raattgift

> inhabitants of a block universe could experience time as sequential without a real sequential ordering of universe states

tl;dr: I don't think Boltzmann brains count as "inhabitants" because their worldlines are so short. Considering together a select set of available Boltzmann brains does not really admit something that looks like a long but complicated worldline. By virtue of being a fluctuation in a thermal bath in equilibrium a BB does not affect the wider universe; a Boltzmann flashlight can't blink out a message in Morse code.

The herd of elephants in the room is the exp(- \Delta S) suppression of fluctuations of size \Delta S out of equlibrium.

I think you are saying that we can imagine a set of some billion billion ephemeral Boltzmann brains each having memories associated with a unique fraction of a false life. I agree we can imagine that, but at the cost of having exact duplicates and many many more ephemeral Boltzmann brains with corrupted and even wholly unrelated false memories.

The true causality is the history of the thermal bath and not the memories of the brains.

In principle we can distinguish between a chosen set of same-false-life-at-different-stages Boltzmann brains and a real human with a very complicated FTL-and-time-travel worldline because at each point on the worldline the latter gets stress-energy ("signals", if you like) from the predecessor point, and also from (and to) each point's neighbours not on the same worldline. That is, our real traveller can detect the thermal bath temperature (which matters in an expanding cosmology) and leaks out metabolism photons to infinity. Ephemeral Boltzmann brains do neither.

The "virtual life" Boltzmann brains -- as you note -- do not have to be ordered in any way. I would go further: brains with immediately neighbouring fractions of the virtual life's false memories can be totally causally disconnected, not just causally disordered.

So I don't think the thought experiment says anything other than the Poincaré recurrence theorem admits states that are close (but not arbitrarily close or exact) to the initial state. That is, BB_final will recur, but so will BB_final-minus-one-nanoseconds-of-false-memory, BB_final-minus-two-nanoseconds-of-false-memory, ... but in some arbitrary point in the system's evolution. I don't think that's surprising.

There will also be brief ephemeral fluctuations into (and out of) mouse brains, cockroach brains, microchips, Jeep Wranglers, brains with memories of having lived lives as little green men from Mars, and so on and so forth. If you have BBs full of false human memories, without some unknown suppression mechanism you will also have BBs full of false nonhuman memories, and nonhuman BBs, especially smaller and less complicated ones (\Delta S being much smaller in those cases).

I also don't think it says anything about our universe, since we simply do not know enough about dark energy to make confident guesses about the very far future (i.e., does it really asymptote to de Sitter with the thermal bath from a dS horizon?). We also don't know if protons are stable that far into the future. However, with what we do know (which is not enough), the far future looks pretty empty. If there aren't RQFT interactions at GUT-scale energies that allow for violations of baryon and lepton numbers, maximum entropy in the far future (>> 10^33 years) still fairly low, but also the path to new nuclei from the (photon-dominated) thermal bath probably means no BBs at all (effectively all baryons are behind horizons by ~10^{10^10} years from now, and significant numbers BBs in our future light cone are expected not much earlier than ~10^{10^50}, although of course if BBs can happen at all, the very occasional individual BB may have its ephemeral moment at any time including today.)

So if there are BBs with false memories of human lives, they are so far in the future that an entire 2020s-style solar system fluctuating into existence and persisting (or a time-traveller who reaches that future) could not recover anything like our present cosmology. At best, via a strong Lorentz boost, they might detect relic and horizon photons, and maybe splatter their windscreens with the occasional BB.

The fluctuated-and-persisting-solar-system scientists would quickly realize its false memories of skies full of stars and galaxies were not true memories. A real time-traveller would probably just try to measure what's left of the CMB or find another marker of the cosmological scale factor.

(The time travel can have been to-the-future-only by something as boring as spending a lot of time moving close to the speed of light.)

Not discussed yet: what to do about fluctuations in fields which obey conservation laws that result in antiparticles. My fast answer would be: that's one reason BBs are so short lived; they are ripped apart by matter/antimatter annihilations.

Boltzmann brains are extremely ephemeral.

An analogy is that of stirring a vat of alphabet soup and noticing that there is a fair number of single-letter words popping into view ("A", "I"), a smaller number of two-letter words, an even smaller number of three-letter words ... a very very small chance of a twenty-letter word ... and a vanishingly small chance of the 189819-letter monster <https://en.wiktionary.org/wiki/Appendix:Protologisms/Long_wo...> popping into view. The stirring doesn't stop just because a multiletter word appears, so multiletter words are quickly broken up and even valid single-letter words get hidden behind the "B"s and "Q"s and other letters in the soup.

Boltzmann brains will fluctuate out of existence on the order of a small multiple of the light-crossing time of the brain-matter that fluctuated into existence. As the brains are human, they won't even have a chance to react. Although their false memories are encoded however true memories exist in our own brains, they'll have no time to have a reminiscence or notice their lack of sensory organs. (Which is probably good, since they would quickly suffer and die from lack of pressure and oxygen).

A Boltzmann-brain with a full encoding of a life worth of false memories (from never-existing sensory input) is a much larger number of letters. Also, in a cold universe, the stirring is slower, and the letters sparser. Boltzmann brains are tremendously unlikely except in a verrrrrrrrry big volume of spacetime. But with a sufficiently big volume of spacetime, or one with an energetic false vacuum, one should expect a lot of Boltzmann brains. This view puts some limits on our own cosmos's vacuum, since we don't see lots of Boltzmann brains (or even much less complicated but RADAR-detectable and/or eclipsing strucures) fluctuating into brief existence in our solar system.

Boltzmann brains are low-entropy. A persisting Boltzmann brain (fluctuating into existence and staying in existence for a long time) is much lower entropy still. This poses problems for hypotheses that the entire early universe fluctuated into existence and then evolved into the structures we see now. Here there are human brains attached to sensory apparatus, whose memories correlate fairly well with their history of input (and recordings by ancestors, and fossil records, and so on): a system with much much lower entropy than Boltzmann brains, so what suppresses relatively high-entropy structures (including Boltzmann brains) from dominating (by count) our neighbourhood?

Also, if the universe supports large low-entropy fluctuations, galaxies that briefly (~ hundred thousand years) fluctuated in and out of existence should be much more common than galaxies with a history consistent with billions of years of galactic evolution, and you'd expect random variations in morphology, chemistry, and so forth; that's not what we see.

This is a bit annoying, as it would be handy to point to Boltzmannian fluctuation theory as the source of the tremendously low entropy in the very early universe, i.e., it could have arisen spontaneously in a less precisely ordered space. Oh well.

> why would ... a universe appear to evolve from a low entropy past following a small set of laws

Thermodynamics.

The issue is: where did the low entropy past come from? Once you have that, evolving into a higher entropy structure-filled present is not too hard -- that's essentially what we have with the standard cosmology from about the electroweak epoch onwards.

So in summary:

> sequences of Boltzman brains who all subjectively experience time as sequential

whatever these might be, they aren't Boltzmann brains, since the latter don't subjectively experience anything as objectively they fluctuate out of existence in something like a nanosecond.

Very briefly, the short existence is driven by interacting fields and the need to keep entropy (relatively) high: if your starting point just before the appearance of the brain is a region that is high quality vacuum, you have to come up with protons, calcium nuclei, ... and all that requires very careful aim to have one split-second "movie frame" of brain. You need much better "aim" which really drives down the entropy (which corresponds a much larger fluctuation) to go from vacuum to a Boltzmann brain that doesn't disintegrate starting in the very next frame thanks to overshoots of momentum.

The higher the entropy of the Boltzmann brain, the clearer the stat mech argument. (If one gets stuck thinking about human brains, C. elegans apparently develop memories and store them in their nerve ring. Why isn't the outer space of our solar system full of those Boltzmann-C.-elegans brains fluctuating in and out of existence with each possessing false memories of sensory stimuli? Smaller fluctuations, so there should be many more of those than human Boltzmann brains).

I don't really understand what you're trying to say.

I think there's two things going on in your comment: you want more information about emergent theories, and you want more information about how time emerges in a theory that is symmetrical under time reversal.

For the first, perhaps you should try Sabine Hossenfelder's video and video-transcript at <https://backreaction.blogspot.com/2020/04/what-is-emergence-...> first, rather than something more technical.

For the second: your paraphrasing, particularly "if you disagree your logic is broken" is in my view unfair to the quoted scientists and the author & editor. However here's a handful of paragraphs on how time can be understood as an emergent property.

tl;dr of below: the behaviour of matter in the bulk breaks the time-reversal symmetry of fundamental physical equations and provides a "clock" that solutions of these equations do not. Since a direction of time can't be obtained by these fundamental equations, but can be obtained by non-fundamental bulk behaviour theories (like statistical mechanics, which captures the collective behaviour of many items described by fundamental theories, with that collective behaviour being qualitatively different than individual behaviour) time can be said to be emergent.

I'm hoping that your "logic is broken" paraphrase is just that you don't understand that any monotonic function on a path through spacetime can serve as a clock, and while there is no a priori correct path, there is always at least one extreme path through spacetime from which one can take a global notion of time. For example, in the FLRW universe, the comoving coordinate time is suitable. However, this time is not the wristwatch time of an observer who sometimes accelerates to a significant fraction of c, and sometimes decelerates to a tiny fraction of c, and the function transforming the two times (comoving time and this particular proper time) is complicated.

Connes & Rovelli in the early 1990s originated the idea of using Boltzmann entropy as a "universal" clock comparable to comoving time: in both cases the behaviour of bulk matter allows for a set of coordinates that most observers can relate to their proper time. Entropy is more general since it's not restricted to an expanding and at large scales isotropic and homogeneous universe; it just requires thermodynamic matter. The details are in papers which are probably too technical for most -- a copy of their 1994 paper in Classical and Quantum Gravity can be found at <https://arxiv.org/abs/gr-qc/9406019>.

One could summarize: galaxy clusters spread apart with high-quality vacuum growing in between them; in galaxy clusters, "metal-poor" gas clouds collapse into stars, chemical enrichment occurs through stellar evolution, successor clouds collapse into stars with more "metal", and so on; black holes form, merge, and grow. All of this can be time-oriented such that the future having more entropy.

There are other "decays" of matter that can serve to break microscopic time-reversal symmetry which have been proposed and even to some extent demonstrated. Practically all of them rely on a sizable collection of in-principle reversible microscopic changes that in practice -- and in large numbers -- will not reverse. Consequently you can examine such a clock and tell if it is ticking forwards or backwards. Again, that's what's meant by time as an emergent property.

Couple minor additions: geodesics are physical in that (i) they are the paths taken by objects in free-fall and (ii) light (massless waves, etc etc) in free space is always in free-fall: all allowable null curves are null geodesics. Massive objects and light may be accelerated (the direction part of the velocity vector changes with scattering even if the magnitude part does not) and during acceleration will not be bound to a geodesic because they aren't in free-fall.

Even though I agree with the way you put it, I'll say it's probably a bit too strong to write that stress-energy is the (sole) source of curvature given the extremely curved spacetime of our expanding universe. However, Einstein was OK with Schrödinger taking that view <https://arxiv.org/abs/1211.6338> (a super-interesting bit of science history), and we don't know enough about the cosmological constant vs dark energy, nor cosmic inflation.

> alpha = (4GM)/c^2*r

r has units of length.

A geometrical space in which closeness is defined and measurable by a numerical distance -- in this case r -- is a Riemannian manifold. "c" is a dimensional physical constant with units LT^-1 or length per time <https://en.wikipedia.org/wiki/Dimensional_analysis#Simple_ca...>. "Time" enters into the manifold making it semi-Riemannian or pseudo-Riemannian, and however you solve your equation, it can be represented in a pseudo-Riemannian manifold. If there are 3 spatial and 1 time dimension, the manifold is Lorentzian <https://en.wikipedia.org/wiki/Pseudo-Riemannian_manifold#Lor...>. Lorentzian manifolds are the spacetimes of relativistic physical theories.

Newton's big G incorporates length and duration; "4M" is the only term in your equation which includes neither.

So it seems less like you have a problem with spacetime (having shown you're OK with length and duration), than that gravitation is identified with spacetime curvature, and that this is captured by the metric tensor which encodes how lengths, durations, and angles change with tiny displacements from a point on the manifold.

> physicists decided that spacetime ... is emergent

Nobody's decided that, but some physicists are chasing that as a hypothesis. The idea is that there is some underlying theory that recovers equations like the one you quote in some low-energy limit of a theory that is not set in a smooth pseudo-Riemannian manifold.

See, "every smooth manifold admits a Riemannian metric" <https://en.wikipedia.org/wiki/Riemannian_manifold#Every_smoo...>. Smoothness is really a question of "no sharp corners", and tends to be expressed in terms like "everywhere differentiable". One can imagine a spacetime that is made up of spacetime-tetrahedra (you and three friends run together towards a point) and see that the triangular features can be non-smooth when you look close but become smooth as you put lots and lots of tetrahedra together and look at them in bulk. (Loop quantum gravity considers something like this).

However, practically all the differential equations we use in practice rely upon smoothness, and modern ones (since the 20th century introduced tensors and general covariance) would break if the universe around us were not very very very very similar to a Lorentzian manifold.

There are alternatives to curvature of the Lorentzian manifold (i.e., they keep special relativity and its flat spacetime) for encoding the gravitational interaction, with various trade-offs and exposure to narrowing limits obtained from astronomical observation. Gauge theory gravity (GTG) is an example of one that is in good shape.

> people who said these things in forums would be dubbed crackpots

I'd reserve crackpot for someone who pesters scientific journals and working scientists (yeesh, some will call you at home) with their non-standard and often quite verbose ideas even after they are shown conclusively to be wrong in some way. Especially if they think the non-standard idea will revolutionise the field. Pursuing a mathematically-expressable theory from which General Relativity (or something very close to it) emerges in some limit (and Newton/Poisson/Gauss gravity in the low-speed low-escape-velocity local limit of that) isn't cranky. Insisting that the new theory is world-changingly revolutionary probably is cranky, but at least they will have shown they understand existing theory and how theirs differs in detail.

What word should be used for someone who denounces an area of research while obviously not understanding the research denounced?

Ignorant? Ignorance is curable. Every working scientist was once an ignorant kid. They read a lot of textook material, got plenty of help from people with more experience, became used to being shown how they misunderstood something or other, and learned how they could rigorously demonstrate how someone else -- including authors and editors of textbooks -- got something wrong. The result: a firehose of papers on arxiv and elsewhere proposing and exploring in detail something that is not the standard model of gravitation (or particle physics, or fluid mechanics, or whatever).

The idea of making the black hole membrane paradigm generally covariant and everywhere locally Lorentz invariant gives me a migraine.

Dropping charges onto a superthin surface (and keeping it cold, we have to consider arbitrarily large SMBHs too) or having the superthin surface emit Hawking radiation is hard to make not-a-toy (step 0: spectral structure evolution; step 1: ultraboost something, Aichelburg-Sexl style pancake; step 2: astronomer near ISCO around a distant SMBH; step 3: Rindler particles from the membrane's pole; step 4: incoming ultra-high-energy cosmic rays, GZK-like cutoff induced above membrane; ...; step N how the hell do they evolve during the PN phase of a BHB merger, and how do you match that up with the numerical relativity?).

(This line of thought has taken me somewhere that seems crazy: following Giddings & Rychkov <https://arxiv.org/abs/hep-th/0409131v1> and Yoshino & Mann (RN metric and during the LHC-will-destroy-the-world silliness) <https://arxiv.org/abs/gr-qc/0605131v3> can UEHCRs on a hyperbolic orbit peel off small black holes from the electromagnetic field around a black hole membrane? If a standard quiescent BH is massive enough there won't be much Hawking anything to collide with, so we won't see evaporation signals; but isn't there a nontrivial electromagnetic field strength close to even a big horizon in the membrane paradigm or anything reasonably like it? [note to self, in case I care later: Parikh & Wilczek (1997) "An Action for Black Hole Membranes" <https://arxiv.org/abs/gr-qc/9712077> just after eqn. (3.8)])

> F) ... why we can't just assume that there isn't spacetime inside black holes

Spacetime isn't a substance.

I guess what you are asking is, can our universe be non-simply-connected 3+1-dimensional manifold (see 2-dimensional version at first diagram @ <https://en.wikipedia.org/wiki/Simply_connected_space>, imagining the additional 1+1 dimensions is an exercise for you) with what we think of as black hole horizons being a region very very very close to a "hole" in the manifold.

The answer is probably not, and depends on the Topological Censorship Hypothesis <https://en.wikipedia.org/wiki/Topological_censorship> being correct. If the universe works the way we think it does pretty much everywhere far enough away from black holes, then a hole-like defect can't last for the billions or trillions of years that an astrophysical black hole will (we have good evidence that some galaxy-centre black holes have been around at least hundreds of millions of years, and it is safe to assume we'll be able to expand that out to billions). Hole defects also can't grow like black holes do by ingesting partner ordinary gaseous stars, or by colliding with one another and merging, or rather the electromagnetic signals would be radically different.

This makes a couple of assumptions about the massless wave function for light. Things get tricky if we introduce an invariant mass to light (i.e., electromagnetic radiation has a sub-infinite range it can travel) or otherwise break the equality of c and the speed of light in free space. Maybe one can contrive a longer lifetime for regions that break simple-connectedness. However, you still have to pile things up around the hole, and there's no reason to expect gravitation of the pile of things will help you there.

Squeezing matter up against the "edge" of a topological hole will also brighten the matter, and you really want it to dim and fade away for observers around here, since that's what we see from astronomy in the aftermath of tidal disruption events, binary merger ringdowns, and infalls of gas clouds. In standard theory black holes get this dimming by directing some near-horizon radiant energy inwards. If there's no inwards, how do you make the heat glow become invisible? As well as the dimming, visible spectral lines shift into the infrared, and the apparent angles and areas of an infalling object should change.

> In other words, that whatever determinations make up the universe are undetermined in those places?

I can't guess what you mean by that.

> E) Any friendly experts around to explain what a "lower dimension" representation of a black hole would look like?

It would be a 2-spatial-dimensional oscillating (that's where the time dimension comes in) membrane around the black hole. Where? Super close to the horizon or super far from it? The answer varies, but the former is more popular. A better question, and I do not know a proper canonical answer in this particular case you've asked about, is: is the membrane or its oscillations tangible, or more precisely, how does one characterize (microscopically) the interaction with light and matter incident upon an oscillation?

Also not very clear in the article is the popularity of adding dimensions beyond the 3+1 spacetime and hiding them where gravitation isn't strong. For example, ADS/CFT comes up in the article but that's an equivalence between AdS_5 × S_5 and N = 4 supersymmetric Yang-Mills theory, or ADS5/CFT4. The value of N is essentially the number of (independent) operations that transform the spins of bosons and fermions; the subscripted 5 on AdS means an embedding of a higher-dimensional contracting, bounded space into 5 spacetime dimensions, and the subscripted 5 on S means there are five extra compact spacelike dimensions as well. There are other (less proven? I don't really pay attention to that area of string theory) correspondences with different numbers of extra dimensions and symmetries compared to our universe. In any of these a black hole (or something very like it) has some complete description on a membrane somewhere around it, and there's still some metaphysics about whether the CFT is outright sourced by the bulk or if ADS & CFT are just equivalent representations of the same bulk system.

"Holography" is a rough analogy - a 2-d film on a credit card looks like a 3-d image of e.g. a bird; a 4-dimensional conformal field's configuration can represent a 5-dimensional object (including a black hole), provided there are extra symmetries in the field theory and extra spatial dimensions available around the object into which one can shove some excess energy.

In these approaches the boundary of the collapsing spacetime and the membrane on which the CFT lives are very far away from everything (our universe doesn't appear to have a boundary or a membrane full of high-energy particles surrounding everything in the sky, after all), the anti-expansion is very slow (as the metric expansion of our universe is pretty obvious with all those redshifted supernovae, quasars, hot clouds of hydrogen, etc), the extra dimensions are made invisible by making them small and/or curled up, and so on.

Various flavours of the holographic principle have their adherents who believe their preferred form of holography say something important about gravitation in our universe, and might explain various features of collapsed stars and supermassive black holes.

A contrasting approach is to assume the Standard Model and 3+1 dimensional General Relativity and to use numerical simulations of gravitational collapses and black hole evaporations and so forth.

There is insufficient evidence from astronomy to really hint at which approach is better, although there are now limits from astronomy on the numbers and natures of possible extra spatial dimensions (they tend to leave imprints on the spectra of distant light sources, for example) and limits from particle physics on the minimum energy levels of extra symmetries beyond the Standard Model.

Lorentzian manifolds come with a definition of causality. The spacetime of Special Relativity is a Lorentzian manifold. An additional condition of time-orientability obliterates the free choice of an observer on a "comes-before"/"comes-after" relation between observable events.

A further condition of global hyperbolicity also determines the "comes-before"/"comes-after" relation between unobservable events. This condition can be fixed by (i) a non-Minkowski metric, or (ii) by constraints on the pattern of events in the gravitation-free metric of Special Relativity (an example of such constraints is thermodynamics). Sloganizing this: "states of matter tells you what configuration came before/came after" in the second case, and also in the first case if the non-Minkowski metric's source is only matter; otherwise you need to do a causality analysis, e.g. by fixing causal cones on curves (paths, trajectories - they don't have to be geodesics) of interest or solving the relevant wave equations).

https://en.wikipedia.org/wiki/Causal_structure

https://en.wikipedia.org/wiki/Causality_conditions

As a practical matter, the initial value formulation of General Relativity <https://en.wikipedia.org/wiki/Initial_value_formulation_(gen...> (and numerical relativity built on that) is popular and of practical use because so far there is no reason to describe a natural system (where gravity isn't just ignored) in a way that breaks global hyperbolicity.

> Because to my mind, anything that is said to emerge implies that the dimension we usually refer to as time is already an implicit hypothesis of this anything being able to emerge

To the mind of a physics theorist, emergent means that one theory can be mathematically derived from another theory.

Often this is a one-way street where one of two theories being compared is more fundamental in the sense that it cannot be derived from the other, but the other can be derived from it. The other theory is the emergent theory.

There are a variety of ways of communicating this idea, none of which are especially satisfactory.

For example, the Charlie Wood article in the link at the top says, "Sean Carroll proposes the following working definition: A system is emergent when you describe it with two theories, one of which is more complete than the other."

There are a variety of attempts to make this more rigorous in philosophy of science literature - if you're interested in how to nail down "emergent theory" and can't find anything on your own, I'll dig up some references.

None of this has anything to do with a definition of time. There are a variety of pairs of time-independent physical theories where one can be derived from the other, satisfying my definition above (and usually Carroll's too). In general it is perfectly reasonable to use different formalisms to describe the same unchanging system, and sometimes one or more of the formalisms can be derived (i.e., can emerge) from another, or at least (using Carroll's definition) one of the descriptions is less general than the others (in the sense that a small change of the system can be captured by the more complete theory, but not by the other less-complete one).

The problem is in the extreme weakness of the gravitational interaction compared to electromagnetism (and even compared to neutrino interactions), not the uncertainty principle. You can use small magnets to hang big things on a fridge door, even though the magnet and the object are being pulled floorwards by the gravitation of the entire planet. You need ENORMOUS vats of super-pure water surrounded by sensitive photodetectors <https://neutrinos.propg.ufabc.edu.br/wp-content/uploads/2019...> (Super-Kamioande, Japan) to occasionally spot light a particle strongly bounced by a neutrino from a significant nearby neutrino-generator. There are bazillions of neutrinos streaming through the chamber in that maintenance photograph. But there are A LOT more gravitons passing through, and that detector will almost never certainly spot an electron being sped up by them!

The idea in the paper is to replace water with something clever that is purer, much closer to absolute zero, and much more voluminous than Super-K. The clever bit is that it doesn't have to be more voluminous (by a lot) than our entire planet because interactions within the medium can (the authors argue) in principle magnify the signal of a deflection by a very precisely characterized (notably in frequency) graviton.

A somewhat unkind way of analogizing it is that they hope to see an avalanche and attribute it to (only) the landing of a very specifically shaped snowflake during a blizzard.

Edit 3: I jumped to some conclusions about what their actual apparatus would be, so some of this doesn't really address what the authors have written (see the link to the actual paper and preprint below). I'm mostly leaving this because it's already written, right in some parts, and the link at the start of "Edit 2" is worth a glance to anyone interested in an ELI12 on Weber-bar style detectors. I also am much less confident know that I know roughly how a telephone works!

It's more in analogy to MiniBooNE. In that, experimenters shoot a high-energy neutrino beam through a suitable medium, recording the electromagnetic radiation from a Z-boson interaction that gives a kick to a target particle. Sometimes these are electrons that give off flashes of Cherenkov radiation; sometimes the neutrino interaction is somewhat more complicated in the radiation ultimately produced. MiniBooNE's detector is colocated with a major neutrino beam generator.

Gravitationally, ideally one would produce a beam of very small merging black hole binaries to be shot through a detector medium. Binaries throw off gravitational waves with frequency proportional to the size of the orbit; a tiny orbit means high frequency, and a local merger is interesting in other ways. If gravitons are the quanta of such HF gravitational waves, the individual graviton energies should be sufficient to scatter particles in a suitable medium (e.g., a light particle like an electron might throw off Cherenkov radiation, which we could detect). We could also rely upon the https://en.wikipedia.org/wiki/Gravitational_memory_effect to leave fingerprints in the less excited bits of the detecting medium.

Since we don't have that ideal, we are stuck with astrophysical sources of gravitational waves, and so roughly the authors' idea <https://www.nature.com/articles/s41467-024-51420-8> (more conveniently at <https://arxiv.org/abs/2308.15440>) is comparable with what the MiniBooNE experimentalists did in arriving at their particular mineral oil: some media produce a "ladder" of events from a small particle deflection to a detectable signal, and all the ladder rungs rely on discrete energy spectra (in this neutrino detection example, the oils form a natural scintillator that produces light given small movements in the medium of charged particles characteristic of certain weak current interactions; in the gravitational case the idea is to use an ultra-low-temperature condensate). Careful tuning "should" pick out monochromatic gravitons from the astrophysical menu http://www.tapir.caltech.edu/~teviet/Waves/gwave_spectrum.ht... -- then it's a matter of waiting a lonnnnnnng time for a detection.

The Weber Bar was a classical stress-strain measuring device; I don't think Weber was thinking in terms of quantum anything as much as how a shock through a suitable substance could produce electrically- or acoustically-measurable side effects, somewhat like piezoelectric crystals. Ultimately his ideas about (classical) gravitational wave detection were so misguided as to be pseudoscientific. I am not very surprised that in pop sci reporting an analogy was drawn to them rather than to the difficulties in detecting Z-bosons but I'm surprised they get much mention (Weber 1960 is cited!) in the actual paper. I'm an optimist so think it's in part because the good science Weber did was tube engineering for very early masers and lasers, and it's not hard to imagine a (backwards) connection from this paper about stimulating high amplitude coherent states of gravitational waves to grasers <https://en.wikipedia.org/wiki/Gravity_laser>.

(In reality the gravitational waves we get here from verrrrrry extragalactic binary mergers won't be effectively monochromatic, so the detection idea seems to die in Section III: you won't be able to correlate a LIGO/VIRGO-style detection with this experiment with any reliability -- the "beep!" from the device (assuming it's not error) is as likely to be from the background. But maybe there are lots and lots of highly-similar EMRIs out there building up the black hole mass hierarchy, who knows.)

Edit: paid more attention to their Table I and how they got there, and well, their smaller devices (mostly leftmost columns) are basically "build better Weber bars". I wonder if there's any hope of someone getting hands on nine tonnes of niobium and getting it to ~ 1 mK. Anyway, good luck to them, publish the low-hanging-fruit results fast!

Edit 2: https://web.mit.edu/klmitch/classes/8.224/project/resonant.h... (Re the NIOBE resonant bar §1.10 of <https://dcc-llo.ligo.org/public/0125/P1600131/001/optomechan...> (disappointingly not 9 tonnes of niobium!) among others) - but decades of experimentalists trying and no confident result...

> I am not a physicist and I am certainly in dangerous half-knowledge territory here.

Gauging is just dealing with the fact that there is no absolute universal fixed value against which can compare a value at some point in a field; but we still want to consider values at one or more points in the field.

Let's do a really simple static model of the atmosphere, with a single scalar value: air pressure at each point. Let's use a simple device: an air pressure gauge which reports some fraction of a pressure measured when we push a "calibrate now" button. We'll call this a calibrated barometer. We can then recover the full air pressure field by measuring at every point in space (not space-time, the staticity means there is no time-dependence to the measurements; we can do them in any order and not have to worry about time of day or season).

Where do we push the "calibrate now" button? At some point on the surface? At mean sea level? At the top of the atmosphere? The choice of any of these will provide different readings on our gauge (i.e., it reports some fraction of the calibrated pressure, will differ when the calibration point is 101 kPa vs some fraction of the value actually measured at a specific point on the surface). But with a bit of care in choices of units, whatever we use as the calibration point, the difference between two different points in space will be the same.

A good choice of gauge lets use our calibrated barometer as an altimeter. In aviation, aircraft pressure altimeters have a calibration knob, which is used to recalibrate during different stages of a flight. Common calibration points are: QFE, field elevation, which lets one know how far above an airfield one is if separated only vertically from it, at the cost of being unable to simply compare the vertical separation between two aircraft above two different airfields; SPS (the pressure of the standard atmospheric pressure, 1013.25 hPa) is a global setting useful for quickly determining the vertical separation between two reasonably nearby aircraft, at the cost of not being able to quickly determine height above terrain, or even the height above mean sea level; QNH is another local setting which lets one compare how high above mean sea level the aircraft is, at the cost of needing to know the height above mean sea level of local terrain, and not being able to easily compare vertical distances with aircraft using one of the other two calibrations.

All three settings are "redundant descriptions" of the aviator's atmosphere. They describe the same column of air, but each makes it easier to pinpoint different hazards scattered through that column (the ground, other aircraft in level flight, the aircraft's operating ceiling).

We could complicate the atmosphere by introducing time dependency (at night in cold dry winter a QNH altitude will be fewer RADAR-measured metres above the same patch of ground), and atmospheric interactions (atmospheric waves, Bernouilli effects from winds). Each complication can be made to vanish via a careful choice of gauge, although it gets harder and harder to write down such a gauge as complications increase. (As a result, in aviation they allow for a certain amount of measurement error and safety margin, and comparisons with different means of measuring altitude like radio altimeters and satellite multilateration.)

In a quantum field theory (QFT), one might choose a gauge in which some particles vanish. A sibling comment pointed out that very commonly one wants to choose a gauge in which gauge bosons like photons don't need to be counted, rather than a gauge in which there is a sea of an enormous number of low-energy gauge bosons. Choosing the gauge does not eliminate the low-energy gauge bosons; in general QFT field values are time-dependent (and usually gauged to admit only "relevant" fluctuations). Low-energy fluctuations can be boosted into "real particles" by relativistic observers, and strongly accelerated observers can count more particles than a weakly accelerated one. Therefore the choice of a gauge for one observer might make calculations for another observer more difficult.

In QED there are several well-known and frequently-used gauges roughly analogous to SPS/QFE/QNH, and one often chooses one of them for convenience. Each of tehse gauges breaks the gauge freedom.

Gauge freedom means simply an uncalibrated system waiting to be calibrated. A common illustration of this is to choose a non-rotating sphere and setting down latitude/longitude. A less-gauge-symmetrical rotating sphere naturally picks out latitudes (the poles and the equator, notably), but there's still gauge freedom in longitude that we can fix by choosing a prime meridian, and gauge freedom in picking out one of the primary compass directions. These choices do not change the sphere or its rotation (or non-rotation), and of course one can choose any other set of coordinates one wants.

Once one has fixed the gauge on the sphere, though, one can more easily compare positions on the surface: is point A in the northern hemisphere, is point B in the eastern hemisphere? Just asking if point B is North-East of point A requires us to at least choose a north pole -- that can be one of two places on a rotating sphere, and it can be anywhere at all on a non-rotating one. The "right hand rule" is the conventional "gauge" for rotating astronomical bodies: anticlockwise rotation around the north pole (right hand: thumb up, fingers curled). But we don't have to use that convention as our "gauge". (We also have a problem for a truly non-rotating spherical object: where's the north pole? We might solve that by using an imagnariy axis parallel to the axis of a relevant body like the local star or the parent galaxy).

Finally, in many gauge theories there are gauge invariant quantities. On our spheres the geodesic intervals between two points are gauge invariant. The gauge tells us something about direction. In practice, fixing a gauge also usually involves choosing (and scaling) units: on our geodesic which might run south-east to north-west (gauge problem), the length might be measured in metres or light seconds (units problem) or kilometres and light-years (scaling problem). We might want to label different points along the geodesic in latitude/longitude (coordinate problem) rather than adapted Cartesian sphere-centred/sphere-fixed ("ECEF" on Earth) or tangential ("Local East-North[-Up]", "LENU") ones.

Crystals are very uniform and yet have very low entropy: at 0 K the entropy of a perfect crystal is zero. See <https://en.wikipedia.org/wiki/Third_law_of_thermodynamics#Ex...>.

Your second paragraph is not a million miles off from Boltzmannian entropy, the log relationship between a macrostate and the set of microstates that match the macrostate. A very carefully layered milk-on-coffee matches no microstates in which there is milk at the bottom of the arrangement or coffee at the top. A fully stirred mix can have a milk molecule and a coffee molecule anywhere in the mix: this matches a much larger set of microstates than the layered case.

It's mostly molecular translation and rotation (hurried up by the stirring) that causes the layered milk-on-coffee to homogenize and come into thermal equilibrium.

But if we take the perfect crystal case, any microscopic rotation or translation within the crystal makes the crystal LESS uniform but also dramatically increases the crystal's entropy.

If we smash the crystal into dust the entropy will become much higher, but the dust will be arranged much less uniformly than when the crystal was intact.

> entropy is a measure of order

Yes.

> or how mixed things are

Maybe.

> Entropy can also be understood as uniformity

Sometimes. There are lots of things in nature which are highly uniform but have very low entropy, with entropy increasing as they become less uniform.

There's no real focused thesis below, more a set of reactions to your comment: Einstein wasn't in practice a lone wolf, he worked in academic environments; he focused on three passions and didn't stray much; he worked "on paper" with very few physical artifacts attributed to him; he was extremely successful where his interests took him, even quite late in life where he failed to meet some of his own hopes; while he is a household name in much of the world, there are other well-known names in his areas of interest (that he admired & used the work of); and after he died the work of thousands of others in those areas of interest carried on.

> 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).

Cool question!

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?

Neutrinos are known to have mass thanks to flavour oscillation. In empty space neutrinos will always be outraced by photons.

What you seem to be trying to remember is that certain types of extragalactic supernovae produce a tremendous number of neutrinos, and those can be detected on Earth before the associated light does. The reason is that both are produced deep within the dying star, and while the star's outer layers are largely transparent to the neutrinos (not completely: it's neutrino pressure that makes the star explode[1]), the deep-in-the-star supernova photons bounce around inside. That's very much not empty space.

https://www.astronomy.com/science/in-a-supernova-why-do-we-d...

We can detect type SN1a supernovae out to about z=4 (redshift of about four in light-years is about twelve billion years of light travel time from the supernova to us). That's not really enough for the delayed pulse of light to catch up to the neutrinos produced also produced in the dying star's interior at the same time. Also, not all of the emitted photons are likely to scatter off gas and dust in any interstellar medium along the way, so the relative delay at Earth of the bright electromagnetic flash is dominated by the dying star's outer layers.

(There are more complicated electromagnetic signals like light echos <https://en.wikipedia.org/wiki/Light_echo> that can follow on much later; there aren't any neutrino equivalents really).

> photons aren't affected by gravity directly because massless but their path, their limit of causality, is affected

Not sure what you are trying to say here, but photons certainly both feel and source spacetime curvature. In empty space, photons always travel along null geodesics. The distribution of all matter, energy and momentum, the expanding background of inter-galaxy-cluster space, and the collapsing background of galaxy clusters (and galaxies, and components of galaxies like their central black holes and stars) picks out what geodesics fill spacetime. Some are null, and massless things can find themselves on ("couple to") them. Some are timelike, and massive things can find themselves on them.

Geodesics are free-fall trajectories, so are inertial as in "things in motion tend to stay in motion", and barring any further accelerations a photon coupled to a null geodesic will stay on that null geodesic and a neutrino coupled to a timelike geodesic will stay on that timelike geodesic.

Some neutrinos and photons start on parallel geodesics within the supernova's exploding core. Each neutrino stays coupled to its timelike geodesic all the way to detection on Earth. The photons are all forced off their initial null geodesic by mostly scattering off nuclear matter near the star's core, find themselves on a second null geodesic, more nuclear scattering, possibly some scattering off ions in outer layers, and each ultimately might end up on a geodesic that it stays on until it reaches Earth.

- --

[1] on neutrinos driving the explosions and how alot of them stick around as they are captured into heavier chemical elements and isotopes https://www.mpg.de/11368641/neutrinos-supernovae

> your velocity through time approaches zero

Proper time, τ. But your proper time and my proper time are different, and are only coordinate times, monotonic labels on timelike curves. That means τ is an affine time.

There are other affine times available. And we have to choose an affine time other than τ for null geodesics, the curves which photons (in vacuum) travel along. So, instead of proper time, for photons there's the affine parameter.

The same rule applies: there is nothing special about the affine parameter. I don't have to use a photon's affine parameter when describing physics any more than I have to use the proper time of an ultrarelativistic electron. And I can convert physics done in one splitting of spacetime into space+time to a different splitting of the same spacetime into space'+time'. The coincidences in the spacetime are unchanged by the switch of how we split -- splitting is just a change of coordinates.

If we divide up spacetime into space+time where the choice of time axis along which to order spatial volumes is my proper time, the emission of a photon in the photosphere of the sun and its subsequent destruction in my eyeball happen in a definite temporal order: there is a time delay. There is still a temporal order if we divide up space+time using your proper time, or that of an ultrarelativistic electron.

There are some special technical aspects of dividing up spacetime into space+time using a photon's affine parameter as the time axis, but it's certainly doable. A photon shares a different 3d spatial volume with many other things at each affine parameter labelled point on the photon's curve. Phases of orbits, stages of an elastic collision, and so forth are among the things "snapshotted" into each 3-d spatial volume the photon finds itself in. Those evolve from one 3-d spatial volume to the next to the next.

So returning to the previous picture: if we split up space+time according to the affine parameter of a photon, there will be some 3-d volumes at which the solar photon is much closer to the sun than to my eyeball, and some 3-d volumes where it is much closer to my eyeball than to the sun. The same is true for the solar photon itself: some affine parameter values put it closer to the sun than to my eyeball, and at some affine parameter the photon's journey ends.

If a photon's trajectory is through curved spacetime, there will be a difference in momentum between two points on the trajectory (we are not restricted to the photon's creation or its destruction), which we can calculate using the affine parameter. The physical interpretation is that the photon undergoes a redshift or blueshift between two points in spacetime.

Note that I did not take the lim v->c approach you did in your first paragraph because there are geometrical differences in a Lorentzian spacetime between a null geodesic and a timelike one, even if the timelike geodesic is associated with a speed arbitrarily close to c. The photon is almost always on a null geodesic. A non-massless observer will never be on a null geodesic.

> Since photons move at c

Photons can be made to move slower than c, in which case they are not on null geodesics, and therefore proper time might be suitable for them.

Photons moving at c must be on null geodesics.

Proper time -- one particular affine time -- is undefined on null geodesics. However, they experience a different affine time. One can interconvert, so it does not make sense to say that photons "experience zero time".

Lastly, if the totality of the photon's curve through spacetime is on a null geodesic, the photon won't be able to experience much of the universe evolving around it as it flys away from its creation. However, segments of a photon's curve can be other than null geodesic motion as (for example) they cross through wispy gas clouds or strong magnetic fields in space. Temporarily slowed light <https://en.wikipedia.org/wiki/Slow_light> can in principle receive news of the world. This could have happened for a photon emitted billions of years ago from a high-redshift quasar en route to the JWST.

Extra reading:

https://en.wikipedia.org/wiki/Initial_value_formulation_(gen...

Blau, Frank, Weiss 2006 (section 3 "Brinkmann coordinates are Fermi Coordinates:", 4 "Null Fermi coordinates, general construction", 5 "Expansion of the metric in null Fermi coordinates") arxiv version https://arxiv.org/abs/hep-th/0603109 (link to publication in Class.Quant.Grav. is on the abstract page).

"What is the physical meaning of the affine parameter for null geodesic?" https://physics.stackexchange.com/questions/17509/what-is-th...

Let's start with the universe since the ignition of the first stars. Your question is also super-interesting in the context of the very early universe, so I'll come back to that further below.

Depending on the constants, with significant fluctuation of them you'd expect spectral line broadening rather than the sharp lines we see in precision interferometry, violations of local Lorentz invariance, different structures in "stacked" spectra (like the Lyman-alpha forest), and instabilities in Keplerian orbits. Present measurement precision of subatomic transition spectra has really boxed you in on this: many physical constants have relative standard uncertainties on the order of 10^-10 or better.

> any measurement ... [sees only] the average

So you'd start wondering: in the limit of infinitesimal fluctuations, is a fluctuating constant just constant rather than an "effective constant"?

Where's there's still wiggle room is in the exact masses of heaver generation standard model particles (top quark, tau mass, W-to-Z mass ratio for example) and somewhat frustratingly Newton's gravitational constant, all of which have relative standard uncertainties worse than 10^-5.

(There's a quick explanation of standard uncertainty and relative standard uncertainty at <https://www.physics.nist.gov/cgi-bin/cuu/Info/Constants/defi...>)

However, assuming cosmic inflation, one might expect incredibly small scale fluctuations in physical constants to be stretched, just like incredibly small scale fluctuations in the densities of matter and radiation. This could lead to later-universe regions of arbitrary size with a significantly different value for one or more physical constants, just like we see regions relatively stuffed with galaxies (filaments) and regions that are relatively empty (supervoids). We'd expect that when we look at different parts of the sky we'd see differences in things like the Lyman-alpha forest, the population and/or spectra and/or light curves of quasars/supernovae/variables, and so on.

So, in order to have the apparently constant physical constants we observe, while keeping your idea that there are tiny fluctuations in them, you'd have to suppress high frequency fluctuations in the constants in the very early universe, because otherwise you'd have to suppress gross effects like different gas and dust chemistry when comparing one galaxy cluster to another.

And we are looking: https://cen.acs.org/physical-chemistry/astrochemistry/Scient...

(The cosmic inflation epoch predates the "freezing-out" of some of the physical constants, so my thinking is that during inflation there must be some precursor constant(s) that determine(s) the mass of the electron (for example) once there are electrons after the electroweak epoch. Even after inflation the ordinary expansion of the universe can stretch fluctuations enough that (assuming your idea) there is likely to be a directional dependence on precision extragalactic astronomy.)

Einstein solved three very different open problems in one year: the photoelectric effect, Brownian motion, and special relativity.

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.

Many tens of thousands of people have studied quantum chromodynamics (and related experimental results) enough that they understand there is a scaling problem in the proton: the more energy you use to probe a proton the more internal structure is revealed. We're orders of magnitude away from being able to probe proton structure at scales where "the problem of time" arises in any practical sense.

You haven't studied QCD or much high-energy physics, but you can improve your understanding of the proton starting with this excellent recent article by Matt Strassler: https://profmattstrassler.com/2024/07/22/the-standard-model-...

> "our assumption of time: that it's a level straight stream that flows forward"

That's not an assumption anyone who's studied physics would recognize, except (being generous) to the extent they read about the history of physical equations before about 1910 which were parametrized by "absolute time", and which have been superseded by relativistic equivalents.

There is no single "assumption" about time; time is treated very differently in different candidates for a fundamental physical theory (and differently again in theories that aren't fundamental; non-fundamental means that although bulk behaviour might be completely and accurately described, it emerges from microscopic behaviour not dealt with in detail by the non-fundamental theory -- examples include Navier-Stokes and Bloch's theorem).

Since no later than the second decade of the 1900s (in the aftermath of de Broglie 1923) it's been known that at some energy scale lengths and durations stop making sense, and since the 1970s (in the aftermath of Wilson 1975) it's been known why they stop making sense, from a mathematical perspective. In the 1960s, DeWitt (and Wheeler) were already pointing out that (as it later was proven) there is a problem with the treatment of the temporal dimension (and causal structure) in relativistic quantum mechanics. This has lead to more attempts at building new physical theories than you're likely to imagine, mostly but not exclusively in quantum gravity. It has also lead to considerable philosophy and foundations of physics work, largely but not entirely swept up in "the problem of time".

There is a huge body of related literature available for you to read at your leisure, and people who would happily engage with you and take your thoughts seriously once you're underway.

> concept of geodesics

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.

The "balls on a rubber sheet" is a pain because nothing is in free-fall: there are dissipative contact forces between the balls and the rubber sheet. Consequently realistic initial [position, velocity] values for the test ball cannot give you a stable circular orbit around the central mass ball. Venus isn't about to fall into the sun. Now try setting up Earth-Moon or the Jovian-Gallilean systems on the rubber sheet.

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...> ?

There are a fair number of extensions to GR that can reproduce the standard cosmology, typically avoiding or recasting DM, DE, or both. Examples include generalized teleparallel gravity and Cotton gravity. In such theories, any solution of the EFEs are solutions of the (sometimes very different) field equations of these families of theories, although the field content may have a somewhat different physical interpretation from GR.

However, generically, these extensions tend to have an under-determination problem frustrating attempts to arrive at a unique spacetime for a given distribution of matter or a unique distribution of matter which can exist in a given spacetime (or both problems). That makes them less attractive than GR, or even possibly outright unsuitable bases for initial-values formulations (and thus are unlikely to overthrow numerical relativity soon).

"[C]an general relativity discard negative mass solutions without the aid of quantum field theory? This would provide an alternative mechanism for the nonoccurrence of negative masses that does not rely on quantum theory at all. Hence, if true, it would show that gravity itself abhors negative masses, regardless of the matter content.

"A natural candidate for the role of a cosmic-weight watcher is the stability of solutions."

...

"While general relativity cannot forbid an equilibrium solution with negative mass — after all any Lorentzian geometry is a solution to the Einstein field equations for the appropriate stress tensor — it may forbid stable solutions with negative mass. This happens in the cases considered in this work. While one can construct a negative-mass star, one cannot expect it to be stable under small hydrodynamical perturbations.

"Notice this gives a classical answer to a problem that may appear to be quantum in nature."

The Chandra X-Ray Observatory (instrumental in producing this image) is under threat. https://savechandra.org/why/

There is excellent evidence for then-relativistic cosmic neutrinos from the cosmic microwave background acoustic oscillations. As with the CMB, these neutrinos cooled into a "relic" field with the metric expansion.

A cooling gas of relativistic neutrinos becomes non-relativistic when the average neutrino momentum becomes comparable to their rest mass. The present cosmic neutrino background (CNB) temperature is about 1.9 kelvins corresponding to ~ 1.7e-04 eV/c^2 which is smaller than some neutrino masses.

This is still "hot" compared to Cold Dark Matter, and CNB also only a small fraction of the required CDM energy density.

The lightest cosmic neutrino background mass eigenstates could be relativistic at present, so how the CNB is split between (FLRW) radiation and dark matter is ripe for research. It will mostly be "hot" DM because of the heavier, colder species. But not hot enough to leave clusters of galaxies, unlike neutrinos produced by present-day astrophysics (and our own laboratory experiments and nuclear power generation).

https://en.wikipedia.org/wiki/Cosmic_neutrino_background

https://bigthink.com/starts-with-a-bang/cosmic-neutrino-back...

> behaves exactly like dark matter

Dark matter is non-collisional, doesn't decay, and doesn't strongly scatter radiation. The last is about gravitational microlensing. You address the first two in another comment, but focused on falling into central black holes of galaxies and Hawking radiation. Black holes merge (cold dark matter doesn't clump, and certainly the absorption cross-section of CDM does not grow with clumping in the event there is some "dark chemistry" in the CDM sector; black holes absorb more radiation as their masses increase, including via merger). The MACHO (massive compact halo object) models which use small black holes have to keep them very sparse and on a restricted set of orbits in order to keep them from merging in galaxy and galaxy-cluster halos where they would be detectable. It's also hard to have galaxy-cluster distributions of small black holes: the density profiles get very different as tiny black holes interact with each other. Additionally, in distributions around the central-bright-galaxy of clusters, it's hard to suppress inverse compton scattering X-rays from dust scattering around (or forming accretion structures around) tiny black holes. So the signature radiation a tiny black hole MACHO model has to worry about is less Hawking than the behaviour of normal matter moving around black-hole-infused space in clusters like Abell 2764 <https://www.esa.int/ESA_Multimedia/Images/2024/05/Euclid_s_n...> or Abell 2744 <https://esahubble.org/images/heic1506c/> <https://en.wikipedia.org/wiki/Abell_2744> for example. It's really hard for simulators to arrive at this kind of structure using mainly MACHOs, and there seem to be lots of these structures. Lots and lots.

It's somewhat easier to do with ~solar mass and bigger black holes (they can be sparser, their orbits are thus less contrived to avoid collisions -- after all star-star collisions are rare unlike dust-dust collisions), although larger-mass BHs run into limits form gravitational microlensing. In particular, BHs of 100 or more solar masses would tend to disrupt wide stellar binaries, particularly in at the outer margins of galaxies (including our own, easy enough to look for out of the plane of the disc). And there are strong limits on BHs between about 10 and 2000 solar masses from ultra-faint dwarf galaxies, where domination at that mass of BH would expand the visible part of those galaxies (especially bright star clusters like the central one in the Eridanus II dwarf satellite <https://en.wikipedia.org/wiki/Eridanus_II>) via dynamical heating.

The MACHO idea was certainly plausible, and projects like OGLE and MOA developed microlensing-observation techniques which are now used for finding low-mass and wide-orbit exoplanets, and "orphan" Neptune-like planets ejected from their birthplace star systems. See for example https://kmtnet.kasi.re.kr/~ulens/

However, there seems to be very little hope that black holes are a large fraction of whatever the detailed description of dark matter might be.

That there are plausible mechanisms for forming primordial black holes at arbitrary masses does not mean they are actually there.

Figure 15 (page 17 of the PDF) is worth the click: it shows the inner pulsar region.

Throw (slowly, compared to c) a black hole (BH) through a Bonnor beam (BB). Throw a white hole (WH) through a Bonnor beam. Ignore technical difficulties in superimposing the exact solutions for the moment. The breaking of the axial/spherical symmetries is deliberate.

Qualitatively what happens, in your view, when the WH touches the beam? Is it just the time reversed picture of the BH intercepting the BB? There's a part of the first spacetime where some of the light is trapped in the BH as it flies off to infinity after its encounter with the beam. Is there a part of the second spacetime in which some of the light is trapped in the WH? If so, where is it if the initial conditions are a Bonnor beam at large spacelike separation from the white hole? Does the WH cut a gap into the beam?

Alternatively, take two widely separated BHs. Grind out the Raychaudhuri equation, bearing in mind the focusing theorem. Now take two widely separated WHs. What's different? How does a circular orbit of two WHs evolve? Outgoing GWs tend to circularize elliptical binary BH orbits. Can a circular binary WH orbit decircularize? How? ("Incoming GWs from initial conditions" is not very satisfying).

The problem I think is confusing the reversal of the entire BH spacetime with a WH stitched into an ordinary Minkowski in the asymptotic limit, or into a cosmology. (Bonnor is essesntially the latter). More broadly, a WH should be able to live with future-directed null geodesics.

Of course, I could only agree with a response like, "well such a WH is almost certainly unphysical", but maybe we could ignore that in order to think about what happens when a plane wave hits a WH.