non-extreme conditions” is basically “is it compatible with everyday observations?” Or to invert it: “is it trivially disprovable?” This is probably a meaningless distinction but I find it cutely fascinating.

derbOac 5y ago
Interesting to think about what's really extreme in the universe, versus what was meant in that passage.
unlaxedneurotic 5y ago
>>“does it reduce to Newton’s Laws under non-extreme conditions” Thomas Kuhn said something about this in his Structures of Scientific Revolutions. Imagine a set of statements, E1, E2, . . . En , which together embody the laws of relativity theory., ..... This enlarged set of statements is then manipulated to yield a new set, N1 , N2 , . . . , Nm , which is identical in form with Newton’s laws of motion, the law of gravity, and so on. Yet the derivation is spurious, at least to this point. Though the N1’s are a special case of the laws of relativistic mechanics, they are not Newton’s Laws. Or at least they are not unless those laws are reinterpreted in a way that would have been impossible until after Einstein’s work. The variables and parameters that in the Einsteinian E1’s represented spatial position, time, mass, etc., still occur in the N1’s; and they there still represent Einsteinian space, time, and mass. But the physical referents of these Einsteinian concepts are by no means identical with those of the Newtonian concepts that bear the same name.

leephillips 5y ago

Always a pleasure to read an appreciation of this turning point in human thought. But, like most accounts, this book excerpt gives the impression that Einstein worked alone to develop his theory. In fact, it was more of a collaboration: https://arstechnica.com/science/2015/12/general-relativity-100-years-of-the-most-beautiful-theory-ever-created/ https://arstechnica.com/science/2015/12/general-relativity-1...

purple5 5y ago
pvarangot 5y ago
Even that article doesn't mention Minkowski. Journalists and writers have such huge egos that can never see past the man in Einstein no matter how hard he tried to explain he was also standing on the shoulders of giants.
- leephillips 5y ago
  Do you think that Minkowski was important in the development of GR? Why, specifically? (I mean in its creation, not in the evolution of its interpretation after 1915.) EDIT: I don’t understand the relationship between the egos of writers and their estimation of Einstein’s role. “Shoulders of giants:” in fact, it was Einstein who jealously guarded his credit for GR and never seemed to mention, in public, the contributions of others, although he did in his private letters.
  - pvarangot 5y ago
    Doesn't Minkowski's work with hyperbolic space predate GR? I thought it was like a stepping stone between Special and General Relativity. I don't understand GR, I'm not even close and I tried for years twice or thrice to teach myself GR and I find it pretty impenetrable. Maybe I see Minkowski's work as a stepping stone because that's one of the paths that I was put into to understand it.
    - leephillips 5y ago
      In my article I talk about the people that Einstein collaborated with in his struggle to arrive at the field equations. Minkowski was not one of those people (although he was one of Einstein’s math teachers in school). I don’t think this work of Minkowski’s that you mention is directly relevant, but, even if it’s part of the mathematical background, Minkowski is not part of that particular story. Now we talk about "four dimensional" spacetime, and that point of view is largely due to Minkowski. But it wasn’t Einstein’s point of view, and for years Einstein remarked that he didn’t see the point—it seemed needlessly formal and academic to him. But he sort of came around later.

jdrc 5y ago

One day we will be able to link Einstein's worldview with the intricacies of human brain. His theory probably aligns with something fundamental about the way we perceive space and time that nobody had tapped into before him. I wonder if there are other such alignments that will ever happen again, before we collectively step back and allow machines to take over the rest of this timeline

bpodgursky 5y ago
I suspect Von Neumann pointed a slightly different direction would have had a pretty good shot at it.
pvarangot 5y ago
Regarding GR I don't think he really perceived or saw time and space much more differently, as much as was well equipped to discuss it with the likes of Minkowski and Poincare and teach himself the tensor calculus. I would really enjoy a discussion with someone versed on the history of GR about this because it's something I've been thinking for a while. How he "saw" special relativity is I think related to riding a bicycle and the Michelson–Morley experiment.
- jdrc 5y ago
  we don't really know either do we? The idea of equivalence is not an intuitive path in the universe of possibilities. We don't know if him or others tried other equally singular paths. And do we know to what extent the MM experiment inspired the constancy of speed of light?
  - pvarangot 5y ago
    Really don't know what? How Einstein experienced time? I think that a sensible man like Einstein that was also very well versed in physics and the social sciences would have extensively written if he really "experienced" time and space differently. But he didn't, he just wrote about physics and formulas and their manipulation to describe a collectively experience reality. I don't know how to attribute an "extent" to how the Michelson-Morley experiment influenced Einstein but Einstein himself quotes Maxwell-Lorentz theory of electromagnetism as heavy inspiration in his papers and books and mentions the Michelson-Morley experiment directly many times. "Relativity: The Special and General Theory" is really approachable and even though I can't find a searchable version right now I am pretty sure grepping for Michelson-Morley and Maxwell there will find references. Einstein was inspired by studying movement of particles like electrons in a CRT to come up with ideas for both Special and General Relativity. He was much more of a working physicist than what popular media tends to portray, it's not that he was some kind of alien magician that had an answer for everything because of his alien magic. He was just super up to date on a lot of things electromagnetism and light, remember he also discovered the photoelectric effect before relativity.

bronlund 5y ago

nmaleki 5y ago

"In 1915, Albert Einstein wrote a letter to the philosopher and physicist Moritz Schlick, who had recently composed an article on the theory of relativity. Einstein praised it: ‘From the philosophical perspective, nothing nearly as clear seems to have been written on the topic.’ Then he went on to express his intellectual debt to ‘David Hume, whose Treatise of Human Nature I had studied avidly and with admiration shortly before discovering the theory of relativity. It is very possible that without these philosophical studies I would not have arrived at the solution.’" https://aeon.co/essays/what-albert-einstein-owes-to-david-humes-notion-of-time https://aeon.co/essays/what-albert-einstein-owes-to-david-hu...

kleton 5y ago

Seems incomplete without at least some token mention of Lorentz and Poincare.

lisper 5y ago
And Minkowski.
not2b 5y ago
Lorentz and Poincare were very important in the development of special relativity. This article is about general relativity. For general relativity there's a good argument that David Hilbert deserves more credit.
- LudwigNagasena 5y ago
  Are Newton, Galileo, Coulomb and Archimedes more important to general relativity?
  - not2b 5y ago
    Than Hilbert? No. Riemann, perhaps. Making it work was all about the proper non-Euclidean geometry. Einstein needed to learn the right mathematics.
  - avmich 5y ago
    > Archimedes, the ancient Greek philosopher, had asserted that heavy objects fall faster than lighter ones. Wasn't that Aristotle?

phkahler 5y ago

Wait, light doesnt bend as an equivalent mass? It behaves that way in other cases like calculating radiation pressure.

sakesun 5y ago

I've read from a cartoon that it started from his curious question of what would happen if a person looking at a mirror in a lightspeed spaceship.

Zamicol 5y ago

The question I've always ask is how did Einstein miss black holes? Schwarzschild immediately saw the obvious and checked the limits of Einstein's work. This is similar to Minkowski seeing the obvious with spacetime, once finally bothering to look at Einstein's work, whom he had taught, years after the 1905 publication.

mrjangles 5y ago
Einstein and all the great scientists from that era didn't miss black holes, they thought the idea of black holes were stupid and looked down on people doing that kind of research. Freeman Dyson talks about this in a few interviews - though he doesn't seem to understand why they thought that as he personally loved black hole research. A singularity is, afterall, a mathematical effect that occurs everywhere in science when the mathematics used to describe the system in one region is no longer valid in another. Only in modern, government funded 'science' do we start to find people taking mathematical errors seriously. Also, to preempt any responses I might get, no, massive dark objects at the center of our galaxy are not even close to being evidence that space-time singularities are real.
- lupire 5y ago
  If you don't believe black holes exist, you need to believe in a theory of physics that explains why they won't form. What is that theory?
  - mrjangles 5y ago
    This makes no sense. When you apply the mathematics of fluid dynamics to the problem of water leaking through a dam wall, you get singularities. It makes no sense to say "you either believe the amount of water in a dam wall becomes infinite and the universe collapses in on itself inside a dam, or you have a better theory, what is that theory?" (you would become a famous mathematician if you had that theory by the way).
    - deleted 5y ago
      [deleted]

paulpauper 5y ago

> No experiment can distinguish free fall in a gravitational field from motion with uniform acceleration (as in the elevator). This has been tested so many times and still holds. Amazing he thought of it.

deleted 5y ago
[deleted]

paulpauper 5y ago

Interesting article. But it's not obvious how you go from principle of equivalence to the equations that describe general relativity, specifically curved space-time. That is a huge leap. Obviously, the author cannot cover all of the inbetween steps. But you don't need special relativity to get to general relativity, nor do you even need equivalence principle. GR is more geometry than anything else.

deleted 5y ago

[deleted]

pmontra 5y ago

One of the commenters in the post wrote this > Einstein didn't use Maxwell's original quaternion equations. He used the dumbed down vectors of Lorentz, Heaviside, Gibbs, Hertz, etc. Make no mistake—this is the reason why Relativity doesn't play well with quantum mechanics. > Maxwell's original equations are scalar in nature. The reduction of these equations by Lorentz, et al. in the early 20th century removed the scalar (time) component entirely, and theoretical physics, whether it knows it or not, has been reeling ever since. [...] Can anybody here explain why this is so important?

gmt2027 5y ago
Maxwell's original paper presented 20 equations. Heaviside's elegant formulation simplified these into the 4 familiar vector calculus equations. I doubt that this has been the obstacle to a unified field theory.
- Qem 5y ago
  Geometric algebra boils them down to a single equation. See https://www.researchgate.net/publication/340037736_CHAPTER_FIVE_Maxwell_Equations_in_Geometric_Algebra https://www.researchgate.net/publication/340037736_CHAPTER_F...
CamperBob2 5y ago
It's important because it suggests that GPT3 or a similar model can now synthesize scientific-sounding gibberish.
blendergeek 5y ago
I am not a theoretical physicist. I have only done first semester college physics and I have read hacker news comments (and physics related articles) for years. However, I can assure you that if it was a simple as using the proper Maxwellian quaternions instead of the dumbed down Lorentz vectors to get a unified theory, this would have been done a long time ago. The comment you ask about seems to make no sense whatsoever. That is why you are having trouble parsing the comment and figuring out what its significance is.
5y ago

29athrowaway 5y ago

Einstein worked at a patent office in Bern, Switzerland and many of the patents at that time had to do with synchronizing clocks.

blendergeek 5y ago
The article being discussed relates to the development of the theory of general relativity. You are thinking of when Einstein developed the theory of special relativity. Special Relativity relates to time dilation where as General Relativity relates to gravity.

Waterluvian 5y ago

An unrelated note: In this article there are these red text excerpts. Sometimes immediately before the location of the text. I get that these probably make more sense in desktop or magazine format, compared to phone. But I find them amusing nonetheless: it’s an ad break where the article advertises itself.

bmitc 5y ago

For some context surrounding the mathematical difficulties of general relativity at the time, I recommend the book Einstein's Italian Mathematicians: Ricci, Levi-Civita, and the Birth of General Relativity. https://www.amazon.com/Einsteins-Italian-Mathematicians-Levi-civita-Relativity/dp/1470428466/ https://www.amazon.com/Einsteins-Italian-Mathematicians-Levi...

Loic 5y ago

How? Thanks to his wife Mileva Marić[0]. [0]: https://en.wikipedia.org/wiki/Mileva_Mari%C4%87 https://en.wikipedia.org/wiki/Mileva_Mari%C4%87

mrtri 5y ago

EMM_386 5y ago

> The effects of free fall can also be achieved with aircraft by shutting off the engines for a period. This is not how this is accomplished. They fly a parabolic trajectory.

dreamcompiler 5y ago
More generally, the plane flies along a spacetime geodesic, the most convenient of which is a ballistic parabola. This does require cutting the engines. Cutting the engines is necessary but not sufficient. In level flight, air still supports the plane even without engine thrust, so the passengers would still feel "weight." The "vomit comet" could achieve the same weightless effect without climbing by cutting the engines and pointing the plane toward the ground. That's effectively the second half of the ballistic parabola. But it would only provide about 12 seconds of weightlessness instead of 25.

rurban 5y ago

Huge cliff hanger. Not a note about the EPR paradoxon and his fights with the standard model of quantum mechanics.