[Dave Lev (OP)]

A white hole, like a black one, is a massive difference in gravitational potential near a location in space, while BBT describes a flat universe with uniform potential everywhere with minor local variations forming over time.

What about the impact of the Dark matter on the difference in gravitational potential in the galaxy?
https://phys.org/news/2015-04-dark-conspiracy.html
It is stated:
"The speeds of stars on circular orbits have been measured around both spiral and elliptical galaxies. Without dark matter, the speeds should decrease with distance from the galaxy, at different rates for the two galaxy types. Instead, the dark matter appears to conspire to keep the speeds steady"
In order to verify if that request is feasible, let's understand how the "Orbit Speed Inside and Outside a Mass Distribution" really works:
http://hyperphysics.phy-astr.gsu.edu/hbase/Mechanics/Keporb.html#c1
In this example they are using a sphere (with radius R) which has a uniform density of matter (or dark matter).
They have found that:
1. Inside the mass distribution the orbital velocity is as follow:
V_orbit = V_R * r / R
2. Outside the mass distribution the orbital velocity is ac follow:
V_orbit = V_R * √ (R / r)

Therefore, if there was a uniform dark matter around the SMBH, then:
1. Inside the mass distribution the orbital velocity, as we go further away from the center, the orbital velocity should increase linearly by the ratio of:
r/R.
As V_orbit = V_R * r / R
2. outside the mass distribution the orbital velocity, as we go further away from the center, the orbital velocity should decrease by the ratio of:
√ (R / r)
As V_orbit = V_R * √ (R / r)

That simple explanation proves that the distribution of the dark matter around the SMBH can't be uniform density.

The Sun is located at about 8.5 KPC from the center.
Its orbital velocity is about 220Km/s.
Actually, that is the average orbital velocity of all the stars in the spirals arms - starting from a radius of 3KPC till 15 KPC.
Hence, in order to keep all of those stars in any radius from 3KPC up to 15KPC at the average orbital velocity of about 220Km/s we can't just use uniform density of dark matter.

Hence, please try to answer the following questions:
1. What is the requested formula of dark matter density in the Milky Way that can keep a constant orbital velocity in the spiral disc (from 3KPC to 15 KPC?
2. Why the dark matter can't keep the same orbital velocity in the Bulge and in the Bar (0 KPC to 3KPC)?
Do you agree that between 0KPC to 3KPC the formula of the dark matter density must be different from that in 3KPC to 15KPC?
3. Up to what radius R the dark matter exists? Why it doesn't go all the way to the infinity?
4. How that special dark matter density could be formed at so different densities/formulas for different radiuses around the Milky Way' SMBH?
5. What kind of force could set those special dark matter densities at any different radius/sphere?

[Origin]

1. What is the requested formula of dark matter density in the Milky Way that can keep a constant orbital velocity in the spiral disc (from 3KPC to 15 KPC?

From Wiki:
A commonly used model for galactic dark matter halos is the pseudo-isothermal halo:[17]

2. Why the dark matter can't keep the same orbital velocity in the Bulge and in the Bar (0 KPC to 3KPC)?

I am not sure what your question is.

Do you agree that between 0KPC to 3KPC the formula of the dark matter density must be different from that in 3KPC to 15KPC?

No.

3. Up to what radius R the dark matter exists? Why it doesn't go all the way to the infinity?

The radius is about 100 to 200 kpc.  I am going to ignore the infinity question.

How that special dark matter density could be formed at so different densities/formulas for different radiuses around the Milky Way' SMBH?

Because dark matter does not 'clump' like regular matter. 

5. What kind of force could set those special dark matter densities at any different radius/sphere?

Gravity.

[Deecart]

5. What kind of force could set those special dark matter densities at any different radius/sphere?

Gravity.
But in my opinion we should before understand how gravity work.
The problem is that we have only some theorical understanding of gravitation, and the observation do not match exactly with the theory. (Per example the Mond theory could be more relevant for big distance or we have to suppose there is some "dark matter" somewhere).

First, there is often a misunderstanding (i suppose not all scientists do the confusion) between the gravitational wave and the gravity field.
The gravitationnal wave is known to travel at light speed (we have received almost simulaneously gravitational waves and light waves coming from some collapsing black holes).
But the gravitationnal wave have no gravitational effect on things they encounter.
They only shortly and temporaly change the length of those things.

So, what about the gravitational field (the one that is curving the space-time) ?
Do the field really expand at light speed ?
Do the field really have the intensity it should have (1/d*d) at some distance d ?
Perhaps this is thrue for short distances (the solar system scale can be considered as a short distance) and false when the distance become bigger.
In my opinion we can not have a law that say the intensity of gravity field is 1/(d*d).
This would contradict (i will not try to develop this idea here because it need a lot of explaination) the energy conservation law (if any).

Therefore i am very puzzled when i see some universe simulation showing that with the actual knowledge we end up with the universe we have actualy (so the simulation show the BB theory and so on is very accurate).

Now, why are there some galaxy with big BH at the begining of the BB ?
In my opinion, this has nothing to do with the gravity question.
It has something to do with the interpretation of what we see in the universe.
We have an observation and we have an interpretation of it.
But is the interpretation right ?

[Origin]

In my opinion we can not have a law that say the intensity of gravity field is 1/(d*d).
This would contradict (i will not try to develop this idea here because it need a lot of explaination) the energy conservation law (if any).

It seems that the 1/r^2 law for gravity makes perfect sense, as it directly follows from the geometry of a point source.
Why would this contradict the conservation of energy?

[Dave Lev (OP)]

1. What is the requested formula of dark matter density in the Milky Way that can keep a constant orbital velocity in the spiral disc (from 3KPC to 15 KPC?

From Wiki:
A commonly used model for galactic dark matter halos is the pseudo-isothermal halo:[17]

Thanks for the formula.
However, don't you agree that it is quite complicated formula?
If we would have to help the galaxy to calculate the requested density for each radius, don't you agree that we have to use a computer to extract the correct dark matter density for any given radius/sphere?
So, how the galaxy could calculate the dispersion of the dark matter density at any radius/sphere based on this formula without using any sort of computer?
Even if the galaxy could use a sophisticated computer for extracting the specific density per radius. How the gravity could help the galaxy to set the correct dispersion of that dark matter all over the galaxy?
You claim that:

Because dark matter does not 'clump' like regular matter.

Quote from: Dave Lev on Today at 13:45:20
5. What kind of force could set those special dark matter densities at any different radius/sphere?

Gravity.

How could it be that the gravity can't clump the dark matter, while the dark matter can clump a regular matter by gravity?

In any case, as the dark matter doesn't clamp by gravity, then how the galaxy could set the correct dark matter density at any given radius by gravity while there is no possibility to move the dark matter or clamp it?
Don't forget that any galaxy is evolving over time.
Therefore, there must be a change in the size/mass of the galaxy over time.
As the galaxy changes its size and mass, then there must also be a change in the dark matter density per a given radius.
So, how the galaxy could change the density of the dark matter over time as it evolves while the dark matter doesn't clamp or move by gravity?

Quote from: Dave Lev on Today at 13:45:20
Do you agree that between 0KPC to 3KPC the formula of the dark matter density must be different from that in 3KPC to 15KPC?

No.

Sorry, you have a sever mistake.
Please look at the following diagram:
https://www.astronomy.ohio-state.edu/thompson.1847/1101/RotCurve2.gif
Don't you see that from 0KPC to 3KPC the orbital velocity is increasing quite dramatically up to 220 Km/s?
While from 3 KPC and upwards it is quite stable on this 220Km/s.
Therefore, how the same density formula could work at those two different segments?
 

The radius is about 100 to 200 kpc.  I am going to ignore the infinity question.

Why the dark matter is concentrated at the galaxy up to that radius?
Why there is no dark matter outside the galaxy?
How the dark matter had been created?
If the galaxy increases its mass/size over time, from where the new dark matter is coming?
If the galaxy decreases its mass/size over time, to where the extra dark matter is ejected or eliminated?

Don't you agree that it is almost impossible mission for the galaxy to calculate the exact dark matter density per radius/sphere, then to set the correct density at the correct radius and finely manage the requested changes in the dark matter density as the galaxy changes its mass/size over time?

There is also an issue with the thickness of the spiral disk.
At 3KPC the thickness of the disc is 3,000 LY, while at the edge of the spiral disk - 15KPC the thickness is 400 LY
This is not correlated to the expectation.
Let's use the Milky Way as an example:
https://www.profmatt.com/ecliptic
It is stated:
"The planets do not all orbit in the same plane as each other: the solar system is not flat"
We clearly see that "the orbital plane of Pluto’s orbit is very different from that of the eight planets"
However, even if it has exactly the same pitch as Neptune, it must go at higher distance from the orbital disc due to its longest radius.
Therefore, it is expected that as the star is located further away from the center, its distance from the disc should be higher.

As this isn't the case in the spiral arms, don't you agree that it proves that the orbital motion of the stars in the galactic disc works on a different mechanism.

Conclusion:
Why can't we just assume that the idea of the dark matter proves that our scientists don't really understand how the spiral galaxy really works?

[Origin]

Now, why are there some galaxy with big BH at the begining of the BB ?

There aren't any, so it is not an issue.

[Origin]

However, don't you agree that it is quite complicated formula?

No it is not.

If we would have to help the galaxy to calculate the requested density for each radius, don't you agree that we have to use a computer to extract the correct dark matter density for any given radius/sphere?

The galaxy doesn't calculate anything, what an odd thing to say.  You don't need a computer to calculate this.
 

So, how the galaxy could calculate the dispersion of the dark matter density at any radius/sphere based on this formula without using any sort of computer?

What are you talking about??  Do you think the galaxy is sentient?

How could it be that the gravity can't clump the dark matter, while the dark matter can clump a regular matter by gravity?

What are you talking about?  'Normal' matter clumps, that is it interact electrostatically to make dust, rocks, planets, etc.  Dark matter does not, it appears to stay as individual, particles that do not in general interact.

"The planets do not all orbit in the same plane as each other: the solar system is not flat"
We clearly see that "the orbital plane of Pluto’s orbit is very different from that of the eight planets"
However, even if it has exactly the same pitch as Neptune, it must go at higher distance from the orbital disc due to its longest radius.
Therefore, it is expected that as the star is located further away from the center, its distance from the disc should be higher.

No that does not logically follow.  It's apples and oranges.

[Origin]

Conclusion:
Why can't we just assume that the idea of the dark matter proves that our scientists don't really understand how the spiral galaxy really works?

Your conclusion is based on ignorance, so it can easily be dismissed.

[Kryptid]

How could it be that the gravity can't clump the dark matter, while the dark matter can clump a regular matter by gravity?

In principle, if you waited long enough, it possibly could. The issue here is that it, so far as we know, only interacts via the gravitational force. That greatly limits the way that dark matter particles can shed energy. Normal matter interacts via both gravity and the electromagnetic force. If you have a cloud of atoms, they can shed energy by releasing electromagnetic radiation. This causes the cloud to cool off and contract over time, until it forms a star or planet or whatever. Gravity, which is far, far weaker than electromagnetism, would not allow a cloud of dark matter to cool off and contract nearly so quickly. So you still have a cloud of dark matter long after a cloud of normal matter has already contracted into stellar or planetary bodies.

[Deecart]

It seems that the 1/r^2 law for gravity makes perfect sense, as it directly follows from the geometry of a point source.
Why would this contradict the conservation of energy?

It is complicated to explain shortly, but i will try my best.

So yes, you are right. If the gravity field would behaviour like the electromagnetic field you should have a 1/d^2 law for the gravitational field.
But first you need to really understand why there can be a 1/d^2 law in the intensity at some distant point for the electromagnetic field.
Lets begin with a source of photons that emit only 1 single photon.
This photon start form the point source and then advance toward infinity.
There is a problem if you want to receive this single photon, especialy if you are at a very long distance because if you consider the photon will spread as a cylinder (like a laser beam would do), the 1/d^2 law intensity would not apply everytime.
By chance, the photon spread as a cone, and you can intercept it much easyer.
So a single photon at a distance d can be received within a large surface onto the sphere wich has the radius d.
Whats the intensity law for this single photon ?
1/d^2 ? No, if you get the photon that is actualy present (because the duality particle wave) you got the full energy of this photon.And very important, if you get the photon within this surface, the photon disappear instantly (so far as we know) preventing anyone to receive the photon at the same time at an other position (the wave function is destroyed).
Now, if you consider a source that emit a tremedous quantity of photons, every second, like a star would do, the intensity of the source can be seen as if it would be distributed onto the surface of a sphere of radius d.
You can divide the intensity by d*d because you are in fact dividing the number of the photons you can intercept on the surface of the sphere.You are not dividing the intensity of the photon (you can not it is a particle), but their number.
It seems obvious at first, but there is something very interresting you need to understand there : As soon as you have interacted with the photon, it stop his travel and disappear and before you interact with it, it is like it is not here (it does nothing).
So : The intensity 1/d^2 can be obtained because of the large number of photons (they are well repartited) BUT you can ONLY obtain this intensity 1 time.
The maximum you can do is receiving all photons emited and you will have the same intensity as that of the star.
Saying you have a pulse of light (it is better to understand) 1/d^2 is proportional with the surface d^d  of the sphere of radius d. Here we dont have a problem with the energy.

Now, if you consider the gravitational field.
Let assume we have, like for the electromagnetic field, "something" that is spreading from the source (the same star as before per example). We dont need really, for the explaination here, to know what this "something" is (some graviton or whatever). But what we know, and it is was distinguish the behaviour of the gravitational field and the electromagnetic field; is that the photon is VIRTUAL (it exists virtualy in the space and has no effect unlike you receive it, and if it interact it disapear) and that the "something" who is responsible for the curvature of space-time is ACTUAL (it has a PERMANENT and real effect, everywhere where it travel).
Therefore, if you consider that it can curve the space-time (and this can be assimilated as some local energy change) everywhere he pass by, you will understand that you could theoritically do the sum of the energy change of the spheres with radius between 0 and the infinity.
Because the "graviton" or whatever it is, change actually the curvature of space-time, this would lead to an infinite energy gain because the radius will become bigger an bigger.
An if you want to interact with it like the photon, it must occupy a large amount of space, bigger and bigger as you go away from the source.
The photon can because it only occupy space without interact with it, but the "graviton" can not (or it is some big mystery) because it is actualy changing the curvature within the space-bigger and bigger it occupy. .

Therefore, my opinion is : The best, and i will finish briefly here, is to consider the "graviton" (or whatever it is) like some fluid that is occupying the area around the star.
The intensity of the fluid production is extremly strong, so the filling around the star is "like if" the "fluid balloon" extend around speed of light, but soon you go further, and because of the constant (proportional to mass) production of this fluid the "balloon" growing rate decrease.
The intensity around the star is proportional to 1/d^2 but soon you go further away the density of this fluid become less than 1/d^2... until some time when the area is well filled and so forth.
More interresting, with this model, you dont only say : What is the intensity of the gravitational field at distance d, but you also need to say WHEN do i consider this intensity..
Older structures, like for the galaxys, have more of this "fluid" then young galaxys.
And when the star is loosing mass... the gravitational effect remain somewhere.

 

[Eternal Student]

Hi.

   I think I got the gist of what you were trying to say.

This is the bit that seems to contain the problem:

Therefore, if you consider that it can curve the space-time (and this can be assimilated as some local energy change) everywhere he pass by, you will understand that you could theoritically do the sum of the energy change of the spheres with radius between 0 and the infinity.

    There isn't any reason to consider the curvature of spacetime as a store of energy.

    Under General Relativity,  spacetime curvature is a consequence of energy being located at a place in space.   It is not a form of energy or a store of energy.    For example, there is no process or piece of equipment that will allow you to straighten out spacetime curvature and charge a battery up while you are doing that.    If there was some process to convert spacetime curvature into another known form of energy then you could have one increase while the other decreases - but that doesn't happen.   Exactly the opposite seems to happen:   Increase the total energy of known forms at a place and the curvature also increases at that place.

Best Wishes.

[Origin]

But first you need to really understand why there can be a 1/d^2 law in the intensity at some distant point for the electromagnetic field.
Lets begin with a source of photons that emit only 1 single photon.
This photon start form the point source and then advance toward infinity.
There is a problem if you want to receive this single photon, especialy if you are at a very long distance because if you consider the photon will spread as a cylinder (like a laser beam would do), the 1/d^2 law intensity would not apply everytime.
By chance, the photon spread as a cone, and you can intercept it much easyer.
So a single photon at a distance d can be received within a large surface onto the sphere wich has the radius d.
Whats the intensity law for this single photon ?
1/d^2 ? No, if you get the photon that is actualy present (because the duality particle wave) you got the full energy of this photon.And very important, if you get the photon within this surface, the photon disappear instantly (so far as we know) preventing anyone to receive the photon at the same time at an other position (the wave function is destroyed).

None of this has anything to do with the 1/r^2 relation ship because you are talking about 1 photon.  As I said before the relationship is due to the geometry of a point source.

Now, if you consider a source that emit a tremedous quantity of photons, every second, like a star would do, the intensity of the source can be seen as if it would be distributed onto the surface of a sphere of radius d.
You can divide the intensity by d*d because you are in fact dividing the number of the photons you can intercept on the surface of the sphere. You are not dividing the intensity of the photon (you can not it is a particle), but their number.

And the intensity (or number of photons) follows 1/r^2 relationship.

But what we know, and it is was distinguish the behaviour of the gravitational field and the electromagnetic field; is that the photon is VIRTUAL

There is a huge difference between a photon and a virtual photon.  Photons emitted by stars are not virtual photons.
The energy aspect was rather succinctly addressed by eternal student. 

[Dave Lev (OP)]

Quote from: Dave Lev on Yesterday at 21:28:06
However, don't you agree that it is quite complicated formula?

No it is not.

Thanks
Please try to answer the following:

1. Dark matter radius -
Why the radius of the dark matter is about 100 to 200 kpc?

Quote from: Dave Lev on Yesterday at 13:45:20
Up to what radius R the dark matter exists? Why it doesn't go all the way to the infinity?

The radius is about 100 to 200 kpc

Sorry, I still don't understand how gravity could set the dark matter so perfectly according to the requested formula up to that distance.

The galaxy doesn't calculate anything, what an odd thing to say.  You don't need a computer to calculate this.

So how the gravity knows the exact requested density at any radius for any sort of galaxy and also to update the density of the dark matter as the galaxy evolves and change its size/mass over time?
Are you sure that the gravity by itself can do the job of the distribution of dark matter without any external help?
If the gravity can do this job so easily, why it stops at 200KPC? Why not up to 1MPC and above?
2. Orbital velocity.
You didn't answer my following question:

Please look at the following diagram:
https://www.astronomy.ohio-state.edu/thompson.1847/1101/RotCurve2.gif
Don't you see that from 0KPC to 3KPC the orbital velocity is increasing quite dramatically up to 220 Km/s?
While from 3 KPC and upwards it is quite stable on this 220Km/s.
Therefore, how the same density formula could work at those two segments so differently?

So please look again in the following diagram and try to explain why from 3KPC to 0KPC the orbital velocity of stars falls down so dramatically?
Why the formula that you have offered can't keep the orbital velocity of 220KPC also for the section of below 3KPC?
Why the dark matter has an impact ONLY on the stars in the spiral disc from 3KPC and above?
3. Bulge (0 - 1KPC) - Why in the bulge each star orbits at different direction and orbital plane?
Why the Dark matter can't force the stars in the bulge to orbit in a disc?
4. Bar (1KPC to 3KPC) - How the dark matter could form the unique structure of the Bar?
5. Ring (3KPC)- Why the ring is always located at the base of spiral arms?
How the dark matter could force/convince billions of stars at that range to move suddenly in one direction and in the same plane/disc and form the ring shape?
Why the ring in all the billions spiral galaxies is always located at the base of the galactic disc?
How the dark matter formula could justify the existence of the ring exactly at the base of the spiral disc (not in the middle and not at the edge)?
6. Spiral disc - As you claim that the dark matter exists up to about 200KLY, how could it be that the spiral disc plan breaks down at about 50KLY?
Why the disc doesn't continue all the way to 200KLY?
7. Thickness of the spiral disc

Quote from: Dave Lev on Yesterday at 21:28:06
"The planets do not all orbit in the same plane as each other: the solar system is not flat"
We clearly see that "the orbital plane of Pluto’s orbit is very different from that of the eight planets"
However, even if it has exactly the same pitch as Neptune, it must go at higher distance from the orbital disc due to its longest radius.
Therefore, it is expected that as the star is located further away from the center, its distance from the disc should be higher.

No that does not logically follow.  It's apples and oranges.

Sorry, I still don't understand how the dark matter with its formula can set any sort of disc and especially its thickness:
a. No disc at the Bulge up to 1KPC
b. Some sort of a disc starts at the Bar 1KPC to 3KPC
b. About 3000LY at the base of the disc/ring at 3KPC
c. About 1,000 LY at 8.5KPC
d. Only 400LY at the edge of the disc (15KPC)
c. No disc after that edge

[Deecart]

    There isn't any reason to consider the curvature of spacetime as a store of energy.

    Under General Relativity,  spacetime curvature is a consequence of energy being located at a place in space.

I agree.

  It is not a form of energy or a store of energy.

You just sayed that spacetime curvature is a consequence of energy being located at a place and then you say that there is no energy needed to create this curvature ?
This is a total paradox.
You state that graviton (or whatever it is, black matter perhaps) do not contain energy but because of its energy it will permanently curve the spacetime while going around without loosing any energy.
But you are perhaps right and GR say this kind of thing, i am not a specialist.

   For example, there is no process or piece of equipment that will allow you to straighten out spacetime curvature and charge a battery up while you are doing that.    If there was some process to convert spacetime curvature into another known form of energy then you could have one increase while the other decreases - but that doesn't happen.   Exactly the opposite seems to happen:   Increase the total energy of known forms at a place and the curvature also increases at that place.

Of course there is.
There is a force wich appears, capable of pulling some mass toward an other, so you can have movement at the place where there was no movement at all before the action of the gravitational field. Therefore you create Work. Work is the transfert of energy.
 

[evan_au]

Lets begin with a source of photons that emit only 1 single photon.... the 1/d^2 law intensity would not apply everytime.

A wavefunction can also be considered to generate a probability.
- If you completely surround a single-photon source with perfect detectors, there is a 100% chance that you will detect the photon at far distance d.
- But if you use a detector with an area of only 1 m², the probability of detection at distance d is much smaller: call it p₁=1/4πd²
       - Since 4πd² m² is the surface area of a sphere, if d is measured in meters
- Now if you move your 1 m² detector twice as far away (2d), the probability that you will detect it has dropped to 25%
p₂ = 1/4π(2d)² = p₁/4

So the inverse square law for radiation still holds for a single photon; the probability of detecting 1 photon can become arbitrarily low if you make your detector smaller, or put it farther away from the source.

[evan_au]

we would have to help the galaxy to calculate the requested density for each radius,

I think you have this equation backwards: https://en.wikipedia.org/wiki/Dark_matter_halo#Density_profiles
- The equation for the density of Dark Matter in a galaxy is an empirical model that tries to explain the observed rotation curve of different galaxies.
- It is not a formula that each galaxy "tries" to follow
- You will notice that there are a number of parameters in the equation, that will take different values for different galaxies

There are a number of galaxies that have been observed with almost no Dark Matter, so the density of stars does seem to explain the rotation curve
- These galaxies appear to have formed from the collision of two gas-rich "normal" galaxies
- The gas clouds collided with each other, forming stars
- But the Dark Matter seems to have continued on its original trajectory, leaving behind a bunch of stars with little or no Dark Matter

The Bullet Cluster is one example where the collision was fairly recent, so the Dark Matter is still relatively close to the collision debris.
https://en.wikipedia.org/wiki/Bullet_Cluster

[Deecart]

There is a huge difference between a photon and a virtual photon.  Photons emitted by stars are not virtual photons.

I dont speak about what we name in physic "virtual photons", i say that the photon, by essence, is a quantic particle that expand in the space within some volume BUT if until you interact with it, the photon is like if there was nothing.
The only moment when you know THERE WAS a photon, is when you have destroyed it. So it is VIRTUAL.
The action of the photon (he give his energy) is localised exactly WHERE you interact with it altought it occupy a bigger volume.

None of this has anything to do with the 1/r^2 relation ship because you are talking about 1 photon.  As I said before the relationship is due to the geometry of a point source.

And the intensity (or number of photons) follows 1/r^2 relationship.

Ok, i see you dident understand what i tried to explain.
I do not blame you because i was thinking like you 3 months ago, before i finaly understood that i was tricked by the mathematical aspect of the 1/r^2 relationship and dident try to understand enought the physicaly phenomenon behind this law.

So, no problem, lets try some other explaination that can eventualy permit you to gain some new insight you can develop by yourself.

First we have to be aware that we dont really know the phenomenon underlying the gravity field.
The GR theory is some mathematical description like the SR theory but we dont really know the detail that lead to the fact we are describing.
Newton was a mathematician too and his law is based on mathematical tought guided by some mystical tought (Newton was also an alchemist).
So, are there some gravitons ? Some paquets of curved space, dark matter, "something" ? etc
SR and GR dont care and you have to guess.

Now, lets try some "GedankenExperiment" to see clearer.
Let us Imagine a massive object apppearing suddenly in some flat space.
Lets say there is something in the space toward infinity around this mass that can interact with light, some very dense fog of some kind.
When "light", or better said "a photon" hit a fog particle, it disappear.
The disappearance has to be regarded as some transformation (or LOSS if we consider it as a part of the total emited energy by the mass in term of photons) of the energy emited by the mass.
Because energy if we want to do physic should be something that should remain (this is some principia, like Newton could have say using his mystical tought) we can also, like Eternal Student dit, talk about transformation and not of loss. But it is the same, it just depend wich system we consider (the total or the part of).
So, what would we see as an external observator when the photons are emited during time ?
I will not explain this because this is very obvious and we can (and if i would so i dont want to talk so long about, my messages are already very long) do many interesting conclusions in the ways the photons will spread among space.

Now, let change and say the photons are now instead some "gravitational field particle" (GFP), that the mass is emitting like previously we did with the photon at the same constant flux rate, and that the fog is "the not curvatured spacetime".
The curvatured spacetime will not interact anymore with the GFP etc.

Good, you say, we have some similar behavior.

Wrong... because the theory (i dont say the theory is right...) say that the expansion of the gravitational field can not be shielded (mass dont hinder the propagation) nor be lowered because its meet some not curvatured space.
Therefore there is some questioning about WHY the GFP should behavior differently of the photon and be able to curve spacetime without not being "discarded" ("loss" of energy of the total emitted energy of the mass).

If you consider the energy you can use to curve the spacetime from GFP at some position d, behavior like those of the photon (... without the fog) you are not consistent.

This is why i mentionned this because it confirm the questioning of Dave Lev.
Why should there be some new law for the Gravitational force that matches the equilibrum of the galaxys and so forth ?
No, you can have this behavior if you consider that there is something (GFP) emited that (like the photon in the fog) disapear when it bends spacetime.
Therefore the impossibility to have a 1/d^2 law, unless there is "no fog" (already some curvature at the same value of the flux).
The energy by surface you can obtain from a constant emitted source of photon into some fog at some distance is not a fixed value. It depends of the anihilation of the fog, so it change during time when the fog progressivly disapear.

I hope it is more clear with this explaination.


 



 

[Deecart]

A wavefunction can also be considered to generate a probability.
- If you completely surround a single-photon source with perfect detectors, there is a 100% chance that you will detect the photon at far distance d.
- But if you use a detector with an area of only 1 m2, the probability of detection at distance d is much smaller: call it p1=1/4πd2
       - Since 4πd2 m2 is the surface area of a sphere, if d is measured in meters
- Now if you move your 1 m2 detector twice as far away (2d), the probability that you will detect it has dropped to 25%
p2 = 1/4π(2d)2 = p1/4

So the inverse square law for radiation still holds for a single photon; the probability of detecting 1 photon can become arbitrarily low if you make your detector smaller, or put it farther away from the source.

I totaly agree with your demonstration.
I just dont give the exact value , so i do not use the Pi or other constants, because this can be discarded when we speak in term of proportionality.
If you want to be very precise the only thing is that you consider that you dont know where the photon will strike.
This is somewhat wrong when you consider some big source of photon.
For a single atom emiting a photon i admit we know it can strike everywhere around the atome.
But for some spherical clusters of atoms, the atome can only be emited in the opposite direction of the cluster starting from his surface, with some angle around the vertical of the surface of the sphere (or it will be absorbed by the cluster shortly after it has been emited).

But why did i speak of this phenomenon ?
Because it can help you to understand that the mathematical point of view permit to consider infinitesimal volumes of space you can add or divide as you want, but in reality the photon, like perhaps the GFP (or not and this is some interresting question) need to be considered as "something" that CANT be divided.
The statistical value (a mathematical consideration) can not be considered to be like the real phenomenon,

[Dave Lev (OP)]

I think you have this equation backwards: https://en.wikipedia.org/wiki/Dark_matter_halo#Density_profiles
- The equation for the density of Dark Matter in a galaxy is an empirical model that tries to explain the observed rotation curve of different galaxies.
- It is not a formula that each galaxy "tries" to follow
- You will notice that there are a number of parameters in the equation, that will take different values for different galaxies

Thanks for your honest and clear explanation
So the idea is that when we can't explain the observed rotation curve by the ordinary matter, we can ask for a special dark matter for help.
For each galaxy we might need different dark matter density, different quantity, and different size of an impact - but as the dark matter comes free of charge we can ask it to fit to any formula which we need.
We only need to write the requested formula of dark matter density for each galaxy - and we get a perfect fit.
However, that fit at its maximal contribution can only explain the observed rotation curve at the galactic disc of spiral arm.
I hope that by now we agree that the dark matter can't explain the following questions:
1. How the disc had been formed exactly from the ring (3KPC) till the edge of the spiral arms ( 15KPC)?
2. Why the dark matter has no impact on the bulge or the Bar (up to 3KPC)?
3. Why the disc breaks down at 50,000 Ly while the dark matter is there up to at least 100,000 LY?
4. How could it be that the thickness of the disc is maximal in the base (3KPC) and minimal at the edge (15KPC)
And many other questions...

There are a number of galaxies that have been observed with almost no Dark Matter, so the density of stars does seem to explain the rotation curve
- These galaxies appear to have formed from the collision of two gas-rich "normal" galaxies
- The gas clouds collided with each other, forming stars
- But the Dark Matter seems to have continued on its original trajectory, leaving behind a bunch of stars with little or no Dark Matter

How can we accept the idea that in some galaxies there is dark matter while in the other there is no dark matter?
Dark matter is not something that we can order based on special delivery.
You have to take a decision.
If there is dark matter - then it must exist in any galaxy in the entire Universe.
If there is even one galaxy in the entire universe where the density of stars does seem to explain the rotation curve, then there is no dark matter in any other galaxy.
Actually, if the dark matter exists at any galaxy and as there are more stars outside the galaxies than in the galaxies - why there is no dark matter also outside the galaxies in the entire Universe?

Quote from: Dave Lev on Yesterday at 21:28:06
How could it be that the gravity can't clump the dark matter, while the dark matter can clump a regular matter by gravity?

In principle, if you waited long enough, it possibly could.

How long do we need to wait?
The age of the Milky Way is estimated for more than 12 BY. So why the dark matter in our galaxy didn't clump yet?

The issue here is that it, so far as we know, only interacts via the gravitational force.

Well, can we claim that as we don't know how the ordinary matter can explain the activity in the spiral galaxy, we have decided that we need some support for extra gravity? Therefore, can we agree that as we have decided that there is a need something that we can't see, can't smell and can't feel, let's call it dark matter and claim that it can only contribute extra gravity?

That greatly limits the way that dark matter particles can shed energy.

Did we even found even one particle of dark matter?
Do we really know how the gravity could spread the dark matter particles in the galaxy so it would fit to the requested formula?
As the dark matter is up to 100,000 LY it is very clear that the solar system and the Earth should constantly collide with dark matter particles as they orbit around the galaxy. So why we can't see a rain of dark matter particles falling on our heads?
If you think that the solar system is not big enough, then what about the spiral arms or ring? The thickness of the ring is 3,000 LY.
Don't you agree that it is quite massive object that should collide with the dark matter - if there was any dark matter?

Normal matter interacts via both gravity and the electromagnetic force. If you have a cloud of atoms, they can shed energy by releasing electromagnetic radiation. This causes the cloud to cool off and contract over time, until it forms a star or planet or whatever.

If the dark matter can't shed its energy, then why do we ignore its impact?
As the total mass of the dark matter is at least 5 times bigger than the ordinary matter, why we can't assume that some of the cosmic energy is due to dark matter/energy?

So you still have a cloud of dark matter long after a cloud of normal matter has already contracted into stellar or planetary bodies.

If the galaxy with its ordinary matter/stars is changing much faster than the dark matter, then then how the dark matter can fit itself to changes in the galaxy?
Do you agree that if in the past the dark matter was OK for the Milky way, then as the galaxy had been surly changed in the last billions years - then the old dark matter density (that can't change fast enough) can't fit anymore to the current milky way?
However, the Milky Way is stable with or without the changes in the dark matter.

In other words - why can't we just agree that our scientists have invented the idea of dark matter as they have no clue how spiral galaxy can work only based on ordinary matter?

[Bored chemist]

So the idea is that when we can't explain the observed rotation curve by the ordinary matter, we can ask for a special dark matter for help.

No.
We MUST ask for something else, and we call it dark matter.