# Does antimatter have a negative mass

1. Jun 9, 2010

### sshort75

If this question has an answer I didn't find it on the rest of the forums.

2. Jun 9, 2010

### haael

Certainly no. It that was the case, then all neutral particles (Majorana) would have zero mass. And we observe neutral particles like Z^0 or pi^0 that have nonzero mass.

Also, negative rest mass has no mathematical meaning. It simply means, that all momentum and energy components are imaginary. What that would mean?
Negative total mass (energy) is possible, but it is perfectly equivalent to positive mass with reversed momentum direction.

Philosophically, negative total mass describes particles that move backwards in time. But in fact particles don't "move" in time, they simply are. It's the same thing as if you drew two lines: one from left to right and second from right to left. After that you see that the lines are identical. The way of drawing a line is irrelevant, both cases lead to the same result.
The same is with negative mass: the particles described by positive and negative values are the same.

3. Jun 9, 2010

### theoryiscool

As stated already, antimatter definately has NOT got negative mass; though in relativistic quantum mechanics, the way one interprets antimatter in via the fact that there exist two energy solutions, one positive and one negative. The positive energy solution is good for household particles(elctrons for e.g.), the negavtive energy solutions are interpreted as positive energy for the antiparticles. This is essentially down to the relativisitc energy equation whereby a square of energy exists.

4. Jun 9, 2010

### mikeph

Why?

Surely an object's momentum direction only depends on how you look at it.

5. Jun 9, 2010

### theoryiscool

I am a little confused by that, surely negative momentum viewed as a particle going in the opposing direction is by virtue of velocity being in the opposing direction. Velocity is the vector, not mass. I could be wrong, my knowledge of this stuff is new to me.

6. Jun 9, 2010

### haael

Total mass and momentum 3-vector together form a 4-vector called 4-momentum. Total mass is its time component. Rest mass is its length. Of course this 4-vector lives in Minkowski spacetime, so total mass and rest mass are related by a known equation:
$$m_t = m_0 / \sqrt{1 - v^2/c^2}$$

In natural units ($$c = 1$$), the rest mass can be expressed as a length of 4-momentum:
$$m_0^2 = m_t^2 - p_x^2 - p_y^2 - p_z^2$$

Consider a particle with some positive total mass and some momentum. This particle would have some rest mass and it would travel by some trajectory.
Now consider a particle with the mass and momentum reversed, i.e. negative, but otherwise the same that the previous particle. This second thingie would have the same rest mass and the same trajectory.
So basically, positive and negative total mass are just two mathematical ways to describe the same physical situation.

In QM some mathematical tricks allow us to distinguish between positive and negative mass and treat one of them as a particle and the other as an antiparticle. But think about Majorana particles (that are identical to their antiparticles). In this case positive and negative total mass would still mean the same.

7. Jun 10, 2010

### tom.stoer

According to Newton we have gravitational mass and inertial mass. They value is identical for each object, but within Newton's theory one is not able to explain, why this is the case. In general relativity it becomes clear why the are are identical.

So in principle we must set up two different experiments, one to measure the inertial mass of an object, one to measure its gravitational mass.

I don't know if one has measured gravitational mass of anti-matter e.g. in a Quadrupole ion trap ("Pauli" trap), but I guess one has. What is constantly being measured is inertial mass, e.g. in colliders. According to these experiments the inertial mass of a particle and of its antiparticle are identical.

8. Jun 10, 2010

### sshort75

Thankyou very much for the answers I should of phrased my question better I was wondering if antimatter had a weight of less than zero. I knew that it was magnetically attracted to matter because of the charge but I did not know if gravity repulsed it. It is my understanding by researching the topic further that there is no conclusive evidence one war or the other.

9. Jun 10, 2010

### tom.stoer

as I said: the gravitational mass (or "weight") should be measurable in a Quadrupole ion trap

10. Jun 15, 2010

### unusualname

tachyons have an imaginary mass, so $$m^2 < 0$$ for those, but it's not physically significant unless they could interact with normal matter, and since they may not even exist that's looking unlikely.

11. Jun 15, 2010

### JesseM

In classical physics a negative-mass object with positive electromagnetic charge would be repulsed by the electromagnetic field of an object with negative electromagnetic charge, rather than attracted according to the usual "opposite charges attract" rule. This is because the electromagnetic force on the negative-mass/positive-charge object would still point towards the negative-charge object, but since acceleration is given by a=F/m, with negative mass the acceleration would go in the opposite direction of the force. So, a negative-mass/positive-charge object and a positive-mass/negative-charge object would behave very weirdly, with the negative-mass object accelerating away from the positive-mass object, while the positive-mass object was accelerating towards the negative-mass object. Not sure if the same would be true in quantum electrodynamics, but since QED should reduce to classical electromagnetism in the large-scale limit I suspect it would, which would probably mean that negative mass in antimatter would have observable consequences in terms of things like tracks left in bubble chambers.

12. Jun 15, 2010

### Fredrik

Staff Emeritus
This isn't correct. Yes you can flip the signs of any or all of the variables that appear squared in that equality without violating the equality, but you will run into a bunch of problems with such things as conservation of momentum in particle collsions and Newtonian gravity (as Jesse already mentioned).

Also, what you call "mass", most people call "energy" these days. When I say "mass", I always mean what you call "rest mass".

Special relativity and quantum mechanics imply that the quantity $$-E^2+\vec p\,^2$$ is the same in all inertial frames, regardless of what particle species we're dealing with. Particles are divided into three classes depending on whether that quantity is negative, zero or positive. If it's negative, the particles are called massive particles (some people call them bradyons or tardyons). If it's zero, they're called massless particles (or luxons). If it's positive, they're called tachyons.

In the first two cases, the "mass" of the particle is defined to be the non-negative real number m that satisfies $$-E^2+\vec p\,^2=-m^2$$. So mass is positive or zero by definition. In the two standard cases, it's defined as the positive square root of $$E^2-\vec p\,^2$$. In the third case, we can define the "mass" to be the complex number m with positive imaginary part that satisfies the equality, or we could write $$-E^2+\vec p\,^2=n^2$$ instead, and let n be a positive real number that labels the particle species instead of mass.

There is. A positron is exactly like an electron but with a positive charge instead of a negative charge. In particular, they have exactly the same mass.

Last edited: Jun 15, 2010
13. Jun 17, 2010

### haushofer

"Philosophically"? I have already problems checking this statement physically or mathematically, let alone "philosophically".

14. Jun 17, 2010

### Galap

Be careful. There are actually 3 kinds of mass that exist. They are all thought to be the same (have equal values), and have been shown to be the same to pretty good precision experimentally. It depends on the types, which are as follows:

Inertial mass: this is the type of mass that makes objects resist motion. This is the mass in the force and momentum equations (F=Ma, P=MV). An object with negative inertial mass would accelerate in the OPPOSITE direction in which a force was applied. I think its very unlikely for antimatter to have negative inertial mass, due to the problems above mentioned

Passive gravitational mass: This determines the magnitude of the acceleration felt in the presence of a gravitational field. The fact that this value is the same as inertial mass explains why all objects fall at the same rate: increasing passive graviatational mass increases the force felt by the object, but increasing inertial mass increases its resistance to the motion. If the values were different in this quantity, different objects would fall at different rates. It seems POSSIBLE that antimatter would have a negative value for this type of mass. I can't think of a reason why it couldn't...

Active gravitational mass: this type of mass governs the strength of the gravitational field generated by an object. an object with negative gravitational mass would repel objects with positive passive gravitational mass. This quantity being variable along with variable passive gravitational mass would have some wierd results, like some one object attracts the other but the other repels it, causing an endless chase. It seems also possible for antimatter to have negative active gravitational mass as well, but something tells me this is less likely than passive.

The bottom line is, since so little antimatter has been produced, the properties of it with respect to gravitation have not been observed. In other words, we don't know which way it will fall. I suspect all three mass types are positive though, as do i think most physicists.