Einstein's Other Theory of Everything
nautil.us
nautil.us
For clarity, here’s what I mean: if you flatten out some silly putty (or pizza dough should work) then pinch and twist together some of the sheet into a lump, that pulls along the surrounding putty. So, if you drew lines on the putty then pulled it into lumps, you’d see the distortion to the lines.
https://www.youtube.com/watch?v=wrwgIjBUYVc
This uses Adobe tools to visualize and take advantage of video format.
Why though? Would it help if the sheet were in a centrifuge?
It bothers me too, why? because it's circular reasoning: acceleration can't explain acceleration.
> Would it help if the sheet were in a centrifuge?
No, for the same reason. (You're imagining a tube-shaped membrane?)
To make it worse, it's developing a wrong idea that hides the right and deeply strange idea: when an object passes a mass and its path seems to deflect what's really happening is that the object is moving in a straight line the whole time and space itself is curved. (The situation is actually a little stranger than that, but I'm no physicist so I won't try to explain any further.)
And anyway explaining gravity v2 in terms of v1’s first approximation isn’t that strange when recursive definitions are going to play a part in lots of higher education anyway. When you’re a kid, 5 is just a concept useful to describe every instance of 5 apples, but later, a number N is perhaps best understood as the successor of N-1.
The actual description of gravity isn't hard to understand, it's just really strange. There is no good reason to introduce confusing and intrinsically incorrect models.
Well, teaching is the usual reason, otherwise physics with trig would all just wait for calculus, and calculus wouldn't get covered before real analysis, etc. Incorrect, or more charitably "useful, prerequisite, & intentionally not rigorous" models are a pretty standard tool for walking students closer to real understanding. Clearly no one is proposing trampolines and bowling balls models because they are expecting to win a Nobel.
> The actual description of gravity isn't hard to understand, it's just really strange.
Hmm, Einstein thought it was pretty hard, and I didn't know that you and Witten had finished quantum gravity or the other latest and greatest.
> Gravity is one of the fundamental forces, there's no recursion in it's definition, indeed we don't "define" it we describe it.
Unpacking this to a first approximation it actually sounds like you're looking for The Truth instead of useful models, that you always know Truth when you see it, that you don't believe that apparently different descriptions can result in formally equivalent stuff. I'm also guessing that you might be strongly inside a "only cares about math because physics" camp whereas I sympathize more with "only cares about physics because math". Lots of interesting conversations in there, but it'll all just be philosophy at that point anyway and you probably wouldn't like it.
> Well, teaching is the usual reason,
Introducing confusing and intrinsically incorrect models is the opposite of teaching.
> "useful, prerequisite, & intentionally not rigorous" models are a pretty standard tool for walking students closer to real understanding.
The funnel model of gravity isn't useful, prerequisite, or rigorous.
> Unpacking this to a first approximation it actually sounds like you're looking ...
A bunch of projection on your part follows.
I'm sorry to be rude, but to me you seem to be intelligent yet deeply confused.
I'm going to bow out of this thread now, again I apologize.
until we crack it.
It's fun to try to peel away defects in the "ball on a rubber sheet" in an effort to arrive at Newtonian limit equations of motion for balls in placed around it. (First advanced question: how do we adapt Einstein-Hilbert to reflect trapping onto the sheet? Does dimensional reduction work?) What sort of membrane in constant acceleration could generate scaled 2+1 timelike geodesics for model solar system objects placed on it? Can one scale this to a model of the solar system with all orbits flattened onto the membrane? For instance, what do the IVs look like for a ~ 1050:1 mass ratio between a model sun and a model Jupiter that is shrunk down to classroom size and retains a good match to Jupiter's real orbital parameters (or if you prefer, lengths and angles) across many orbits? Without destroying this scale model orbit, can we add the inner solar system? Can we get sensible orbits of scale model Galilean moons?
(And of course all of the above has completely neglected the rotations of these bodies about their axes, which is clearly always very wrong with a typical in-classroom rubber sheet + balls demonstration. We can blame friction for that.)
I'm not sure what you're representing on silly putty: are the drawn lines solutions to geodesic equations? What would the twists-pulls of the putty in a scale model ~kg:g Sun and Jupiter system look like? Or are you thinking about a relativistic regime somewhere in the right half of this diagram : <https://en.wikipedia.org/wiki/Post-Newtonian_expansion#/medi...> ?
The balls on a rubber sheet model is actually really great, but not in the way it's typically presented (rolling a ball down the curvature). Instead, just use a pen to draw lines to show the concept of geodesics.
Start like this:
1. Imagine that you can move without friction if you stay at the same vertical level.
2. Draw a line on a flat rubber sheet, that's a line in free space. It's just a straight line that can go on to infinity.
3. Now put a ball onto the rubber sheet, so you get some curvature. Now the lines near the ball that stay on the same level are not straight lines, but circles.
Ok, you brought in the "g" word. I think that makes it fair to ask how you plan to calculate the analog of spacetime intervals along your rubber sheet.
The general curves (not just geodesics) down to the heavy central ball all end up where the ball and sheet are in contact unless blocked by earlier contact with the central ball. How do you recover anything like the behaviour of a smaller ball bound to a non-spacelike radial geodesic with one end normal to the central ball's surface and the other "at infinity" (or at least in the part of the sheet that is asymptotically parallel to the ground)?
How do we show students, using your adapted rubber sheet, that spacetime curvature around a spherically symmetrical mass is symmetrical in all the spatial dimensions and that there is a curvature induced on the timelike dimension too.
What's the relationship between your pen lines and the Christoffel symbols (notably \Gamma^{1}_{00}) or Euler-Lagrange?
How does your "3." work with highly eccentric elliptical orbits? How about a grazing hyperbolic orbit? Think Halley's comet and 1l/`Oumuamua.
Describe it as an artistic representation of the theorized behavior.
Pull a Maxwell, whose theory of electromagnetism only worked when he got rid of the imaginary levers; get rid of descriptions in terms of physical things.
As a visual it’s fine. The debate here is the language. Only one aspect needs to change.
I like to imagine a sponge. If you could somehow make dense lumps inside the sponge (may be apply heat in its center somewhere using microwaves?) everything around that lump will be feel a tension/attraction towards that lump. That's my mental model.
When you see those stretched rubber sheets, they rarely/never show the grid lines moving. So let's say you place a small *stationary* object at a specific grid point (coordinate), and there's a large object that deforms the grid itself. Nothing about that visual provides any new intuition about why the small object would leave it's current grid position and move towards the larger one.
The visual tries to explain gravity by appealing to your existing notion of gravity.
Afaiu, the answer is that moving through time in a gravitational gradient makes you constantly “fall flat” on an x/time 2d graph due to time dilation gradient, thus affecting x and spatial momentum. Apparently mass affects time and time creates gravity. Idk if that’s a fringe idea or mainstream.
"using gravity" in the experiment is convenience of the experiment - gravity is freely abundant to use, both as a source of curvature and source of "making objects not leave the sheet"
if you want to hold the sheet by yourself, and hold the objects to the sheet by yourself - you are free to do it, enjoying your victory of "not using gravity"
but the point is not in the means, but in the end - create curvature, keep contact
An inert object will sit on it kissing it and never go anywhere. The curvature of a sheet doesn’t matter cause there’s no “down” and no forces. If you push it “in” a little and release, the sheet tension will push it back out but not “to” the well. You may start accelerating the system to create gravity-like situation, but that’s the point.
These models are also an intuitive way to illustrate why the speed of light is a limit.
A ball rolling on a rubber sheet, or a boat on a lake, etc, can travel faster than waves in the rubber or water. So why can't matter travel faster than light? With ball-on-sheet type models, you need to resort to abstract relativity arguments about mass going to infinity, time slowing, causality, etc.
But if particles are actually just waves or knots or whirlpools or whatever, they clearly can't possibly travel faster than the speed of waves in the medium.
Maybe matter didn't crack because the right tools weren't available.
And also Poincaré getting close to it.
Others may have gotten close to one of these solutions, but nobody else came anywhere close on all three.
General Relativity as his own research programme was designed to capture the consequences of constraining the speed of propagation of changes of gravitational influence; it was literally about relativizing gravity. GR was not designed to explain Mercury specifically (or even really motivated by Mercury), the theory just happened to explain why its orbit traces out a daisy-like pattern rather than a perfect ellipse. GR also correctly predicted a deflection of background starlight around the limb of the sun (1919 eclipse and eclipses since), stellar gravitational redshift (Sirius-B initially, many many objects since), and gravitational redshifts induced by Earth (all reliable results were posthumous: Pound-Rebka and similar since 1959, and more recently precision lunar and satellite ranging).
Indeed, Einstein liked to explain that his mental toy in understanding relativistic gravitation was someone jumping off the roof of a house, or the behaviour of things (e.g. flashlights/torches) riding in office-tower elevators/lifts (which date from the 1870s). That's a far cry from precision measurement of Mercury's perihelion!
There were no real astrophysical or terrestrial problems calling out for General Relativity. Even after General Relativity was a published theory, real gravitational problems were solved with low-order correcting terms to Newtonian gravitation and with linearization: an approach which Einstein practically invented, and which he used himself when thinking and writing about early problems in cosmology (the discovery of Cepheid variables opened up a lot of those).
There were quickly alternatives to General Relativity which predicted some but not all of these early classical tests of the theory. Eddington's 1922 book was the first shot in a body of literature analysing different theories of gravitation and how they differ in their predictions of dozens of tests of General Relativity. Will's work in particular is useful: https://en.wikipedia.org/wiki/Parameterized_post-Newtonian_f... -- you can see how it's used in practice in this open access paper https://www.nature.com/articles/s41467-017-02558-1
That said, there are mathematical tools available now that weren't available to Einstein in the early 20th century, and he might have chosen to arrive at a different (but equivalent) formulation of General Relativity. The standard Hamiltonian and a variety of modern Lagrangian formulations are particularly useful, and it could have been nice to have had <https://en.wikipedia.org/wiki/Initial_value_formulation_(gen...> before the 1960s (even though it arguably only shines brighter when you have 21st century supercomputers).
Indeed, one can imagine Einstein starting with Lie theory, such that Special Relativity from the start is just the theory of spacetime with SO(3,1) symmetry at every point. But Cartan, Killing, and Noether came decades later and were motivated by Einstein. And quite a bit of group theory developed as the Standard Model developed after Einstein was already dead (notably Goldstone's theorem, 1960s). So to first formulate General Relativity as a GL(4,R) group theory with spontaneous symmetry breaking to SO(3,1) one would need to rearrange an awful lot of physics history.
Any of these alternative-universe mathematical origins would just have been using different tools to arrive at the central result: we inhabit a Lorentzian spacetime in which there is an exact matching of moving matter and a metric tensor (at each point in spacetime) encoding durations, spatial lengths, and angles, or the equivalent set of orthonormal vector/covector fields.
And worse, the physical content of the theory -- however formulated -- probably would still have been considered interesting but practically useless until the 1970s.
Something I don't understand about GR is whether Einstein had real, empirical evidence to guide him or whether it all just sprang fully-formed from the world of ideas into his waiting mind. I know about his thought experiments, but those are, well, thought experiments. Did he have concrete observations to base his theory of GR on?
Forgive my lazy approaches to citation and linking below. I didn't have much time, and ran into the realization that you and I are probably the only HN users who will ever read this.
> concrete observations
No, certianly not. As far as I remember all of the early tests of post-Newton/pre-GR but "relativity compatible" gravitation were motived by sketched-out systems in Einstein's 1907ish-1912ish writings, with the observations and experiments taking place years later.
> base his theory of GR on
The entire programme of Einstein gravitation started from purely theoretical considerations, starting with thoughts about accelerated bodies in special relativity and relativistic ballistic bodies (which aren't accelerated beyond the initial impulse: c.f. Newton's cannonball (1728) -- ignoring friction a cannon ball's descent back to the ground is free-fall so the motion in free-fall must therefore be inertial, and in fact the whole trajectory up and down, or into orbit, or out to infinity after it is shot out of the cannon must be inertial <https://physics.weber.edu/schroeder/software/NewtonsCannon.h...>).
General Relativity certainly didn't spring fully formed from Einstein's mind -- it took about eight years for him to develop the ideas and mathematics along the way.
"Doc" references below are to translations of his early papers at https://einsteinpapers.press.princeton.edu/vol2-trans
(It's also handy to see how interested in diffusion and dissipation -- and thermodynamics more generally -- he was before his famous Brownian motion paper, 1905, Doc 16.)
Relativity, 1905 (Doc 24 ("Does the inertia of a body depend on its energy content?"))
First articulation of equivalence principle (observers in free-fall are in inertial motion), 1907 (Doc 47, "On the relativity principle and the conclusions drawn from it"; this is practically a short textbook and is awesome in total, but for your question the relevant bit is in part V, starting at the bottom of p. 301 (direct link because pagination is often weird on the site) <https://einsteinpapers.press.princeton.edu/vol2-trans/315>).
A choice quote: from the end of part V §19: 'There exist "clocks" that are present at locations of different gravitational potentials and whose rates can be controlled with great precision: these are the producers of spectral lines. it can be concluded from the aforesaid that the wave length of light coming from the sun's surface, which originates from such a producer, is larger by about one part in two million than that of light produced by the same substance on earth.' (Footnote 1 is also interesting for noting that his initial thinking was about a uniform gravitational field, which does not exist in nature, and thus he was forced into assuming that his thinking also applied in a more realistic gravitational field; this was well before he started developing the mathematics of General Relativity in 1911-1915 and of course also before Schwarzschild 1915).
Such a small spectral shift was untestable in 1907; it took until 1959-1960 (Pound-Rebka experiment, "Apparent Weight of Photons") and the 1970s (Harfle-Keatin and Gravity Probe A) to demonstrate and measure the effects of Earth's gravitational time dilation.
Now we advance a few years to 1911:
https://einsteinpapers.press.princeton.edu/vol3-trans
and in particular Doc 23, "On the influence of gravitation on the propagation of light"
There is a lot of interesting stuff in that paper, including an early rough estimate of the deflection of light around the sun and Jupiter. However it's important to note that there are no tensors and no (pseudo-)Riemannian geometry in the 1911 paper: the theory with those (and the general covariance and curved spacetime they encode) was still about four years away. His light deflection estimates were illustrative of generic effects in any sort of principle-of-relativity-compatible gravitation (again, he was personally in no position to be thinking about a geometric theory, not yet having started learning differential geometry) rather than serious predictions, let alone existing observations that he needed to capture.
It is really only after 1912 that Einstein begins developing a description of gravitation in terms of curved spacetime. By then there were several observations (motivated by Einstein's pre-GR work!) showing that Newtonian gravitation becomes inaccurate near the sun, with Newton's formulation (and also Poisson's and Gauss's and other equivalents) proving difficult to adapt via correcting terms.
So: SR first; then thoughts about accelerated v freely-falling observers where relativistic effects are expected, including some thought experiments and some sketches that could be weakly checked by astronomy; becoming convinced that non-Euclidean geometry could represent some of these effects; then learning (and developing) relevant mathematics; then GR; then modelling systems and predicting behaviours using GR; then early precision astronomical and eventually (and sadly, posthumously) laboratory tests of those.
It's possible to imagine that astronomical discoveries could come before a fully non-Newtonian theory of gravitation. Let's omit General Relativity and the early work in the 1920s-1930s, the theoretical developments of General Relativity from the 1950s&1960s, and more (thanks to computers) in the 1980s, but keep the dates of astronomical discoveries. We then wonder how what we realized were "manifestly relativistic" astrophysical systems would have been dealt with by theoreticians.
The "Newtonian gravitation needs to go" trigger would probably have been clearly non-Keplerian orbits like pulsar+other binaries (Hulse-Taylor, 1970s; the orbit is contracting/speeding up) precision studies of stellar orbits in the Milky Way's central parsec (1990s; there is an unseen compact mass distorting the innermost stars' orbits), or could have come as late as the discovery of PSR J037-3039 (a two-pulsar binary, 2003) or PSR J30337+1715 (a pulsar a close binary with a white dwarf and with another white dwarf orbiting the central pair, 2007, which has been used to test the strong equivalence principle). However, in our history, predictions of "highlight" aspects of these astronomical oddities date from early work with GR in the 1920s and 1930s.
Another trigger could be compelling evidence for the non-ballistic trajectories of distant galaxies, which started racking up in the 1990s. Einstein and others toyed with an accelerated expansion in the late 1920s-1930s (that other galaxies were distant was freshly discovered then), and rejected the idea for want of astronomical evidence.
In all of these, with some thought, a pattern would emerge: in all these systems there are orbits or trajectories which appear to reach velocities comparable to the speed of light. Corrections in powers of v/c might seem obvious. However, with our real history, Einstein was doing this in about 1916 or so, because it was easier to calculate orbital evolutions that way, and the approach was (allegedly) easy to extract from (or trace back to) GR. I wish I had a handy reference for that. Perhaps some proper historian of relativity will update <https://en.wikipedia.org/wiki/Post-Newtonian_expansion#Uses>.
Likewise linearized gravity captures the speeding-up of orbits implying the loss of non-electromagnetic energy radiated out of the binaries/triples/central parsec as gravitational waves. It is somewhat easier to relate to GR than expansions in v/c. But what form would early theories take when thinking about the decay of the Hulse-Taylor orbit?
>> So: SR first; then thoughts about accelerated v freely-falling observers where relativistic effects are expected, including some thought experiments and some sketches that could be weakly checked by astronomy; becoming convinced that non-Euclidean geometry could represent some of these effects; then learning (and developing) relevant mathematics; then GR; then modelling systems and predicting behaviours using GR; then early precision astronomical and eventually (and sadly, posthumously) laboratory tests of those.
From this I take that Einstein was mainly a theoretician, which is perhaps a little bit surprising. It is to me, because I have an idea of physics as a discipline with a very strong empirical component.
In the AI and machine learning community there is a bit of a debate about the lack of a theory of intelligence, or artificial intelligence, to guide research. Turing award winner Yann LeCun for example has argued that a theory is not necessary because very often technological advances precede theoretical understanding. He's used the Wright brothers as an example and claimed there was no theory of aerodynamics before their first powered flight, but I think he's wrong about that: George Caley set the foundations of aerodynamics a good 100 years before the Wrights.
I asked my question just because I was curious but as I was reading your answer it occurred to me that it is relevant to that debate, that I'm very interested in (and have my own strong opinions about). Einstein comes across as a powerful example of how far a dedicated, competent theoretician can go without a need for empirical results. A little bit scary to be sure, and certainly a lone theoretician plugging away at a theory on their own will not go very far, there needs to be the right environment, a scientific community that can properly evaluate such work. In any case, despite what LeCun says I am convinced that there can be no true scientific progress without theoretical understanding. Even if empirical results come first, we only really make progress when our understanding of the world improves. But all that is a bit political; apologies if you find that disagreeable.
And now I wonder whether Einstein was really one of a kind, as we're taught since school. There must have been others, other physicists, and possibly astronomers, who made progress only based on mathematics and theoretical understanding, and didn't have direct empirical confirmation of their results for a long time; or possibly never -because those results were confirmed after their death; yeah, sad for uncle Albert :( .
Thanks again for your erudite and thorough reply!
> Clearly this is a subject of passion to you
Not exactly - the passion here is for physical theories of gravitation, with a side helping of obviously unphysical uses of gravitation (e.g. spacetimes with arbitrary numbers of dimensions), and wrong theories of gravitation. This thread was more history of science, which isn't a passion. It's just that I've read a lot of 20th century scientific papers on gravitation, which are often interesting but rarely of practical relevance.
(It also goes into "metahistory" of science or metaphysics or whatever which is even less of a passion, so I'm afraid I won't engage with your summary of LeCun. I'm not familiar with him (yes I know, it's HN, but...), there's no obvious overlapping expertise. I'm not sure I'd get it right if I were to comment much more on the relativist/astrophysicist "dance" I mention below, and I simply would not know what I'm talking about when it comes to AI, computer vision, etc.)
> Einstein was mainly a theoretician
Yes, very much.
We can tie this to the article at the top: late in his career he pursued theories which didn't bear fruit for one reason or another.
In astrophysics and physical cosmology there has been centuries of "dance" between theoreticians and experimentalists -- sometimes, the former have 'go look for this particularly' ideas which can pan out; sometimes the latter produce a 'huh, we weren't expecting and can't explain this result'. Theory and observation co-evolve.
Again, though that goes into the history and philosophy of science more broadly, and that's too far from my island of comfort. There are many many HN commenters who will share their thoughts on this stuff quite readily.
> whether Einstein was one of a kind, as we're taught since school
He was, but it doesn't really matter -- he died before there were tools for theoreticians like supercomputers, before the cosmic microwave background was discovered, before neutrinos were observed in a lab, before ultra cold atomic gasses could be made and studied in a lab, before the first practical atomic clock, before the discovery of astrophysical masers, before the first lasers, and so on and so forth, before CCDs, before good slew studies of the "variable universe" <https://www.astronomy.ohio-state.edu/asassn/index.shtml>. Some of this stuff would probably have been harder to invent without his photoelectric effect paper (for which he got the Nobel prize in physics) or special relativity. But if all those tools and techniques had been around when he was at his most intellectually productive, it would have been interesting to see how he would have adapted his thinking, and what he would have chosen to work on.
(Not to mention that scientists can collaborate with one another much more easily these days, and don't have to wait for access to experimental results as long as before there was the Internet. Just the way he would do things now day-to-day would be incredibly different. It's really hard to imagine being stuck with the long long lonnnnnnnnnng waits he had to put up with, but on the other hand he wasn't distracted by streaming entertainment, computer games, social media, etc etc, and had more time to fill as a result -- notably while travelling via HORSE (!), train, and ship to academic conferences, instead of flying or being remote.)
> There must have been others
Sure, physics and the mathematics of physics are totally littered with surnames like Gauss, Laplace, Lagrange, Lorentz, Poincaré, Newton, Leibniz, Galileo -- many of them were "polymaths" that studied many areas of science and even many non-scientific things (for example: economics, social sciences).
By comparison,Einstein stuck to his three lanes (thermodynamics, quantum theory, and gravitation), writing down theories that used groundbreaking formulae and theories named for / developed by all of the above and more.
Interestingly, one experiment/invention of Einstein's that I do know (there may be others; I just deal in theories he developed alone and with collaborators) came from his interest in thermodynamics: https://en.wikipedia.org/wiki/Einstein_refrigerator
I would imagine Einstein would have been interested in the cooling of electronic equipment and especially computers, had he lived into the 1980s. He also would likely have been interested in computer display technology (CRTs use and LEDs/OLEDs are related to the photoelectric effect) and digital photography (which has uses in astronomy, obviously).
> A lone theoretician plugging away on their own
is pretty rare, since it is so easy to get feedback from other theoreticians, results from experimentalists, and so on. There are many single-author theory papers still, but they generally aren't written by recluses.
Einstein certainly didn't work in a vacuum, particularly when it came to General Relativity and his later Grand Unified Theory work. He got help from mathematicians and published a number of papers with coauthors.
Finally, because he didn't work in a vacuum it is safe to say that if he were suddenly resurrected today with all his previous memories intact, he would have a lot to catch up on to be able to make sense of most papers in quantum mechanics and gravitation. He'd have to learn how to browse the web safely; he'd have to pick up some LaTeX and probably a bit of computer programming. These are all things a modern physics student will pick up no later than their first year at university. There's quite a lot of graduate-level stuff in regular use that postdates Einstein too, that he would have to become familiar with. I'm pretty sure he would still be productive and even prolific very quickly, but he would need help from others practically right away. (That wouldn't be alien: he had help from Hilbert, Levi-Civita, Noether, and many others, during his career).
No matter how expert one is in one's "silo", there will always be people much more expert than you in other fields, even closely-related other fields. And even in your "silo" you won't always be preeminent (and even then can learn from others).
To clarify, I didn't think that Einstein was "A lone theoretician plugging away on their own", that was a more general stereotype and kind of hypothetical. My understanding is that even in his time Einstein had ready enough access to others' work and there are at least two famous results of his collaboration with Podolsky and Rosen I'm aware of. It's an interesting question how differently he would have worked in today's world. Even the idea of scientific research is very different today than in his time. I don't reckon he had to spend so much time writing grant proposals as modern senior academics, for instance (fortunately I'm just a post-doc at this point, but I observe the effect it has on my PI; basically, their research career is over. Which is where I come in I guess. Bit of a digression this).
>> (It also goes into "metahistory" of science or metaphysics or whatever which is even less of a passion, so I'm afraid I won't engage with your summary of LeCun. I'm not familiar with him (yes I know, it's HN, but...), there's no obvious overlapping expertise. I'm not sure I'd get it right if I were to comment much more on the relativist/astrophysicist "dance" I mention below, and I simply would not know what I'm talking about when it comes to AI, computer vision, etc.)
I appreciate this. I, too, don't try to have an opinion about everything and anything and prefer to stick to my area of expertise. There are enough different disciplines in AI research that I can probably keep learning until I'm dead; which is what I intend to do.
Thank you for the conversation and I appreciate also your kind deviation from the matters of your immediate interest. It has been a pleasure to read.
“Creating” is a vague(r) term, do you mean “quantization”? Afaik the open-loop geometry of fermions is something any quantization scheme has to start with, the details are how one includes gravity, so without more details, one wouldnt be able to tell how LQG is different from string theory :)
As it happens with so many cool ideas it did not germinate something useful.
Edit: edited after 57 minutes - pedantic nerd here :)
Well, at least, not so far.
The lack of news from the "deep" frontiers of fundamental physics might end tomorrow or might last a millenium. Its impossible to tell.
The pace of our increasing understanding of universe is not particularly predictable beyond these periods that benefit from simple scaling rules (ever bigger detectors etc.)
I can only barely understand the explanation for things like monstrous moonshine, but I’m with Conway on this stuff anyway.. there has to be a reason, it can’t just be a coincidence. Or in more classical terms, maybe nature abhors a vacuum, but not in the original sense. Lots of math is just too cool to not use somewhere.
She is a real physicist and not a kook, but she has been criticized for presenting her views (e.g. superdeterminism) as having much more acceptance than they actually do. She ignores and misrepresents counter-arguments regularly. Her ideas about, e.g. the explanatory power of entanglement wrt processions of moons around (IIRC) Jupiter are certainly well outside what I’d describe as regular astrophysics.
The golden standard of science communication was set by Sagan, and he always carefully pointed out when he was expressing a personal opinion, as opposed to one shared by the majority. Sabine Hossenfelder is no Sagan.
So proceed with caution. :)
As far as criticism goes, I appreciate how professionally you stated this PSA. Most don't make the same points as gracefully. Best of luck with your studies.
Some claim matter falling into a black hole never really does from the point of view of an outside observer. I've seen weird sounding descriptions like it "spreads out over the surface". What if electron orbitals are some kind of equivalent to that?
When I ask these (admittedly naive) questions, physicists will usually say something like "oh you have to treat that with quantum mechanics". But why? Isn't trying to resolve it using more conventional means (including concepts from relativity) a good idea? I feel like it's not right to reject one approach simply because nobody has figured out how to make it work while another does. That's different from showing that it can't work. Or have such approaches somehow been categorically proven inviable?
Only in Newton's mechanics. With special relativity, it'll approach the lightspeed.
> Some claim matter falling into a black hole never really does from the point of view of an outside observer. I've seen weird sounding descriptions like it "spreads out over the surface".
It doesn't. To an outside observer, the object falling towards the black hole just becomes progressively dimmer and more red, until it disappears.
I have heard both answers. It's spread out over space and is not like the classical pre-Bohr models, but it's described by a classical wave equation, and can be viewed at as a differential equation solution; a function over 3D space (For a time snapshot; or 4D spacetime with rotating phase). In this definition, you are not doing quantum mechanics until dealing with things like anti-symmetry, spin statistics, exchange interactions etc.
Quantum mechanics successfully explains why the electron does not collapse: because its time evolution is given by the Schrödinger equation. Unlike your idea, it even correctly produces the energy level of the ground state and everything to an astonishing degree.
Quantum mechanics is arguably the most correct theory we ever had, so ignoring it and trying to find an alternative approach is extremely unlikely to work. People may start listening if you can also produce the correct energy level of the ground state.
Not in atoms, no. But I mentioned scattering, which is a different scenario.
It explains the case where an electron and a proton scatter off each other and do not form a bound hydrogen atom.
No, it won't. A correct relativistic analysis of the relative motion of the electron and proton will show their relative speed never reaching c, let alone exceeding it. You can't just plug numbers into Coulomb's Law for this case, because Coulomb's Law by itself is not relativistically correct. You need to use the full Maxwell's Equations and the relativistic Lorentz force law.
> So that's an event horizon due to a different force.
No, it isn't. No force in the relativistic sense produces an event horizon. In relativity, gravity is not a force, it's spacetime geometry, and so is an event horizon in spacetimes where one is present.
> physicists will usually say something like "oh you have to treat that with quantum mechanics".
They are correct in the sense that once the electron and proton get close enough together, classical relativity and Maxwell's Equations are no longer a good model. But as above, you don't need to do that to realize that your claim about reaching the speed of light is wrong.
Sorry if this is a bit pedantic, but as someone trying to study this at the moment, I don't see this the same way and I'd like to validate my interpretation: You can just plug numbers into Coulomb's law, that part is correct. But then the problem of infinite velocities comes from interpreting the 'F' side of the equation, assuming Newton's law (F=ma), rather than using its relativistic counterpart.
Coulomb's law: F = qq'/r^2
Lorentz force law: F = q(E + mu x B)
For the 2 particle case, both of these say the same thing (substitute into the Lorentz eq E = q'/r^2, B = 0 and you get the same thing).
The promotion from non-relativistic to relativistic mechanics is a change of what 'F' means.
nonrelativistically: F = p' = m v' = m x'' = m a
relativistically: F = p' = \gamma m v' = \gamma m x'' = \gamma m a
where \gamma is the Lorentz factor.
Interpreted this way, infinite velocities are avoided.
But, as r->0 we still have an infinity problem - namely infinite energy! This necessitates a quantum mechanical correction to both the Coloumb and Lorentz laws.
TLDR: relativity is necessary when things start to move 'very fast', qm is necessary when things are 'very small'
In the fundamental quantum field theory picture you don't even have forces and particles in the original sense anymore. The dynamics are then described by interaction between the em field and charged fermionic fields. Stuff like Coulomb's law (or any other force potential) only emerges as a macroscopic low energy approximation for specific field configurations.
Looking further a redefinition E is necessary when including the \beta factor [2]. So that was a mistake on my part - relativity does change the rhs of Coulomb's law.
Admittedly the problem as stated (two particles falling towards each other) constrains things in such a way that there is no off-axis contribution. Or to put it another way, 1d electromagnetism doesn't have magnetism.
[1] https://physics.stackexchange.com/questions/142159/deriving-...
[2] https://en.wikipedia.org/wiki/Coulomb%27s_law#In_relativity
Only if the impact parameter is exactly zero. But that is an extremely unlikely edge case.
It doesn't even hold in ordinary QM (because there are no point charges anymore, only charge densities) and it fails completely in QFT for interacting fields. What you linked is an intro example from many textbooks that shows how the tree level diagram in the nonrelativistic limit can indeed yield the Coulomb potential. At the tree level you will often see such "classical" behaviour. But if you consider higher order corrections, the picture changes rapidly. See the Uhling potential for a practical example, but for higher loops this gets analytically intractable very quickly. The world starts to work very differently once you reach these length scales.
In general I think it's fine to use Coulomb's law as an approximation in this case because the proton is much heavier than the electron and so we can just stay in the proton's reference frame and let the electron fall in from infinity (and we're ignoring QM and just doing relativistic EM here). We could also switch to a tritium nucleus and make it a bit better of an approximation, or indeed add a whole bunch more neutrons and get lucky that they don't beta decay to make it an arbitrarily good one. It is true that if the proton starts moving that you will no longer have a pure Coulomb field with respect to the original reference frame, as after a Lorentz boost the E field gets squished into the transverse direction somewhat, and you'll gain a B field swirling around the proton...
Staying with the frozen proton approx, if we plug numbers in we get quite a bit of energy: set the proton radius r_p to 1E-15, and we get U = q_e^2 / ( 4 \pi \eps_0 r_p ) ~ 1.4 MeV, or a gamma of about 4, so yeah, it would be moving faster than c if we stayed with Newtonian mechanics. But there's another wrinkle: the 1.4 MeV of liberated potential energy won't all go into the electron's relativistic kinetic energy, because it is accelerating like crazy, especially in the final femtometers, and that acceleration (essentially Bremsstrahlung, although its not braking here) will generate an intense pulse of EM radiation as well - a decent fraction of the 1.4 MeV will go into that instead. You could perhaps estimate how much using the Larmor formula (in general calculating this radiation reaction force precisely becomes very complex, because the excitation of the EM wave modifies the acceleration, which modifies the excitation of the EM wave etc... And, now looking on Wikipedia, I'm not surprised to see that the first QM version of the calculation was done by Sommerfeld).
So yeah, the electron will zip through the proton, with much of the potential energy converted to an EM pulse that zips off to infinity, and so the electron is now bound to the proton, and will continue to zig zag back and forth, emitting more radiation until it comes to a rest inside the proton. So yeah, we do need QM after all.
This is extremely unlikely unless the relative motion is very slow, or, to put it another way, the total center of mass energy is very close to the rest energy of electron + proton, so there is a significant probability amplitude for capture into a bound hydrogen atom.
The post I originally responded to was obviously not considering such a case since it claimed the electron could exceed the speed of light.
Even if that's true (I'm not sure it always is--see below), that case is extremely rare. A much more common case is Bremsstrahlung, which you mentioned upthread--and as the Wikipedia article you referenced notes, the electron in this process starts out free and remains free after the radiation is emitted; it does not become bound to the proton.
> My reading of phkahler's original statement is that the electron will wind up going faster than the speed of light (which is incorrect, due to gamma) due to falling down the potential well, and not due to having non-zero kinetic energy at infinity...
That may have been the original intent, yes (and, as you note, it's wrong because it neglects the gamma factor). However, even in that case, what matters is not the electron's energy at infinity in the proton's rest frame, but its energy in the center of mass frame. If the electron is really falling in from far enough away that the relativistic gamma factor is relevant, which is what was implied by pkahler's original statement, then its energy in the center of mass frame (or more precisely the center of momentum frame, since in relativity you have to take momentum and energy into account) will be relativistic, i.e., large enough that it's by no means guaranteed that it will emit enough energy in radiation to become bound to the proton.
Not if you want to get correct answers in problems that involve moving charges.
> relativity is necessary when things start to move 'very fast'
In electromagnetism, relativity is necessary whenever charges are in motion. Whether or not they are moving "ver fast" is irrelevant. Coulomb's Law is only valid when you have a charge at rest.
That said, the post I originally responded to obviously was talking about charges moving "very fast" since it claimed an electron falling towards a proton could exceed the speed of light.
Now you can get quite good at predicting where you will end up after a while, and even be able to remember how to get places. But does that mean you are thinking 4 dimensionally? No, you’re still thinking in 3 dimensional shadows.
I get the feeling that is analogous to what happens when you try to do what you’re describing.
Such claims are wrong. The correct statement is that the outside observer never sees the matter reaching or falling inside the event horizon. But that's not because it never happens; it's because the spacetime geometry prevents light emitted at or beneath the horizon from getting back out to the outside observer.
In some ways, yes, but none of that changes the particular thing I said about BH physics.
A big if indeed, but if that hypothesis is correct, then the GR solution that applies is no longer the standard black hole solution. The "firewall" is not vacuum--more precisely, it does not have a vanishing stress-energy tensor. Which means "the intuition one builds from a pure GR understanding" for the "firewall" case will need to be a pure GR understanding of a different solution from the standard BH, and of course such an understanding can be perfectly correct.
In other words, if you're going to talk about a "firewall" solution, then saying "well, GR doesn't model that correctly because it's not a standard GR black hole" is simply wrong. GR can model lots of other things besides standard (vacuum solution) black holes. You just have to use the correct GR model for the actual stress-energy tensor that is present. Of course statements about a standard vacuum black hole will not be correct for a different non-vacuum solution; but that is not contradicting anything I said, because the post I was responding to was assuming a standard vacuum black hole, and my statement was correct for that case.
The real question is whether such a "firewall" model, with a nonzero stress-energy tensor, would even have an event horizon. As far as I know nobody has actually answered that question; the treatments I have seen have simply assumed that there is one without taking into account the fact that the "firewall" stress-energy tensor is non-vanishing. If there is an event horizon in such a model, then my statement would still be correct for that model, since my statement was based on general properties of event horizons.
It's one thing to use analogies to guide your intuition, but physical theories are written in the language of math, and not the language of analogies!
You don't have to use QM to describe protons and electrons at a fine level, but it is very hard to do otherwise, because whatever new theory you want to invent would also have to agree with QM on all the experiments where we have observed quantum effects. You can make an even bigger theory, but you can't throw away the existing approach without reinventing most of its results.
You're welcome to try, of course. But be aware you'll need cold hard math, not just high-level ideas
You have grown up with a set of different analogies based on more modern theories: which is to say, you're letting the tail wag the dog: we have those analogies to explain physics to laymen, but the analogies don't inform the physics.
I think something to keep in mind is humility. In the Bayesian sense it's quite unlikely for you to have picked up something that physicists missed or didn't try to work out before accepting Quantum Mechanics.
https://www.researchgate.net/publication/383609891_Gravity_M...
Here's a page about John Brandenburg, one of the authors: <https://rationalwiki.org/wiki/John_Brandenburg>
PS: this looks like anyone could reproduce or refute it in their basement for a few hundred dollars given all the details in the slides. I'm hoping some amateurs step in.
Interestingly if you look at the most popular programming languages they were created by someone 37.5 years old, on average [0].
Einstein set forth some of the most foundational and tested theories ever.
And that https://en.wikipedia.org/wiki/Black_hole_electron
"...the angular momentum and charge of the electron are too large for a black hole of the electron's mass: a Kerr–Newman object with such a large angular momentum and charge would instead be "super-extremal", displaying a naked singularity, meaning a singularity not shielded by an event horizon."
And 2 singularities having worm-hole connection is the entanglement.
For example, the vast majority of the mass of a proton is explained by the immense energy of the three quarks and gluons being bound together by the strong force. The mass of the quarks themselves is only a tiny portion of that (about 1%), while gluons are massless.
The mass of the atom is further increased by the energy of the electromagnetic force. A hydrogen atom has one proton (1.6726×10^-24 g) plus an electron (9.1×10^-31 g), but the mass of the hydrogen atom is slightly higher than their sum (1.6735×10^-24 g).
The mass of a composite particle is at least partly coming from the famous E = mc².
The Higgs mechanism is ultimely just a way for elementary particles to have this type of energy as well, even in a void and without any other forces present. There is nothing special about it and spacetime, it works like any other field.
https://en.wikipedia.org/wiki/ER_%3D_EPR
Unfortunately the author doesn't seem to know about this idea.
Check out the current Scientific American special publication.
e.g. they figured out how to entangle the electron and proton of a hydrogen atom with a complementary particle that is being pulled into a black hole, like if there were a way to entangle or entrain a local atom with hawking radiation from a black hole, where as the effect of entanglement, the local atom adopted the dialated time/gravity of its remote counterpart in the black hole. the effect would be that states of matter which only existed on the ephemeral femtosecond scale here would be stabilizied for longer time periods because its "clock" had been slowed down by its adopted clock entanglement via hawking radiation in a kind of black-hole-time.
maybe better for a movie script or fiction, but people who think of these things reason them through logically before doing the math as well.
the naive intuition is that lensing hawking radiation might stabilize unstable elements for longer periods.
I’m not aware of any theoretical or experimental way to straight up entangle unrelated particles remotely but I don’t know QM enough to say it’s straight up impossible but it would violate my understanding of how entanglement works.
That being said it is an interesting thought experiment although in practice I doubt you’d measure anything particularly interesting through the entanglement and more importantly it’s not clear entanglement would survive near a black hole since we don’t have a unified model of gravity and QM.
when I looked up whether other particles could be entangled in the same way, the analogy seemed to map, but the logical errors appear to be, a) assuming there is time between the entangled photons as there's no t in p = mv, b) then that there is time dependent information between the photons, then c) extrapolating that some property of black holes might operate on that relationship.
thank you for indulging!
You can entangle two photons in a lab, keep one of them and send the other far away. For example, you can construct the pair in a way that both give the same polarization. If you measure one and the result is horizontal, then the result of measuring the polarization of the other is horizontal. If you measure one and the result is vertical, then the result of measuring the polarization of the other is vertical.
But a trick that is usually untold is that you can put a device in the path of the photon that is going far away to rotate it 90 degrees. The important part is that the photon in the lab is not affected. You can't make any measurement in the photon that you keep in the lab to check if the photon far away passed through the device to rotate it or not. But now if you measure one and the result is horizontal, then the result of measuring the polarization of the other is vertical. If you measure one and the result is vertical, then the result of measuring the polarization of the other is horizontal.
Operating on one half of an entangled pair does not transmit information to the other half. Therefore, the is no action or causation. Choices of vocabulary which imply otherwise are incorrect.
It also doesn't work by "hidden variables" - there isn't some secret value which we just don't know yet. So while it's probably least inaccurate to describe what happens in terms of our knowledge of the remote particle changing, is closer to the new facts we learned coming into existence as we learn them, rather than discovering an existing fact. Except that's also not quite right (information can never be created or destroyed).
The various interpretations are ways of trying to map what actually happens onto easily-understandable descriptions using standard classical-world vocabulary, which doesn't work very well because QM has fundamental differences from the macroscopic world that we live in and drive our language from. Where they disagree with eachother or with the math is because those mappings aren't perfect.