A Dark matter and energy explained by negative mass

[KarlM]

Any thoughts on this paper?
https://arxiv.org/abs/1712.07962

 

[mountevans]

It looks like it just came out. I am still reading through it, but I don't see any discussion of what this negative mass dark fluid could be made of.

Also, what would the geodesics around such a fluid look like?

 

[yahastu]

https://phys.org/news/2018-12-universe-theory-percent-cosmos.html

Very interesting paper here. In addition, I would point out that if approximately 95% of the mass in the universe is negative rather than positive, then perhaps its actually 100% -- a perfectly equally balanced universe of positive and negative mass, which seems rather elegant.

 

[Bandersnatch]

I would point out that if approximately 95% of the mass in the universe is negative rather than positive, then perhaps its actually 100% -- a perfectly equally balanced universe of positive and negative mass, which seems rather elegant.

How is 20:0 less imbalanced than 19:1, let alone perfectly balanced?

 

[yahastu]

How is 20:0 less imbalanced than 19:1, let alone perfectly balanced?

Because a generic property of inflation is that the universe began from a small quan-
tum fluctuation. According to Vilenkin, “A small amount of energy was
contained in that [initial] curvature, somewhat like the energy stored in a strung bow. This ostensible violation of energy conservation is allowed by the Heisenberg uncertainty principle for sufficiently small time intervals. The bubble then inflated exponentially and the universe grew by many orders of magnitude in a tiny fraction of a second.”

If the there is the same amount of negative mass as positive mass then the sum total is zero and that makes the idea that the whole thing sprang into existence out of some vacuum potential more plausible to me

 

[Bandersnatch]

But the point is, the paper doesn't claim there to be the same amount of positive and negative mass. It claims that all the energy density currently attributed to dark energy + dark matter is negative mass density. So, it proposes an already unbalanced state with a 19:1 ration of negative:positive mass.
A 100% negative mass density would have 0% positive mass in it.

Also, if I'm reading this paper correctly, this model does away with inflation, going for cyclic cosmology instead.

 

[mitosis]

I'm surprised this hasn't yet generated more discussion. Seems like an elegant theory.

 

[Elroch]

This is the most interesting new hypothesis I have come across in a long while, the idea that a single hypothetical substance (field/particle) could explain the two phenomena that are currently explained by dark energy and dark matter separately. It is this that J.S. Farnes (https://www.researchgate.net/profile/Jamie_Farnes) explains in his paper which is on Arxiv at https://arxiv.org/pdf/1712.07962.pdf

The first thing I thought was "how can a single substance explain both the 'missing mass' that is needed for anomalous galaxy rotation and accelerating expansion of the Universe?" The answer is given rather clearly in the paper by an extremely simple diagram whose most important feature is the fact that with a material which has negative mass, force and acceleration act in opposite directions (Newton would have been happy with this, since it is what F=ma says!). The result is that negative mass, which has positive energy according to Einstein's energy momentum equation (and which makes E=mc^2 a wrong simplification for negative mass!) repels itself, but is attracted to positive mass.Positive mass is repelled by negative mass, but since there is negative mass in all directions, this does not make galaxies fly apart. Farnes assures us that the calculations show it can explain the effect for which dark matter was invented and easily explains the accelerating expansion of the Universe.

Farnes does not claim the hypothesis is definitely true: he identifies experimental tests that can test his hypothesis and discriminate between it and other more established ideas.

 

[Chris W Kullander]

How would negative mass affect spacetime? Also what happens when it comes into contact with "positive" mass?
https://phys-org.cdn.ampproject.org...s/2018-12-universe-theory-percent-cosmos.html

 

[fresh_42]

Several threads about this subject have been merged.
Because of the highly speculative nature of this paper, I want to remind all participants to stay as close as possible within a debate about the publication.

 

[PeterDonis]

Sabine Hossenfelder has posted about this paper:

http://backreaction.blogspot.com/2018/12/no-negative-masses-have-not.html

 

[PeterDonis]

One thing I am having trouble understanding in the paper: The author appears to be arguing that negative mass can have the same effect as a negative cosmological constant. But I don't see how he is arriving at that result. A negative cosmological constant is a negative energy density, but a positive pressure of equal magnitude, so the "source" term $\rho + 3 p$ is positive. A negative mass, as he is modeling it, appears to be a negative energy density with zero pressure, which makes $\rho + 3 p$ negative. So a negative mass should have the opposite effect to a negative cosmological constant.

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.

 

[PeterDonis]

negative mass, which has positive energy according to Einstein's energy momentum equation

If you mean $E^2 - p^2 = m^2$, that equation can't tell you about the sign of the mass or the energy or the momentum, since all of them are squared.

The paper says that negative mass means negative energy density $\rho$ in the Friedmann equations, which are derived from the Einstein Field Equation. So according to the paper, negative mass has negative energy.

 

[Elroch]

Chris, based on the symmetry and the basic dynamics, the effect of the hypothetical negative mass on space-time has to be the opposite of that of positive mass. . For example, regions near a positive mass have to experience gravitational blue shift compared to regions near a negative mass.

The question is really what is the stress energy tensor for a negative mass density. I believe it has to be -1 times the stress-energy tensor for a positive mass with similar distribution to have the correct properties.

 

[PeterDonis]

what is the stress energy tensor for a negative mass density

Just knowing the energy density can't tell you the stress-energy tensor. You have to make an assumption about it. The assumption the paper appears to be making is that "negative mass" means negative energy density $\rho$, and zero pressure, similar to ordinary matter having positive energy density $\rho$ and zero pressure. Basically, this means that the negative mass the paper postulates, like ordinary matter, is cold.

 

[Elroch]

Yes, Peter. I had spotted my mistaken understanding about the sign of the energy when I couldn't edit it, and you are right that it is merely that the energy-momentum equation is consistent with either sign of energy rather than implying it is positive. A question is whether all positive energies breaks any conservation laws.
My previous post was saying exactly the same as yours: some assumption has to be made about the stress energy tensor. However, that assumption is strongly guided by the basic dynamics you want to produce by definition of what a negative mass is, and assumed symmetries probably provide the rest.

 

[mitosis]

Sabine Hossenfelder has posted about this paper:

http://backreaction.blogspot.com/2018/12/no-negative-masses-have-not.html

Great respect for Sabine Hossenfelder. I found her response to a poster named DreamChaser to be of particular interest, DreamChaser said that they liked the study because it was elegant in offering an explanation for both dark energy and dark matter (I will admit that I also found this appealing) and was therefore simpler solution. This was her reply:
Sabine Hossenfelder said...

DreamChaser,

It does not, please look at the paper. You need to introduce some weird stuff new stuff, then you need to introduce the creation tensor, then you need to assume you have no problem with vacuum stability, then you need to somehow assume that you get around the issue with the spin-2 field while still using GR, then you need to explain how come that a negative cosmological constant is actually in agreement with all the data, and even if you have done that you'd still have to bend over backward to demonstrate that the solution actually does fit the rotation curves which, frankly, I am rather skeptic about because I cannot see how you get the right scaling behavior (Tully-Fisher and all).

B.

 

[mitosis]

Here's Sean Carroll's take on the study: https://twitter.com/seanmcarroll/status/1071066682234261504

 

[Elroch]

Sean Carroll's main point is why I am uncomfortable with negative energy and why I assumed (inconsistently with Franes, it seems) that the energies are all positive and it is only the gravitational interaction that is flipped. I am yet to be completely convinced that this is impossible, but that is not really for this discussion.
[Doing a back of an envelope calculation, I find that the simple dynamics based on gravitational interactions as described in the paper conserve energy and momentum with either sign of energy associated with the rest masses. The weird feature is that the total energy of negative mass goes down as it goes faster, because the (m v²) / 2 term in a Newtonian approximation is negative). This is what makes it possible to conserve energy in the situation where a negative mass chases a positive mass. Another concern of mine is whether with such weird dynamics any system with both types of matter could be stable].

 

[yahastu]

Bandersnatch, yes I see what you mean about the positive/negative mass ratio...I had it wrong

I have been thinking about some of the interesting implications/predictions of this theory:

1) If this is dark matter, this explanation tells us why it is "dark" -- specifically, dark matter would be "dark" because these negative mass particles are mutually repulsive, they would never clump together into anything that would reflect light. Additionally, because most negative mass gets ejected outside of the galaxy into the halo, we wouldn't expect there to be much of it nearby to Earth.

2) I found it interesting in section 3.4 where it is pointed out that the runaway motion that is described for positive-negative mass pairs could explain cosmic rays. This theory should be capable of predicting the frequency or density of cosmic rays as a function of one's location in space, which could potentially be used as an additional testable prediction.

3) Because positive masses attract and clump together, I think this implies that any positive mass objects in free space would experience some amount of uniform pressure from all directions from negative mass particles that are colliding with it. It begs the question what these collisions would look like. Since the positive mass particles are clumped closely together, I would think that the EM force would hold them together strongly, and so negative mass particles wouldn't be able to break apart positive mass objects, since gravity is weaker than EM.

4) It would make intergalactic space travel significantly more difficult. In addition to the already known difficulties of needing to escape the planet's gravitational field, and then needing to escape the gravitational attraction of the galaxy you are trying to leave, you would also need to fight your way though the repulsive force of this very large negative mass halo. If you did succeed in crossing the tipping point in getting far away from your home galaxy, once you got outside of the negative mass halo it would then provide a propulsive effect...but entering a new galaxy would again be very difficult.

5) The author explains that this theory corresponds to an Anti-de Sitter space which undergoes a cycle of expansion and contraction. It seems not hard to visualize why this would be so...if we assume all positive mass fits within some finite extent, and negative mass is always created within this radius driving expansion, the negative mass would eventually be ejected outside of the positive mass universe and form a large scale halo of negative mass surrounding the entire universe in the same way that it is proposed to do for galaxies. Eventually, the ratio of negative mass "inside" the universe vs "outside" would change, until it reaches a tipping point where there is so much negative mass outside the universe that it begins to compress and slow down the inflation, and then crunches everything back down.

6) If this theory is correct I think it also tells us what we could expect to happen if someone tried to fly "to the edge of the universe"...basically, it would become increasingly difficult to travel beyond the edge of positive mass, because you'd be fighting against the repulsion of the negative mass halo, so you'd basically just fly until the repulsive mass effect canceled out whatever you were using for thrust.

 

[PeterDonis]

A question is whether all positive energies breaks any conservation laws.

The only conservation law in GR is that the covariant divergence of the stress-energy tensor is zero at every event. That means that locally, stress-energy can't be created or destroyed. Our best current model of the universe, with only positive energies, satisfies this property.

The main open question in this regard is what came before the Big Bang--or before inflation if you think inflation is the best answer to what came before the Big Bang. But the issues with the various proposed solutions have nothing to do with violating conservation laws: none of them do.

 

[Elroch]

RIght: I meant whether energy and momentum are conserved at low energies in local Lorentz frames according to the defining interactions, which would seem desirable. As far as I can see this can be so with all positive energies, but that doesn't mean something else doesn't go wrong.

 

[PeterDonis]

If this is dark matter, this explanation tells us why it is "dark" -- specifically, dark matter would be "dark" because these negative mass particles are mutually repulsive

This has nothing to do with whether or not the negative mass particles can absorb or emit electromagnetic radiation. If they are postulated not to do so, that is an additional assumption that has to be added to the model.

The author explains that this theory corresponds to an Anti-de Sitter space

But that requires that negative mass acts like a negative cosmological constant. As I pointed out in post #12, I don't see how that can work.

If this theory is correct I think it also tells us what we could expect to happen if someone tried to fly "to the edge of the universe".

As far as i can tell, there is no edge of the universe in the proposed model in the paper; the universe is spatially closed without a boundary (spatially a hypersphere).

the edge of positive mass

The proposed model appears to be homogeneous on large distance scales, just as our current mainstream model of the universe is, so there is no "edge of positive mass" any more than there is an "edge of negative mass"; both are evenly distributed, on average, throughout the universe.

 

[PeterDonis]

I meant whether energy and momentum are conserved in local Lorentz frames according to the defining interactions

The paper does not appear to treat this question at all; it simply assumes a negative energy density for the "negative mass" without discussing at all the question of local Lorentz invariance or what fundamental interactions the negative mass particles do or do not participate in. In other words, his model is a large-scale phenomenological model, not a fundamental model of some new fundamental particle or interaction.

 

[PeterDonis]

Another concern of mine is whether with such weird dynamics any system with both types of matter could be stable

I think this is highly unlikely, for the reason to be given below.

I found it interesting in section 3.4 where it is pointed out that the runaway motion that is described for positive-negative mass pairs could explain cosmic rays.

Unfortunately, the presence of these "runaway motion" solutions predicts a lot more than that: as Hossenfelder points out in her article, it predicts that these pairs of positive-negative mass particles should be constantly being created everywhere and emitting huge amounts of energy all over the place. (An often used term for this is "the vacuum is unstable".) Obviously we do not observe this at all.

 

[Elroch]

Actually, I think that problem is due to having negative energy particles.

I am thinking of the first order approximation, like Newton's gravitation as an approximation to GR.. I believe this is useful for the dynamics of a galaxy consisting of components all moving at small fractions of the speed of light, and may be sufficient to describe the halo of negative matter around a positive matter galaxy,

 

[yahastu]

Sean Carroll's main point is why I am uncomfortable with negative energy and why I assumed (inconsistently with Franes, it seems) that the energies are all positive and it is only the gravitational interaction that is flipped. I am yet to be completely convinced that this is impossible, but that is not really for this discussion.

Sean argues that it fails Occam's razor because he says "dark matter and dark energy are a simpler theory that explain the same effect"...but is that really so?

Dark matter is not something that was predicted in advance by any theory. Rather, it was observed that galaxy rotation curves do not agree with the predictions of GR. Rather than rejecting or revising GR due to its inability to match observations, it was argued that the theory is infallible, and therefore there must be some type of "dark matter" that exists and can explain the observed rotation curves without modifying GR...but there is still no consensus on what this dark matter would actually consist of, or how exactly it would be distributed to account for the observed failure of GR to properly predict galaxy rotation curves. Farnes points this out in section 3 when he says, "This provides a resolution to the cuspy-halo problem (eg, de Blok 2010) and to my knowledge makes negative masses the only dark matter candidate that can provide a non-contrived solution."

Farnes negative mass proposal is a specific example of a theory to resolve the galaxy rotation problem, and it happens to do so by defining a type of "dark matter" distributed almost exactly as predicted...so if it is is correct, it would be a concrete proposal for "dark matter" that can finally replace the vague and undefined concept of "dark matter" which is currently lacking a concrete theory.

 

[yahastu]

Unfortunately, the presence of these "runaway motion" solutions predicts a lot more than that: as Hossenfelder points out in her article, it predicts that these pairs of positive-negative mass particles should be constantly being created everywhere and emitting huge amounts of energy all over the place. (An often used term for this is "the vacuum is unstable".) Obviously we do not observe this at all.

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. I think that they would only come about when a negative mass particle happens to encounter a free positive mass particle of equal mass which happens to be found in isolation from any other positive masses...a pretty rare scenario.

In any case, when a positive mass encounters a negative mass, it wouldn't lead to the creation of new energy...rather it would just lead to their existing mass energy being converted into pure energy after they accelerated to the speed of light and turned into photons. Conservation of energy would be preserved due to this effect.

It does however seem to raise the question of how these negative masses, which are constantly being created, have energy, and persist indefinitely do not violate conservation of energy

 

[Elroch]

Regarding vacuum instability with negative energy particles, to preserve conservation laws you would appear to need to spontaneously generate four species: positive energy particles, their antiparticles, negative energy particles and their antiparticles, to satisfy both energy conservation and other conservation laws. Admittedly photons would do for two of these, and negative energy particles could also feasibly be their own antiparticles.
It seems plausible to someone with my limited knowledge that this would be an unlikely interaction (is this notion even meaningful given the Lorentz invariance of the vacuum?). If it was unlikely but not impossible, it might be a handy way of generating the negative mass, along with some photons. (Is this how cosmic rays got mentioned?)

 

[yahastu]

This has nothing to do with whether or not the negative mass particles can absorb or emit electromagnetic radiation. If they are postulated not to do so, that is an additional assumption that has to be added to the model.

If negative masses exist and are mutually repulsive than this would make them behave like an extremely thin gas, and would fail to absorb or emit EM radiation for the same reason that we can see through air...they are spatially separated so much that they simply don't create any significant interaction. Their density would be less than any conventional gas because the mutual repulsion is driven by gravity rather than collisions.

But that requires that negative mass acts like a negative cosmological constant. As I pointed out in post #12, I don't see how that can work.

If negative masses exist in free space, and are created so as to maintain equal pressure, then their effect would be to push all positive masses apart from each other. This would cause all positive masses to expand through spacetime (rather than causing spacetime itself to expand), but I think perhaps the point is that when you take into account the creation term, we no longer need to invoke the concept of spacetime itself expanding...

 

[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.