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Watsisname
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10 Feb 2018 17:18

midtskogen wrote:
Source of the post What is "matter"?  Warped spacetime, or is matter only one if more ways spacetime can be warped?

The latter.   A bit loosely speaking: mass-energy warps space-time, and matter is just mass-energy in a particular form: one which is "bound up" in some way and has a velocity slower than light.  "Dark matter" is considered a type of matter because it has mass and cannot be moving at or even near speed of light (or else it will not explain observations).

Example of something which is not matter and bends space-time?  Light.  A photon of light is itself massless, and of course moves at the speed of light.  Oddly however, if you build a system containing many photons moving in different directions with respect to each other, like a mirrored box with many photons bouncing around inside it, then the system will have mass.  A massless box filled with massless photons bouncing around is not massless!  It will curve the space-time.  In principle one could even bring so many photons into a small enough region of space that they generate a black hole.  Think about that: a black hole made of massless light!


A bit more precisely, in the technical jargon of general relativity, we say that "4-momentum" is the source of space-time curvature.  What the actual tensor equations of general relativity describe is a relation between the amount of 4-momentum passing through a space-time region (the "stress-energy tensor") to the amount of curvature generated (the "metric tensor").  A little while ago I discussed on the SE Discord channel why a system of photons moving in different directions relative to each other has mass, despite the photons themselves being massless, using principles of 4-momentum.  I think this is a really interesting and counter-intuitive thing and I'll reproduce it here:



4-momentum is the generalization of momentum to the four dimensions of space and time together.  Something which does not move through the space does move through time, and you can imagine a "velocity" with which it does.  (It will be rate of change of time coordinate, dt, with respect to the proper time dτ: the time interval measured by the object itself.)  Every component of the 4-velocity is the rate at which the coordinates (t, x, y, z) change with respect to the time measured in the frame of the particle itself.

It turns out that this "time component" of the 4-velocity is in fact the energy of the particle (divided by speed of light), and the "spatial components" of the 4-velocity are the regular 3-dimensional momenta.  So we can write 4-velocity as a vector with components [E/c, px, py, pz].

Relativistically, the energy of any object is

E2 = m2c4 + p2c2

Where m is its mass (which is invariant), c is speed of light, and p is the regular 3-momentum.  Notice that if the speed of the particle is zero, then the momentum p is zero, and this reduces to the famous equation E=mc2.  Whereas for a massless particle like a photon, m=0, and then E=pc.  (This is why photons have momentum despite having no mass.)

Let's rewrite this equation and choose units where the speed of light c=1 (like 1 light year per year).  Then we can solve for the mass as:

m2 = E2 - p2

Now we can combine this with the principle of 4-momentum.  The mass of a particle can be found by its 4-momentum, and the mass of a system can be found by combining the components of the 4-momenta of each of its constituent particles.  Let's go through a couple of examples using photons.

A single photon has energy E and momentum p=E/c.  Again let c=1, so both its energy and its momentum are simply E.  Now consider a photon moving purely in the +x direction.  Its 4-momentum will be [E, px, py, pz] = [E, E, 0, 0].  Now compute the mass.  m2 = E2 - px2 = E2 - E2 = 0.  The photon is massless.

Now consider two photons moving in tandem in the +x direction.  The 4-momentum of the system will be [E+E, E+E, 0, 0] = [2E, 2E, 0, 0], and the (squared) mass will be (2E)2 - (2E)2 = 0.  This system is massless, since the photons are moving together.

Finally, let the photons move in opposite directions.  Then the 4-momentum of the system is [E+E, E-E, 0, 0] = [2E, 0, 0, 0].  Will this system still be massless?  Check:  m2 = (2E)2 - (0)2 = 4E2.  Or, m = 2E.  Not massless!  As if by magic, we obtained mass from things that have no mass.  The photons themselves are massless, but the system is not, because the photons are moving with respect to each other.  Their respective 4-momenta generates gravitation.

If this seems totally weird, it is. :)  But it has very important consequences in particle physics.  You can collide two (sufficiently energetic) photons together and produce new particles of matter!  Matter from not-matter.   

Another important consequence shows up in cosmology.  The very early universe was much hotter and denser than today, and the energy contained in the form of photons was enormous compared to the energy in the form of non-relativistic matter.  The gravitating effect of all those photons moving through the space was not negligible, and we must account for it when studying the universe's early evolution.
 
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11 Feb 2018 00:25

"Dark matter" or "dark mass-energy"?
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Watsisname
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11 Feb 2018 01:20

I think the former rolls off the tongue a bit better. 

Matter also better describes what it is in the framework of "weakly interacting massive particles".  Because dark matter forms structures on the size of galaxies and clusters, it must be something with speeds slower than light, like matter particles.  "Mass-energy" is too general of a term and does not capture this property.  There's another aspect to this in that matter dilutes as the size of the universe cubed (as you'd expect), whereas mass-energy in the form of radiation dilutes as the size to the fourth power (because the radiation is redshifted by the expansion).  And mass-energy in the form of a cosmological constant is not diluted at all.  So again "dark matter" is the better name because it specifies that it behaves just like regular matter in terms of how much it is diluted by expansion.

You may also encounter the name "Cold Dark Matter" (as in LCDM standing for "Lambda + Cold Dark Matter").  The "Cold" specifically refers to the slow (non-relativistic) speeds of the dark matter.  As opposed to, say, cosmic rays, which can be highly relativistic.
 
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11 Feb 2018 10:13

Watsisname wrote:
Source of the post Because dark matter forms structures on the size of galaxies and clusters

That also makes it somewhat intangible.  It makes me wonder if we're really missing something fundamental because we're stuck with something we haven't yet thought of questioning.  We see these huge structures, but perhaps the real issue is that we don't understand the geometry of the universe and don't admit what would first seem like imperfections in how we now understand the geometry.  How can we know that dark matter and dark energy aren't some new form of epicycles? They stuck for long because people weren't ready to rethink in a way that would appear to question the perfection of the circle.
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11 Feb 2018 12:42

The size of the gravitationally bound structures formed by dark matter is a clue to its properties, not a feature of intangibility.  That it collapses into bound systems at all indicates that it is "cold" particles of matter.  Otherwise it would uniformly fill space.  That it does not collapse into structures smaller than galaxies indicates that it does not significantly radiate or interact through collisions.

midtskogen wrote:
Source of the post How can we know that dark matter and dark energy aren't some new form of epicycles?

By testing their predictions.

Epicycles were ad hoc adjustments to force a model to remain consistent with observations.  They lacked predictive validation.  Dark matter as a form of massive weakly interacting particle is a model that is built to explain some previous set of observations, but also makes predictions that we can go out and test against further observations.  

Example:  
Consider the above observation (which comes from rotation curves) that dark matter forms haloes that the galaxies are embedded in, leading to the hypothesis that there is an excess of weakly interacting nonluminous matter.  This hypothesis makes a prediction.  If it is weakly interacting, then a collision between two galaxy clusters should separate the matter that interacts collisionally from the dark matter.  Since most of the luminous mass of a galaxy cluster is in the form of gas, which collides with itself, this gas gets piled up during the collision in shocks.  The stars on the other hand have small cross sections compared to the distances between them, and they pass through the collision mostly unscathed.  The dark matter, too, must pass through the collision.

Prediction:  If stars and dark matter pass through the collision, while the gas does not, then gravitational lensing by a colliding cluster should show this separation.  We should see excess gravitation that follows with the stars, not the gas.  And in fact, we do:

Image

This is combination of observations in visible light showing the stars and galaxies, with x-ray data which shows the gas (pink).  Location of mass determined by gravitational lensing of the background galaxies is shown in blue.  The data show that the majority of the mass goes with the stars.  Whereas by census, we know that the majority of the regular matter is in the form of gas.
 
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11 Feb 2018 13:06

midtskogen wrote:
Source of the post Perhaps the real issue is that we don't understand the geometry of the universe and don't admit what would first seem like imperfections in how we now understand the geometry.

This is actually understood quite well because it is easy to measure: the paths of light rays traces the geometry!  

On large scales the universe is homogeneous and isotropic, for which general relativity permits only three possible geometries: constant negative curvature, flat, or constant positive curvature.  Each affects the path of light rays differently.  If positively curved then light rays are focused, if flat then they remain parallel, and if negatively curved then they are de-focused.  Observations indicate the universe's geometry is very close to flat.  (This hints that something is missing, because there is far too little regular matter to make the geometry flat.)

On smaller scales, geometry of space-time is determined by the local mass distribution.  Again, the passage of light traces the geometry of the space-time, so we can study the geometry by examining the lensing of background objects.  By general relativity, this also tells us how the mass is distributed, as in the above image of the Bullet Cluster.


Many have speculated that these observations are actually evidence that our understanding of gravity is flawed on large scales, leading to "Modified Gravity" models.  But no successful modified gravity model has been found which explains all cosmological observations (rotation curves, lensing, velocity dispersion, separation of matter from dark matter, evolution of expansion rate, cosmic web formation, and large scale geometry / CMB angular power spectrum).  It is easy to explain one or two of these with modified gravity, but not all through a single model.  If one supposes our understanding of gravity or geometry is wrong, then additional matter and energy are required anyway.  

Occam's Razor says take the simpler route: don't use a more complex model than necessary to agree with observations.  Dark matter and energy alone agree with observations, so modifying our understanding of gravity and geometry on top of it does not appear necessary.
 
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11 Feb 2018 17:33

Is a singularity, or rather the event horizon from an outside perspective, a place where location and "identity" are the same thing? Location, as the where something is, and the Identity, as what something is. And could this be, remaining only as an outside observer, be considered nothing? As in something that is neither location or identity, and yes I understand an event horizon itself, the idea, the "object", has a location and an identity, but rather what would be inside the volume of it. From an outside observer, shouldn't it be like a point on a grid, larger than infinitesimal but expressing no defined internal locations? I suppose someone falling into it wouldn't say this, should they be completely indestructible, they would observe the universe as a white hole, an anti-event horizon, pushing them away, consisting of an infinite amount of internal volume, and the now "new" universe, the internal of the black hole event horizon, be the gradient decline from a region that has dimensions, to a region that has none, a universe lacking in volume, where going outwards is anti-hyperbolic, with a point of infinite convergence. Where the what something is, and where, become the same? Like a 0-dimensional point. Sorry if this is worded a little weirdly, its more like an perspective question on an astronomical phenomena.

ADDED:
lol, re-reading this... you technically do, if my perspective is right, actually pop out of a white hole on the other side of a black hole, but not at the singularity, rather at the event horizon. The white hole being our entire universe.
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11 Feb 2018 18:14

Is a singularity, or rather the event horizon from an outside perspective, a place where location and "identity" are the same thing?


Kind of, in some sense of terminology, I suppose. :)

But first, let's distinguish two types of singularities being discussed here.  The singularity at the center of the black hole is a physical singularity -- a curvature singularity where the curvature of space-time becomes infinite and everything is inevitably crushed.  The event horizon on the other hand is a coordinate singularity.  It is a location where certain coordinate systems built to describe the space-time geometry (such as Schwarzschild coordinates) become badly behaved.  The geographic poles of the Earth, in latitude-longitude coordinates, are also examples of coordinate singularities.  But the Earth's surface is not badly behaved there.  The singularity here is a consequence of the choice of coordinates, not a feature of the geometry itself.


So with that aside, what can we say about the nature of the horizon?  From the outside perspective, the event horizon is a place where anything falling into the black hole gets redshifted to invisibility and frozen in time (these happen on the same timescale, so you don't really see the thing get frozen on the horizon).  It just looks like it vanishes onto the horizon.  All observable properties of that object are lost.  Quite quickly in fact.  So in this sense you could say that things that fall into the horizon become the horizon according to outside observers.  Another implication is that according to outside observers, there is nothing within the horizon.  There is no interior because all events that transpire there are never known to the outside observers.

Personally, I prefer to say that the horizon is a surface in space-time.  It is a boundary, demarcating a region where some light signals can escape to infinity, from the region where none can.  The power of this definition is that it follows directly from the geometry of the space-time, and is useful for computing where it is.  Simply choose an event, release a bunch of light rays from it, and trace the trajectories of those rays.  If any escape to infinity, then the event is outside the horizon.  If all terminate at a singularity, then the event was inside the horizon.



Terran wrote:
Source of the post you technically do, if my perspective is right, actually pop out of a white hole on the other side of a black hole, but not at the singularity, rather at the event horizon.

No.  For a non-spinning black hole, all allowed (time-like and light-like) paths that pass through the horizon terminate at the singularity.  There is no other side, no white hole for them to pass out through.

You would be correct about passing out through a white hole if we consider a rotating or charged (or both) type of black hole, but in that case this result is only valid in the mathematically extended vacuum solution, where there is no matter at all except at the central singularity.  But the moment you introduce any particle to this solution and have it pass through, the geometry breaks down and you do not get a white hole.  

There are some cool visualizations of what the idealized mathematical extension to the geometry for the inside of a charged black hole would look like on this page, as well as the reasoning for why this is not physically valid description of what actually happens. It's analogous to saying that you can mathematically describe a waterfall which falls down a canyon and then smoothly flows back up the other side.  A simple and elegant solution, but it is never observed in nature.  Instead the waterfall breaks down into turbulence at the bottom.  This is a good analogy for what actually happens to the space-time inside a real black hole.
 
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12 Feb 2018 02:30

Watsisname,
Once again thank you for your time and effort explaining these things. I want you to know that I'm making a compilation of your responses. This information has a lot of explanatory value. Your posts should not be buried by the flow of this forum. I hope others are doing the same, this is so interesting and well written. Thank you. The main reason I say this is because I'm afraid you get bored or your pattience ends one day. I want to encourage you to continue this attitude because is helping a lot :)


Watsisname wrote:
Source of the post like on this page

Link is broken


midtskogen wrote:
Source of the post How can we know that dark matter and dark energy aren't some new form of epicycles?

I personally think this is a bad example for your point (If I understanded correctly). Epicycles can explain everything (yep, even today). Epicycles were rejected in part because there was a simplier explanation and because many realized this fact that epicycles can be used to explain nearly any shape possible. Adding epicycles you could even explain why a planetary orbit has the shape of Homer's head, this is because the operation of including more and more epicycles is equivalent to adding more and more terms in a Fourier series (and as you know, with that series you can follow any function to whatever precission you want).
My point here is that there is an epistemological issue here. Even today's orbits could be approximated with enought epicycles, but we abbandoned the idea because when something can explain every possible situation without mistake that something is considered unfalsifiable and therefore is not scientifically tollerable.



This is not the problem with dark matter as far as I can tell. The explanations given here can't be applied to any possible landscape and because of that the concept could be falsified and the observable parameters can be constrained to a set of values that can be only fitted in certain situations no mater how you tune the theory to adjust it. There could be plenty of explanations for sure but considering dark matter a kind of strange-behaved matter is not like epicycles since it has limits as a theory. For example, immagine you don't know what momentum is and try to call it strange-matter, you could say that momentum is made of particles that can be exachanged between objects but are never destroyed but does momentum particles have momentum? does momentum particles have mass, inertia? well, if not, the matter concept should be thrown away since it barely makes sense. Not everything can be explained as matter because the idea has constraints (in contrast with epicycles that can explain every possible shape).
 
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12 Feb 2018 02:54

Watsisname wrote:
Source of the post Epicycles were ad hoc adjustments to force a model to remain consistent with observations.  They lacked predictive validation

Well, not really.  Ptolemy had only one layer of epicycles, and when this model was tested with better observational accuracy and longer observational records, it did fail validation.
FastFourierTransform wrote:
Source of the post Epicycles can explain everything (yep, even today).

I wasn't thinking about epicycles-on-epicycles.
Watsisname wrote:
Source of the post the paths of light rays traces the geometry!  

On large scales the universe is homogeneous and isotropic,

Yes, those are fundamental assumptions.  I don't want that not to be true, or we'll be very lost now, but we can't exclude that possibility.  As you said, Occam's razor will decide.  If the models simply get too complex by preserving our assumptions, the assumptions will have to go to allow something simpler.
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12 Feb 2018 04:12

midtskogen wrote:
Source of the post Yes, those are fundamental assumptions.  I don't want that not to be true, or we'll be very lost now, but we can't exclude that possibility.

Thankfully, we don't have to take them as assumptions.

That light rays follow null geodesics in space-time is verified by the lensing of stars by the Sun during solar eclipses, and the Shapiro delay.  It is also verified with higher precision by gravitational microlensing events.  And if all goes well this year, it will be tested in the strong field regime by the observations of SgrA* by EHT. :)

That the universe is on large scales isotropic is verified by observations of the Cosmic Microwave Background, the Cosmic X-ray Background, and distribution of distant objects like radio galaxies.  These all show that the universe is very isotropic.  (This is why fractal cosmologies can be excluded with high confidence.)

That it is homogeneous is a bit more difficult to test (we must check distribution across volumes rather than across surfaces), but there are still several viable approaches.  An obvious method is to survey galaxy redshifts, but this is limited to fairly small scales.  One can reach further with GRBs and radio sources.  An even more powerful test is the Lyman-alpha forest, which probes homogeneity across a very wide range of scales.

So yes, they are assumptions, but they are testable assumptions, and evidence indicates that their use in cosmology is valid.  Otherwise we would indeed be in trouble, because much of our understanding of the universe and its evolution is based on them!


FastFourierTransform wrote:
Source of the post Once again thank you for your time and effort explaining these things. I want you to know that I'm making a compilation of your responses. This information has a lot of explanatory value. Your posts should not be buried by the flow of this forum. I hope others are doing the same, this is so interesting and well written. Thank you.


Thanks!  I enjoy writing these more thorough explanations, and I appreciate the feedback on them.

FastFourierTransform wrote:
Source of the post Link is broken


Oops!  Fixed. :)
 
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12 Feb 2018 07:23

Watsisname wrote:
Source of the post No.  For a non-spinning black hole, all allowed (time-like and light-like) paths that pass through the horizon terminate at the singularity.  There is no other side, no white hole for them to pass out through.

The last part was kinda important for what I was referring to :/
Terran wrote:
Source of the post The white hole being our entire universe.

As in the other side is the interior of the black hole. The white hole is our universe, infinite in internal volume, and has dimensions. The interior of the black hole a region of no volume or dimensions. Looking back after falling in. You never leave the black hole in this perspective. And it still terminates.
Watsisname wrote:
Source of the post Kind of, in some sense of terminology, I suppose.


Yay!
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12 Feb 2018 19:29

Terran wrote:
Source of the post The last part was kinda important for what I was referring to :/

Aye, but sadly it does not change the answer.  The idea of connecting the universe to black hole or white hole geometries is a popular one, but it doesn't work.  Along with the problem of black holes not having another side, the expanding universe does not have the space-time geometry of a white hole.

White hole geometries are time-reversals of Schwarzschild geometry, with the gravitation being due to a spherically symmetric distribution of mass or a point source, with comparitively empty space around it.  The geometry of the universe on the other hand is uniform (constant curvature), due to the distribution of matter and energy also being uniform.
 
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12 Feb 2018 20:34

Watsisname wrote:
Source of the post the expanding universe does not have the space-time geometry of a white hole.

Would it not seem that way standing at a point within the event horizon. What would be the difference from looking out of the event horizon and looking into a white hole that is in a dimensionless universe?
Watsisname wrote:
Source of the post White hole geometries are time-reversals of Schwarzschild geometry

Wait... What? I thought black holes cannot be time reversed? As in the space around them can but that black holes themselves are neutral? That a black hole is an inversion in spacetime. Or would that just be perpendicular? As I understand it, a black hole looks the same time forwards or time backwards, only acting like a white hole when the local entropy is reversed, from chaos to order, otherwise you just get an anti-black hole instead of a negative black hole (white hole). Or am I just wrong on this account, since there should be a distinction from negative matter and antimatter?
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13 Feb 2018 01:51

Terran wrote:
Source of the post Would it not seem that way standing at a point within the event horizon. What would be the difference from looking out of the event horizon and looking into a white hole that is in a dimensionless universe?

You cannot stand at a point within the event horizon. :)  Nor can you hover at a point inside the horizon. You are swept into the singularity.  Remember, inside a horizon, no stationary observers can exist, because their path would have to be space-like (faster than light).

As for looking into a white hole in a dimensionless universe, the concept makes no physical sense.  A white hole can't exist in a dimensionless space.  Nor can any observer, to make such an observation.  

Terran wrote:
Source of the post Wait... What? I thought black holes cannot be time reversed?

In practice?  Of course not.  The idea is purely notional.  A white hole is by definition the time reversal of a black hole.  Under a transformation that reverses the direction of time in the Schwarzschild metric, things which would be falling into black holes will instead fall out of them.  Instead of space flowing inward through the event horizon at speed of light, space flows out of it at the speed of light.

You can think of this as reversing the arrow of time and increase in entropy if you like.

Terran wrote:
Source of the post Or am I just wrong on this account, since there should be a distinction from negative matter and antimatter?


Matter and antimatter have the same gravitational effects.  "Negative" matter would be a source of antigravity, and produce a white hole instead of a black hole if you could bring enough of it (and if such stuff exists) into a small enough region of space to form an event horizon.  Same principle as forming a black hole, but with gravitational repulsion.

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