A Dark matter and energy explained by negative mass

[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).

 

[Bandersnatch]

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.

Nobody's disputing this. Both comments you responded to were arguing with yahatsu's claim about global behaviour of the universe.

 

[Auto-Didact]

Nobody's disputing this. Both comments you responded to were arguing with yahatsu's claim about global behaviour of the universe.

Actually, it isn't clear that that is necessarily so, because he is explicitly using a scaling up argument from small to large scale. It is only in the large limit that his statement is incorrect; somewhere under this limit his or Farnes' point might apply.

 

[PeterDonis]

So it makes no sense to claim that opposite sign masses repel (i.e. that they are accelerated in opposite directions)

"Repel" might not be the best choice of words. What GR says is that, for gravitational masses of opposite signs, the potential energy decreases as they get farther apart, whereas for masses of the same sign the potential energy increases as they get farther apart. What these things imply about the actual motions of negative masses depends, as you note, on what assumption is made about the relationship between inertial mass and gravitational mass. I believe the implicit assumption in the paper is that inertial mass = gravitational mass.

The two key points of Hossenfelder's critique appear to me to be:

(1) If inertial mass = gravitational mass and negative gravitational masses are present, that means negative inertial mass is present, and that is highly questionable as it makes the vacuum unstable; but if negative inertial masses are not allowed, then we can't have inertial mass = gravitational mass, we must have inertial mass = absolute value of gravitational mass (at least that's the simplest assumption), and then you have all the issues of the dynamics not matching what the paper claims.

(2) The paper does not actually derive the dynamics from a field equation; Farnes just puts in by hand the dynamics the way he thinks they should be. But this means the model might not be consistent; and in fact it does not appear to be.

 

[PeterDonis]

the rate of production is certainly extraordinary low per unit volume per unit time

The rate of production of what? Actual cosmic rays we observe, or the runaway particles predicted by Farnes' model? If the latter, where are you getting your numbers from?

 

[Elroch]

The rate of production of what? Actual cosmic rays we observe, or the runaway particles predicted by Farnes' model? If the latter, where are you getting your numbers from?

Actually neither: I was thinking of the possibility of the spontaneous production of pairs of positive energy particles and negative energy particles each in particle-antiparticle pairs which, given that it cannot break any conservation law by definition is possible according to quantum field theory, and that such production might be needed to explain the characteristics of the cosmological expansion. However, the latter is by no means clear. I do not have a good understanding of Franes' reasoning about this:
Note that the system with some positive and some negative mass, sustained "chasing" is a very precise case where the total mass is zero and the initial velocities are identical and aligned, which is so special as to be irrelevant. If the net mass is positive, the system becomes bound with a fixed speed, if it is negative, the masses rapidly separate, and these are the only cases that are really relevant.

 

[Elroch]

"Repel" might not be the best choice of words. What GR says is that, for gravitational masses of opposite signs, the potential energy decreases as they get farther apart, whereas for masses of the same sign the potential energy increases as they get farther apart. What these things imply about the actual motions of negative masses depends, as you note, on what assumption is made about the relationship between inertial mass and gravitational mass. I believe the implicit assumption in the paper is that inertial mass = gravitational mass.

The two key points of Hossenfelder's critique appear to me to be:

(1) If inertial mass = gravitational mass and negative gravitational masses are present, that means negative inertial mass is present, and that is highly questionable as it makes the vacuum unstable; but if negative inertial masses are not allowed, then we can't have inertial mass = gravitational mass, we must have inertial mass = absolute value of gravitational mass (at least that's the simplest assumption), and then you have all the issues of the dynamics not matching what the paper claims.

(2) The paper does not actually derive the dynamics from a field equation; Farnes just puts in by hand the dynamics the way he thinks they should be. But this means the model might not be consistent; and in fact it does not appear to be.

The word "repel" suggests the assumption that masses tend to accelerate in a way that tends to reduce potential energy (an easy slip to make). According to the line of reasoning I followed (with inertial mass proportional to gravitational mass), this is true for positive masses and the exact opposite is true for negative masses. This latest weird observation is a conclusion from the Newtonian reasoning, not as an assumption. The consequence is that when the total mass is negative, two masses are always driven apart, when it is positive they are bound if there is not too much kinetic energy in the centre of mass frame.

I too am concerned about the vacuum being unstable if the energy of the negative mass particles is negative (another assumption, I believe), but as far as I understand it can be almost stable if the interactions that produce a set of particles (eg two photons, a negative mass particle and its antiparticle) that conserve all laws are very unlikely due to potential barriers involving some interaction involving a massive particle (like for weak interactions). Given that physicists treat seriously the idea that the vacuum might not be in its ground state and undergoes a transition to its ground state with very low probability, perhaps that is not too unreasonable.

 

[LURCH]

The paper claims that acceleration up to light speed is possible because the overall mass of the system is 0. I've never heard of this being a criterion before. The fact that the two objects are gravitationally interacting does not make them a single particle. I just don't see how it works. However, if we do accept this as a valid premise, then it looks like all we've done is swapped "massive particles accelerating to light speed" with "massless particles traveling at sub-light speed". This would appear to add an infinite rate of acceleration to a scenario that was already difficult (for me, at least). That would be the result of an acceleration acting on an object with zero mass, correct?

I didn't see anything in the paper that addresses this, nor the possible effects on galactic collisions (that I mentioned in Post #57). If anyone has seen these topics discussed in the light of the implications of this new theory, please post a link. I have not yet read Hossenfelder, so maybe something in there may shed further light.

 

[Elroch]

Franes does say "the pair can eventually accelerate to a speed equal to the speed of light", but I believe this would take an infinite time from the point of view of an observer watching this (the particles are in an accelerating frame to him, so experiences something like the "twin paradox"). There is no "infinite rate of acceleration", just a finite one. For velocities to rise indefinitely, it would be necessary for the masses to be perfectly matched and the particles to have exactly zero initial relative velocity, so it simply would not occur naturally. (I think it classifies as an neutral equilibrium: even if the masses had a perfect sum of zero, if their velocities were very slightly different they would move apart).
Given that negative mass is a rather exotic hypothetical, it is not so surprising you are as unfamiliar with this as I was: you are very familiar with massless particles moving at the speed of light though.
I believe Zitterbewegung was as surprising a property when Dirac created his relativistic model of the electron, and happens to involve an interference between positive and negative energy states. This is a meaningful phenomenon affecting the emission structure of the hydrogen atom. (I am not claiming there is a very close relationship to the present topic, but it is reminiscent).

 

[LURCH]

Franes does say "the pair can eventually accelerate to a speed equal to the speed of light", but I believe this would take an infinite time from the point of view of an observer watching this (the particles are in an accelerating frame to him, so experiences something like the "twin paradox").

If this is true, then it would be very badly misstated. Saying that something takes an infinite amount of time to occur is the same as saying it “never” occurs, which is exclusive of the statement that it “eventually” occurs. Farnes says they accelerate to light speed, and that this is possible because the total mass of the system is zero.

There is no "infinite rate of acceleration", just a finite one. For velocities to rise indefinitely, it would be necessary for the masses to be perfectly matched and the particles to have exactly zero initial relative velocity, so it simply would not occur naturally.

Aren’t these the exact conditions necessary for runaway pairs? If so, are you pointing out that there can’t be any such phenomena?

you are very familiar with massless particles moving at the speed of light though.

Yes, and it is another difficulty I am having with this concept. Farnes says that these pairs can get up to light speed because they are massless. But if that is true, then they cannot move at sub-light speeds, so they can’t “accelerate to” light speed. However, if they do exist and do accelerate, then it would seem that their rate of acceleration must be infinite. When mass is zero, acceleration is infinite, isn’t it? I suppose this could mean that the acceleration is instantaneous; meaning that the speed is c as soon as the pair is spawned. This would avoid the problem of massless particles moving at sub-light speed.

Still a lot more for me to think through...

 

[PeterDonis]

I was thinking of the possibility of the spontaneous production of pairs of positive energy particles and negative energy particles each in particle-antiparticle pairs

That might be necessary if one actually worked out a quantum field theory that had the phenomenological model in Farnes' paper as a Newtonian approximation, yes. But Farnes has certainly not done anything to work out such a theory. (Nor do I think one could be worked out consistently, but that's probably off topic here.)

 

[PeterDonis]

The word "repel" suggests the assumption that masses tend to accelerate in a way that tends to reduce potential energy

Yes, it does, and if inertial masses are all positive that is in fact what will happen. But, as you note, if particles with negative gravitational mass also have negative inertial mass, they will move to increase potential energy, not reduce it. Which seems to me to be yet another serious problem for Farnes' model.

 

[PeterDonis]

The paper claims that acceleration up to light speed is possible because the overall mass of the system is 0.

I don't buy this either; I think it's just unjustified hand-waving (which quite a few of the claims in the paper seem to me to be). The individual particles are either massless or they're not. If they are, then they can't have negative mass and the whole model breaks down. If they aren't, then they can't move at the speed of light.

 

[Auto-Didact]

(2) The paper does not actually derive the dynamics from a field equation; Farnes just puts in by hand the dynamics the way he thinks they should be. But this means the model might not be consistent; and in fact it does not appear to be.

After having read all the comments there, I see Hossenfelder saying "You cannot start from a Lagrangian and then just postulate what you want to happen in the Newtonian limit", honestly stating afterwards that she might be wrong but will not accept Farnes idea without a full derivation. That is understandable of course, since doing this has become somewhat standard methodology in theoretical physics in the last century.

Having said that, it is very important to realize that settling for nothing less than a Lagrangian formulation or other type of first principles derivation is actually possibly a too strong focus on a very particular methodology, since it is not the only possible methodology for a theorist to construct a novel theory; phenomenological modelling, i e. putting things in by hand and then simply comparing the results to experiments, is another valid methodology of theorization.

It is therefore largely unjustified to say that a theorists' theorization is unscientific or 'not proper physics' simply because the theorist uses phenomenological modelling instead of giving a first principles derivation, especially if this other methodology has proven to be successful for theorization as phenomenological modelling of course has been in countless cases; for theories in some large scale limit (e.g. hydrodynamics) it actually isn't even directly clear whether a first principles derivation such as a Lagrangian formulation is necessary or even wholly appropriate.

The fact remains that historically most of physics was initially modeled phenomenologically with a first principles derivation only following later (e.g. Newton followed by Lagrange/Hamilton, Faraday followed by Maxwell, Planck followed by Dirac et al., etc). Moreover, both in fluid dynamics and in nonlinear dynamics, i.e. the proper context which Farnes' equations are actually from, phenomenological modelling is still the standard theorization methodology.

Farnes does this pretty well by directly picking up a historically abandoned line of research by Einstein - a different interpretation of GR - which was subsequently made respectable by Bondi and procedes to logically build the new case naturally rederiving known results (Eq. 15). Farnes procedes to not only give simulations which qualitatively match observations, but also a brief review reinterpreting known empirical data reformulated based on new Bayesian priors.

Moreover, Farnes directly gives a host of falsifiable predictions. The correct next step in research based on phenomenological modelling is for others to try reproducing his simulations and then doing a statistical comparison with observational data. If the theory is consistent with the data, then others will naturally start to chew much more on his equations, which is about when I'd advise him to start worrying a bit more about actually trying to give a full derivation from first principles.

 

[PeterDonis]

phenomenological modelling, i e. putting things in by hand and then simply comparing the results to experiments, is another valid methodology of theorization.

Proposing a phenomenological model that does not have any known basis as an approximation to some underlying theory derived from first principles is one thing; yes, that's often done in science.

Proposing a phenomenological model that appears to violate properties that are believed to be essential to even have a basis as an approximation to some underlying theory derived from first principles is something else. Doing that, I think, is much more risky and much harder to defend on the grounds that you're only trying to construct a phenomenological model and the details of the underlying theory can catch up later.

Farnes does this pretty well by directly picking up a historically abandoned line of research by Einstein - a different interpretation of GR

Where are you getting this from?

Farnes directly gives a host of falsifiable predictions.

Yes, and at least one--the "runaway" solutions--is arguably already falsified.

 

[Auto-Didact]

Proposing a phenomenological model that appears to violate properties that are believed to be essential to even have a basis as an approximation to some underlying theory derived from first principles is something else. Doing that, I think, is much more risky and much harder to defend on the grounds that you're only trying to construct a phenomenological model and the details of the underlying theory can catch up later.

It is risky, but because this approximation is based on Newtonian field theory - our old and sometimes forgotten friend - his interpretation makes intuitive sense even if it won't end up working; I'd prefer if he directly derived it on the basis of the Newton-Cartan formalism.

Where are you getting this from?

Farnes' paper (Einstein 1918)

Yes, and at least one--the "runaway" solutions--is arguably already falsified.

That's good, I'm all for quick falsification, as long as the necessary care is taken. i.e. in this case that the model is treated as a preliminary theory in nonlinear dynamics. Since it seems to address the two most important separate core issues simultaneously (nonlinear dynamics & open system non-equilibrium statistical mechanics) it is extremely interesting mathematically, regardless of its physical correctness.

In any case, runaway doesn't seem to be typical in any of his simulations, nor does it increase when varying the dimensionless group which might affect it; this is to be expected given that the geometrodynamics is highly nonlinear.

Moreover, this is to be expected intuitively as well since runaway only occurs in the highly idealized situation of identical dislikes colliding symmetrically, i.e. in the naive 'particle physics setting'.

Given the above, there actually isn't that much reason to believe that runaway should be too big of a problem for the model, since the negative masses might also just be effective negative masses, as Farnes himself also says.

What I'd actually be more worried about is that creation tensor; I've seen similar constructions though, it would be very interesting to see if those were really mathematically consistent with Farnes' proposal.

 

[LURCH]

and at least one--the "runaway" solutions--is arguably already falsified.

If we then discard the idea of runaway pairs, does the proposed theory fall apart? I would contend that the creation of runaway pairs would be an oddity, rather than a necessary prediction from this model, and that the rest of the concept could continue to exist, even if (as has been proposed) this particular phenomenon is not possible. Perhaps the conditions required to generate these pairs really are unattainable, and so they cannot form in any real-world situation. What does that leave us with?

I have been doing some more thinking about galactic collisions, and have expanded that thinking to include cluster and supercluster formation. I have not yet run the simulator program that Farnes created, but I’m having trouble understanding how, under the proposed conditions, any two galaxies could be gravitationally drawn toward each other at all. If all galaxies are more than 80% negative mass, then they can fairly be described as negative mass structures, with traces of impurities. It seems that they should all be repelling one another.

EDIT: Auto-Didact posted his while I was still typing.

 

[Auto-Didact]

I have been doing some more thinking about galactic collisions, and have expanded that thinking to include cluster and supercluster formation. I have not yet run the simulator program that Farnes created, but I’m having trouble understanding how, under the proposed conditions, any two galaxies could be gravitationally drawn toward each other at all. If all galaxies are more than 80% negative mass, then they can fairly be described as negative mass structures, with traces of impurities. It seems that they should all be repelling one another.

Intuitively, I would say by Landau damping with galaxies as the analogues of electrons.

 

[LURCH]

Intuitively, I would say by Landau damping with galaxies as the analogues of electrons.

An interesting notion. Will need to ponder it a while.

Meanwhile, the more I think about it, the more problems are eliminated by discarding the runaway pairs. Reactionless propulsion, perpetual motion, light speed travel; they all go away. Now I only need to cope with spontaneous creation ex nihilo, and I’m practically on board with this!

Except for the galactic collisions, of course.

 

[Elroch]

If this is true, then it would be very badly misstated.

Yes, the phrasing I quoted exactly should not be in the paper.

Aren’t these the exact conditions necessary for runaway pairs? If so, are you pointing out that there can’t be any such phenomena?

It is not something that will happen in the real world at all because it require the two particles to have exactly opposite masses and exactly identical velocities, exactly aligned with their relative position. This happens with probability zero. So what matters are the less extreme interactions where masses don't agree and velocities are distributed widely.

Yes, and it is another difficulty I am having with this concept. Farnes says that these pairs can get up to light speed because they are massless. But if that is true, then they cannot move at sub-light speeds, so they can’t “accelerate to” light speed. However, if they do exist and do accelerate, then it would seem that their rate of acceleration must be infinite. When mass is zero, acceleration is infinite, isn’t it? I suppose this could mean that the acceleration is instantaneous; meaning that the speed is c as soon as the pair is spawned. This would avoid the problem of massless particles moving at sub-light speed.
.

You don't need to be concerned because even with the perfect conditions for runaway pair, they merely accelerate indefinitely, never reaching the speed of light.

 

[Elroch]

Yes, it does, and if inertial masses are all positive that is in fact what will happen. But, as you note, if particles with negative gravitational mass also have negative inertial mass, they will move to increase potential energy, not reduce it. Which seems to me to be yet another serious problem for Farnes' model.

This was a surprise to me and I am concerned about it too, but not to the extent I would be if, say, it implied that entropy decreased! For it to be a genuine problem for Farnes' ideas we need it to lead to some inconsistency. It would be good to look at this from the point of view of the principle of least action and Lagrangians.

 

[Elroch]

That might be necessary if one actually worked out a quantum field theory that had the phenomenological model in Farnes' paper as a Newtonian approximation, yes. But Farnes has certainly not done anything to work out such a theory. (Nor do I think one could be worked out consistently, but that's probably off topic here.)

In physics we presently deal with gravity as a classical phenomenon acting on particles that are quanta of field theories and the same would be true here. We don't have a quantum gravity theory, so it would be unreasonable to object to Franes not having one for gravity extended to negative masses: this is a separate matter to an analogous theory to the known field theories for normal matter. At least we do know that there are theories analogous to what I describe for the interaction of many or all of the particles in the standard model, all expressible in Feynman diagrams.
We are as much in the dark about the physics of dark matter as about Franes' hypothetical substance.

 

[PeterDonis]

this approximation is based on Newtonian field theory

That doesn't address the issue I raised at all. Neither would deriving it from Newton-Cartan theory (if it could be done).

Farnes' paper (Einstein 1918)

This refers to Einstein's postulating a positive cosmological constant in order to have a static universe. Farnes claims that "negative mass" can have the same effect as a negative cosmological constant. Also, as has already been commented here, this claim does not appear to be correct.

 

[PeterDonis]

If we then discard the idea of runaway pairs, does the proposed theory fall apart?

You can't "discard" the idea. It's a prediction of the model. As Hossenfelder points out in her article, if you want your theory to be consistent with GR, you can't choose the mass and independently choose the dynamics. The mass determines the dynamics.

 

[PeterDonis]

It is not something that will happen in the real world at all because it require the two particles to have exactly opposite masses and exactly identical velocities, exactly aligned with their relative position

That is how "runaway" pairs are described in the paper, in order to make the idea intuitively plausible. But the actual interaction Farnes postulates between negative and positive mass particles will cause their motion to approach that exact "runaway" solution regardless of their initial relative velocity (as long as that velocity is small, which it should be under the postulated conditions in the paper), if they approach each other closely enough for their two-body interaction to dominate their dynamics (which should happen often under the postulated conditions in the paper).

 

[PeterDonis]

We don't have a quantum gravity theory, so it would be unreasonable to object to Franes not having one for gravity extended to negative masses

I'm not talking about a quantum gravity theory. I'm talking about a quantum field theory, on a classical background spacetime, that has a field with negative mass in it. As Hossenfelder points out, any such theory makes the vacuum unstable. This has been a well known property of standard QFTs for decades.

At least we do know that there are theories analogous to what I describe for the interaction of many or all of the particles in the standard model, all expressible in Feynman diagrams.

None of the Standard Model particles fields have negative mass. That's not just a coincidence; it's true for a good reason (see above).

 

[Auto-Didact]

That doesn't address the issue I raised at all. Neither would deriving it from Newton-Cartan theory (if it could be done).

I didn't say it did, I'm only saying that in order to obtain a first principles derivation, it might be easier to proceed backwards towards a modified GR Lagrangian by unlimiting from a modified Newton-Cartan theory than from a modified Newtonian theory alone.

This refers to Einstein's postulating a positive cosmological constant in order to have a static universe. Farnes claims that "negative mass" can have the same effect as a negative cosmological constant. Also, as has already been commented here, this claim does not appear to be correct.

I'll post the entire paper, in order to make the point clearer:

When I wrote my description of the cosmic gravitational field I naturally noticed, as the obvious possibility, the variant Herr Schrödinger had discussed. But I must confess that I did not consider this interpretation worthy of mention.

In terms of the Newtonian theory, the problem to be solved can be phrased more or less as follows. A spatially closed world is only thinkable if the lines of force of gravitation, which end in ponderable bodies (stars), begin in empty space. Therefore, a modification of the theory is required such that “empty space” takes the role of gravitating negative masses which are distributed all over the interstellar space. Herr Schrödinger now assumes the existence of matter with negative mass density and represents it by the scalar $p$. This scalar $p$ has nothing to do with the internal pressure of “really” ponderable masses, i.e., the noticeable pressure within stars of condensed matter of density $\rho$ ; $\rho$ vanishes in the interstellar spaces, $p$ does not.

The author is silent about the law according to which $p$ should be determined as a function of the coordinates. We will consider only two possibilities:
1. $p$ is a universal constant. In this case, Herr Schrödinger’s model completely agrees with mine. In order to see this, one merely needs to exchange the letter $p$ with the letter $\Lambda$ and bring the corresponding term over to the left-hand side of the field equations. Therefore, this is not the case the author could have had in mind.

2. $p$ is a variable. Then a differential equation is required which determines $p$ as a function of $x_1... x_4$ . That means, one not only has to start out from the hypothesis of the existence of a nonobservable negative density in the interstellar spaces but also has to postulate a hypothetical law about the space-time distribution of this mass density.

The course taken by Herr Schrödinger does not appear passable to me, because it leads too deeply into the thicket of hypotheses.

Farnes is taking this pathway, as is clear in Eqs. 12, 13, 14, 15, 23 and 29 among others.

I'm not talking about a quantum gravity theory. I'm talking about a quantum field theory, on a classical background spacetime, that has a field with negative mass in it. As Hossenfelder points out, any such theory makes the vacuum unstable. This has been a well known property of standard QFTs for decades.

When speaking about relativistic gravity, QFT is frankly speaking completely irrelevant because it is fundamentally incapable of dealing with the concept of multiple vacua which are necessarily there per the equivalence principle in geometrodynamics; this has already been shown using the Newton-Cartan formalism. If QFT is fundamentally unable to accurately handle positive gravitational masses, why would you expect the situation to change for negative masses?

 

[Elroch]

That is how "runaway" pairs are described in the paper, in order to make the idea intuitively plausible. But the actual interaction Farnes postulates between negative and positive mass particles will cause their motion to approach that exact "runaway" solution regardless of their initial relative velocity (as long as that velocity is small, which it should be under the postulated conditions in the paper), if they approach each other closely enough for their two-body interaction to dominate their dynamics (which should happen often under the postulated conditions in the paper).

Why would you think that? I have just written a little simulation where the velocities do not perfectly match to start off with, and the particles steadily drift apart over time as I would have guessed. Note that the two particles are not bound: intuitively, as they get further apart, the negative mass loses potential energy and the positive one gains it, and the two effects balance perfectly.
I summarised somewhere that when the net mass of a two particle system is positive, it can be bound and when it is negative it never is. When the total mass is zero only a neutral equilibrium is possible, not a stable one.

 

[PeterDonis]

I have just written a little simulation where the velocities do not perfectly match to start off with, and the particles steadily drift apart over time as I would have guessed

I'm not sure why you would guess that. See below.

intuitively, as they get further apart, the negative mass loses potential energy and the positive one gains it

Potential energy is not a property of either particle in isolation; it's a property of the two-particle system. As the two particles get further apart, the potential energy of the two-particle system decreases for this case (whereas for two masses of the same sign, it increases).

If we assume that the negative gravitational mass particle also has negative inertial mass, then it will accelerate in the direction of increasing potential energy, i.e., towards the positive mass particle. The positive mass particle will accelerate in the direction of decreasing potential energy, i.e., away from the negative mass particle. Since the potential depends on the distance between them, the two particles will have identical accelerations: same magnitude, same direction. If they have a nonzero relative velocity to start off with, that will not affect this fact. So I would not expect the particles to steadily drift apart, since if they get further apart, the acceleration of both decreases.

I can't comment on your simulation since I haven't seen the source code. The two-body problem should be solvable analytically, but it might take a little time before I can try that.

 

[andrew s 1905]

PeterDoins and Elorch , I don't think you will resolve your difference with words. Why not write down the equations and assumptions and or constraints you are implicitly using in your verbal description of what will happen then it should be possible to clear up the issue one way or the other.

Regards Andrew

 

[Davephaelon]

Per my comment on Sabine Hossenfelder's Backreaction blog at 10:40 AM, December 9, 2018, using the analogy of Pac-man icons eating each other should negative-matter in a galactic halo meet the positive matter in the galactic disc, this would seem to afford a potential way to test Jamie Farnes model. Assuming the negative-energy matter in his model is constituted of the same baryonic matter that makes up our positive-energy matter, with the energy sign reversed, and the negative-energy electrons and protons generally don't coalesce into atoms due to mutual gravitational repulsion, then numerous free, negative-energy electrons and protons might be passing through the Milky-Way's galactic disc gobbling up their positive-energy counterparts. Further assuming that on a time averaged basis that the disappearance of electrons and protons in a chunk of positive-energy matter is not perfectly balanced, then for some period of time that chunk of positive-energy matter would not be electrically neutral. By conducting an experiment similar to the search for fractional charges in bulk matter, it might be possible to check for occasional, tiny charge imbalances in an aggregate of ordinary matter in a carefully controlled laboratory setting.

 

[Elroch]

I'm not sure why you would guess that. See below.

Potential energy is not a property of either particle in isolation; it's a property of the two-particle system. As the two particles get further apart, the potential energy of the two-particle system decreases for this case (whereas for two masses of the same sign, it increases).

If we assume that the negative gravitational mass particle also has negative inertial mass, then it will accelerate in the direction of increasing potential energy, i.e., towards the positive mass particle. The positive mass particle will accelerate in the direction of decreasing potential energy, i.e., away from the negative mass particle. Since the potential depends on the distance between them, the two particles will have identical accelerations: same magnitude, same direction. If they have a nonzero relative velocity to start off with, that will not affect this fact. So I would not expect the particles to steadily drift apart, since if they get further apart, the acceleration of both decreases.

I can't comment on your simulation since I haven't seen the source code. The two-body problem should be solvable analytically, but it might take a little time before I can try that.

It doesn't really matter why I would guess the particles continue to drift apart over time if their initial relative velocities are not equal: it's a fact, as my elementary finite difference simulation, based on the definitions of the forces and Newton's laws (with negative masses) confirms. This is important, as my guesses cannot be relied upon! The line in your reasoning which is misleading is "So I would not expect the particles to steadily drift apart, since if they get further apart, the acceleration of both decreases." The confusion here is between the acceleration of the centre of the particles (which does decrease as they get further apart) and their relative velocity, which is unaffected by that. The drifting apart is solely due to the initial relative velocity persisting in this special case where the sum of the masses is zero.

One valid way to reason about potential energy is to work in a frame centred on the midpoint between the two particles and to observe that the net mass is like a mass of zero at that point, with the distance to either of the two masses providing the other co-ordinate. This is a co-ordinate transformation similar to that used for modelling two body systems like the hydrogen atom. Given that the radial forces on the two particles are equal and opposite (instantaneous Newton's third law or conservation of momentum), the rate of change of potential energy with their common distance from their centre (dV/dr, say) is zero (for two separate reasons!)

Anyhow, working in this midpoint centred frame, if the particles have an initial relative velocity, they are either getting closer or further away along the line between them. While this is happening the potential energy is not changing, so the relative velocity is just maintained. This is the rather dull result of my simulation too.

 

[Lindsayforbes]

Sabine Hossenfelder has posted about this paper:

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

Peter, I read the press stuff and the paper, but Sabine's blog is highly critical. She is pretty well informed.

 

[kent davidge]

@PeterDonis, who is Sabine Hossenfelder?

 

[Elroch]

google is your friend, kent. ;) Sabine Hossenfelder is a German researcher in quantum gravity.

Note that Sabine made what I identified as an slip in her blog post. It was about whether negative masses repel each other, where she claimed that Franes had got it wrong (but in fact he had got it right because of the odd fact that the acceleration of a negative mass is in the opposite direction to the force on it). She has accepted my correction in the comments to the blog post but has not explicitly responded to it.

Correction: she has responded and appears open to being convinced that the reasoning about what has to be true in a Newtonian approximation is indicative of what has to be true in general relativity, which I am now rather certain is the case (supported by Hermann Bondi and those who followed him).

 

[Elroch]

A short light discussion of some more anti-intuitive (but consistent) behaviour of negative masses. The observation that if you were able to push a negative mass like a normal mass, this would cause acceleration of the mass towards you is bizarre. However, the notion of pushing involves contact of two surfaces and a force which derives from the electromagnetic force. We cannot assume that anything like this would be possible with a negative mass, if such a thing existed.
Negative mass can be positively amusing - Richard Price, University of Utah

 

[PeterDonis]

it's a fact, as my elementary finite difference simulation, based on the definitions of the forces and Newton's laws (with negative masses) confirms. This is important, as my guesses cannot be relied upon!

Neither can your simulation if I can't see the source code. Is it available somewhere?

 

[PeterDonis]

who is Sabine Hossenfelder?

Aside from the excellent advice @Elroch gave you, there is also the fact that I posted a link to an article on her blog, which has an "About" page that directly answers your question.

 

[PeterDonis]

The confusion here is between the acceleration of the centre of the particles (which does decrease as they get further apart)

No, that's not correct. The acceleration of each particle gets smaller as the distance between them increases--because the "slope" of the potential "hill" between them gets smaller as the distance between them increases. There is no "acceleration of the centre of the particles" if we are considering an isolated two-body system; the system as a whole has no external forces on it and moves in a straight line at a constant speed.

This is a co-ordinate transformation similar to that used for modelling two body systems like the hydrogen atom.

And it doesn't work for the case under discussion, because the reduced mass $\mu = m_1 m_2 / (m_1 + m_2)$ is undefined.

if the particles have an initial relative velocity, they are either getting closer or further away along the line between them. While this is happening the potential energy is not changing

Yes, it is; if the distance between the particles is changing, the potential energy is changing, since it depends on the distance between the particles.

This is the rather dull result of my simulation too.

Do you see why I don't trust the results you are claiming from your simulation?

 

[Elroch]

I thought I should make it a little more user friendly first. Python with standard numpy and matplotlib libraries only. It was written in a jupyter notebook, so should work nicely if pasted into one. The graphs show the behaviour quite nicely when there is an initial relative velocity. The maximally simple implementation is in theory more vulnerable to numerical errors than say Runge-Kutta, but it confirms the expected behaviour perfectly here.

import numpy as np
import matplotlib.pyplot as plt

n_step = 100

# x's are positions in 2D, v's are velocities, "neg" means negative mass, "pos" positive mass
# g determines the strength of gravity

x_pos = np.zeros((n_step, 2))
x_neg = np.zeros((n_step, 2))
v_pos = np.zeros((n_step, 2))
v_neg = np.zeros((n_step, 2))
x_rel = np.zeros((n_step-1, 2))

x_neg[0]  = np.array([0, 0])
x_pos[0]  = np.array([1, 1])
v_pos[0]  = np.array([0, 0.1])
v_neg[0]  = np.array([0, 0])

g = 0.1

for i in range(1, n_step):
    x_rel[i-1] = x_pos[i-1] - x_neg[i-1]
    v_pos[i, :] = v_pos[i-1] + g * x_rel[i-1] / (np.sum(x_rel[i-1]**2) ** (3/2))
    v_neg[i, :] = v_neg[i-1] + g * x_rel[i-1] / (np.sum(x_rel[i-1]**2) ** (3/2))
    x_pos[i, :] = x_pos[i-1] + v_pos[i]
    x_neg[i, :] = x_neg[i-1] + v_neg[i]
 
plt.plot(x_pos[:,0], x_pos[:,1])
plt.plot(x_neg[:,0], x_neg[:,1])
plt.title("The paths of the two particles")
plt.show()
plt.plot((v_pos[:,0] + v_neg[:,0])/2)
plt.title("First component of velocity of particles")
plt.show()
plt.plot((v_pos[:,1]+v_neg[:,1])/2)
plt.title("Second component of velocity of particles")
plt.show()
plt.plot(x_rel[:,0])
plt.title("First component of relative position")
plt.show()
plt.plot(x_rel[:,1])
plt.title("Second component of relative position (the one with an initial non-zero relative velocity at the start)")
plt.show()

 

[Elroch]

No, that's not correct. The acceleration of each particle gets smaller as the distance between them increases--because the "slope" of the potential "hill" between them gets smaller as the distance between them increases. There is no "acceleration of the centre of the particles" if we are considering an isolated two-body system; the system as a whole has no external forces on it and moves in a straight line at a constant speed.

And it doesn't work for the case under discussion, because the reduced mass $\mu = m_1 m_2 / (m_1 + m_2)$ is undefined.

Yes, it is; if the distance between the particles is changing, the potential energy is changing, since it depends on the distance between the particles.

Do you see why I don't trust the results you are claiming from your simulation?

Firstly, with two body system with total mass zero, the centre of the system does exhibit the weird acceleration given Newtonian dynamics, because the two forces are in opposite directions, but F=ma makes both accelerations in the same direction. The centre of the particles has the average of these two accelerations.

EDIT: I find I do agree with you on the dependence of potential energy on distance for two masses of opposite sign. When they are close together, they have more potential energy. But this does not mean they tend to move apart, because negative masses accelerate to where they have more potential energy.