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I've read somewhere an article which posited that our 3D universe might be inside a 4D black hole. When you cross a black hole's event horizon, the radial coord

I've read somewhere an article which posited that our 3D universe might be inside a 4D black hole. When you cross a black hole's event horizon, the radial coordinate becomes timelike, so you lose one degree of spatial freedom. Movement is still possible in the tangential directions however, so what you get is basically an N-1 dimensional universe. So maybe our 3D universe is actually matter that fell into a 4D black hole, and our 3D black holes contain 2D flatland universes. And of course, the outer 4D universe might be in a 5D black hole, etc.

unyttigfjelltol 1y ago
Yes, and then there's the parlor game of guessing what familiar property of our known universe is actually a spaghetified fourth dimension. I guessed c once. It would be a constant. Maybe all the constants are spaghettified remains of a superior universe.
- jfengel 1y ago
  I don't think c is a good candidate, because it's not really a parameter. It's just a correction factor for our mis-judgment in picking different units for time and space. In "natural units", we define the units so that the important conversion factors (c, G, h-bar, etc) work out to exactly 1. You can say that c is one light-year per year and then forget about it. The true parameters of the universe are the dimensionless constants: the fine structure constant, proton-electron mass ratio, 3+1 dimensions, etc.
  - throwawaymaths 1y ago
    > I don't think c is a good candidate, because it's not really a parameter. dont be so sure! there is no way to experimentally know if c is a parameter or not. there are consistent physics formulations which have variable, even anisotropic c. physicists dont usually explore them (e.g. tangherlini relativity) though because the math is considerably harder.
    - raattgift 1y ago
      Physicists (and in particular the subset doing physical cosmology) don't usually explore parametrizations of c because they're not clearly physical (and sometimes even clearly unphysical), or alternatively don't help solve astrophysical or cosmological problems. Relativists sometimes like to explore things that make using the Tangherlini transformations rather than the Lorentz transformations look positively benign. (To be clear, the Tangherlini synchronization system is clearly unphysical, requiring infinite speeds. His thesis also proposed using a distinguished global frame, which is not really philosophically different from how the standard cosmological frame is used, and seems OK because the distribution of stress-energy can pick out useful systems of coordinates in standard relativity. Unfortunately his method frustrates and probably outright breaks comparisons between inertial reference frames related by a boost, which the standard cosmology does not, and it's hard to see an alternative method that preserves his central ideas.) But why even be stuck with 3+1d spacetime like Tangherlini? He was trying to do physics. But an unphysical metric signature with 47 plusses and no minuses is really cool! In our observed universe, FAPP, c is the same everywhere after recombination, and we get that from spectral lines. You have to play really weird games to preserve the Lyman-alpha forest's apparent isotropy while introducing spacetime (or redshift-space, here) anisotropy. Things like BAOs make the problem even harder. If we strip away all that pesky radiation and the information its structure encodes, analysing variations of c gets a lot easier. A relatively recent paper (Lewis & Barnes 2021) I enjoyed considered anisotropy in the one-way speed of light in an FLRW cosmology with zero energy density (well, really the convenient Milne model, which is also far from spatially flat). "So far, we have considered two cases, where either the speed of light is isotropic, or the extreme case where the anisotropic speed is 1/2 in one direction, and infinite in the other. The question remains whether this holds true in general case, for an arbitrary κ": https://www.cambridge.org/core/journals/publications-of-the-astronomical-society-of-australia/article/oneway-speed-of-light-and-the-milne-universe/193D9277D6E2DC7A825979FF1ECE4C84 https://www.cambridge.org/core/journals/publications-of-the-... (arxiv: <https://arxiv.org/abs/2012.12037 https://arxiv.org/abs/2012.12037>). "For more general cosmological models, where the presence of mass and energy results in curved space-time, the picture is more complicated as there is no simple mapping of the modified Lorentz transformations into the general relativistic picture. We leave this discussion for a future contribution." Sadly there doesn't seem to be a future contribution yet, at least going by published citations (<https://scholar.google.com/scholar?cites=2012575105829699847&as_sdt=2005&sciodt=0,5&hl=en https://scholar.google.com/scholar?cites=2012575105829699847...>). (Of those, I've put the Chamberlain paper on my to-read pile; you'd appreciate how it relates to Tangherlini, "credence is given to one-way infinite light-speed inward to each particle in direct comparison against Einstein’s isotropic (c=constant) light-speed"). Of course there's also the excellent Magueigo 2003 VSL overview <https://iopscience.iop.org/article/10.1088/0034-4885/66/11/R04 https://iopscience.iop.org/article/10.1088/0034-4885/66/11/R...> copy <https://cds.cern.ch/record/618057/files/0305457.pdf https://cds.cern.ch/record/618057/files/0305457.pdf> preprint <https://arxiv.org/abs/astro-ph/0305457 https://arxiv.org/abs/astro-ph/0305457>. And even if you can make sense of an f(c) cosmology in the early visible universe, you will get to epochs before recombination and try to make sense of the later universe's chemistry, which of course relates to big bang light nucleosynthesis, baryogenesis and electroweak ssb. How do you abolish Lorentz symmetry in those epochs? Good luck! (I mean, I think if you are doing physical cosmology you ought not to ignore gauge theory...)
- AtlasBarfed 1y ago
  I thought that's what the high dimension counts of string theories were: taking constants and turning them into dimensions. Or is that too simplified?
- jldl805 1y ago
  Gravity, obvs.
account-5 1y ago
What's in a 1D black hole?
- SlightlyLeftPad 1y ago
  /dev/null I presume
- modderation 1y ago
  I'm guessing it'd look something like this on a 1-dimensional number line: --- > | > >> . << < | < --- The dot in the middle would be the singularity, the pipes the event horizon, and the contents would be increasingly warped spacetime that may or may not exist, depending on your interpretation of things.
codethief 1y ago
> When you cross a black hole's event horizon, the radial coordinate becomes timelike, so you lose one degree of spatial freedom. The second half is incorrect. Since the time coordinate becomes spacelike in turn you'll still have 3 spatial degrees of freedom. Dimensions can't just vanish if you believe that spacetime is a 4D Lorentzian manifold (as physicists do). Moreover, the singularity is not a place you can poke with a stick, once you've entered the black hole. It lies in your future, in the same way as your death.
- BoiledCabbage 1y ago
  > The second half is incorrect. Since the time coordinate becomes spacelike in turn you'll still have 3 spatial degrees of freedom. Dimensions can't just vanish if you believe that spacetime is a 4D Lorentzian manifold (as physicists do). Can we say that one of the spatial dimensions (the radial dimension) and the time dimension combine into a single dimension? After crossing the event horizon aren't they 1:1 correlated?
  - raattgift 1y ago
    No, there's no change in dimensionality. The swapping of timelike and radial dimensions are a "game" frequently played with families of coordinates, including Schwarzschild coordinates. One can apply any system of coordinates on a physical system without changing the behaviour of the physical system: coordinates are unphysical. Think of navigating around in a neighbourhood: you can talk about going forward a few blocks then turning left, after which you go forward two more blocks; or for the same journey, going "city north" a few blocks then going "city west" two blocks. Here assuming that (initially) "forward" is in the "city north" direction (and "city north" is not necessarily exactly magnetic north nor a section of a meridian of longitude). After the left turn, "forward" is "city west". There's an analogue to the discussion's (ab)use of Schwarzschild coordinates. In Schwarzschild spacetime, without applying any system of coordinates, just floating in free-fall far from a black hole extremizes your travel in the timelike dimension. (You can do this at home: you stay put at some point on Earth (whether you use GPS latitude/longitude/altitude or some other system of coordinates) but your wristwatch keeps ticking). Inside the black hole horizon, just floating in free-fall extremizes your travel in the direction of the singularity. Far from the black hole, accelerating as strongly as you can in any direction takes travel from the timelike dimension and puts it into one or more spatial dimensions. In particular, you have the freedom to increase the spacetime interval between you and the singularity. Within the horizon, however strongly you accelerate the spacetime interval between you and the singularity shrinks. This behaviour seems to invite the use a different set of coordinates applied to a patch of space around an observer far from the black hole and a patch of space around an observer inside the horizon. It's some human cognition thing, and in the early 20th century it took decades to discover systems of coordinates that work for observers far from the black hole, at the horizon, and inside the horizon. And even today, most people don't seem to try to enhance physical intuitions by swapping among arbitrary systems of coordinates (including no coordinates) on a single physical system like a black hole and a pair of observers (one inside the horizon and one far outside the black hole). The Schwarzschild black hole interior is still locally Lorentz-invariant everywhere (because the whole Schwarzschild spacetime is a Lorentzian manifold). The various local interactions of the Standard Model will keep working inside a black hole. In a really tiny patch around every point, everything behaves as if its in Minkowski space (flat 4-d (3 spatial + 1 time) spacetime). (That's one of the problems of quantum field theory on curved spacetime: the "focusing-pressure" [for experts: this is encoded in the Weyl curvature tensor; my "scare quotes" take a view of this in a Raychaudhuri equation way] gets so high that the unknown ultraviolet behaviour of the Standard Model (a quantum field theory) becomes relevant. The Weyl behaviour in Schwarzschild is that quasispherical objects are strongly prolated with the long axis aligned radially: a soccer ball or basketball starts looking like an American or Canadian or Rugby football ball. The radial stretching "spaghettifies" by ripping apart weaker bonds (like intermolecular ones, and molecular ones, and ionizing atoms), but the tangential squashing ("focusing") must eventually generate more nuclear interactions, probably up to quantum chromodynamics (QCD) energies possibly before the radial stretching starts generating hadronization. How this works in the Standard Model is just unknown. However simpler "test" quantum field theories (fewer, or even no, interactions; and often no colour-confinement-like processes) raise really difficult questions. Finally, back to the Standard Model as local theory: how does any allegedly quantum nonlocality behaviour work? Local here in the sence that states can be distinguished by local measurements alone. Related questions: can you entangle particles deep inside a black hole? If an entangled pair fall in together, how does the entanglement evolve? Or obsessing black hole information people, what if you throw in only one half of an entangled pair and locally measure the outside half? Nobody has great answers for these sorts of questions at present, and there's no near-term hope of testing any proposals in laboratories or via astrophysical observation.
deleted 1y ago
[deleted]
twothreeone 1y ago
What? Wouldn't that mean an object's speed in some direction determines how time passes once it crossed over, and conversely, it would experience its old time dimension as spatial and be able to "move through (old) time" freely after crossing the event horizon?? My head hurts.
mousethatroared 1y ago
You can't have the curl operator in 4D.
paulnovacovici 1y ago
I’ve always like to explore the idea of our universe being in a static 5th dimension where the 5th dimension represents randomness/entropy. The same way to think about exploring a 2d plane in a 3 dimensional space where the 3rd dimension is constant. We just happen to be in a random big bang in this 5th dimensional space

unyttigfjelltol 1y ago

Yes, and then there's the parlor game of guessing what familiar property of our known universe is actually a spaghetified fourth dimension. I guessed c once. It would be a constant. Maybe all the constants are spaghettified remains of a superior universe.

jfengel 1y ago
I don't think c is a good candidate, because it's not really a parameter. It's just a correction factor for our mis-judgment in picking different units for time and space. In "natural units", we define the units so that the important conversion factors (c, G, h-bar, etc) work out to exactly 1. You can say that c is one light-year per year and then forget about it. The true parameters of the universe are the dimensionless constants: the fine structure constant, proton-electron mass ratio, 3+1 dimensions, etc.
- throwawaymaths 1y ago
  > I don't think c is a good candidate, because it's not really a parameter. dont be so sure! there is no way to experimentally know if c is a parameter or not. there are consistent physics formulations which have variable, even anisotropic c. physicists dont usually explore them (e.g. tangherlini relativity) though because the math is considerably harder.
  - raattgift 1y ago
    Physicists (and in particular the subset doing physical cosmology) don't usually explore parametrizations of c because they're not clearly physical (and sometimes even clearly unphysical), or alternatively don't help solve astrophysical or cosmological problems. Relativists sometimes like to explore things that make using the Tangherlini transformations rather than the Lorentz transformations look positively benign. (To be clear, the Tangherlini synchronization system is clearly unphysical, requiring infinite speeds. His thesis also proposed using a distinguished global frame, which is not really philosophically different from how the standard cosmological frame is used, and seems OK because the distribution of stress-energy can pick out useful systems of coordinates in standard relativity. Unfortunately his method frustrates and probably outright breaks comparisons between inertial reference frames related by a boost, which the standard cosmology does not, and it's hard to see an alternative method that preserves his central ideas.) But why even be stuck with 3+1d spacetime like Tangherlini? He was trying to do physics. But an unphysical metric signature with 47 plusses and no minuses is really cool! In our observed universe, FAPP, c is the same everywhere after recombination, and we get that from spectral lines. You have to play really weird games to preserve the Lyman-alpha forest's apparent isotropy while introducing spacetime (or redshift-space, here) anisotropy. Things like BAOs make the problem even harder. If we strip away all that pesky radiation and the information its structure encodes, analysing variations of c gets a lot easier. A relatively recent paper (Lewis & Barnes 2021) I enjoyed considered anisotropy in the one-way speed of light in an FLRW cosmology with zero energy density (well, really the convenient Milne model, which is also far from spatially flat). "So far, we have considered two cases, where either the speed of light is isotropic, or the extreme case where the anisotropic speed is 1/2 in one direction, and infinite in the other. The question remains whether this holds true in general case, for an arbitrary κ": https://www.cambridge.org/core/journals/publications-of-the-astronomical-society-of-australia/article/oneway-speed-of-light-and-the-milne-universe/193D9277D6E2DC7A825979FF1ECE4C84 https://www.cambridge.org/core/journals/publications-of-the-... (arxiv: <https://arxiv.org/abs/2012.12037 https://arxiv.org/abs/2012.12037>). "For more general cosmological models, where the presence of mass and energy results in curved space-time, the picture is more complicated as there is no simple mapping of the modified Lorentz transformations into the general relativistic picture. We leave this discussion for a future contribution." Sadly there doesn't seem to be a future contribution yet, at least going by published citations (<https://scholar.google.com/scholar?cites=2012575105829699847&as_sdt=2005&sciodt=0,5&hl=en https://scholar.google.com/scholar?cites=2012575105829699847...>). (Of those, I've put the Chamberlain paper on my to-read pile; you'd appreciate how it relates to Tangherlini, "credence is given to one-way infinite light-speed inward to each particle in direct comparison against Einstein’s isotropic (c=constant) light-speed"). Of course there's also the excellent Magueigo 2003 VSL overview <https://iopscience.iop.org/article/10.1088/0034-4885/66/11/R04 https://iopscience.iop.org/article/10.1088/0034-4885/66/11/R...> copy <https://cds.cern.ch/record/618057/files/0305457.pdf https://cds.cern.ch/record/618057/files/0305457.pdf> preprint <https://arxiv.org/abs/astro-ph/0305457 https://arxiv.org/abs/astro-ph/0305457>. And even if you can make sense of an f(c) cosmology in the early visible universe, you will get to epochs before recombination and try to make sense of the later universe's chemistry, which of course relates to big bang light nucleosynthesis, baryogenesis and electroweak ssb. How do you abolish Lorentz symmetry in those epochs? Good luck! (I mean, I think if you are doing physical cosmology you ought not to ignore gauge theory...)
AtlasBarfed 1y ago
I thought that's what the high dimension counts of string theories were: taking constants and turning them into dimensions. Or is that too simplified?
jldl805 1y ago
Gravity, obvs.

account-5 1y ago

What's in a 1D black hole?

SlightlyLeftPad 1y ago
/dev/null I presume
modderation 1y ago
I'm guessing it'd look something like this on a 1-dimensional number line: --- > | > >> . << < | < --- The dot in the middle would be the singularity, the pipes the event horizon, and the contents would be increasingly warped spacetime that may or may not exist, depending on your interpretation of things.

codethief 1y ago

> When you cross a black hole's event horizon, the radial coordinate becomes timelike, so you lose one degree of spatial freedom. The second half is incorrect. Since the time coordinate becomes spacelike in turn you'll still have 3 spatial degrees of freedom. Dimensions can't just vanish if you believe that spacetime is a 4D Lorentzian manifold (as physicists do). Moreover, the singularity is not a place you can poke with a stick, once you've entered the black hole. It lies in your future, in the same way as your death.

BoiledCabbage 1y ago
> The second half is incorrect. Since the time coordinate becomes spacelike in turn you'll still have 3 spatial degrees of freedom. Dimensions can't just vanish if you believe that spacetime is a 4D Lorentzian manifold (as physicists do). Can we say that one of the spatial dimensions (the radial dimension) and the time dimension combine into a single dimension? After crossing the event horizon aren't they 1:1 correlated?
- raattgift 1y ago
  No, there's no change in dimensionality. The swapping of timelike and radial dimensions are a "game" frequently played with families of coordinates, including Schwarzschild coordinates. One can apply any system of coordinates on a physical system without changing the behaviour of the physical system: coordinates are unphysical. Think of navigating around in a neighbourhood: you can talk about going forward a few blocks then turning left, after which you go forward two more blocks; or for the same journey, going "city north" a few blocks then going "city west" two blocks. Here assuming that (initially) "forward" is in the "city north" direction (and "city north" is not necessarily exactly magnetic north nor a section of a meridian of longitude). After the left turn, "forward" is "city west". There's an analogue to the discussion's (ab)use of Schwarzschild coordinates. In Schwarzschild spacetime, without applying any system of coordinates, just floating in free-fall far from a black hole extremizes your travel in the timelike dimension. (You can do this at home: you stay put at some point on Earth (whether you use GPS latitude/longitude/altitude or some other system of coordinates) but your wristwatch keeps ticking). Inside the black hole horizon, just floating in free-fall extremizes your travel in the direction of the singularity. Far from the black hole, accelerating as strongly as you can in any direction takes travel from the timelike dimension and puts it into one or more spatial dimensions. In particular, you have the freedom to increase the spacetime interval between you and the singularity. Within the horizon, however strongly you accelerate the spacetime interval between you and the singularity shrinks. This behaviour seems to invite the use a different set of coordinates applied to a patch of space around an observer far from the black hole and a patch of space around an observer inside the horizon. It's some human cognition thing, and in the early 20th century it took decades to discover systems of coordinates that work for observers far from the black hole, at the horizon, and inside the horizon. And even today, most people don't seem to try to enhance physical intuitions by swapping among arbitrary systems of coordinates (including no coordinates) on a single physical system like a black hole and a pair of observers (one inside the horizon and one far outside the black hole). The Schwarzschild black hole interior is still locally Lorentz-invariant everywhere (because the whole Schwarzschild spacetime is a Lorentzian manifold). The various local interactions of the Standard Model will keep working inside a black hole. In a really tiny patch around every point, everything behaves as if its in Minkowski space (flat 4-d (3 spatial + 1 time) spacetime). (That's one of the problems of quantum field theory on curved spacetime: the "focusing-pressure" [for experts: this is encoded in the Weyl curvature tensor; my "scare quotes" take a view of this in a Raychaudhuri equation way] gets so high that the unknown ultraviolet behaviour of the Standard Model (a quantum field theory) becomes relevant. The Weyl behaviour in Schwarzschild is that quasispherical objects are strongly prolated with the long axis aligned radially: a soccer ball or basketball starts looking like an American or Canadian or Rugby football ball. The radial stretching "spaghettifies" by ripping apart weaker bonds (like intermolecular ones, and molecular ones, and ionizing atoms), but the tangential squashing ("focusing") must eventually generate more nuclear interactions, probably up to quantum chromodynamics (QCD) energies possibly before the radial stretching starts generating hadronization. How this works in the Standard Model is just unknown. However simpler "test" quantum field theories (fewer, or even no, interactions; and often no colour-confinement-like processes) raise really difficult questions. Finally, back to the Standard Model as local theory: how does any allegedly quantum nonlocality behaviour work? Local here in the sence that states can be distinguished by local measurements alone. Related questions: can you entangle particles deep inside a black hole? If an entangled pair fall in together, how does the entanglement evolve? Or obsessing black hole information people, what if you throw in only one half of an entangled pair and locally measure the outside half? Nobody has great answers for these sorts of questions at present, and there's no near-term hope of testing any proposals in laboratories or via astrophysical observation.

deleted 1y ago

[deleted]

twothreeone 1y ago

What? Wouldn't that mean an object's speed in some direction determines how time passes once it crossed over, and conversely, it would experience its old time dimension as spatial and be able to "move through (old) time" freely after crossing the event horizon?? My head hurts.

mousethatroared 1y ago

You can't have the curl operator in 4D.

paulnovacovici 1y ago

I’ve always like to explore the idea of our universe being in a static 5th dimension where the 5th dimension represents randomness/entropy. The same way to think about exploring a 2d plane in a 3 dimensional space where the 3rd dimension is constant. We just happen to be in a random big bang in this 5th dimensional space