# 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 at 11:42 AM

### 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 at 11:58 AM
9. Sep 16, 2017 at 3:22 PM

### 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 at 8:29 AM