A Dark matter and energy explained by negative mass

[Elroch]

Whether particles interact with electromagnetic radiation depends simply on whether they have an electric charge. Any other interaction of photons would be a surprising additional assumption.

 

[yahastu]

Whether particles interact with electromagnetic radiation depends simply on whether they have an electric charge. Any other interaction of photons would be a surprising additional assumption.

That is of course true...but even if they have a charge (and interact with EM fields) they would still be undetectable in EM because their predicted property of being self-repellent means that they would be more sparsely distributed than any known gas (hence would not reflect any light or have enough energy to emit any significant blackbody radiation), and their property of being attracted to positive masses would cause them to rapidly collide with and presumably be converted into energy (photons) when in the proximity of any physical measurement device, so I don't see how it would be possible to detect them in EM even if they have a charge.

 

[PeterDonis]

it was observed that galaxy rotation curves do not agree with the predictions of GR.

No, it was observed that the mass distribution needed to match galaxy rotation curves using GR (actually using Newtonian gravity since there is no significant correction to Newtonian gravity from GR in this regime) was different from the visible mass distribution. But there is no requirement in GR that all mass must be visible. It is perfectly possible to have mass that emits no radiation and hence can only be observed by its gravitational effects.

This is twice now that you have made the incorrect claim that galaxy rotation curves "do not match the predictions of GR". Please do not make this claim again; if you do, you will receive a warning.

it was argued that the theory is infallible

This is not correct; nobody has ever claimed that GR is infallible.

Again, please do not make such incorrect claims; if you do so again you will receive a warning.

 

[PeterDonis]

Dark matter is not something that was predicted in advance by any theory.

Neither is "negative mass".

 

[PeterDonis]

Farnes only proposed a creation term of negative mass particles, not positive ones...so I don't think you'd have positive-negative mass pairs spontaneously appearing in the vacuum.

He may have proposed a creation term for only negative mass particles, but that obviously violates energy conservation. To maintain energy conservation, you have to create a pair of particles, with masses of equal magnitude and opposite sign. The fact that Farnes just skates by this obvious fact, and handwaves his "creation term" into existence instead of trying to derive it from first principles and test it against conservation laws, does not inspire confidence.

Also, the "runaway solutions" do not require creation of a particle pair from the vacuum. They should happen whenever a negative mass particle and a positive mass particle interact. Since according to the proposed model, negative mass particles are everywhere, these interactions should be happening everywhere all the time, and we should be observing them constantly. We don't.

when a positive mass encounters a negative mass, it wouldn't lead to the creation of new energy

It doesn't have to. The "runaway solutions" involve the negative mass particle having increasingly negative energy, and the positive mass particle having increasingly positive energy. The sum of their energies remains constant (and would be expected to be zero on average). But we would observe this as a positive mass particle acquiring huge amounts of energy in a very short time (since according to the proposed model we cannot directly observe the negative mass particles, so we can't observe the huge amounts of negative energy that keep the total energy constant).

 

[PeterDonis]

If negative masses exist and are mutually repulsive

They aren't. Negative masses attract each other, just like positive masses. Negative masses and positive masses repel each other. As Hossenfelder points out in her article, this is required for consistency with GR.

If negative masses exist in free space, and are created so as to maintain equal pressure

The negative mass postulated in the paper has zero pressure, as far as I can tell; it is modeled as "cold" negative mass, just as ordinary matter and dark matter in standard cosmology are modeled as "cold" positive mass.

 

[martinbn]

This apparent error seems to me to be related to what I find to be a glaring omission throughout the paper: the author only considers the first Friedmann equation and never considers the second (he writes the second down as equation 3 and then never mentions it again). But a proper understanding of the dynamics requires both equations.

This is a good point. The second equations, his (3), is the one with the second time derivative. So it is the evolution equation. The other one, his (2), is more like a constraint equation.

 

[yahastu]

No, it was observed that the mass distribution needed to match galaxy rotation curves using GR (actually using Newtonian gravity since there is no significant correction to Newtonian gravity from GR in this regime) was different from the visible mass distribution...
you have made the incorrect claim that galaxy rotation curves "do not match the predictions of GR".

I think there are two separate issues here: (1) whether or not GR can explain the observed motion of galaxies assuming the presence of additional dark matter, and (2) whether or not the observed motions of galaxies matched the predictions of GR.

As for #2, I apologize for the way it came out, I am not trying to say anything controversial...I was just making a historical observation. To clarify my meaning, it was discovered in 1884 by Lord Kelvin that the mass of the Milky Way, as estimated using Newton's law of gravity from the observed velocity dispersion, was inconsistent with the observed mass of visible stars. In other words, the observed velocity dispersions did not match the predictions made at that time using Newton's law of gravity. The fact that observations didn't match the prediction didn't necessarily mean that Newton's law of gravity was false...it simply meant that the predicted outcome did not match the observed outcome, which meant at least one of the assumptions was false...Lord Kelvin concluded that the error was in the mass estimation (not gravity) when he said "many of our stars, perhaps a great majority of them, may be dark bodies" (ie, dark matter)...this discrepancy was further validated in 1922 by Kaptyn. GR was formulated in 1915, around this same time that it was discovered that Newton's law of gravity by itself was not properly explaining galaxy rotation curves, but as you noted already, GR did not differ significantly from Newton in this regard. So, when I said that "observed galaxy rotation curves do not match the predictions of GR," I was really just pointing out that dark matter was proposed as a solution to erroneous initial predictions assumed by Newton's gravity (or equivalently GR).

As for #1, if the observed galaxy rotation curves are to be explained by some distribution of dark masses with the known equations of gravity, then it is critical that the distribution of those invisible dark masses also be explained by gravity, right? Otherwise, we could arbitrarily add additional terms into the equations for gravity (e.g., change gravity to be inverse cube of distance), and then simply compensate for those differences by postulating some increasingly complex distribution of invisible matter such that the observed motions of positive masses are predicted accurately. It would be like using a high order polynomial equation to predict an arbitrary function. Therefore, the question of whether or not dark matter can be used to explain galaxy rotation curves really comes down to the question of whether or not the combined distribution of visible matter + dark matter can be explained using the laws of gravity. Correct me if I'm wrong, but my understanding is that this is currently not the case -- adding dark matter greatly reduces the discrepancy between model and observation, but still does not bring them into complete alignment...with the most significant discrepancy remaining being called the "cuspy halo problem," wherein the dark matter distribution that would be dictated by the laws of gravity does not correctly match the dark matter distribution that would be necessary to compensate for observed galaxy rotation curves.
https://en.wikipedia.org/wiki/Cuspy_halo_problem

He may have proposed a creation term for only negative mass particles, but that obviously violates energy conservation. To maintain energy conservation, you have to create a pair of particles, with masses of equal magnitude and opposite sign. The fact that Farnes just skates by this obvious fact, and handwaves his "creation term" into existence instead of trying to derive it from first principles and test it against conservation laws, does not inspire confidence.

I agree this seems like a very valid point, and suggests that at best the theory is incomplete, though it seems elegant in many other ways...and given that there is not yet any alternative theory which doesn't have it's own subtle issues, I'm not ready to completely dismiss the idea on this basis. Farnes admits that it is just the initial workings for a theory, not fully worked out.

Also, the "runaway solutions" do not require creation of a particle pair from the vacuum. They should happen whenever a negative mass particle and a positive mass particle interact. Since according to the proposed model, negative mass particles are everywhere, these interactions should be happening everywhere all the time, and we should be observing them constantly. We don't.

Positive masses attract each other into close proximity and then become bound together by the much stronger EM force, whereas in this model negative masses are proposed to repel each other, and hence negative masses would never be bound together by the EM force...so we should expect the vast majority of interactions between positive and negative masses to be between a clump of positive masses that are bound together by EM vs. an individual free negative mass, as such these interactions would not lead to the runaway solutions because they are not equal in mass.

It doesn't have to. The "runaway solutions" involve the negative mass particle having increasingly negative energy, and the positive mass particle having increasingly positive energy. The sum of their energies remains constant (and would be expected to be zero on average). But we would observe this as a positive mass particle acquiring huge amounts of energy in a very short time (since according to the proposed model we cannot directly observe the negative mass particles, so we can't observe the huge amounts of negative energy that keep the total energy constant).

Is that not exactly what we observe with cosmic rays -- positive mass particles that have unexpectedly high energy? This seems like an additional explanatory selling point of Farnes theory rather than a problem.

They aren't. Negative masses attract each other, just like positive masses. Negative masses and positive masses repel each other. As Hossenfelder points out in her article, this is required for consistency with GR.

That is certainly not how Farnes describes them in Fig. 1. The entire premise of this theory requires negative masses being mutually repulsive in order to explain the halo formation. I missed the link to Hossenfelder's article...but isn't Farnes already modifying the field equations of GR for this theory, so I don't see how one could use inconsistency with GR as a basis for dispute when that is his very premise

The negative mass postulated in the paper has zero pressure, as far as I can tell; it is modeled as "cold" negative mass, just as ordinary matter and dark matter in standard cosmology are modeled as "cold" positive mass.

If empty space is filled with negative masses which are attracted to positive masses, that would seem to imply that positive masses are being continually bombarded with negative masses from all directions -- how is that not pressure?

 

[Elroch]

1. Regarding the predictions of galaxy rotation, a theory needs to be able to predict the evolution of this over time. This is much more demanding than agreement at one instant, and only a tiny fraction of possibilities could be achieved by any mass distribution.
2. I don't know why you think the EM force takes over when masses get close. The Sun keeps bound in a small region because of gravity, not any electromagnetic interaction of the plasma. Indeed gravity holds it together and EM forces stop it from collapsing more, so it is opposing the binding. The two need to be in equilibrium so the form is stable.
3. You are right, if you have a positive mass and a negative mass, if the negative mass is smaller, you can have a bound system. If it is larger the masses always separate. If they are the same, you can get them staying the same distance and moving in the same direction at an accelerating speed. I believe that if the kinetic energy in the centre of mass frame is more than the gravitational binding energy, they diverge, just like two positive masses.
4. I am rather sure that this choice of definition of mass is the one consistent with general relativity (sticking my neck out here as this is not in any sense my field). For example, it should correspond exactly to the ADM mass or Komar mass defined in general relativity having a negative sign. Intuitively (at least at low energy) the meaning is clear: positive masses produce valleys into which things fall, and negative masses make hills down which things tend to roll. This is true both for negative mass things and positive mass things. Of course, being GR, these hills and valleys also involve the time dimension, which means the visualisation is loose.
5. Pressure is about repulsive interaction. There is no assumption of any interaction other than gravity between positive and negative masses: they could pass straight through each other without being detected (apart from a changing gravitational interaction).

 

[yahastu]

Regarding the predictions of galaxy rotation, a theory needs to be able to predict the evolution of this over time. This is much more demanding than agreement at one instant, and only a tiny fraction of possibilities could be achieved by any mass distribution.

Nobody is disputing that. The notion of a theory of gravity agreeing at only an instant of time doesn't wouldn't even make sense, since it's a theory describing the motion of masses from any initial positions.

I don't know why you think the EM force takes over when masses get close. The Sun keeps bound in a small region because of gravity, not any electromagnetic interaction of the plasma. Indeed gravity holds it together and EM forces stop it from collapsing more, so it is opposing the binding. The two need to be in equilibrium so the form is stable.

For the interaction I was discussing, gravity is weak at the atomic and subatomic level in comparison to EM because the masses involved are incredibly small. According to this theory, because all negative masses repel other negative masses, they would never glob up to form anything more than a subatomic particle -- so when they interact with a positive mass, which is actually a collection of many positive masses bound together by the EM form through chemical bonds etc, the gravitational interaction of this 1 tiny negative mass would not be strong enough to break apart the chemical bonds between positive masses that are bound together through EM. That is the reason why this theory does not predict frequent occurrences of the "runaway particle" ...because that only occurs when a positive and negative mass of exactly equal mass meet up in relative isolation of other masses, and the vast majority of the time that positive mass meets negative mass, they will not be of equal mass.

You are right, if you have a positive mass and a negative mass, if the negative mass is smaller, you can have a bound system. If it is larger the masses always separate. If they are the same, you can get them staying the same distance and moving in the same direction at an accelerating speed. I believe that if the kinetic energy in the centre of mass frame is more than the gravitational binding energy, they diverge, just like two positive masses.

I am rather sure that this choice of definition of mass is the one consistent with general relativity (sticking my neck out here as this is not in any sense my field). For example, it should correspond exactly to the ADM mass or Komar mass defined in general relativity having a negative sign. Intuitively (at least at low energy) the meaning is clear: positive masses produce valleys into which things fall, and negative masses make hills down which things tend to roll. This is true both for negative mass things and positive mass things. Of course, being GR, these hills and valleys also involve the time dimension, which means the visualisation is loose.

I'm not sure what you're replying to here...

Pressure is about repulsive interaction. There is no assumption of any interaction other than gravity between positive and negative masses: they could pass straight through each other without being detected (apart from a changing gravitational interaction).

The paper proposes that the gravitational interaction between negative-negative particles is repulsive, and that gravitational interaction between positive-negative masses is for positive masses to be repelled by negative masses, and negative masses to be attracted to positive masses. Thus we have a situation where negative masses expand to fill the vacuum (like a gas), and exert pressure on any positive mass by pushing on them from all directions...or effectively causing them to behave that way due to the way that positive and negative masses deform spacetime

 

[PeterDonis]

f the observed galaxy rotation curves are to be explained by some distribution of dark masses with the known equations of gravity, then it is critical that the distribution of those invisible dark masses also be explained by gravity, right?

I'm not sure what you mean. You don't "explain" the distribution of matter by gravity. You use an assumed distribution of matter as the source in the known equations for gravity.

the "cuspy halo problem," wherein the dark matter distribution that would be dictated by the laws of gravity does not correctly match the dark matter distribution that would be necessary to compensate for observed galaxy rotation curves.

No, that's not the cuspy halo problem. The cuspy halo problem is that when we try to simulate how galaxies with dark matter distributions might have formed, what comes out of the simulations doesn't match the distributions that we infer from observations of galaxy rotation curves. But in order to make such simulations we have to assume initial conditions. The obvious conclusion from the cuspy halo problem is that we have a very poor understanding of the initial conditions. In other words, we have a poor understanding of how the galaxies we observe evolved. But that doesn't mean the mass distribution we infer from their rotation curves is wrong.

in this model negative masses are proposed to repel each other

Yes, and as I've already pointed out (and as Hossenfelder points out in her article), that's not consistent with GR. In GR, masses of the same sign attract each other. Since the Friedmann equation used throughout the article depends on GR being correct, the model is not self-consistent.

Is that not exactly what we observe with cosmic rays -- positive mass particles that have unexpectedly high energy?

No. Most cosmic rays have energies that are not "unexpectedly high". Very rare cosmic rays are observed that have unexpectedly high energy. But according to the model proposed in the paper, cosmic rays with those high energies should not be "unexpected"--we should be seeing them constantly. And they shouldn't be "cosmic"--they shouldn't just be coming from far away from the Earth. They should be coming from everywhere, including right here on Earth.

That is certainly not how Farnes describes them in Fig. 1.

I know. His Fig. 1 is inconsistent with GR. He has evidently not bothered to check all of the assumptions of his model for consistency. Again, this does not inspire confidence.

If empty space is filled with negative masses which are attracted to positive masses, that would seem to imply that positive masses are being continually bombarded with negative masses from all directions

In GR, masses of unlike signs repel. They don't attract. So again, the model is not self-consistent.

how is that not pressure?

Pressure in a cosmological model is a indication that the masses in question have relativistic energies. The model in the paper appears to be assuming that the negative masses, like the positive masses in the standard model of our universe, have non-relativistic energies and therefore have zero pressure in the model.

 

[Elroch]

Peter, are you saying masses of the same sign attract each other in GR? Anyhow, Franes definitely assumes positive masses attract everything and negative masses repel everything.

To first order, interactions are additive (n masses attract n times as much as 1 mass). A positive mass and a negative mass of equal magnitude sum to a mass of zero, so the negative mass has to have the opposite effect on all objects to the positive mass, in order for the superposition of the two to have zero effect. [I am thinking here of a large mass that is influencing small masses, for simplicity].
But the argument works the other way too, I believe. If you have a small probe mass, to first order, this has some force on it due to another mass (of either sign). The total force on the sum of a small probe mass and a negative probe mass of the same size is zero, so the force on the negative probe mass is in the opposite direction.
But this means that the acceleration of the negative probe mass is in the same direction as that of the positive mass probe mass! Which is the opposite to the result I was trying to derive. :D
I am not sure I see any way of getting round the dramatic inconsistency between this and what Franes assumes is true without throwing away his reasoning.

 

[PeterDonis]

Peter, are you suggesting masses of the same sign attract each other in GR?

Yes. Hossenfelder's article explains why in more detail.

A positive mass and a negative mass of equal magnitude sum to a mass of zero, so the negative mass has to have the opposite effect on all objects to the positive mass, in order for the superposition of the two to have zero effect.

This is perfectly consistent with masses of the same sign attracting each other--and masses of opposite sign repelling each other, as I said. A source consisting of a positive mass and a negative mass of equal magnitude would have an effect on a test mass that sums to zero, whether the test mass itself is positive or negative, since the positive and negative source masses would have opposite effects on it either way.

I am not sure I see any way of getting round the dramatic inconsistency between this and what Franes assumes is true without throwing away his reasoning.

I don't think there is one. Franes has, as I said before, simply failed to check his assumptions for consistency.

 

[Elroch]

If it wasn't obvious, it was only when I was writing the second last sentence of my post that I realized my simple reasoning was directly inconsistent with the assumptions of Franes's paper.

 

[yahastu]

The cuspy halo problem is that when we try to simulate how galaxies with dark matter distributions might have formed, what comes out of the simulations doesn't match the distributions that we infer from observations of galaxy rotation curves. But in order to make such simulations we have to assume initial conditions. The obvious conclusion from the cuspy halo problem is that we have a very poor understanding of the initial conditions. In other words, we have a poor understanding of how the galaxies we observe evolved. But that doesn't mean the mass distribution we infer from their rotation curves is wrong.

Have the simulations actually shown that the distribution of dark matter in the stable state is highly sensitive to initial conditions? For the same reasons that we expect regular masses to reach a dynamic equilibrium, I would imagine that any dark matter would reach it's own type of dynamic equilibrium relative to the regular masses, and as such I don't see why it would be very sensitive to the initial distribution (I do see why it would be sensitive to initial quantity, but that is assumed known).

Yes, and as I've already pointed out (and as Hossenfelder points out in her article), that's not consistent with GR. In GR, masses of the same sign attract each other. Since the Friedmann equation used throughout the article depends on GR being correct, the model is not self-consistent.

From Hossenfelder's critique (http://backreaction.blogspot.com/2018/12/no-negative-masses-have-not.html), "The deeper reason for this [why it is not consistent with GR] is that the gravitational interaction is exchanged by a spin-2 field...Once you work with General Relativity, you are stuck with the spin-2 field and you conclude: like charges attract and unlike charges repel.".

In trying to understand that explanation better, I found this:
https://www.reddit.com/r/askscience/comments/fdm3s/can_anyone_explain_what_a_spin2_field_is/

"Spin-2 fields and spin-2 bosons come up whenever you apply quantum field theory to gravitation. It was once believed that if you could couple a spin-2 field to the stress-energy tensor, you would reproduce exactly the Einstein-Hilbert action, which means you would have a quantum-field-theory formulation of gravity. Which would be a big deal. But it turns out that isn't possible, for mathematical reasons."

Based on that explanation, it sounds like GR being a spin-2 field is not a standard assumption of GR, but rather a more controversial hypothesis that was made in attempt to unify gravity with GR which failed.

Furthermore, if gravity is described by a spin 2 field, that would seem to be predicated on the assumption that there is an actual spin-2 particle (the graviton), however I believe that explanation is not believed by most physicists today. If the graviton does not exist, then GR is not a spin-2 field, and Hossenfelder's argument that Farnes violated GR is invalidated. What are your thoughts on that?

Hossenfelder also adds to his critique by saying:

"Farnes in his paper instead wants negative gravitational masses to mutually repel each other. But general relativity won’t let you do this. He notices that in section 2.3.3. where he goes on about the “counterintuitive” finding that the negative masses don’t actually seem to mutually repel."

However, looking at section 2.3.3, it is clear that Hossenfelder misquoted Farnes, who said nothing of the sort. Here is what Farnes actually said: "This is a counterintuitive result, as although negative masses are gravitationally repelling one another, the cosmological effect appears to be for the negative energy associated with the negative masses to cause the universe to recollapse...the solution expands from a big Bang, reaches a maxima, then recontracts to a Big Crunch"

If Farnes was assuming a finite universe, it would be rather obvious that a situation of negative masses repelling would mandate an expansion phase followed by a contraction phase, as I already pointed out...because negative mass would migrate towards the boundary of the universe, form a halo around it in the same way that it is hypothesized to do around galaxies, and the ratio of negative mass outside would continually increase until eventually the gravitational "forces" inwards from the negative masses would overcome the gravitational "forces" outward from the finite positive mass, leading to a collapse. I think that is all Farnes was saying. (not using the word "force" literally, I am referring to the effect caused by warping of spacetime)

 

[PeterDonis]

Have the simulations actually shown that the distribution of dark matter in the stable state is highly sensitive to initial conditions?

Since the dynamics are chaotic, this would be expected. My understanding is that the simulations have not explored a very wide range of initial conditions.

For the same reasons that we expect regular masses to reach a dynamic equilibrium

But we don't expect this for astronomical systems. The solar system, for example, is not in dynamic equilibrium; its dynamics are chaotic, and it does not settle into a particular equilibrium state that it then remains in indefinitely.

 

[PeterDonis]

In trying to understand that explanation better, I found this

A reddit thread is not a good source for learning science. Try a textbook. Plenty of textbooks on GR explain what it means to say that the gravitational interaction is spin-2, and why that implies that like masses attract and unlike masses repel--by contrast with a spin-1 interaction like electromagnetism, in which like charges repel and unlike charges attract.

it sounds like GR being a spin-2 field is not a standard assumption of GR

Gravitation arising from a spin-2 quantum field is not a standard assumption of GR--of course not, since GR is not a quantum theory.

But saying that gravitation is a spin-2 interaction is not the same as saying that it arises from a spin-2 quantum field. Hossenfelder explains the difference in her article; it sounds like you need to go back and read it again more carefully.

looking at section 2.3.3, it is clear that Hossenfelder misquoted Farnes

That does appear to be true for the particular quote you gave. However, it does not in the least change the substance of Hossenfelder's critique, which does not depend on her having quoted Farnes correctly in this case.

 

[yahastu]

Since the dynamics are chaotic, this would be expected. My understanding is that the simulations have not explored a very wide range of initial conditions.

Individual particle motions are chaotic, but that does not mean the overall characteristic behavior is chaotic. The fact that we have a termed called "the cuspy halo problem" means that, regardless of initial conditions, they always tend to observe a cuspy halo. Nobody would be talking about that as a problem if it was something that just happened to crop under one particular random initialization. This implies that the overall radial dark matter distribution is not dependent on initial conditions.

 

[yahastu]

A reddit thread is not a good source for learning science. Try a textbook. Plenty of textbooks on GR explain what it means to say that the gravitational interaction is spin-2, and why that implies that like masses attract and unlike masses repel--by contrast with a spin-1 interaction like electromagnetism, in which like charges repel and unlike charges attract.

Sure, I'd be happy to refer to a textbook -- I know you said that "plenty of textbooks" exist, but considering that different people seem to have different opinions, can you recommend a specific one that you know supports your view?

 

[PeterDonis]

Individual particle motions are chaotic, but that does not mean the overall characteristic behavior is chaotic.

In some cases, like an ideal gas, yes, there are properties of the overall system that are not chaotic. However, a galaxy is not an ideal gas. I have already given the solar system as an example of a system whose overall behavior is chaotic. Galaxies are much more like the solar system than they are like an ideal gas.

The fact that we have a termed called "the cuspy halo problem" means that, regardless of initial conditions, they always tend to observe a cuspy halo.

Please give a specific reference that supports this claim. As I have already said, it does not seem to me that the simulations you refer to have sampled a wide range of initial conditions.

Nobody would be talking about that as a problem if it was something that just happened to crop under one particular random initialization. This implies that the overall radial dark matter distribution is not dependent on initial conditions.

This is not valid reasoning, it's just you guessing. Go find a specific reference that supports your claim.

I'd be happy to refer to a textbook -- I know you said that "plenty of textbooks" exist, but considering that different people seem to have different opinions, can you recommend a specific one that you know supports your view?

The two classic GR textbooks, Misner, Thorne & Wheeler, and Wald. But I'm sure those aren't the only ones. The properties of a spin-2 interaction in a classical field theory are not at all controversial.

 

[PeterDonis]

negative mass would migrate towards the boundary of the universe

A finite universe does not have a boundary; that would violate the Einstein Field Equation. A spatially finite universe would have the spatial geometry of a 3-sphere: a 3-dimensional space with a finite volume but no boundary (just as the Earth's surface is a 2-sphere, a 2-dimensional surface with a finite area but no boundary). Negative mass in a finite universe would, on average, be expected to have uniform density, just as positive mass does.

 

[yahastu]

Please give a specific reference that supports this claim. As I have already said, it does not seem to me that the simulations you refer to have sampled a wide range of initial conditions. This is not valid reasoning, it's just you guessing. Go find a specific reference that supports your claim.

Basically, my reasoning is that no galaxy has the same initial conditions, each one starts as a random cloud of dust and gas...yet we have observed a common tendencies for galaxies to form, they generally have a consistent visual appearance, and we can generally characterize their rotation curves as deviating from what would be expected without dark matter in a common way, indicates that the dark matter distribution in the stable state must be independent from the specific random distribution of their constituent particles in the interstellar medium from which they formed.

The two classic GR textbooks, Misner, Thorne & Wheeler, and Wald. But I'm sure those aren't the only ones. The properties of a spin-2 interaction in a classical field theory are not at all controversial.

Thank you

A finite universe does not have a boundary; that would violate the Einstein Field Equation. A spatially finite universe would have the spatial geometry of a 3-sphere: a 3-dimensional space with a finite volume but no boundary (just as the Earth's surface is a 2-sphere, a 2-dimensional surface with a finite area but no boundary). Negative mass in a finite universe would, on average, be expected to have uniform density, just as positive mass does.

I did not mean a boundary in spacetime. Spacetime itself would need to extend infinitely. I only meant a finite extent to the subset of spacetime that contains regular matter.

 

[kent davidge]

Jamie Farnes' channel with simulations is https://www.youtube.com/channel/UC8ltFtaETXDphec0l-VxMsg/videos

 

[Bandersnatch]

I did not mean a boundary in spacetime. Spacetime itself would need to extend infinitely. I only meant a finite extent to the subset of spacetime that contains regular matter.

You know those Friedman equations you've seen the author use in his paper? They assume large-scale homogenous distribution of matter in the universe. This implicitly precludes any such subset from existing.

 

[Auto-Didact]

My two favourite areas of physics in one thread; I'm going to try taking off my GR thinking cap and put on my nonlinear dynamics thinking cap for a bit.

But we don't expect this for astronomical systems. The solar system, for example, is not in dynamic equilibrium; its dynamics are chaotic, and it does not settle into a particular equilibrium state that it then remains in indefinitely.

I think a mentioning of the time scale is necessary: despite chaos, the solar system is known to be stable for at least millions of years, due to tidal friction effects, resonances and whatnot. This means two things: a) that the answer to any particular scenario depends on the time scale involved, and b) the full answer requires a multiple scale analysis.

I did not mean a boundary in spacetime. Spacetime itself would need to extend infinitely. I only meant a finite extent to the subset of spacetime that contains regular matter.

Again, as with the above, the scale decides the answer: how large are you roughly taking these regions of spacetime to be? Galaxy sized or much larger?

You know those Friedman equations you've seen the author use in his paper? They assume large-scale homogenous distribution of matter in the universe. This implicitly precludes any such subset from existing.

The Friedman equation is an approximation only valid on scales larger than several hundred megaparsecs; it seems people quickly tend to forget that actually solving GR equations (not that weak field linearized bollocks) is mathematically, ahem, pretty involved i.e. actual geometrodynamics requires nonlinear dynamics.

 

[PeterDonis]

my reasoning is that no galaxy has the same initial conditions, each one starts as a random cloud of dust and gas...

Yes.

yet we have observed a common tendencies for galaxies to form, they generally have a consistent visual appearance

No, they don't. Galaxies have varied visual appearances: elliptical, spiral, and barred spiral are three main types, but there are significant variations within them and there are many irregular galaxies that don't fit any of the types. Also intergalactic space is not empty, it has huge clouds of dust and gas in it that have not collapsed into galaxies.

we can generally characterize their rotation curves as deviating from what would be expected without dark matter in a common way,

Please give a reference to support this claim. It seems much too strong to me.

I only meant a finite extent to the subset of spacetime that contains regular matter.

There is no such thing. The universe, on average, has the same density of matter everywhere. This is true in the proposed model in Farnes' paper just as it is true in the standard mainstream cosmological model.

 

[LURCH]

Have to admit, I’m seeing the article in a rather skeptical light, but trying to keep an open mind (also, I’m only on p.15). Will be following the link to Hossenfelder’s response next, but what I’ve read so far has brought up a question that I don’t see addressed yet.

Wouldn’t these “halos” of negative mass effect events like galactic collisions? If both the Milky Way and Andromeda galaxies are, by mass, mostly made of “negative mass” matter, largely concentrated in halos around the outer boundaries of these galaxies, and those halos are mutually repulsive, should the two galaxies still be able to attract one another gravitationally? I can see a possible response in pointing out that the positive mass in each galaxy is attracted to both the negative mass and the positive mass in the other galaxy, but that doesn’t seem to work if the majority of the matter is of negative mass.

Even if this does not prevent the collision, it should have a predictable and measurable effect, shouldn’t it? I don’t know if this poses a problem to the model, or just an opportunity for observation to test it.

I also see a problem with the runaway pairs, but will read on before asking about that.

 

[Elroch]

There is a crucial problem with some of what has been said earlier in this discussion (including me) which involves a careless assumption which is valid when all masses are positive.

First, I'll make my assumptions clearer than before. Assume inertial mass is proportional to gravitational mass (this is well tested for positive masses, but it is at least conceivable that for a negative mass, the inertial mass would be proportional to the absolute value of the gravitational mass, or something more complicated, so it is necessary to make this assumption clear). Assume also we are in the low energy domain where GR is approximated almost perfectly by Newtonian physics: any theory extending GR surely has to have such an approximation.

Here's the main point: given the assumption about inertial mass and gravitational mass, If a positive mass attracts a negative mass then the negative mass has to repel the positive mass in order for momentum to be conserved. So it makes no sense to claim that opposite sign masses repel (i.e. that they are accelerated in opposite directions): this cannot happen. It is possible that one reason someone might think they do is to subconsciously assume that force and acceleration are in the same direction for a negative mass, when in fact they have to be in opposite directions.
[To derive Newton's third law for masses which may not be positive, just observe the sum of the two interaction forces F₁₂ +F₂₁ is the force on the system of two masses as a whole. Thus this sum has to be zero to satisfy momentum conservation].

Anyhow, continuing while taking this into account does lead to the dynamics assumed and described by Franes, with positive masses attracting everything, negative masses repelling everything. This does lead to the strange behaviour where an inertial observer can watch a positive mass and an equal negative mass accelerate together, with the negative mass chasing the positive mass.
[Note, to an observer at one of the masses, the relationship of the two masses can appear entirely stationary. The nearest analogy I can think of to this is a thought experiment I played around with when I was young, where an object behind a massive object that is being accelerated can itself appear to be both stationary relative to the large object and experiencing no acceleration].

Anyhow, it seems to me that any reasoning about GR that led to the conclusion that like masses attract and unlike ones repel has a sign missing somewhere.

The cosmologist Hermann Bondi analysed the role of negative mass in general relativity (with a hope of showing it couldn't exist, at which he was unsuccessful) and states: "In general relativity, a negative mass repels all masses, a positive attracts all".

 

[Auto-Didact]

No, they don't. Galaxies have varied visual appearances: elliptical, spiral, and barred spiral are three main types, but there are significant variations within them and there are many irregular galaxies that don't fit any of the types.

Read what he means, not what he writes! Galaxies, just like cells, can obviously be classified into similar classes of structures: you are doing so yourself in your very reply!

Please give a reference to support this claim. It seems much too strong to me.

Actually this claim is pretty standard, see for example, pp 350, 351 of Hartle; it's a bit more difficult to find in MTW probably due to my copy being from the 70s (NB: Weinberg's book belongs in the trash). Clearly @yahastu just isn't worded as carefully (i.e. as pedantic) as it could be worded. On small scales, i.e. definitely less than the megaparsec scale, dark matter is inconsistent with the galaxy rotation curves predicted by Newtonian dynamics; dark matter was first hypothesized for this by Zwicky in the 1930s.

There is no such thing. The universe, on average, has the same density of matter everywhere.

Again on average on large scales; on 'small scales' such as the size of dozens to roughly thousands of galaxy (Milky Way) sized objects this is obviously not true.

 

[Elroch]

No. Most cosmic rays have energies that are not "unexpectedly high". Very rare cosmic rays are observed that have unexpectedly high energy. But according to the model proposed in the paper, cosmic rays with those high energies should not be "unexpected"--we should be seeing them constantly. And they shouldn't be "cosmic"--they shouldn't just be coming from far away from the Earth. They should be coming from everywhere, including right here on Earth.

While this is true and needs quantification, the rate of production is certainly extraordinary low per unit volume per unit time. cf the energy density of dark energy is equivalent to 7x10^-27 kg/m³ and the corresponding rate of production has a time constant similar to the age of the universe. In any case, most of the cosmic rays would have come from a long distance if they can travel such distances, if the rate of production is roughly uniform in space-time. (If so, the cosmic rays are distributed roughly uniformly against distance of origin, like in the Olber paradox, until the distance is so large the expansion of the Universe becomes significant).