You probably found a video discussing Olbers's paradox <https://en.wikipedia.org/wiki/Olbers%27s_paradox>.
4,580 karma · joined February 11, 2016
Precision measurements by satellites around Earth and spacecraft scattered around the solar system reveal the nonlinearity of gravitation, as do precision measurements of systems like Hulse-Taylor and PSR J2222-0137.
A linear superposition law for gravitation is consequently unavailable - again, this can be seen in the solar system, where a linear superposition model helped find a real mass (Neptune, where ultimately the telescope targetting was driven by Urbain Le Varrier's detailed study of the orbit of Uranus in the 1840s, assuming the validity of Newtonian gravitation), but misled astronomers into decades of futile searches for "Vulcan", a hypothetical body inside Mercury's orbit.
There are a bunch of ways one can capture the nonlinearity of observed gravitation. A nice slogan: gravitation self-gravitates. A nice theoretical framework: Newton-Cartan gravity is great for exploring the failure of linear gravity. An easier theoretical approach: the relativistic two-body effective radial potential energy <https://en.wikipedia.org/wiki/Two-body_problem_in_general_re...> or less encyclopedically <https://spaceengine.org/articles/the-anomalous-advance-of-th...> where you can see the same effective potential term written slightly differently, with more about Mercury's orbit.
Quoting the latter:
Again I don't want to get lost in math, but it's worthwhile
just to look briefly at what the math is saying here.
Notice this still has the exact same two terms from the
Newtonian effective potential: an attraction that goes as
-1/r, and a repulsion that goes as +1/r^2. But a new term
is added: another attractive term that goes as -1/r^3. This
means that at very small radii, the -1/r^3 term dominates,
and gravitation becomes attractive again, dominating even
over the centrifugal effect of your orbital velocity.
No linear theory of gravitation is viable for known planetary and astrophysics. At best one can come up with a quasi-linear theory.
This is calculationally unfortunate: solving the full nonlinear Einstein Field Equations exactly is fiendishly hard. Where one can use a linear approximation, essentially every physicist would choose to do so. Indeed, Einstein invented linearized gravity (and various other approximation techniques). Unfortunately, linear theories of gravity can only ever be approximate, as they fail to deal with multibody systems, systems where orbital velocities are even only thousands of kilometres per second, where one wants to trace out radiation (including gravitational radiation), and so forth. Convincing proof of incompatibility between any possible linear theories of gravity and numerous observed physical orbits have been known since the 1960s. Roman Sexl did some really interesting work (alone and with collaborators like Otto Nachtmann) in that area in that decade.
These days one can turn to box 7.1 (sec. H) of Misner Thorne & Wheeler as a textbook starting point.
None of this really has anything to do with quantum mechanics, except with respect to a correspondence principle (e.g. Fraunhofer-like spectral lines have their origin in quantum mechanics, and we can see how gravity rather than just motion affects them).
ZFS is essentially an object store database at one layer; the checksum-hash deduplication table is an object like any other (file, metadata, bookmarks, ...). There is one deduplication table per pool, shared among all its datasets/volumes.
On reads, one does not have to consult the dedup table.
The mechanism was fairly easy to add. And for highly-deduplicatable data that is streaming-write-once-into-quiescent-pool-and-never-modify-or-delete-what's-written-into-a-deduplicated-dataset-or-volume, it was a reasonable mechanism.
In other applications, the deduplication table would tend to grow and spread out, requiring extra seeks for practically every new write into a deduplicated dataset or volume, even if it's just to increment or decrement the refcount for a record.
Destroying a deduplicated dataset has to decrement all its refcounts (and remove entries from the table where it's the only reference), and if your table cannot all fit in ram, the additional IOPS onto spinning media hurt, often very badly. People experimenting with deduplication and who wanted to back out after running into performance issues for typical workloads sometimes determined it was much MUCH faster to destroy the entire pool and restore from backups, rather than wait for a "zfs destroy" on a set of deduplicated snapshots/datasets/volumes to complete.
The paper:
Yusef-Zadeh et al., Non-stop Variability of Sgr A* using JWST at 2.1 and 4.8 micron Wavelengths: Evidence for Distinct Populations of Faint and Bright Variable Emission <https://arxiv.org/abs/2501.04096>.
Figure 1 therein shows views of our galactic centre in various wavelengths, and is worth the click & scroll even for non-experts.
Incredible.
https://scholar.google.com/citations?user=19WGkFsAAAAJ&hl=en
be sure to check past the first 20 papers or so, like, oh, say his 1990 paper with Michael Peskin (438 citations), a copy of which can be found at <https://www.slac.stanford.edu/pubs/slacpubs/5250/slac-pub-53...>.
The reverse of your question is interesting: a quasar host galaxy or a Seyfert galaxy isolated deep within a supervoid should be much less redshifted than similar cluster and filament galaxies (one would have to "weigh" the galaxies, and so would lean on angle-diameter-distance and other geometrical relations, relative redshift of hydrogen-alpha (and millimeter CO and 21cm neutral hydrogen spin-flip etc.) at the galactic limbs and in globular clusters). The side-effect of Timescapes running clocks much slower in filaments is that they run much faster in supervoids. Many known voids have small numbers of galaxies in them (the emptiest of voids have something like a tenth of the radio-generating matter compared to large galaxy clusters, so they're nothing like "empty", which in turn drives the focus to the evolution of Timescape's "void fraction") so looking for faster-running galaxies in voids is not an impossible observational test.
Going forward again, the late-time Integrated Sachs-Wolfe structure would be anisotropic, with strong nonlinear differences between ISW radiation through filaments (because of the significant gravitational backreaction central to Timescapes) and ISW radiation through voids. Coarsely, that's not what we see (nonlinear effects are subdominant) and is an obvious target of study of the Timescapes proponents.
https://en.wikipedia.org/wiki/Sachs%E2%80%93Wolfe_effect#Lat...
There is only a microscopic chance of the white dwarf member undergoing runaway fusion becoming a Type Ia SN. So microscopic it would be truly surprising astrophysically.
Neutron star-black hole mergers (NSBH; yes sorry the name is the other way around from the easier way to think about the mass ratio) mergers are relatively rare in our detectors. Detections GW200105 and GW200115 were moderate mass ratios, ~9:1.9 and ~6:1.5 solar masses respectively. In both cases there was nearly no optical signal, which is easy to interpret as the NS essentially falling right into the BH.
Astrobites, whose writers are graduate students who summarize papers in (or at least close to) their fields in a way meant to be accessible for undergrads, has a 2021 article at <https://astrobites.org/2021/06/30/first-nsbh-merger/> which includes a link to a video simulation of a NSBH. Another simulation, explicitly compatible with the GW200115 (6.1:1.4) detection, can be seen at <https://www.youtube.com/watch?v=Rd3p3xPtWn4> which also shows the NS deformed into a prolate shape which falls right into the BH in this way. The prolation does not rise to a tidal disruption, and essentially no mess is left around outside the BH to influence the ringdown (GW waveform traced on bottom).
Higher mass ratios are even less likely to produce an optical component -- as one takes the mass ratio higher, the NS's tidal deformation (the prolation) will effectively vanish into negligibility.
Smaller mass ratio NSBH mergers are likely to disassemble the NS in a "kilonova" event comparable to a collision between two neutron stars.
There is a small zoo of simulations at <https://www.aei.mpg.de/145347/gravitational-waves>. The same group did <https://www.youtube.com/watch?v=-pdNYuWWN_w> (which does not seem to be in the "zoo"), which shows a tidal disruption in a low-mass-ratio NSBH merger. The matter left outside the BH will initially be extremely hot and optically bright. AFAIK there is no known NSBH merger with a definitive kilonova; the low mass ratio GW230529 had a significant optical signal but it is not entirely clear that the more massive of the pair was a black hole.
> lose degeneracy
Oh yes, binary neutron star mergers (BNS) are very busy with nuclear physics, producing all sorts of heavy atomic nuclei in the ejecta. Gold is certainly one of those elements (see e.g. <https://en.wikipedia.org/wiki/R-process>).
> "slice" the degenerate matter away
The apparent horizon is not a razor.
Apparent horizons are not often at the same location in spacetime as event horizons in these mergers. An event horizon is not even in-principle measurable by us: you'd need know the entire contents of the future light cone out to the infinite future. An apparent horizon is physically measurable locally (but not too locally, because General Relativity guarantees an ultralocal patch of flat spacetime at every point in a general curved spacetime), essentially by measuring whether a beam of light (visible by being shot through a dust, like how one can see the beam from a laser pointer shining through a mist of water or a cloud of chalk dust) tangent to the emitter's trajectory curves inwards.
The self-gravitation of a neutron star is too great for a larger BH to overcome outside the horizon except when the BH is very small (low mass ratio approaching unity, and there are observational and astrophysical-theory reasons to suspect that BHs with NS masses are rare, which makes studying GW230529 exciting). However tidal deformations can heat the NS so there is the possibility of exciting standard model physics inside it during its final pre-merger orbit even for moderate mass ratios, given a highly noncircular NSBH orbit.
Me neither (to say the least), but my comment was an attempt to fairly characterize CCC in this thread's context.
> Is CCC on a positive cosmological constant?
AFAIK it's not a requirement of Penrose's approach, but with a positive CC the aeon/future_aeon conformal boundary is spacelike, so you can have global hyperbolicity (and importantly a(t) is always positive and describable by classical EOMs, and the overall structure is just flat de Sitter with a radiation fluid).
[For clarity, here I'm the one extrapolating from the radiation fluid, and afair I'm not summarizing someone's attempt to do this rigorously.]
> it restarts
The conformal rescaling isn't exactly a restart; a Eulerian observer A crossing into its future aeon could encounter a highly similar scaled-up obsever B running much more slowly (and made from fundamental particles with much longer de Broglie wavelengths compared to A's, those having gotten there by freezing out of A's cold sparse ultra-long-wavelength massless boson gas, which to B is B's hot dense ultra-short-wavelength early conditions).
> Infinity is a big number though
Yeah, I think that's why CCC proponents are OK with past-aeon's (pseudo) heat death managing to be a rescaled future-aeon's low entropy initial conditions.
On the other hand, they seem to think in merely large-but-finite timescales when they talk about final BH evaporations leaving a lower-entropy mark on the pseudo heat death that can carry across the boundary (and rescaled to possibly sub-horizon perturbations from B's perspective) be detectable in future aeon's structure formation.
> confused
Sorry about that. Perhaps I lost some train of thought that if made explicit would have made it clearer why I might have been talking about both nucleated and fluctuated structure. I don't remember and am unlikely to re-check the context.
> it restarts once there's nothing left but energy
The "nothing left but energy" part is a requirement that matter (in the broadest sense) must be conformally invariant so that its active gravitation as a source allows for the CCC conformal rescaling of the FLRW metric, which is how a predecessor "aeon" is connected mathematically to its successor.
Of the Friedmann dusts, only lightlike radiation can be rescaled this way. Equivalently, all the matter left in the universe at the end of an aeon must be on null geodesics.
Because local Lorentz invariance is fully baked into the Standard Model of Particle Physics (SM), and because the SM has particles with nonzero rest masses (which in a Lorentzian patch cannot couple to null geodesics), NOBODY knows how to do this in a consistent way (let alone in a way that matches actual evidence from particle physics).
(If we restrict to QED we need to convert all electrons and positrons into photons and impose some unknown mechanism to suppress statmech fluctuations back to a non-conformally-invariant condition. In reverse order, two-photon physics are maaaaaaybe supressible adiabatically. However, there just aren't enough positrons to find and annihilate every electron (adiabatic expansion makes that even less likely!), and electrons on their own don't decay into photons. Of course, once we add in the weak and strong forces, we are far beyond quantum electrodynamics, with all sorts of new ways in which reaching a conformally invariant stress-energy state becomes implausible. Oh yeah, and now do dark matter.)
WRT previous comments in this thread, any black hole (BH) at the end of an "aeon" must radiate only massless bosons. This puts a pretty strong lower limit on the mass of Hawking-radiating BHs crossing an boundary between "aeons", or destroys the mathematics of the hypothesized conformal rescaling by virtue of having incompatible non-conformally-invariant field theories on both sides of the Einstein Field Equations.
Binary BHs don't fit cleanly into the FLRW rescaling picture either: among other things they source a metric that isn't locally isotropic and homogeneous (a dust of high mass isolated singleton Birkhoff-theorem BHs is mostly fine though, and in principle you could get through through BH mergers and a stronger cosmological coupling (some types of "fifth force"/quintessence, for instance, to break apart wide BH binaries/triples/multiples)).
There are maybe escapes from some of these constraints in extra dimensions and lattices, but I've been under the impression that one of the attractions of CCC is that it's compatible with the FLRW metric of the standard cosmology.
Does CCC work with small perturbations on the boundary between aeons? Who knows. However, it probably works with small perturbations near that boundary, because we do perturbative FLRW routinely these days. So maybe there's some mechanism (e.g. in dark energy) that makes small deviations from conformally invariant field configurations entirely vanish at the aeon boundary. But we have no astrophysical or particle physics evidence for that at all.
Finally, the article at the top is about inhomogeneous cosomology -- i.e., Timescapes metric is not FLRW metric -- and whatever one's position on CCC, it rests on the standard view that at large scales the universe is homogeneous and that any inhomogenities, anisotropies, and backreactions vanish at smaller scales (and so admit perturbation theory).
https://en.wikipedia.org/wiki/Sachs%E2%80%93Wolfe_effect
Note that in the next paragraph I depart significantly from the vocabulary that the Timescapes programme proponents have been using for the past twenty years.
ISW and comparable spectroscopy is easy enough to think about in terms of an accelerating cosmic expansion, i.e., relative voids are becoming spatially bigger with the expansion. It becomes much less intuitive how to fit the data if one keeps relative voids at roughly constant volume instead implying that there is a significant false vacuum above the ground state and in voids the false vacuum is slowly decaying to that state. (Outside the supervoids, near matter, this false vacuum decays much more slowly still). Because "vacuum" in the voids isn't really vacuum, one is stuck with a running function on the constant c (it gets faster with time from the formation of the CMB; this is because the false vacuum evolves towards a real vacuum) or adapting lightlike geodesics by imposing refraction (since the false vacuum is a medium).
The usual terminology is reasonably capture in the first paragraph here at <https://en.wikipedia.org/wiki/Inhomogeneous_cosmology#Inhomo...> ("Inhomogeneous universe"). The following short section ("Perturbative approach") is what is done in the standard cosmology when one wants to do detailed studies of filamentary distributions and other structures that are lumpy at some (larrrrrge) length scale of interest: the perturbed homogenous background is practically always the standard FLRW.
The justification for perturbation theory on FLRW is that even though there are dense spots (notably most galaxies' central black holes), principles like the Birkhoff theorem capture the idea that as you get far enough away from a galaxy it behaves more and more like a small shell, and this happens at intragalactic scales for these SMBHs: gravitationally, even to its arms' structure, it makes practically no difference whether Andromeda's central bulge has a lot more stars/gas/dust or whether it has one, two, or six central SMBHs (at enough spatial separation that they're not mutually orbiting in a way that would generate gravitational radiation our observatories are sensitive to).
The same idea applies to galaxies->galaxy clusters->filamentary structures: as you "zoom out" the density variations become less important: filaments are pretty sparse on average.
The Timescapes programe wants a sharper difference in matter sparseness between voids and filaments, and proposes that gravitational backreaction by the matter is responsible for generating that: the presence of matter steepens the density of matter over time (without the visible matter clearly becoming denser). I don't personally see how that's much different from a false-vacuum decay in the voids, conceptually. (ETA: well, it depends somewhat on how the Timescape void fraction evolves, but the local universe VF doesn't run void clocks fast enough, unless we do violence to the Copernican principle.)
(Also ETA, mostly a note-to-self: I also don't understand how they capture the angular diameter turnover point in their dressed geometry <https://journals.aps.org/prd/abstract/10.1103/PhysRevD.80.12...> PDF available from institution at <https://ir.canterbury.ac.nz/items/36fe829a-0e7a-45d6-8db6-c2...> (cf <https://astronomy.stackexchange.com/questions/21006/understa...>.))
Finally, I think the most important result of this latest Timescapes paper is a reminder to everyone that supernova data are a mess. A good X-mas present would be a couple readily visible Milky Way supernovae.
-
Nucleated objects could be long-lasting, which blunts the Boltzmann brain (Bb) picture, as under fluctuation theory the Bb is ephemeral and time-reversible. On the other hand, it's historically been attractive to think of the nucleation of a inflating patch of spacetime (with low enough entropy that structure like galaxies might form as it expands and fragments gravitationally).
I'll give it a try. This is very much a hand-wave.
tl;dr: Boltzman brains (Bb) from energy gradients: a "formless" high-energy fluctuation in a cold gas returns to thermal equilibrium through a Bb state.
The classical cartoon for a Standard Model of Particle Physics human Boltzmann brain (SMBb) is a cold (too cold for metabolism) Maxwell-Boltzmann gas or soup of atoms which in principle could condense into biological molecules via chains of endothermic and exothermic reactions. The gas is on average too cold for the endothermic parts, though, which essentially means no products comparable to those from anabolism.
From fluctuation theory randomly there will be high-temperature regions which allow for endothermy. In a hot bubble, which quickly cools by dissipation, complex molecules are (briefly) energetically favourable as their formation also lowers, locally, the temperature of the hot spot in which it's embedded.
The Boltzmann brain formed in this way is liable to be cooked apart by the heat of the hot spot outside the small region that cooled as the Bb condensed in it.
You've been wondering about how an SMBb might form. The starting point is a cold gas of photons. In that gas regions with vast amounts of gammas can fluctuate out of equilibrium: this is the hot spot. Particle pair productions and complicated decay chains serve to cool the hot spot (inelastically scattering gammas, among other processes), and consequently forming complex bound states embedded within the super-hot-but-rapidly-cooling spot is energetically favourable. Yes one has to have some luck (or some extra constraint or mechanism) in matter/antimatter asymmetry, which should be encoded in the grand canonical ensemble for interacting particles.
The SMBb will be torn apart by gammas and other radiation in the hot spot in which it is momentarily a cold spot.
One might compare this with a different extremely hot "hot spot" in which complicated states can form briefly. High-entropy pulsional pair-instability supernovae (PPISN) <https://online.kitp.ucsb.edu/online/stars-c17/woosley/pdf/Wo...> (see especially the graph on slide 5) are massive stars whose core rises to pair production temperatures. The pair-production cools the core of the very hot (~ 0.3 GK), very massive star; the cooling means less radiation supporting the star's bulk above the core. Gravitation from the sheer mass of the star itself drives a thermal runaway. However, during the runaway, there will be further cooling via nuclear processes that tend to generate a large neutrino flux. Soon however the star and all the heavy daughter products which condense during the pair-producing phase tend to be violently explosively disassembled.
The "hot spot" for a Standard Model Boltzmann brain might be several terakelvins hotter than a PPISN's core (the SMBb bubble ought to be gamma gas reaching QCD or even GUT temperatures), but won't be massive enough to self-gravitate. Animatter is the least of the SMBb's worries, given all the hotter radiation surrounding the cold spot formed by condensing into the brain itself.
Schrödinger or Schroedinger: it is just you on HN <<https://duckduckgo.com/?q=%22Schr%C3%B6edinger%22+site%3Anew...> who has used "öe", multiple times.
Boltzmann brains have nothing to do with Schrödinger: statistical mechanics works fully classically, and nobody treats Boltzmann brains in a quantum mechanical way because a Boltzmann brain is an unembodied ephemeral human brain. Natural human brains have a history of being warm and electrically noisy (any quantum features decohere faster than thought), while fluctuated-out-of-equilibrium human brains aren't around long enough to have their temperature measured, nor to produce much electrical noise.
A quantum-mechanical Boltzmann brain emerging from a gas of photons in (cold) equilibrium in which fluctuations take photons out of equilibrium and into the farrrr UV is going to be on the short-lived end of Boltzmann brains: things like annihilations and complicated decay chains will dissolve them away quickly. Which is the point. Boltzmann brains, unlike the bowl of petunias in The Hitchhiker's Guide to the Galaxy, should not have time to compose poetry.
Very hot thermal radiation is what destroys classical Boltzmann brains. They sort-of are a cool spot in an extremely violently hot bubble in an otherwise cold (colder than brains!) gas of almost everywhere uniform temperature.
> Yes I am familiar with the physics ...
> Quoting a university [physics] textbook on a philosophical argument
... which is philosophizing about actual physics ...
> is an interesting choice.
Well, what textbooks or other sources do you rely upon when philosophizing about fluctuation theory? What have you read or taught from?
> pop sci/undergrad classroom interpretations
?
Bbs are arguments against the early low-entropy state of the universe being a fluctuation out of thermal equilibrium, and of a future universe fluctuating out of the approximately de Sitter state of the far future.
Expanding steady state was an effort to capture the increasing evidence (including redshift relations) in favour of a Lemaître-style dense early universe, and to avoid several problems with ~static universes.
Since a steady-state cosmology has neither an early low-entropy configuration nor a late homogeneous equilibrium state (steady-state means homogeneity & isotropy in time as well as space: the "perfect cosmological principle"), I'm not sure how a BB argument arises in such a model. In an expanding steady-state model, is there some mechanism for making BBs other than to have them appear with the other components of new gas which under self-gravitation fragments into systems with negative heat capacity?
Landau and Lifshitz vol 5 <https://en.wikipedia.org/wiki/Course_of_Theoretical_Physics#...> is the standard textbook. There's an older copy on the Internet Archive <https://archive.org/details/landau-and-lifshitz-physics-text...>. (Having the background of L&L vol 9 makes a classroom demonstration even easier: a small handful of electronic parts for a resistive-capactive low-voltage DC electric dipole, a decent oscilloscope or other apparatus to measure and record fluctuating voltage, and a thermometer).
The probability of an out-of-equilibrium structure spontaneously fluctuating (briefly!) into existence depends on the complexity of the structure, and Boltzmann brains are much much much less complex than the whole Earth, solar system, Milky Way, or the early universe in which these structures' precursors originated. So therefore any theory compatible with statistical physics in which the early low-entropy state of the universe is a fluctuation in a higher-entropy "gas" is imperiled.
For the philosopher or two who wrote comments above in this thread, https://plato.stanford.edu/entries/statphys-Boltzmann/ is probably of interest.
Discounting Brain-in-a-Vat (because it's cognitively useless), the problem in a nutshell is that we inhabit a universe which appears (a) to have had a hot dense phase in approximate thermal equilibrium, (b) a future sparse phase in approximate thermal equilibrium, and (c) a whole bunch of structure in between those. Is the structure a fluctuation in (a)? Could (a) be a fluctuation in (b)? These are reasonable questions about which one can ask: is there astrophysical or laboratory evidence available to determine the answers?
One problem is that if (a) (early conditions) is a fluctuation in (b) (late conditions), wherein (a) simply evolves into (c) (complex structure with galaxies and so on) and then (b), what mechanisms could suppress simpler configurations than (a)?
A huge huge huge number of low-entropy Boltzmann brains fluctuating into existence is vastly more likley (on Boltzmann entropy grounds) than an early very-very-very-very-very-low-entropy universe compatible with the standard model of particle physics and the cosmic microwave background and galaxies all over the sky, in which there is a nonzero chance of human brains arising via evolutionary processes.
A tiny change in a Boltzmann brain as it fluctuates into existence could lead to a significant loss of false memory; a tiny change in a maximally-hot maximally-dense phase in the early universe could lead to completely different chemical elements (or none at all).
So Boltzmann brains highlight some metaphysical ratholes one can fall into with respect to the fine-tuning of the (a) state, and have provoked work on how (a) could be so generic an outcome that the evolution of (a)->(c) is "unsurprising". The hard part is coming up with observables which usefully compare a given hypothetical solution and our own sky.
Singleton black holes from collapsed stars move in their galaxy about the same as uncollapsed star: on the order of 200 km/s or so (faster towards the middle but still in the disc where motion is roughly circular around the galaxy's centre, slower in the bulge where motion is randomly around the galaxy's centre). Really unusually high-velocity stars move about 65-100 km/s faster than these, which is still not that fast, and "hypervelocity stars" (we've seen some twenty, compared to the 100 billion or so stars in our galaxy) move about only five to ten times faster still, but we're still at only about a thousandth of the speed of light.
Black hole binaries can be arbitrarily wide, even up to many thousands of light-years, taking hundreds of thousands of years or more to orbit each other, possibly at speeds comparable to those of stars in galaxies. MEERKAT just announced its pulsar timing array results which focuses on orbital periods of some tens of years ("nanohertz gravitational waves"), which means not moving very fast. Here's a nice cartoon: https://physics.aps.org/articles/v16/116 LIGO is sensitive to much higher frequencies, once a black hole binary's mutual orbit has shrunk considerably - at the final chirp, they are moving at double-digit percentages of the speed of light and the orbital periods are in the milliseconds. In that regime black hole horizons do have bumps raised on them: https://www.youtube.com/watch?v=Y1M-AbWIlVQ
The black holes can't rip apart though: everything inside stays inside.
I'm afraid I can't figure out what you're talking about in terms of frozen in time, time dilation, or atoms compacting.
I did. In particular I did not miss the whole preceding apparent horizon vs event horizon context of §VIII or the second half of the second column of p. 17, all of which conflicts with your:
It hasn't finished forming because as its gravitational
field increases its time distortion increases. Its
formation is "frozen in time" (actually just very very
slow), it is *never fully formed*.
And then this choice statement and your previous paragraph in mixed order:
> That was 37 years ago! We may have figured out one or two things about black holes since then
"Tell all physicists you don't read physics papers without saying you don't read physics papers..." [1]
I mean, did you even look at the range of dates in your One Good Paper's bibliography?
For starters, Ginzburg & Frolov was just a useful foundational paper (which I suspected you had never heard of) that shows that generically in curved spacetimes, different observers count different numbers of particles, and in particular one observer's vacuum can be another observer's cloud of electrons, positrons, and photons. This was a nice way of saying that your "relativity does not allow observers to disagree on observations of what" is just wrong.
I gave you a google scholar link to the 37 year old paper paper so that it would be clear anyone with a slightly different academic background (and I hoped you) that it's a foundational theory paper. Frolov is the well-known author of two standard textbooks on the physics of black holes (with Novokov and with Zelnikov), both of which deal with Frolov's 37-year-old paper in the context of evaporation and of different observers counting different particle numbers and how that an acceleration between past and future observers accounts for Hawking quanta. Both Frolov textbooks appear early on the first page of google scholar results.
(The 37-year-old concern is especially funny. Frolov's 21st century textbook, like practically all textbooks on gravitational phenomena and theory, even reference papers which are now more than a hundred years old, oh no! Choosing a recent GR textbook -- Carroll 2014 -- the author lists under Advanced General Relativity: Hawking & Ellis 1973, de Felice & Clarke 1990, Sachs & Wu 1977; and in the Graduate section: Wald 1984, MTW 1973, Weinberg 1972, ...)
> modern (2024-era) numerical methods
which are built to be compatible with ... what? Analytical and/or perturbation theory, right?
(BTW, Stark & Piran published their computer results in 1985: <https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.55...>. Again, can be found by placing sci-hub.se/ before that URL. That's 39 years ago! "We have performed an extensive series of tests [including] known perturbation solutions.")
One more kick at the ridiculous dead horse: at the bottom of p. 17 one finds, "We are not the first to propose a picture like the one presented throughout this section. As far back as theoriginal discovery of the Hawking effect, similar ideas were invoked in [4], and by various comments of [2, 3]". The dates of those are respectively 1974, 1975, and 1976. Oh no!
Could it be that among the "one or two things about black holes since then" that "We" may have "figured out" is that early theory papers (the 80s are not early) turn out to have good support in things like astrophysics, magnetohydrodynamics, gravitational wave observations, Hulse-Taylor / PSR J0737−3039 etc. etc.?
- --
[1] https://journals.aps.org/125years but uh oh that was 2018 and surely the list would be totally different now!
Can a BH form in a finite time as viewed by a
distant observer? (Answer: Yes.)
It hasn't finished forming because as its gravitational
field increases its time distortion increases. Its
formation is "frozen in time" (actually just very very
slow), *it is never fully formed.*
If there is a paradox in your model, then your model
is broken, end of story.
Static and non-static observers in general curved spacetimes immersed in relativistic QFTs generically disagree on particle counts. The Unruh, Hartle-Hawking, Rindler, Minkowski and Boulware vacuums seem especially apposite search terms for someone who isn't among "the slow people at the back of the class".
(Ginzburg & Frolov 1987 is a good starting point: https://iopscience.iop.org/article/10.1070/PU1987v030n12ABEH... (one can also stick "sci-hub.se/" in front of the URL). It is cited a lot <https://scholar.google.co.uk/scholar?cites=12518697499517381...>).
Uhhh... one of those words should go.
Let's keep it fully classical and drop "photon": we're interested in gravitational effects rather than quantum ones (uncertainty, fluctuations, tunnelling, details about scattering and more). Really what we want is something to illuminate (pardon the pun) interesting null geodesics, so a thin collimated beam -- a pencil of light -- will do.
The relevant surface here is the apparent horizon, which can be measured by infalling apparatuses, and not the event horizon, the location of which is determined by the configuration of the entire spacetime. (See Visser PRD 2014 <https://journals.aps.org/prd/abstract/10.1103/PhysRevD.90.12...> or the corresponding arxiv version <https://arxiv.org/abs/1407.7295>).
> stay in place forever
Note the region inside the shell and the downward-pointing wedge in Fig 1. of Visser 2014 is flat Minkowski spacetime. Everything in that region will work like Special Relativity, as one would expect from the shell theorem.
In particular, a pencil of light directed outwards through the apparent horizon in Fig. 1. will ride the AH down to the singularity, but a receiver intercepting the pencil of light just inside the shell would notice nothing unusual: spacetime is flat there.
Eventually the collapsing shell collides with observers floating weightlessly inside it, and they have a bad time. But they can direct a pencil of light inwards just before the shell hits them.
The References in your "speculative paper" include at least five citations of the same author's previous work, at least one of which didn't even find its way into SCIRP's OALJ, and does not cite the Ludwig paper.
The full text also has such writing and editing gems, in the published version, as "the disk, the bugle and the halo of dark matter" immediately before eqn 23.
The paper's central argument is not obviously worth untangling, because the decomposition into the g and k fields (eqn 10) isn't Lorentz-invariant which raises questions about higher speed observables like cosmic rays, lensed background, "kicked" post-merger BHs, and even stars flung out of globular star clusters. There is no general transform avaiable in his equations of motion between two subsystems (e.g., outer stars and inner stars) related by a Lorentz boost. As far as I can tell the notational approach (and even the expression "gravitic field" to stand for the the gravitomagnetic field B_g) is unique to the author. It's so atypical (for quite ordinary equations) that I'd be surprised if there was any sort of reviewer or editor at all.
The author <https://people.epfl.ch/stephane.lecorre/> is a computer engineer in the university's architecture department, and claims a master's degree in theoretical physics <https://www.researchgate.net/profile/Stephane-Le-Corre-2>. I admire his continuing interest in and even investigations of "Astrophsics" (sic), but would not point to him as a persuasive expert as you have.
The Ludwig paper (EPJC 2021) is by comparison cited by 60, only a couple of which are self-cites. Whatever take one might have on Springer's approaches to open access journals, EPJC has an IF of almost 5.
Ludwig is an electrical engineer and plasma physicist. With the many cites on his set of related papers, it's clear he was not ignored by virtue of not being an astrophysicist or relativist. So we can't blame Le Corre's background for the lack of published engagement with his no-dark-matter-needed papers.
I don't think that Ludwig's gravitomagnetic vortex model is particuarly interesting in galaxy rotation curves because the fall-off off of the Lorentz force pulling outer margins of the galaxy inwards must have some arbitrary per-galaxy cutoff that also suppresses wild lensing effects at the cutoff point; we're interested mainly in doppler corrections on the HII spectrum rather than luminous stars (we don't necessarily need DM to explain flat rotations for the outer stars - we do need DM for rotating HI gas well beyond those outer stars) so the cutoff point is beyond the optical limb (meaning we should see wild lensing even in HST/WFC3); the gravitomagnetic effects must be smaller than the gravitoelectric effects (and capturing that somewhat in (v/c)^2 terms corrections to Newtonian/Keplerian orbits (v ~ 0.001 c in Andromeda-like galaxies) should be on the order of 10^-6 whereas in this approach we'd need corrections on the order of 10^-5 and higher for lower-mass lower-v dwarfs); and because the formulation does not work well with elliptical and irregular galaxies (both of which can have low circumferential rotational support - blobs of gas move radially in and out) without treating them differently from discoids (and when you do that in this approach you get divergences at galactic cores); and even for discoids there must be a minimum rotational support. More prosaically, the problem with the model is to avoid having to stabilize satellite dwarfs around a galaxy: you have to make the attractive Lorentz force not pull them right into the parent's middle and you have to avoid having satellites tear the crap out of the outer orbits of the parent galaxy's HI gas.
The paper's central idea certainly does not succeed as a general theory for flat rotation curves of HI dust as opposed to stars in circular orbits in a thin-disc plane.
However Ludwig's wasn't an obviously misguided idea, the paper's arguments are pretty clear, he's done follow-on work that is interesting, and the academic dialogue it produced is well deserved. But to say that anyone could use this paper to point to which mathematical object in GR (or which physical aspect of GR) stabilizes the relevant HI and dwarf orbits is, I wager, a huuuuge stretch.
Finally, quoting you:
> For example, properly accounting for GR effects is enough to explain the observed rotational curve for our Galaxy without the need for any dark matter hypothesis
This is not at all borne out by your choice of papers. Ludwig's text doesn't even mention the Milky Way.
It turns out that one can knit together simplified models and build up a good description of a real complex system, but this has been known since at least the dawn of thermodynamics, if not since the time of Newton.
Indeed, Nasa and its counterparts have been working for decades with an approximation of the solar system: new bodies inside Neptune's orbit keep being found practically every year. It's not remotely likely that we know all the bodies of the solar system even out to Neptune (much less beyond), let alone their orbital parameters and how those evolve over mere millions of years <https://en.wikipedia.org/wiki/Stability_of_the_Solar_System>. Does that mean publishing the results of studies of long-running models of our solar system "can only be fodder for academic careers"? Even if it spots anomalies that lead to the actual discovery of very dim bodies?
> collect your academic points
The academic points mostly come from being cited by an author poking holes in your paper. Go investigate google scholar.
This is called the academic dialogue. And yes, a variety of scores are kept (e.g. the loathsome h-index).
But I guess you don't care, because you are happy writing obviously ignorant nonsense on hacker news for engagement and upvotes, right?
> There is one universe but an infinite number of spacetimes
There is possibly one unique spacetime that fully describes the universe, but guess what, we simply do not have enough computer power on the planet to validate such a model.
Here's the recent state of the art in computational cosmological simulation, n-body with n in the hundreds of billions:
https://flamingo.strw.leidenuniv.nl/ (their page)
https://skyandtelescope.org/astronomy-news/largest-ever-comp... (decent write up)
There are more than a hundred billion stars in this galaxy; there are more than a hundred billion galaxies in our sky. And there are more than a hundred billion particles in a star. And there are lots of motes of dust and blobs of gas between stars. So we're quite a few orders of magnitude too small in n in our n-body simulating to be able to pick out our own universe, exactly described, from a large set of simulations.
We also obviously don't have an infinite number of observations, since neutrinos and gravitational waves are hard to detect at all (and we only see a small part of the frequency space of both), we've only just started having really good views in the near infrared (JWST), our views in X-Rays and gamma rays are fuzzy because of technological limits, and so on and so forth. We are just at the start of https://en.wikipedia.org/wiki/Multi-messenger_astronomy four centuries after Galileo used a telescope to find the four biggest moons of Jupiter. (Incidentally, three moons of Jupiter were just discovered two years ago, because hey telescopes are not all-powerful and all-seeing. Guess how they figured out where to point the Victor M. Blanco Telescope?).
> The whole thing is a joke
Honestly, it's amazing that you aren't embarrassed by how obvious your ignorant contrarianism is.
Write back if you're actually interested in expanding your knowledge rather than mocking people you don't know whose work you know very very very very little about.
Ha ha just joking, I know you don't care.
The volume deviation is carried in the Ricci tensor
https://en.wikipedia.org/wiki/Ricci_curvature#Direct_geometr...
http://arxiv.org/pdf/gr-qc/0401099v1 (section 5.2)
https://math.ucr.edu/home/baez/gr/outline2.html (bullet point 9)
The highest-scoring answer at https://physics.stackexchange.com/posts/36411/revisions is a fairly reasonable attempt to calculate the volume deviation for nonspinning ~spherically symmetric bodies with the masses of the Earth (~ 10^2 km^3) and the Sun (~ 10^12 km^3), compared to the Euclidean-Newtonian volumes. Qualitatively, dropping these symmetries and the uniformity of the matter will tend to make the volume deviation larger.
> there is no volume
The volume deviation becomes enormous for compact (relativistic) objects, and for black holes one has to exercise care in even defining a volume, since naive choices of coordinates will show a divergence. Typically the choice of a 3-space inside the horizon has a time-dependency, and most choices of 3-space will tend to grow towards the future.
Christodoulou & Rovelli's (C&R) approach: https://arxiv.org/abs/1411.2854 ("it is large" for the largest volume bounded by a BH's area should win some sort of award for understatement). https://arxiv.org/abs/0801.1734 (reference [5] of the 2014 C&R paper) takes a slightly different path to the same conclusion.
YC Ong (several other references, and a number of related later papers) has a nice article at https://plus.maths.org/content/dont-judge-black-hole-its-are... The prize quote: "To give an idea of how large the interior of a black hole could become, this formula estimates that the volume for Sagittarius A, the supermassive black hole at the centre of our Milky Way Galaxy, can fit a million solar systems, despite its Schwarzschild radius being only about 10 times the Earth-Moon distance. (Sagittarius A is actually a rotating black hole, so its geometry is not really well-described by the Schwarzschild solution, but this subtlety does not change the result by much.)" And: " These examples show that, in addition to the surprising property that the largest spherically symmetric volume of a black hole grows with time, in general, the idea that volume of a black hole grows with the size of its surface area is wrong. In other words, by comparing two black holes from the outside, we cannot, in general, infer that the "smaller" black hole contains a lesser amount of volume. "
The area of a Schwarzschild horizon is straightforward to define, and unique for constant mass. (Procedurally you could count the number of unique tangent planes at r_{schwarzschild}, but there are other ways of arriving at the area).
If your sweater "weave" represents a set of orbits around the black hole and your ant free-fall along those rather than walk, you are getting close to a solution of the geodesic equations for a black hole. A free-falling ant will stick quite firmly to geodesic motion around a black hole. However, there are definitely plunging orbits that will take the orbiting-ant inside the horizon, and there is an innermost stable circular orbit (ISCO) that isn't solid like the yarn: a small perturbation of an orbiting-ant there will knock it into or away from the BH. But an un-knocked ant can circle forever.
The ISCO (3r_{schwarzschild} for a Schwarzschild black hole) is quite a lot of ant-lengths above the horizon of a BH (2r_{schwarzschild}). Spinning black holes have a narrower gap between the ISCO and the point of no return.
The point of no return for a spinning hole is just that: the ant can't backtrack, but will continue moving "forward" from there, and for a massive enough black hole it could do so for an hour or more before it feels the discomfort that precedes spaghettification. The "no drama" conjecture holds that the freely-falling ant won't even notice crossing the point of no return, although astrophysically it is likely to have noticed things falling inwards on different trajectores even above the point of no return (at ISCO around an astrophysical black hole the ant has a good chance of being knocked by something on an intersecting trajectory).
> fabric of spacetime
Misleading terminology. It's not a substance. Spacetime is nothing more than a collection of possible trajectories, and none of them needs to be realized. (Our universe has an enormous number of unrealized trajectories compared to ones on which real bodies move).
> bunched up in a very thin shell
The "thin shell" is just a set of points of no return, and for an astrophysical black hole where exactly each point is can be rather fuzzy since it depends on the outside universe which is filled with moving ants (and galaxies).
In any spacetime you care to do an ADM split on, there are an infinite number of real-valued smooth scalar fields whose gradient is everywhere non-zero and timelike available to serve as the coordinate time.
In the standard cosmology the at-rest isotropic and homogeneous distribution of matter provides an obvious coordinate time function, but physics still has to work for other inertial and accelerated observers, so there is nothing preventing anyone from using a non-comoving observer's proper time in the ADM split.
Nits:
* Hamiltonian formulation of general relativity
* ADM formalism
The expansion is in the metric, and most visible (and most amenable to interpretation as an expansion of space) when using comoving coordinates. However, we are allowed to work in any system of coordinates, and when we do a general coordinate transform, we lose the interpretation of the metric expansion as an expansion in space.
("We see in both [Milne & de Sitter] cosmologies that the interpretation of redshift as an expansion of space is dependent upon the coordinates one chooses to calculate z." -- https://academic.oup.com/mnras/article/422/2/1418/1036317 final sentence in §3.4 de Sitter space).
The standard cosmology's FLRW spacetime (and also de Sitter space, where the vacuum constant positive scalar curvature makes for an easier-to-understand expansion history) is time-orientable. There are more points in spacetime in the future direction from an arbitrary point anywhere in the entire spacetime, than in that point's past.
However, the real distribution of matter is in our universe lumpy, as is easily demonstrated right here on Earth. Standing on the ground you can tell that locally there is neither isotropy nor homogenity (you can see quite far up into the sky, but not so far into the ground). Moreover, there are differences in isotropic pressure, convection, heat conduction, and shear stresses between the air and ground, none of which are features of the perfect fluids in the FLRW model. So locally the FLRW metric is not suitable, and since the Earth is very much not vacuum de Sitter is even less suitable. Consequently it should not offend anyone to read that Manhattan isn't undergoing cosmological expansion. Most things within ten kiloparsecs of here are gravitationally collapsing. It requires coordinate contortions to interpret interplanetary or interstellar space in the Milky way as expanding, and switching to different systems of coordinates will blow up that interpretation.
A "swiss cheese" universe with collapsing vacuoles in an expanding cosmology reflects that it's only when we go from ~kpc length scales to ~Gpc length scales that the distribution of matter behaves enough like perfect fluids to allow for an exact solution to the Friedmann equations. The collapsing vacuoles are usually modelled like Lemaître-Tolman-Bondi with a thin shell boundary; this results in a vacuole that time-orientable and has fewer spacetime points in the future direction. "Hole" time functions and "cheese" time functions must be different (hole clocks tick slower as they fall towards the centre).
(It's also a relief to see that eminent names in the field make a lot of typos.)