# A Negative mass and antimatter

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1. Sep 12, 2017

### The Count

In physics we cannot easily imagine “negative” energy for a particle (not a field) in order to have “negative” mass, although the first concept of Dirac for antiparticles was that they were “holes” that were opposite to particle existence and there was a minus in front of mc2.Regardless of whether we use the Dirac sea interpretation, a negative-energy particle in field theory is always interpreted as an antiparticle.

Here we can also give an answer to the problematic feature of "negative rest energy" if we regard that
Eo=(-mo)c2<0
comes from
E2=m2c4 +c2p2
so for rest mass and zero momentum we truly have
Eo2=(-mo)2c4
which gives back the well known
Eo=(mo)c2>0

In the beginning we have to distinguish inertial mass, active gravitational mass, and passive gravitational mass.
Active and inertial mass of course can be negative, meaning that the motion will be opposite than expected. If we regard, as until today is accepted, that these 3 are one and only feature, we could also solve the problem of equations of motion of a negative mass particle (-m). We will just add a minus in acceleration too (either as opposite motion, or as negative length).
Experimentally found here
https://m.phys.org/news/2017-04-physicists-negative-mass.html
Theoretically fits to the notion that in GR spacetime is the "field" of mass, so negative gravitational charge (mass) gives negative field(spacetime).
As for "negative" time, in physics we cannot accept time travelling backwards, but we can accept opposite arrow of time for antiparticles in Feynman diagrams and also conversion of a particle to antiparticle in case it changes sides (or time evolution…) in the particle equation.

So
F = (-m) (-a) = G (-m) M /r2 => a = -GM/r2.
(Either we use r or -r, the result stays the same)
It seems to accelerate away from a positive passive mass particle, opposite than normal mass does.
In the case of the positive mass charge close to a negative mass' field (passive mass)
F = ma = G m (-M) /r2 => a = -GM/r2.
The positive charge/mass seems also to run away from a negative passive one.
Perhaps it is opposite mass repelling and not an unknown "dark energy" that is causing the universe to expand at an ever increasing rate. We will also in this way solve the baryon asymmetry problem, where all antimatter seems vanished.
Of course for both negative masses we have usual behavior of same positive mass
F = (-m) (-a) = G (-m) (-M) /r2 => a = GM/r2.

In GR the important quantity is the energy, not the mass, so the appropriate question would be, "are there negative energy states"?
We could accept opposite/negative curvature in spacetime. We have not accepted the correlation between covariant-contravariant with matter-antimatter respectively, but we can accept that changing sides of the equation changes contra-variant to co-variant and vise versa, or when we have contravariant vector instead of covariant, the Christoffel symbol changes signs, which means opposite curvature. When we multiply a covariant metric with its contravariant one, the result is the unit tensor or the Cronecker Delta, that means flat space (no curvature)! Matter with antimatter gives us no matter (particle annihilation), like opposite curvatures cancel (destructive interference).

In QFT negative mass doesn't make much difference. For a scalar (spinless) object, the expression in the Lagrangian (ie. the physical description) is always m2, so if m<0 you get the same thing. Therefore whether or not the mass is positive or negative is just a matter of definition.

For a fermion, the mass in the Lagrangian is linear but you can just redefine your fermion field to make it positive. All antiparticles have all features opposite (charges/quantum numbers & spin direction) except mass. All particles have antiparticles except these with no mass and no charge.

Finally seems impossible, at least yet, for our experiments to distinguish gravitational repelling while gravity is 1038 times weaker than any EM field close.

Can anybody think of a reason not to regard negative mass as existent and not to correlate it to antimatter?

Last edited: Sep 12, 2017
2. Sep 12, 2017

### Staff: Mentor

We have extremely accurate measurements of the energy and mass of antimatter particle. They are clearly positive.

We also have indirect evidence that antimatter must fall down, as most of the energy of hadrons is neither matter nor antimatter, and the relative contribution is different fr different materials. Direct measurements of antimatter falling in gravitational fields will follow in the next years.

You can arbitrarily add minus signs in all formulas exclusively for antimatter, but that is a meaningless complication that doesn't change the physics.

3. Sep 12, 2017

### The Count

If I am not mistaken, the mass of antimatter is calculated from equations of motion through EM field, which could show the amount of mass and not clearly the sign, as showed.
As for energy I have mentioned in the equations that it could count as positive, even with negative rest mass.
Also for hadrons I am not sure where the sign of mass is counted.

Finally I would appreciate a comment in all my points in my first post, at least to the ones that have mistakes.

4. Sep 12, 2017

### Staff: Mentor

Half of particle physics?
(the other half is matter)
See above: You can arbitrarily introduce additional signs, but where is the point?
Antimatter behaves exactly like matter (apart from CP violation, but that is off-topic here). There is no reason to introduce separate sign conventions for it everywhere.

And what about particles that are neither matter nor antimatter, like mesons? Do you want to give them a positive or negative mass, and why?
The whole approach is a mistake.

5. Sep 12, 2017

### ZapperZ

Staff Emeritus
No, you cannot use this as experimental evidence for your argument here. Read this thread and references therein:

This negative mass is the effective mass. This is nothing new. Solid state and condensed matter physicists have dealt with negative effective mass for a long time.

Zz.

6. Sep 15, 2017

### The Count

To Mfb

I am not quite sure what you mean. If you are suggesting that (probably or almost) all experiments and physicists take antimatter's mass as positive, shows more like the status quo, rather than a proof. I am aware that this is the status quo, but I have difficulty finding one experiment that undoubtedly shows that the sign is positive. The most solid proof would be "antimatter falling in matter gravitational fields", which is, as you said, not yet accomplished. What is usually seen/said/believed/used is not always correct, or at least not proved to.

I am not suggesting that everybody is crazy except me, but I am wondering how solid is this assumption.

When you say "behaves" you mean that follows the known rules of particle physics, as all particles.
But they seem almost totally different particle than their matter-relatives. As I have mentioned:
1. All antiparticles have all features opposite (charges & spin direction, generally all quantum numbers like quark flavor numbers, isospin, baryon number, lepton flavor, lepton number, weak isospin, hypercharge, which is a combination of weak isospin and electric charge, parity, (sort of)chirality ) except mass!
2. All particles have antiparticles except these with no mass and no charge. And when they have charge, antiparticles change to opposite properties, but not with mass?
3. All antiparticles run "backwards" in time in Feynman diagrams. I find this much more stranger and unnecessary (for physics, not maths), than negative mass.
4. As you also mentioned antimatter breaks CP and T symmetry. CP is charge and (kind of) space (parity), so if charge changes signs, so should parity-space. Also time "changes" sign. If spacetime is the field of mass (As GR says), then opposite fields leads us to opposite charge-mass.

What more could anyone need to say that they behave more like opposites (at least in mass) than "exactly alike"?

For my mind, seems much more strange to try to find patent-like solutions for Baryon Asymmetry, antimatter-universe loss and "dark energy" repulsion, than to just introduce negative mass (like negative charge in EM), matter-antimatter repulsion and have the most simple and logical explanation to these three great problems of Cosmology. I am not assuming that it will be easy, just more logical and simple.

This is truly a good question. The first thought is that they should have zero mass, because they are consisted of particles and antiparticles. First the fact that they are not the same particle (or else they would annihilate) reassures that they wouldn't add to zero mass. But we also know that 95% of the mass of any hadronic group of particles (protons, neutrons) does not come from their part's masses, but from the interaction (gluons) between their parts (quarks). So while still we have no way to know the sign of the meson's mass, we could just say for now that they have their mass from interactions between the parts and we are sure of the "volume" of the mass but not it's sign (in a way that we could know the volume of an arrow, but not it's direction).

Last edited: Sep 15, 2017
7. Sep 15, 2017

Staff Emeritus
Light, which is neither matter nor antimatter, falls down. The effective g is within 2% g for matter.

If antimatter "fell up", you could build a perpetual motion machine - light falls down and produces a matter-antimatter pair. These are tied together producing an object of zero net weight and lifted, allowed to recombine to light, which falls and gains energy. This repeats, producing energy at every cycle.

8. Sep 16, 2017

### dukwon

Unflavoured neutral mesons (such as the $J/\psi$) are made of a quark and its own antiparticle, and they have non-zero mass. They often decay via annihilation.

Last edited: Sep 16, 2017
9. Sep 16, 2017

### Staff: Mentor

Not with antiprotons, but indirectly we have these tests already.

The energy of regular matter has three contributions:
- rest mass of valence quarks (about 1%)
- rest mass of electrons (about 0.05%)
- QCD binding energy (about 99%)
The first one is clearly associated with matter. The second one counts as matter for historical reasons, but in the Standard Model it would make more sense to call it antimatter (note that it is just convention - both options work). The third one is neither matter nor antimatter, but it is present in both (and also in mesons).

Different elements have different relative contributions of these three components, and comparing them it has been shown that all three fall down at the same rate with very high accuracy. We also know light falls at the same rate. Why exactly should antiquarks deviate from that?
Z bosons don't have antiparticles (or they are their own antiparticles, if you like). Z bosons have mass.
In terms of composite particles, many mesons are their own antiparticles, and they all have mass.
This is purely a convention for notation.
The symmetry breaking is not a feature of individual particles, it doesn't make sense to assign it to antimatter.
It does not.
Negative mass for antimatter wouldn't give an explanation for anything. You can't just say "repulsion" and then claim everything has been solved. You have to do the maths. People did that. It doesn't work.

10. Sep 18, 2017

### nikkkom

11. Sep 18, 2017

### vanhees71

12. Sep 23, 2017

### The Count

If I am not wrong light doesn't fall down, it just follows geodesics that are curved by the Earth's mass.

As far as the machine, I must admit that I never heard of something like this. I can only guess that due to momentum conservation and to ridiculously weak gravitational force, both particles will keep on the initial photon's direction (and possibly with components opposite symmetrically to each other) and won't be seriously affected by Earth's gravitational field. If we assume that in special conditions gravity was most important, I would guess that there is no reason to be lifted as "zero net weight object", only possible negative mass particles would be lifted.

That's an interesting point. My guess would be that as mentioned the majority of groups of quarks get their mass from the binding QCD gluon interaction and not from the initial rest masses of their components. It is very interesting to notice that all flavourless mesons seem to have mass almost as the total mass of their components, but all other mesons have plenty of mass percentage to address to gluon binding. This possibly means that their rest mass could all come from gluon interaction and not from their components' initial masses (that could indeed add to zero in case of negative mass of same antiparticle).

13. Sep 23, 2017

### The Count

QCD of antimatter could also possibly be negative. Due to meson's mass, lifetime and concetration incompetence, we cannot measure gravitational repulsion.
I already explained why antimatter could logically have negative mass. As I said, I am just trying to see how certain we are about non existing negative mass.

You are correct about Z having mass. Even though it decays to a fermion and its antifermion, which probably shows a symmetry between masses as also in charges.
I guess that it could have antiparticle, but with no "negative mass distinction" we think it is the same...

It's strange. I would say that it is one of the strangest convention in physics, that due to the fact that it works, everyone (after first resistance) stops arguing. It's like imaginary numbers usage in quantum physics. Maths work, but there is no physical analog or paradigm. We can all understand that physics is not as free as maths, it has to have an explanation close to our (physical) reality.

Which one of all? Spacetime isn't the field of mass? Or opposite fields doesn't lead us to opposite charge-mass? In my mind GR doesn't cope with antimatter as particle physics. Can you please give me a clue of which of the following is wrong?

As I said it won't be easy. I would appreciate if you could help me with studies that have tried to work out the maths and didn't work.
I am aware that there are still theories of repulsive gravity and specifically due to antimatter.

Just for first step answers, if matter and antimatter are existent in the same quantities then it would be more logical than the Baryon Asymmetry.
Next, since we measured preferred repulsion through "dark energy" 3 times greater than the attraction from gravity of (dark) matter, total result is: repulsion 2 times (3-1=2) stronger than what gravitational attraction (from known dark matter) should implement. This is kind of equivalent of saying that there exists the same quantity of (dark) antimatter that both (with matter) give (by repulsion) the same result: repulsion 2 times stronger than matter gravitational attraction should implement. I know it is oversimplified, but gives a hint.

14. Sep 23, 2017

### king vitamin

In relativistic quantum physics, the only way you can have negative mass is if you have a completely negative spectrum. That is, the dispersion would be

$$E = -\sqrt{p^2 c^2 + m^2 c^4}$$

This follows already from the Wigner classification of all possible quantum states with Poincare symmetry, so you don't even need to introduce QFT to see this. So a negative mass particle could decay into more negative mass particles with larger and larger momentum, and the vacuum is totally unstable. It's not even a sensible theory.

15. Sep 23, 2017

Staff Emeritus
I think you're moving from asking questions towards promoting a personal theory. We don't do that at PF.

Yes, that's the GR explanation. However, GR also says matter and antimatter fall at the same rate. So if you want to go down the "GR says" path, you need to take it all the way.

Even in GR, light "falls down" in the sense that it gains energy when going from a higher to a lower elevation. So it doesn't even help you.

You can't simultaneously argue that antimatter falls up but is unaffected by gravity.

Last edited: Sep 25, 2017
16. Oct 1, 2017

### The Count

I am sorry if I crossed any lines. As I said before "I am wondering how solid is the assumption that there is no negative mass". When I searched for similar threads I understood that anyone that questioned the positivity of mass was getting discouraged from thinking as a possibility mass to be negative, as if it was measured or totally out of question, and I thought that it was not very solid as an assumption. Since I haven't thought of it as a new theory, every point that you made against this firstly made me look for an answer from known and accepted physics and, when the first one failed, secondly I tried to build an argument that could fit to known physics and be logically stable. If the second part is thought of as a new personal theory and is forbidden in this site I am sorry, I didn't know that.

As I mentioned, GR never introduced negative mass and I know that, but this doesn't mean that forbids such assumptions. I mentioned above possible ways for GR to be "friendly" to negativity of mass.

As far as light is concerned, I would agree that "falls down" "gaining energy" because of matter-mass curvature. But we could assume that also light could be bent in opposite curvature (antimatter) in the same way, but this time "gains energy by falling up". I tried to find diagrams that could help. Only "charged" massive particles could feel attraction or repulsion, and not massless-uncharged that just follow geodesics.

I said that is "ridiculously weak" to change it's speed or to have obvious difference from close EM fields altering its path. We have not managed to count change of motion in lab with vertical speed to Earth and clearance (as much possible) of close EM fields and we will see it in space? I am just saying that the effect couldn't be noticeable.
But even theoretically I have not understood why "an object of zero net weight will be lifted" and not keep on geodesic path towards the Earth.

I am not sure whether this is the only alternative. Since we have squared masses, negative doesn't play any role. I have to admit here that I am not very keen on "Wigner classification" that copes with only positive mass as I searched. I would appreciate some more explanation or at least how one can be led to the equation that you presented, with negative sign for negative mass.

17. Oct 1, 2017

Staff Emeritus
You continue to defend this theory of yours. I've asked the mentors to close this thread.

18. Oct 1, 2017

### Drakkith

Staff Emeritus