One of the most important things we will ever learn about the universe is just how big it is, practically, for our purposes. In the last century we’ve learned that it it is far larger than we knew, in a great many ways. At the moment we are pretty sure that it is about 13 billion years old, and that it seems much larger in spatial directions. We have decent estimates for both the total space-time volume we can
The point of my comment was not to present an impossibility theorem, but to suggest that there are several highly nontrivial challenges that any theory of negative mass particles must confront and I know of no plausible solution to any of these, but maybe someone will find a way around them.
You're right that there are many known examples of forces getting stronger or weaker as the universe evolves (both the strong and the weak forces did this in opposite ways in the early universe). However, with regard to negative mass particles, there is generic tension between having a sufficiently large coupling to populate them after inflation while keeping this coupling sufficiently small to avoid all the problems associated with radiating extremely large numbers of conventional particles (and other tachyons) in a runaway process that endlessly fills the universe with more stuff.
I agree that zero coupling is implausible, but it isn't obvious that the coupling can't become very low at current pressures and temperatures, even if high enough in the early universe.
RE: 3) To be clear, I would never deprive him of his first amendment rights ;) Let's see where it goes
Apologies for missing your paragraph on this earlier, but I agree with your observation that there may be a loophole if such particles don't couple to the matter we know and love.
However, the cosmological challenge of having completely decoupled particles is that it's not easy to populate them in the early universe. One might argue that they were around from the beginning as an initial condition, but it is overwhelmingly likely (though not yet fully established) that the very early universe underwent a phase of "inflation" during which it was expanding at an exponential rate.
This inflationary expansion dilutes the number densities of all possibly pre-existing particles by at least a factor of ~10^30 (and often much more depending on as yet unknown details about this phase). Inflation ends when the field that drives this expansion (the "inflaton") transfers its energy to create more familiar particles through some coupling, so there is no known way of filling the universe with an appreciable number of completely non-interacting particles.
1) I accept your claim. 2) This is the issue I pointed to in my 4th to the last paragraph. But there need not be a coupling to allow such emissions. 3) He should be allowed to offer evidence and analysis regarding his hypothesis even if he doesn't answer all the questions a high energy journal wants answered. I agree a good next step is to try to explain a wider range of empirical patterns, beyond what he considered in this paper.
1) Dark energy does not have a negative energy density. This quantity is strictly positive, but it does exert negative pressure, which gives rise to accelerated cosmic expansion. If we think about this as a substance, it seems very exotic since no other known form of matter has negative pressure. However, we can equivalently think of accelerated cosmic expansion as just a modified version of the original (minimal) General Relativity which includes an additional term (the cosmological constant) that enables accelerated expansion without spoiling any of the deeper principles of the theory.
2) Negative mass particles (tachyons) are problematic in quantum theories because their kinetic energy (which is proportional to mass) is negative. Thus, they can always lower their energy by going faster and conserving energy by emitting arbitrary numbers of other, positive mass particles; they would never stop doing this.
That said, it is technically possible for a spin-0 particle (like the Higgs boson) to *very temporarily* have a negative mass (and it likely did have one in the very early universe). However, the resulting instability from this negative mass changes the vacuum energy state of the universe and forces the Higgs to acquire a positive "vacuum expectation value" which is responsible for giving masses to the known elementary particles. In this new vacuum, all known particles (including the Higgs boson) all have positive masses.
None of these issues were known when Einstein made his original casual speculations about negative mass particles.
3) The Farnes article is woefully inadequate and would not have been published in a journal of high energy physics. It fails to address any of the issues related to the theoretical consistency of negative mass particles (It's not clear whether he's aware of them) and fails to confront the overwhelming evidence that favors the existence of dark matter. Although rotation curves get the most attention in the popular press (probably because they're the easiest to explain), they're probably the weakest link in the overall picture. There is even more compelling evidence from:
The statistical patterns encoded in the cosmic microwave background light leftover from the big bang
The statistical distribution of galaxies and galaxy clusters in the universe across all known distance scales.
Gravitational lensing (the bending of light around massive objects which can be used to "weigh"objects like galaxies independently of their internal dynamics)
To my knowledge, no known alternative to dark matter (modified gravity or some other kind of exotic substance) addresses any of these to a satisfying degree, whereas dark matter accounts for all of them. For a historical overview of this evidence, see https://arxiv.org/abs/1605....
Feynman famously stated that antimatter, such as positrons, could be thought of as normal matter moving backwards in time. At this point, we're not sure if the symmetry extends to gravity; early results suggest that it doesn't but are not conclusive. If it does, antimatter would have negative mass for gravitational purposes.
My own background is in semiconductors. Semiconductors have "holes" with mass which is "negative" relating to the surrounding medium (a hole is the absence of an electron relative to the rest of the medium). Holes nevertheless attract and are attracted by electrons - forces aren't really affecting the hole (because there's nothing there), but they're affecting the surrounding medium in ways that cause the hole to move. The effective mass can be considered positive for inertial purposes and the force regarded as negative. Negative mass might work something like this for gravity.
shouldn't negative masses be ATTRACTED to one anotherand repulsed from positive mass?F=m1m2/r^2 the two negative signs cancel each other and you get the same direction for the force as with positive mass
I see. My reply to Robin was correct as to the forces experienced, but incorrect as to the resulting acceleration of the neg mass particle (because I didn't account for the sign of that mass in the acceleration formula a = f/m). Thanks!
I don't get this. It seems to me that a positive-mass particle would set up the usual gravitational field, in which the negative-mass particle would feel a repulsion (I.e. negative the force that a positive test mass would feel). And that the neg-mass particle would set up a negative gravitational field, one in which the positive mass particle would feel a repulsion. So the particles would move away from each other with ever-decreasing acceleration. If I am confused can someone help straighten me out?
Gravity, with negative masses, obeys the opposite rule of electrostatics: like masses attract, unlike masses repel.
In the 2-particle scenario, the particles experience a mutual repulsion. The positive mass experiences a force pointing away from the negative mass, and it accelerates in the same direction away from the negative mass.
The negative mass experiences an equal, but opposite force pointing away from the positive mass. However (the weird bit), because it’s mass is negative, it accelerates in the opposite direction of the force, towards the positive mass.
If the masses are equal in magnitude and both initially at rest, the outcome is that the negative mass ‘chases’ the positive mass, both moving with the same constant (proper) acceleration, forever.
I accept your claim that this tension exists. Yes, any theory must deal with many difficulties.
The point of my comment was not to present an impossibility theorem, but to suggest that there are several highly nontrivial challenges that any theory of negative mass particles must confront and I know of no plausible solution to any of these, but maybe someone will find a way around them.
You're right that there are many known examples of forces getting stronger or weaker as the universe evolves (both the strong and the weak forces did this in opposite ways in the early universe). However, with regard to negative mass particles, there is generic tension between having a sufficiently large coupling to populate them after inflation while keeping this coupling sufficiently small to avoid all the problems associated with radiating extremely large numbers of conventional particles (and other tachyons) in a runaway process that endlessly fills the universe with more stuff.
I agree that zero coupling is implausible, but it isn't obvious that the coupling can't become very low at current pressures and temperatures, even if high enough in the early universe.
RE: 3) To be clear, I would never deprive him of his first amendment rights ;) Let's see where it goes
Apologies for missing your paragraph on this earlier, but I agree with your observation that there may be a loophole if such particles don't couple to the matter we know and love.
However, the cosmological challenge of having completely decoupled particles is that it's not easy to populate them in the early universe. One might argue that they were around from the beginning as an initial condition, but it is overwhelmingly likely (though not yet fully established) that the very early universe underwent a phase of "inflation" during which it was expanding at an exponential rate.
This inflationary expansion dilutes the number densities of all possibly pre-existing particles by at least a factor of ~10^30 (and often much more depending on as yet unknown details about this phase). Inflation ends when the field that drives this expansion (the "inflaton") transfers its energy to create more familiar particles through some coupling, so there is no known way of filling the universe with an appreciable number of completely non-interacting particles.
1) I accept your claim. 2) This is the issue I pointed to in my 4th to the last paragraph. But there need not be a coupling to allow such emissions. 3) He should be allowed to offer evidence and analysis regarding his hypothesis even if he doesn't answer all the questions a high energy journal wants answered. I agree a good next step is to try to explain a wider range of empirical patterns, beyond what he considered in this paper.
A couple of minor technical points here.
1) Dark energy does not have a negative energy density. This quantity is strictly positive, but it does exert negative pressure, which gives rise to accelerated cosmic expansion. If we think about this as a substance, it seems very exotic since no other known form of matter has negative pressure. However, we can equivalently think of accelerated cosmic expansion as just a modified version of the original (minimal) General Relativity which includes an additional term (the cosmological constant) that enables accelerated expansion without spoiling any of the deeper principles of the theory.
2) Negative mass particles (tachyons) are problematic in quantum theories because their kinetic energy (which is proportional to mass) is negative. Thus, they can always lower their energy by going faster and conserving energy by emitting arbitrary numbers of other, positive mass particles; they would never stop doing this.
That said, it is technically possible for a spin-0 particle (like the Higgs boson) to *very temporarily* have a negative mass (and it likely did have one in the very early universe). However, the resulting instability from this negative mass changes the vacuum energy state of the universe and forces the Higgs to acquire a positive "vacuum expectation value" which is responsible for giving masses to the known elementary particles. In this new vacuum, all known particles (including the Higgs boson) all have positive masses.
None of these issues were known when Einstein made his original casual speculations about negative mass particles.
3) The Farnes article is woefully inadequate and would not have been published in a journal of high energy physics. It fails to address any of the issues related to the theoretical consistency of negative mass particles (It's not clear whether he's aware of them) and fails to confront the overwhelming evidence that favors the existence of dark matter. Although rotation curves get the most attention in the popular press (probably because they're the easiest to explain), they're probably the weakest link in the overall picture. There is even more compelling evidence from:
The statistical patterns encoded in the cosmic microwave background light leftover from the big bang
The statistical distribution of galaxies and galaxy clusters in the universe across all known distance scales.
Gravitational lensing (the bending of light around massive objects which can be used to "weigh"objects like galaxies independently of their internal dynamics)
To my knowledge, no known alternative to dark matter (modified gravity or some other kind of exotic substance) addresses any of these to a satisfying degree, whereas dark matter accounts for all of them. For a historical overview of this evidence, see https://arxiv.org/abs/1605....
Feynman famously stated that antimatter, such as positrons, could be thought of as normal matter moving backwards in time. At this point, we're not sure if the symmetry extends to gravity; early results suggest that it doesn't but are not conclusive. If it does, antimatter would have negative mass for gravitational purposes.
My own background is in semiconductors. Semiconductors have "holes" with mass which is "negative" relating to the surrounding medium (a hole is the absence of an electron relative to the rest of the medium). Holes nevertheless attract and are attracted by electrons - forces aren't really affecting the hole (because there's nothing there), but they're affecting the surrounding medium in ways that cause the hole to move. The effective mass can be considered positive for inertial purposes and the force regarded as negative. Negative mass might work something like this for gravity.
Yes, the force is the same but the acceleration is opposite, due to F = ma.
shouldn't negative masses be ATTRACTED to one anotherand repulsed from positive mass?F=m1m2/r^2 the two negative signs cancel each other and you get the same direction for the force as with positive mass
This is one of those things that really takes an intro course, a page won't do it.
Robin can you recommend a page for someone to better understand the terms you're using, especially entropy and negative matter?
That's also my guess. It sounds like how two particles with similar charge would repel each other. So there seems to be something I'm missing.
I see. My reply to Robin was correct as to the forces experienced, but incorrect as to the resulting acceleration of the neg mass particle (because I didn't account for the sign of that mass in the acceleration formula a = f/m). Thanks!
I don't get this. It seems to me that a positive-mass particle would set up the usual gravitational field, in which the negative-mass particle would feel a repulsion (I.e. negative the force that a positive test mass would feel). And that the neg-mass particle would set up a negative gravitational field, one in which the positive mass particle would feel a repulsion. So the particles would move away from each other with ever-decreasing acceleration. If I am confused can someone help straighten me out?
Gravity, with negative masses, obeys the opposite rule of electrostatics: like masses attract, unlike masses repel.
In the 2-particle scenario, the particles experience a mutual repulsion. The positive mass experiences a force pointing away from the negative mass, and it accelerates in the same direction away from the negative mass.
The negative mass experiences an equal, but opposite force pointing away from the positive mass. However (the weird bit), because it’s mass is negative, it accelerates in the opposite direction of the force, towards the positive mass.
If the masses are equal in magnitude and both initially at rest, the outcome is that the negative mass ‘chases’ the positive mass, both moving with the same constant (proper) acceleration, forever.
The scenario is directly and easily calculated via the most basic Newtonian physics.