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midtskogen
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27 Apr 2018 04:08

Watsisname wrote:
Source of the post I'm mainly trying to imagine how hidden or wrapped up dimensions could be shown experimentally

So we should see space bend without any associated matter, and matter should be detectable by radiation.  We can either say that it is caused by some extra-dimensional influence/structure, or call it "dark matter" which is matter that is invisible, radiationless, does not interact with matter, etc, removing all attributes normally associated with matter save a single one (influence on space).  I can't see how we can distinguish between these two options, but the former description is simpler, I think.
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27 Apr 2018 06:53

Yeah, to that extent they are predictively identical models, and in fact physically equivalent as well, provided we don't care about the physics near or within those extra dimensions.  You could treat each clump of matter locked away in a pocket of hidden dimension as a particle in our universe.  It's similar to treating charged particles as points in classical electromagnetism, which gives the correct predictions as long as you don't care about what goes on very close to them, where their finite size and wave nature becomes important.

However, I think a hidden dimensions model does beg for some explanation for why it should bend space in the correct way, with the correct mass densities and kinetic energy distribution to explain the additional gravitation and how it is distributed in clusters.  For example, why should the gravitational anomalies due to matter in hidden dimensions not have relativistic speeds and be uniformly distributed in the universe?

Another thing to consider is that free neutrons also gravitate and do not interact with light, so they have the necessary properties of dark matter without requiring extra dimensions.  The only key differences are that free neutrons are unstable and interact by the strong force, whereas dark matter must be stable for astronomical timescales and be more weakly interacting.  Dark matter properties are a lot like a combination of certain properties of neutrons and neutrinos.
 
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27 Apr 2018 11:43

Blaming hidden dimension doesn't have any more explanatory power.  I didn't mean to imply that dark matter is still "matter", but in a such hidden dimension.  Since we don't know what causes what we observe, the label should be vague, and we should make as few assumptions about it as possible.  We think we live in this sheet shaped spacetime dented by matter.  Which is mathematically convenient. But let's assume for the moment that the sheet could be worn and crumpled.  We need a detailed map to figure out what the patterns might be.
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02 May 2018 01:41

Einstein has provided us with just such a map.  It is the general theory of relativity. :)  

Use the motions of particles and light rays to measure the geometry of the space-time.  (For example, light always travels along "null geodesics", or straight lines in space-time that have a length of zero.)  Then general relativity relates the geometry of the space-time to the density of energy and flux of momentum through that space-time, described by the stress-energy tensor.  

In other words, if you measure the distortion of space-time, then the theory tells you the nature of the source.  Or, if you provide the source, then the theory predicts the distortion it will cause.  



What can act as a source?  The most obvious is matter.  Matter is mass which is bundled up in the form of particles that move slower than light.  Matter is mass is energy, and energy curves space-time.  

But even massless particles, like light, act as a source, because they carry momentum.  (Recall the example where I show the surprising result that a massless box filled with massless photons is not, in sum, massless).

Perhaps even more surprising is that electric and magnetic fields are also sources.  According to electrodynamics, these fields contain an energy density, and a flux of momentum.  Even if no actual charges are present within them.  This means there is energy stored in the empty space within a capacitor, or inside an inductor, and these fields bend space-time.

So in brief, there are several ways in which space-time can be distorted.  It is all encapsulated in "stress-energy", or "4-momentum", but these can take several possible forms, of which matter is just one.



Where does "dark matter" fit into this framework?  What we observe in galaxies and clusters are motions that indicate an additional source of gravitational field that is not attributed to the visible matter.  The source of this additional gravitation is extended ("puffed up") around the galaxies more than the stars and gas are, and it also can become separated from the gas (which is the majority of the visible matter) in galactic collisions.

This suggests that the explanation of these gravitational anomalies is not that we need to modify our understanding of gravitation.  We instead treat its source as a new mass distribution. To be bound up in clusters, it must have slow speeds, and probably the most natural way to describe something that generates gravitation and has slow speeds is with a distribution of massive particles.  They must also be weakly interacting, to be consistent with its lack of collisions and electromagnetic detection. There may be many different models for how it is massive yet weakly interacting, like the hidden dimensions idea.  A population of black holes (with the correct mass distribution) also works!  Or perhaps something even more exotic.  To know what it is on that level, we need more direct observations.
 
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02 May 2018 01:52

Aside:  It is not actually necessary to use general relativity to study dark matter (the gravitational field in galaxies and clusters are weak enough, and the motions slow enough, for Newtonian gravity to be adequate).  But when describing gravitation as a curvature of space-time, it is natural to speak in terms of general relativity. :)

It is necessary to use general relativity to understand accelerated expansion of the universe through dark energy, and in fact it is necessary for understanding the expansion history of a universe with any sort of mass-energy contents.  Newtonian gravity can help get an intuition and "almost" correct equations describing expansion.
 
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02 May 2018 06:11

Protons decay, protons don't decay, Protons decay, protons don't decay, Protons decay, protons don't decay....

Protons have a charge equal to 1.602 x 10-19 Coulomb. Since the charge of the proton is the smallest amount of charge an object can obtain, it is obvious that any of the charges we encounter in daily lives are integer multiplications of the charge of the proton. The proton consists of two up quarks and one down quark. If we were to try some matter antimatter annihilations with different spins or masses we might finally see a proton decay into some weird quark pairings? Or hadrons? (with charge and no charge? Or perhaps never? Or an average of every 10^34 or 36 years?)

And what does the topology of empty spacetime have to do with decaying particles?

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02 May 2018 07:06

Slightly aside, it's interesting how people figured out that the proton (or electron) has the smallest, fundamental unit of charge.  

If you spray a fine mist of mineral oil, each droplet (which is very small -- something like micrometer sized) may pick up a few electrons.  Then you can levitate that drop in an electric field (which tells you the electric force being applied, such that it balances the gravitational force).  If you also measure the terminal velocity of the drop when there is no field applied, that tells you the force due to air drag, which relates to the radius of the drop.  Then with some algebra and knowledge of the oil's density, you can derive the charge on the drop from those two measurements.

So the experiment, which I did a few months ago in lab, involved measuring the charge on a number of droplets in this way, and showing that they all differ by integer multiples of some fundamental charge.  (This is the Millikan oil drop experiment).   A very neat bit of physics, though finicky and difficult to achieve good precision with in practice.  I was able to clearly show the quantization of charge, but my derived value of e was off by about a factor of 2.  In more modern experiments they achieve far better precision. :)

Anyway, proton decay, if it happens, must be an exceptionally rare event -- something like a half life of 1030 years or more.  It has never been unambiguously observed.  The decay must conserve charge (and other quantum numbers), so a proton would decay into a positron and a neutral pion.  Positron of course carries the +e charge (and also the 1/2 spin), while the pion then decays into 2 photons.

What does it have to do with topology of empty space-time?  Probably little if anything, but I don't know a whole lot about it.
 
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03 May 2018 01:19

Watsisname wrote:
Source of the post What we observe in galaxies and clusters are motions that indicate an additional source of gravitational field that is not attributed to the visible matter.  The source of this additional gravitation is extended ("puffed up") around the galaxies more than the stars and gas are, and it also can become separated from the gas (which is the majority of the visible matter) in galactic collisions.

What I meant by "map" is to get detailed knowledge of the distribution of "dark matter".  Does it form lumps, or is it only thinly distributed, etc?  The idea of a halo of dark matter around galaxies seems to dominate still, and it would be good to get more confidence about that, and if that's the only thing we see.  (I didn't quite understand what you meant by becoming "separated from the gas").  As always, it's easier to explore explanations with more information available.  Could dark matter be linked somehow to regular matter?  If it appears around galaxies and not nearly so much in the vast space between then, there must be some interaction, but how does it stay outside the galaxy and not sink to the centre, or at least gets a flattened shape, if it interacts gravitationally with regular matter?  It seems to complicate galaxy formation hyptheses.

Can we fairly confidently rule out the possibility that there is no dark matter, just regular matter, and that our mathematical model of how regular matter bends spacetime is wrong?  That it works well on smaller masses and at the star neighbourhood scale, but breaks down at the galactic scale?  Perhaps, I'm speculating freely, regular matter in galactic quantity has a kind of distant ringing effect on spacetime.
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03 May 2018 17:39

There are several ways to determine the distribution of the dark matter.  One is to use general relativity to map the curvature, as I describe above.  You can use the gravitational lensing of light rays from background galaxies to map the distribution of mass in a foreground galaxy or cluster, and then compare that with the observed distribution of matter in the form of stars and gas.

More recent research has also been able to use this technique to resolve the sub-structure of the dark matter haloes.  There is a good lecture on some of this research which I shared in the astronomy videos thread.


midtskogen wrote:
Source of the post I didn't quite understand what you meant by becoming "separated from the gas").

What I mean is that they can get physically separated in space.  Normally the gas and dark matter overlap within a cluster.  If they overlap it not easy to tell if the gravitational anomaly is due to misunderstanding of gravitation due to regular matter, or if it is actually additional unseen matter.

But when two clusters of galaxies hit each other, then the gas and dark matter can be separated.  Gas particles are numerous enough that they directly hit each other and get piled up, while the stars are far enough apart that they mostly pass through the collision unscathed.  Dark matter also only interacts gravitationally (it doesn't exert pressure on itself like gas does), so it passes through the collision along with the stars.  The gas becomes physically separated from the stars and the dark matter.  This is observed in the Bullet Cluster, which I explain and show in more detail here.

Now consider that there is much more mass in the form of gas than in the form of stars, so if what we're calling dark matter is actually a flaw in our understanding of gravity due to normal matter, then we should see that the gravitational anomaly follows the gas.  But it doesn't.  It follows the stars.  This should hopefully answer your question "Can we fairly confidently rule out the possibility that there is no dark matter, just regular matter, and that our mathematical model of how regular matter bends spacetime is wrong?"  

This observation of the separation of dark matter from regular matter is actually what convinced the cosmological community to follow dark matter models over modified gravity models.



Another way to determine the dark matter distribution is to observe the gas which surrounds the galactic clusters.  The gas is kept in equilibrium within the cluster by a balance of gravitational forces and pressure forces, much like the hydrostatic equilibrium that maintains a star.  We can determine the pressure within the gas by measuring its density and temperature.  Then hydrostatic equilibrium tells us the gravitational force acting on the gas at that distance, and thus the total mass enclosed.  Doing this calculation across a range of distances from the center of the cluster, and comparing that to the visible distribution of matter, reveals the distribution of dark matter.

This technique doesn't give us a nice 2D image of the distribution of dark matter like gravitational lensing does, but instead gives us a map in the sense of how the density of dark matter changes with distance from the center of the cluster.  What we're seeing is that this dark matter density does have a different function of distance from the center than either the stars or the gas.


midtskogen wrote:
Source of the post If it appears around galaxies and not nearly so much in the vast space between then, there must be some interaction, but how does it stay outside the galaxy and not sink to the centre, or at least gets a flattened shape, if it interacts gravitationally with regular matter?  It seems to complicate galaxy formation hyptheses.


If you imagine (or simulate) a universe filled with only gravitationally attracting particles of dark matter, then following the Big Bang, these will develop the cosmic web structure.  Regions with higher dark matter density collapse under their own gravity to form the filaments and sheets, while regions with lower dark matter density get emptied out as that matter falls into the sheets, and expanded to form the voids.  In other words, the cosmic web forms the same way whether you fill the universe with regular matter or with dark matter.  They have the same gravitational physics and this structure arises purely by gravity.  

Then the differences in their physics come into play on the more local scale.  Regular matter can collide with itself, and also radiate its energy away as light.  This is what allows regular matter to collapse into smaller structures like stars and planets.  (Think back to the hydrostatic equilibrium argument:  if a system of particles is in equilibrium, then the only way for it to collapse more is to lose energy, but it can't lose energy without radiating it away.)  Dark matter has no (or at least negligible) self-collision, and it does not radiate, so it cannot collapse into smaller objects.   We don't expect there to be "dark matter stars" or "dark matter asteroids".  

So dark matter does play a huge effect on the formation of galaxies, by accelerating or "seeding" their growth, and we see this in the Lambda-CDM simulations (I show some examples in my post to Gnargenox on the previous page).  The additional dark matter forms the cosmic web structure and higher density haloes of matter more quickly, and the regular matter goes along for the ride, forming the galaxies and the interesting objects within. :)
 
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03 May 2018 23:16

Here's a fun, if not morbid question, inspired by elsewhere here on the forum.

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If Space Engine showed the universe the way we perceive it, then galaxies and nebulae would look dim, desaturated, and boring. You would also be blind before you could see the details in the surfaces of hot stars, or in the accretion disks of black holes and white dwarfs. I think it is also better to show things the way they are, not as how we are tricked by illusions in the brain, or in the above examples, by limitations of our vision. :)


What would it take to make a standard consumer computer screen bright enough to actually blind someone, either with and/or without cgi graphics?
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04 May 2018 00:30

PlutonianEmpire wrote:
Source of the post What would it take to make a standard consumer computer screen bright enough to actually blind someone, either with and/or without cgi graphics?

The monitor would have to be roughly 10 million times brighter than typical consumer monitors to match the sun (160 cd/m2 vs 1.6*109 cd/m2).  To build such a monitor I would suggest mounting 6.2 million lasers (for 1920x1080 resolution) which would point at the viewer's eye.  Each individual laser wouldn't have to be very powerful, but all would need to be extremely accurate to hit the eye precisely where they need to.  The number of lasers must be doubled for both eyes (which also would allow stereo vision).  I think this setup would be able to render even the brightest stars with lasers no brighter than what's commercially available, but not supernovas seen from within the star system.  That would probably require sustained fusion right in front of your eyeballs.
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04 May 2018 00:41

Watsisname wrote:
Source of the post Now consider that there is much more mass in the form of gas than in the form of stars, so if what we're calling dark matter is actually a flaw in our understanding of gravity due to normal matter, then we should see that the gravitational anomaly follows the gas.  But it doesn't.  It follows the stars.  This should hopefully answer your question "Can we fairly confidently rule out the possibility that there is no dark matter, just regular matter, and that our mathematical model of how regular matter bends spacetime is wrong?"  

Can we actually observe that separated gas and the lack of dark matter associated with it?
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04 May 2018 03:24

Yes.  X-ray data, taken with the Chandra X-Ray Observatory, trace the distribution of gas, which is hot and ionized by the collision.  The gas distribution is shown in pink.  The lensing of the images of background galaxies (visible light, Hubble) maps the gravitational mass of the foreground cluster.  The distribution of gravitational mass is shown in blue.


Image

Another figure showing the same thing but in the form of contour levels for the gravitational mass and gas mass. This is figure 9 from Paraficz et al 2016.

Image

For galaxy clusters, the mass of stars is significantly less than the mass of gas.  A census of the different mass components for the Bullet Cluster can be found in figures 11 and 12 of the paper.

So if what we're calling dark matter didn't get separated from the gas, or if it is instead a flaw in our understanding of the gravitational field due to regular matter, then the data would not show this separation.  The greatest lensing would be associated with the gas, not the stars.  What we observe is the opposite.  Yet the stars only account for about 1/10th of the total mass, and the mass of gas is several times greater than the stellar mass.


Great answer by the way with the user-blinding monitor full of lasers!  :P
 
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04 May 2018 06:50

Can gravitational lensing be correlated with galactic rotation, both being caused by Dark Matter, rather than two separate observations of phenomenon?
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04 May 2018 17:53

Gnargenox wrote:
Source of the post Can gravitational lensing be correlated with galactic rotation, both being caused by Dark Matter, rather than two separate observations of phenomenon?

No, galaxies rotate too slowly, and rotation doesn't affect space-time in the correct way.  So rotation curves and gravitational lensing are independent measurements of the mass distribution -- one from deflection of light rays in curved space-time, and the other from Kepler's Laws for orbiting masses.

The rotation of mass (its angular momentum) does in fact modify the gravitational field.  But instead of making the lensing stronger (as if more mass was there), it causes the space to be whirled around, called "frame dragging".  You might be familiar with it in the context of spinning black holes dragging the space-time around them.  This frame dragging effect occurs around any rotating mass, and has even been measured in the space-time around Earth.

If you compute the angular momentum of a rotating galaxy, or even a massive star, it is quite large.  Often it is so large that the object would need to shed some angular momentum in order to be able to collapse into a black hole.  But these objects are so extended in size compared to their Schwarzschild radii, that the rotation's effect on the space-time is very small.  Anything which is not extremely massive, compact, and rapidly rotating (such as a spinning black hole or millisecond pulsar) will have very weak frame dragging.

To give a very rough idea, consider that the frame dragging speed at some distance from the center of a galaxy cannot be faster than the speed the galaxy is rotating.  Spiral galaxies turn out to be in approximately rigid body rotation, and for the Milky Way this is about 250km/s.  Assume (very incorrectly) that the frame dragging velocity is also this fast.  Then in the time it takes for a light ray to pass across the Milky Way (30kpc ~ 100k years), the frame dragging would have shifted it by just 25 parsec.  This is barely resolvable over intergalactic distances, and far too small to explain the observed gravitational lensing by galaxies or clusters.  This is also severely overestimating the effect the rotation could possibly have!



But what if the rotation of galaxies actually is somehow generating the observed lensing that we're attributing to dark matter, in some way general relativity doesn't predict or explain?  If that's the case, then we should easily notice the discrepancy around stars and planets.  Like galaxies, the Sun also has an angular momentum which would make it nearly extremally rotating if collapsed into a black hole.  Yet the lensing we observe around it is consistent with the predictions from Schwarzschild (non-rotating) geometry.

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