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:
Everybody was working on it and it was much more of a race to an inevitable interpretation of the world, than most
credit historically. Certainly not a single man vision.
Though special relativity was coming no matter what, I don't think we would have had general relativity without Einstein for at least another couple decades, likely longer. We would have had it without Hilbert. Hilbert got the key insights from Einstein, but he did a lot of the necessary work on the math, important work but work other mathematicians could have done. That's the difference.
Everybody as in, the leading experts in theoretical physics of the time:
"It was noted by Sir Edmund Whittaker in his 1954 book that David Hilbert had derived the theory of general relativity from an elegant variational principle almost simultaneously with Einstein's discovery of the theory.[B 1] Hilbert's derivation of the theory predated that of Einstein by five days.[B 2]"
Be careful however, as unfortunately some, for other reasons, historically tried to appropriate this work, and use to try to diminish the contributions of Einstein. Something that of course, is very much incorrect.
That equation is associated with SR, not GR. I’m not aware of anyone, aside from Einstein and the small group at Göttingen who were working with him, and a couple of his friends, such as Grossmann, who were helping him with the math, even being aware of this work on gravity. But I’m willing to learn. Please provide some names. Who were the “experts of the domain at the time”? For that matter, what is this domain?
The equation is not more associated with SR or GR, more than its historical context where it was derived from. Its just a principle of physics SR, GR or any
other theory.
Who are the people? The Berlin Group, David Hilbert, Carl F. Gauss, Bernhard Riemann, Ernst Mach,Henri Poincaré, Hendrik Lorentz. The domain are the studies on the understanding the most basic fundamentals of physics derived from the analysis of electromagentism that most leading physicists of the time were busy with. Although Hilbert and Poincare are monsters of pure mathematics they were just doing physics by the side.
Looking at the biography of Hilbert, it starts to look like almost obvious what happened. In no way it diminishes the stature of Einstein to recognize it.
Hilbert was a monster:-) Hilbert did invariant theory, calculus of variations, commutative algebra, algebraic number theory, geometry, spectral theory of operators and its application to integral equations, mathematical physics.
Einstein by the contrary, always needed help with Mathematics, since
the times at University. That was how he met his first wife...
Hilbert was following the work of Einstein but this latest one was struggling to make any progress for years. In the summer 1915, Hilbert's was interested in general relativity, and he invited Einstein to Göttingen to deliver a week of lectures on the subject.
Suddenly within a few weeks, Einstein comes up with his Field equations while Hilbert follows with his foundations of physics. The fact that Hilbert fully credited Einstein as the originator of the theory, and did not engage in any public priority dispute is pretty clear was as a statement to the
previous work Einstein did for years. With the collaboration and common work that happened its pretty clear, Einstein did not have the mathematical prowess and skill, to come up with those sudden breakthroughs...
He had even better than mathematical prowess: an intuition and creativity. Einstein's thought experiments were what led him to the discovery. What's the difference between someone with superior raw mathematical talent and strong mathematical talent plus creative intuition? I would argue, in particular with regards to physics, it makes all the difference.
"...a paradox upon which I had already hit at the age of sixteen: If I pursue a beam of light with the velocity c (velocity of light in a vacuum), I should observe such a beam of light as an electromagnetic field at rest though spatially oscillating. There seems to be no such thing, however, neither on the basis of experience nor according to Maxwell's equations. From the very beginning it appeared to me intuitively clear that, judged from the standpoint of such an observer, everything would have to happen according to the same laws as for an observer who, relative to the earth, was at rest. For how should the first observer know or be able to determine, that he is in a state of fast uniform motion? One sees in this paradox the germ of the special relativity theory is already contained.[p 1]: 52–53 "
> Suddenly within a few weeks, Einstein comes up with his Field equations
It wasn't a few weeks, it was months. Einstein visited Hilbert in June/July 1915. He didn't publish his field equation until November 1915 (and even then it took him several tries before he got the final one).
This is sort of a myth. Einstein was a poor mathematician in comparison with Hilbert, but that goes for most of us. He was fairly strong by the standards of the era.
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.
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.
> Do you think that Minkowski was important in the development of GR? Why, specifically?
Minkowski came up with the concept of spacetime as a 4-dimensional geometric object. That was a crucial insight required for the development of GR: just take this geometric object, which was flat in SR, and allow it to be curved.
IIRC Einstein himself, who initially was dismissive of Minkowski's idea, later changed his mind and recognized its importance, and said so in a number of his writings about relativity. Unfortunately, Minkowski died the year after he came up with his idea, so he never got to see where it led.
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.
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.
> 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.
Probably you are right, but... maybe its just me, but this coincidence seems too much of a coincidence. I can't resist hypothesizing, would it be possible to Minkowski somehow influence Einstein, maybe indirectly. For example, Minkowski was interested in curved spaces, it is possible that he somehow implanted his ideas into Einstein's mind, isn't it? Not consciously, but as it happens with teachers passionate with their subject by bringing his favorite topic in his lectures for any reason or even without any reason.
> 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.
This fact also can be incorporated into my hypothesis, though with an additional assumption: teenager Einstein was exhausted by his teacher's constant remarks about curved spaces, and was conditioned to roll his eyes hearing about curved spaces. So he naturally continued to roll his eyes at curved space-time.
Yeah, it is just a hypothesis, a wild guess, and even if it was true, it wouldn't mean that Minkowski was a collaborator, but what a fun story it may be. A story about a passionate teacher shaping a mind of genius into a curved space despite all lack of mutual enthusiasm.
On a more serious note, I can remark, that this hypothesis consistent with all I know about a human mind. Einstein might have a mental model for a curved space, and his mind might have used this model to propose new thought experiments, but Einstein disliked the very idea to the point of not noticing how his mind relies on it, and he worked hard consciously to find another model to rely on. Moreover there are psychological theories stating that a mind must have at least two different models/representations of a problem domain to deal with it successfully, so this hypothetical inner conflict might benefited Einstein's genius by urging him to construct his second mental representation of gravity.
The way I understand it, out of all the fathers of general relativity, Einstein was one of the only ones who really did physics. That is, applying the formulas to real life observations, or thought experiments, something that Einstein was particularly famous for.
Einstein got a lot of help with the maths, but I think he deserves full credit for the physical application.
Accepted practice for listing authors on scientific papers is always changing. In older papers you often have people listed in an acknowledgement who, today, would absolutely be on the author list.
A collaboration.. and even the article says 8 years of hard work and missteps and still we stick to the "Einstein's genius" narrative. I think the genius narrative is disingenuous to the person and discounts all the effort and furthermore putting everyone else in the position of "are you a genius? No right? So don't hope to do Einstein level work."
Well, I think it could also be disingenuous to presume that anyone could do what he did if you just put in the hard work. If hard work was all you need, we would have a lot more Einstein level discoveries than we do.
We do have a lot more Einstein level discoveries than most people may realize. If anything, we have so many discoveries that it's hard to single one out for special consideration. The big difference between now and then I'd argue is that progress is much more incremental today so that it never seems like you just wake up and there's one major breakthrough that comes out of nowhere. Instead we're constantly being exposed to small improvements that add up to significant advances over a 15-20 year period.
What would you say are some examples where you look back what the state was 15 years ago vs the progress we made till the present and the jump would seem just as profound. Just curious.
I felt the same way - it seemed like the early 20th century made so much progress with those visionaries compared what what is being made now. Obviously I am not well informed because that is likely not the case.
"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.’"
> 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?
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.
i am a former string theorist, pretty much turned and expanded Maxwell Einstein and Yang Mills in any possible ways, and those comments are garbage.
> original quaternion equations
quaternions are a 3/4d thing, you can write maxwell in any dimensions. sure you can rewrite some 3/4 d physics with quaternions but really no one does that for the last 30 years. we routinely use the group SU(2) or SO(3) but almost never it's quaternion representation. it's really not that practical.
> dumbed down vectors
i don't think it is the vectors that are dumb in this case...
btw it's not only a vector, it's a connection in a U(1) bundle over some spacetime manifold \cal{M}.
> Relativity doesn't play well with quantum mechanics
What in the f**** f**....
it works really well, we call that quantum field theory and it's the best theory ever found by mankind. it works so well CERN didn't found any deviation in 30 years or so.
> Maxwell's original equations are scalar in nature
Oh. My. God.
No. Any Maxwell or Yang Mills is a gauge theory with A_\mu the gauge potential which IS A SPACETIME VECTOR that takes value in some adjoint representation of some group. For Maxwell this group is U(1) so the gauge field aka photons is a real valued vector.
> removed the scalar (time) component entirely
a vector is a vector. a scalar is scalar.
a vector transforms with rotations a scalar does not..
> Can anybody here explain why this is so important
it is not important. it is the dumbest things i heard in a long time.
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.
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.
No one "missed" black holes. There are obvious degenerate singularities that appear when you take a simple exact solution like the Schwarzchild solution past sensible physical reality by e.g. pretending conveniences like "point masses" really exist. It took decades of theoretical development to show that black holes were actually possible, and it was still very surprising that they turned out to observably exist.
He didn't miss the possibility; he just convinced himself that this possibility could not actually be realized, and published, IIRC, at least two papers giving his arguments for why. Unfortunately for him, both arguments were invalid.
> Schwarzschild immediately saw the obvious
No, he didn't. He did come up with the solution that is named after him, but he had no idea it described what we now call a black hole.
The earliest recognition and acceptance of the fact that the Schwarzschild solution describes what we now call a black hole (though that term wasn't invented until several decades later) was in the classic paper by Oppenheimer and Snyder in 1939 that describes the gravitational collapse of an idealized exactly spherically symmetric body with zero pressure.
It's a little unfair to Schwarzschild. He discovered his solution, the first solution to Einstein's equations, while serving in WWI and actually before Einstein published his paper on general relativity. Schwarzschild died just a couple months after his paper describing the solution was published.
How is telling the truth about what he did and did not do unfair?
> He discovered his solution, the first solution to Einstein's equations, while serving in WWI
Yes.
> and actually before Einstein published his paper on general relativity.
Before the official publication in 1916, yes. As I understand it, Einstein sent Schwarzschild a preprint and Schwarzschild based his work on that.
> Schwarzschild died just a couple months after his paper describing the solution was published.
Yes, and this was undoubtedly a tragedy.
None of the above, however, contradicts what I said, which is that Schwarzschild did not realize that his solution described what we now call a black hole. The post I was responding to said Schwarzschild "saw the obvious", meaning saw a black hole in his solution. He didn't. Nobody did until the 1930s.
> The Schwarzschild radius is the defining boundary of a black hole
In our modern understanding, yes.
> which Schwarzschild first calculated.
He calculated that there was a constant that appeared in his metric, proportional to the mass, and with units of length. But he had no idea that this constant was related to the boundary of a black hole. Of course he didn't have much time to explore his solution further, since he was killed not long after sending his paper to Einstein. It's an interesting what if question to ask what he might have found if he had had years more to do physics.
> why did Schwarzschild beat Einstein in calculating the Schwarzschild radius first?
Einstein wasn't working on the specific solution for the case of a spherically symmetric vacuum surrounding a mass. He already knew that, to a first approximation, this solution would look like Newtonian gravity, and that the next order correction terms would explain the extra precession of Mercury's perihelion (which had been observed in the 19th century) and would predict gravitational redshift and the bending of light by the Sun (neither of which had yet been observed). Einstein was more interested in deriving the general form of the field equation than investigating further the specific properties of that particular solution. Whereas Schwarzschild focused on that solution.
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.
Aren't you conflating black holes with singularities, here?
Questions about singularities, I would assume, are inherently non-scientific in the sense that it would be impossible to ever come up with testable predictions about their behaviour. However, black holes, as 'a region of spacetime where gravity is so strong that nothing — no particles or even electromagnetic radiation such as light — can escape from it' (definition ripped from Wikipedia), seem like a testable concept with some evidence for their existence.
Fuzzballs were first proposed as a consequence of superstring theory in 2002, so it would be quite a feat for a scifi author to have come up with them in 1977.
Not the same thing as a black hole. A black hole is a region of spacetime that cannot send light signals to infinity, i.e., bounded by an event horizon. In the simplest such models, there is a singularity inside the event horizon; but that does not mean every possible model with an event horizon must contain a singularity.
Btw, the problem Einstein and others of his time had was with the event horizon, not the singularity; the singularity did not become a significant object of study until a decade or two after Einstein died.
I'm guessing from these responses that 'singularity' has turned into kind of pop-culture term expressing the center of a black hole.
A singularity is just where physical quantities go to infinity. There are many singularities at the event horizon. For example, as you fall into a black hole and approach the event horizon the time of an observer a distance away begins to speed up and approaches infinity - the universe comes to an end before you actually reach the event horizon. Many unphysical things like that happen. These are all singularities.
Importantly also, the energy density of space-time approaches the plank energy and this is a region where general relativity and quantum field theory do not agree with each other. So we know the equations are non-sense in this region for sure.
> I'm guessing from these responses that 'singularity' has turned into kind of pop-culture term expressing the center of a black hole.
It's not a pop culture term at all. It's a precisely defined technical term in GR. Everything I said about it is taken from that precise technical definition.
> A singularity is just where physical quantities go to infinity.
Correct. (Although this itself is something of a pop science version of the actual technical definition. But it will do for this discussion.)
> There are many singularities at the event horizon.
Wrong. All physical quantities are finite at the event horizon. Your counterexamples are based on misconceptions which have been well understood and corrected in the GR literature for decades.
> as you fall into a black hole and approach the event horizon the time of an observer a distance away begins to speed up and approaches infinity
Wrong. If you are free-falling into a black hole, light from the rest of the universe is redshifted, not blueshifted.
If you are hovering at a constant altitude above a black hole's horizon, light from the rest of the universe is blueshifted; but the blueshift is finite for any altitude above the horizon. It is impossible to hover at the horizon.
> the universe comes to an end before you actually reach the event horizon.
Wrong.
> Many unphysical things like that happen.
Wrong.
> the energy density of space-time approaches the plank energy
Wrong. The black hole is a vacuum solution: the stress-energy tensor is zero everywhere.
> this is a region where general relativity and quantum field theory do not agree with each other. So we know the equations are non-sense in this region for sure.
Wrong. The area at which GR and QM create compatibility problems is within a Planck time of the singularity, not the horizon.
As I said above, all of these misconceptions have been known of and corrected in the GR literature for decades.
I didn't believe you so I looked this all up and indeed everything you said is correct. My GR professor was famously one of the worst academics at the department and he never taught us any of that. His specialty was GR too.
Anyway, your response was needlessly hyperbolic. The only two misconceptions you are correcting here is that tidal forces can be quite weak at the event horizon and the universe does not come to an before passing through it.
> My GR professor was famously one of the worst academics at the department and he never taught us any of that. His specialty was GR too.
This is disappointing, but unfortunately I don't find it surprising. I have learned GR by self study over many years, starting with borrowing my office mate's copy of Misner, Thorne & Wheeler when I was in graduate school; I never actually took a course in it. But the reports I had from people who did were that the professors did not do a good job of explaining things. Unfortunately being good at research and being good at teaching are two very different things and not many people have both.
> The only two misconceptions you are correcting here is that tidal forces can be quite weak at the event horizon and the universe does not come to an before passing through it.
I did correct those two misconceptions, but those weren't the only ones in your post.
There's no particular reason to believe the singularity in the math describing black holes has physical existence. Lots of equations have singularities and usually it just means that you're using them outside the domain in which they're defined.
Maybe some heretofore unknown force kicks in and keeps the material inside the black hole from forming a singularity. Maybe they're actually fuzzballs:
You don't really have to have a fully worked-out explanation of why the black hole singularities aren't physical- nobody can see inside the black hole, so all we can say is that the existence of black holes is consistent with there being a physical singularity in the middle. But really anything could be happening in there, we just don't know. The singularity the GR predicts is arguably evidence against GR holding at the center of the black hole; there's very probably something else going on.
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).
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.
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.
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.
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
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.
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?
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.
I did not mean that Einstein had a different intuition of time. It s pretty much impossible to derive an absolute spacetime from experience where time is monotonic. I wasn't talking about that, but about the ability of the brain to entertain and adopt counterintuitive notions in general. He was one of the few for whom this ended up being successful. He did know about the MM experiment but i wonder if that was the primary motivator for his hypothesis.
For all we know, Einstein did not “entertain and adopt counterintuitive notions” of time and space at an intuitive level. He just had the right perspective, used the right math, and was just as amazed by the physics that came out of this as everyone else.
i m pretty sure if you ask people about something like the relativity of simultaneity , 100% of people who havent studied relativity will call it counterintuitive
Physics is full of concepts that are counterintuitive. Inertia is an early example of one such concept. But ideas are adopted based on their explanatory power, and one way you get places is with an ethos called 'shut up and calculate'. I.e., don't think too hard about the 'counterintuitive' nature of what the theories predict, crunch the numbers and figure out what the predictions are and leave the implications to the philosophers.
Once you accept that the speed of light is constant in all reference frames, relativity falls out from that. That in itself is a bit hard to accept, though, which was why it was some number of years between the Michelson-Morley experiment in 1887 and Einstein's paper on SR in 1905. GR basically also comes from 'shut up and calculate' after accepting the principles behind SR but adapting them to non-inertial reference frames (and also the insight behind gravity being a fictitious force), but the mathematics is much more complicated than SR, which I assume is why it took Einstein over a decade to work it out.
> Physics is full of concepts that are counterintuitive. Inertia is an early example of one such concept.
Huh?!? Try to start a car by pushing it -- or stopping it, even on flat ground, after it's gathered momentum rolling down some slope -- a few times, and inertia becomes utterly intuitive. I'd imagine that worked for medieval oxcarts, too. Or for moving blocks of stone for the pyramids, or Stonehenge.
Perhaps, but prior to Galileo (or perhaps Avicenna?), Aristotelian physics dominated and motion was explained by 'impetus' (this didn't originate from Aristotle, but instead came long after him). Aristotle distinguished between 'natural' motion, which is the motion of falling objects and 'violent' or 'unnatural' motion, which is caused by some agent (a human throwing a stone, for instance). In the theory of impetus, the agent imbues an object with some impetus, and this impetus is only ever temporary, the object stopping once its impetus is exhausted.
Today, sure, we know that friction is a force that acts against the momentum of a moving object, but these were alien concepts a thousand years ago.
The very idea of using the 1887 experiment from Stone Age to defend GR seems ridiculous. I understand why you are doing that: there are no modern experiments, which you can use to defend your point, but still. Moreover, interpretation of Michelson-Morley experiment as «it proves that physical vacuum does not exist» is frivolous. Let me quote Wikipedia:
> The Michelson–Morley experiment of 1887 had suggested that the hypothetical luminiferous aether, if it existed, was completely dragged by the Earth. To test this hypothesis, Oliver Lodge in 1897 proposed that a giant ring interferometer be constructed to measure the rotation of the Earth; a similar suggestion was made by Albert Abraham Michelson in 1904.
> the first interferometry experiment aimed at observing the correlation of angular velocity and phase-shift was performed by the French scientist Georges Sagnac in 1913. Its purpose was to detect "the effect of the relative motion of the ether".
> In 1926, an ambitious ring interferometry experiment was set up by Albert Michelson and Henry Gale. The aim was to find out whether the rotation of the Earth has an effect on the propagation of light in the vicinity of the Earth. The Michelson–Gale–Pearson experiment was a very large ring interferometer, (a perimeter of 1.9 kilometer), large enough to detect the angular velocity of the Earth. The outcome of the experiment was that the angular velocity of the Earth as measured by astronomy was confirmed to within measuring accuracy. The ring interferometer of the Michelson–Gale experiment was not calibrated by comparison with an outside reference (which was not possible, because the setup was fixed to the Earth). From its design it could be deduced where the central interference fringe ought to be if there would be zero shift. The measured shift was 230 parts in 1000, with an accuracy of 5 parts in 1000. The predicted shift was 237 parts in 1000.
So, Michelson-Morley experiment confirmed that physical vacuum is dragged with Earth, and then Michelson–Gale–Pearson experiment confirmed that it is not completely dragged by Earth. It far from «physical vacuum doesn't exist» mantra from «shutup and calculate» guys.
In this century,
* the existence of Higgs boson, which gives mass, and Higgs field, which exists at every point of our Universe, was proved in 2012;
* the existence of gravitational waves in physical vacuum is proved by LIGO/Virgo interferometers.
Thus, today we have Higgs field, which is presented at every point, which can be used as 0 point, but we cannot detect it. However, we can use CMB (light from distant galaxies with red shift z=1000) as 0 point.
> The very idea of using the 1887 experiment from Stone Age to defend GR seems ridiculous.
Previous comment about SR, although GR is a natural extension of SR for non-inertial reference frames.
> Moreover, interpretation of Michelson-Morley experiment as «it proves that physical vacuum does not exist» is frivolous.
The interpretation of it is that it proves the constancy of the speed of light. This is the case whether SR is assumed or Lorentz ether theory. The two theories result in identical predictions, except LET assumes the existence of an ether but without any way of detecting it.
> So, Michelson-Morley experiment confirmed that physical vacuum is dragged with Earth, and then Michelson–Gale–Pearson experiment confirmed that it is not completely dragged by Earth.
Michelson-Morley rules out a stationary ether, at least without length contraction which Lorentz added to attempt to repair the theory. Michelson-Gale-Pearson rules out ether drag. SR and LET are compatible with both experiments. Whether or not the ether is real is philosophical quibbling without a method for separating LET from SR.
> * the existence of gravitational waves in physical vacuum is proved by LIGO/Virgo interferometers.
This is one of the predictions of GR, so I'm not sure what your point here is.
> Thus, today we have Higgs field, which is presented at every point, which can be used as 0 point, but we cannot detect it. However, we can use CMB (light from distant galaxies with red shift z=1000) as 0 point.
> IMHO, relativity is not necessary at this point.
The Higgs field, just like other fields in quantum field theory, is a relativistic field; its Lagrangian is Lorentz-invariant.
> Previous comment about SR, although GR is a natural extension of SR for non-inertial reference frames.
Sorry, but SR is a special case of GR now, so not a big deal.
> The interpretation of it is that it proves the constancy of the speed of light. This is the case whether SR is assumed or Lorentz ether theory. The two theories result in identical predictions, except LET assumes the existence of an ether but without any way of detecting it.
Now we have LIGO and Virgo interferometers, which clearly shows that speed of light in pure vacuum is not constant.
Now we know that if we will put an interferometer into space, it will detect deviations in speed of light. (We know it as gravitational lensing).
Now we know that gravitational waves exist and are conducted by a medium (Higgs field/Higgs boson).
Now we know that gravitation is a bit faster than light, so photons are not flying on 100% of C, thus they are not immortal, so they are losing energy with time (Red Shift).
If you say that GR/SR is still valid, despite opposing results from experiments, then those experiments are irrelevant for GR/SR at all. Regardless of what experiment will found, scientists will be able to find a way to explain results in terms of GR. With enough number of constants, a formula can make paintings or generate music after all.
> Michelson-Morley rules out a stationary ether, at least without length contraction which Lorentz added to attempt to repair the theory. Michelson-Gale-Pearson rules out ether drag. SR and LET are compatible with both experiments. Whether or not the ether is real is philosophical quibbling without a method for separating LET from SR.
If we put a sail into a box, to test the existence of a wind, then we may find that there is no wind in the box, if the box is tight enough. It can be interpreted as «there is no wind, so no atmosphere, we are on a Moon», or it can be interpreted as «there is no wind in the box». IMHO, the second variant is valid.
For me, Michelson-Gale-Pearson experiment doesn't rule out drag. Fizeau shows that drag exists, but it works in heavy mediums. Physical vacuum is too lightweight to change the course of photon just by itself. It will work at the scale of the Solar system.
> The Higgs field, just like other fields in quantum field theory, is a relativistic field; its Lagrangian is Lorentz-invariant.
Nobody says that Higgs field is stationary. It expected that it will move and behave like any other field, with currents and gradients of stength. However, the average of Higgs field of our visible Universe can be used as a reference frame. I interpret CMB as light of distant galaxies with z=1000, so it can be used as representation of this average. For example, the Sun moves at a cumulative 369 km/s relative to the Cosmic Microwave Background (CMB) in direction 264°l, 48°b.
No, they say that arms are expanded and contracted, but this means that measured speed of light must c±delta, while measured speed of light is in c...c-delta range. AFAIK.
Moreover, if arms are just expanded/contracted, i.e. it's density wave, then gravitational waves and light from distant mergers should arrive at the same time ± few milliseconds, while light arrived 1.7 seconds later, i.e. light is slower by 1E-15.
Moreover, somebody told me that density wave is not possible for gravitation, because gravitons should be massless(of course) spin-2 particles. IMHO it a wave of flips or deflections.
Anyway, Higgs «field», which gives mass, exists, so a medium, which exists at any point of our Univers, exists, so gravitational waves are waves in a g-medium, which is connected to the Higgs medium somehow, thus, for gravitation, c is speed of gravitation in the medium.
For light, it should be same. I see no reason to say that c is the speed of gravitation in g-medium, while light propagates in pure nothing and c is the top speed in the pure nothing. Nonsense.
I agree, that for most calculations those details are unnecessary and can be avoided. However, existence of something is not depended on it necessity for us.
Moreover, AFAIK (I'm not a real scientist, so beware), Higgs «field» and medium for gravitational waves (g-medium?) are two different mediums, because Higgs boson is spin-0 and it gives mass, while graviton is spin-2 and is massless.
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.
>>“does it reduce to Newton’s Laws under non-extreme conditions”
Thomas Kuhn said something about this in his Structures of Scientific Revolutions.
<i>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.
</i>
<i>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.</i>
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.
https://arstechnica.com/science/2015/12/general-relativity-1...