# If a particle had negative mass where would it go?

1. Aug 21, 2006

### PRDan4th

If an oblect or sub atomic particle had negative mass, would it "fall" up? And if so where would it go? If the universe is infinite the particle would find a place as far away from all other positive mass objests as possible and we would never see it or know it existed at all! It could agglomerate with other negative mass particles and as such create another universe of anti matter.

Any thoughts along this line of thinking?

Pete

2. Aug 21, 2006

### ZapperZ

Staff Emeritus
Why is there suddenly a rush of questions on "negative mass" all of the sudden? Was there a TV show on this, or did some webpage started doing something?

Zz.

3. Aug 21, 2006

### rbj

I think this is a slightly different twist than that other thread, Z.

From a POV of gravitation, and using the Equivalence Principle (which implies, for this case, that gravitational mass is the same thing as inertial mass), what you get with the concept of negative mass is contradiction.

A positive mass, $M$, will attract another mass, $m$, positive or negative. For the negative mass, $m$, the gravitational force from $M$, will be in the opposite direction than if $m$ were positive. But then when using Newton's 2nd law, if its mass is negative, it will move in the opposite direction of the force applied to it. Two negatives means it will still fall.

But the problem is that a negative mass $M$ will always repel the other object $m$ whether positive or negative mass.

You can set up a curious situation with two masses $M$ and $m$ of equal magnitude but opposite sign. Do they move toward each other or away from each other? It seems that the negative mass will move toward the positive mass, but the positive mass will move away. Kinda like a dumb thing I remember seeing in high-school where a cute (and popular) girl is being followed around by a less cute (and less popular) guy that is in love with her.

I think if we had two masses of equal magnitude and opposite sign (and no electric charge), we could construct a perpetual motion machine out of it.

4. Aug 21, 2006

### Danger

I remember a couple of decades ago Dr. Robert Forward proposed just such a situation for a space drive system in an Omni article.

5. Aug 21, 2006

### WhyIsItSo

Pardon my towering ignorance, but doesn't the current state of Physics "know" that matter and antimatter will attract each other and suffer mutual annihilation?

6. Aug 21, 2006

### rbj

i don't think that antimatter is negaive mass, is it?

7. Aug 21, 2006

### WhyIsItSo

I suppose not, I just thought that must be what he meant.

Reason being, I thought mass was always a positive number $$(0,\infty )$$.

Guess I'll just quietly go away

8. Aug 21, 2006

### rbj

it's a reasonable assumption. i just don't think that's what they say it is.

9. Aug 21, 2006

### Andrew Mason

It is not clear whether an anti-particle has negative mass or an opposite charge (opposite to its normal counterpart). It may not be possible to tell the difference. It may be that the laws of physics are the same whether you think of charge or mass as the quantity having positive and negative attributes. I have not yet seen any test that would distinguish the two possibilities.

Positive and negative mass seems a bit contrived. But when you think about it, so does positive and negative charge.

When you consider that the collision of a particle with its anti-particle causes matter annihilation, negative mass may be a better model.

AM

10. Aug 21, 2006

### Rach3

No, they would both accelerate away from each other.

11. Aug 21, 2006

### Rach3

The classical physics of negative mass is consistent. For instance, air bubbles in water.

12. Aug 21, 2006

### rbj

it's not what the math says. if inertial mass is the same as gravitational mass (sometimes gravitational mass is differentiated as "passive" and "active" gravitational mass, but i'm not doing that), then a positive mass attacts both negative and positive masses and a negative mass repels both negative and positive masses if we stay consistent with the signs. if you want to hear it from a physicist a lot bigger and more authorative than me, check out

non sequitur. we're not talking about air bubbles in water.

13. Aug 21, 2006

### rbj

matter is maybe annihilated, but there's some energy left. wouldn't the energy equivalent of a negative mass particle be negative energy?

14. Aug 22, 2006

### yaminohohenheim

i'll try to spare the mumbo-jumbo and make it quick and simple:
physicists define mass as always positive, negative mass is nonexistent.

this is unless you get into theoretical physics involving hypothetical particles such as tachyons.

15. Aug 22, 2006

### yaminohohenheim

and it's not an arbitrary definition by the way, there are many formulas that, when derived properly, prove that mass is a constantly positive quantity, such as the classic equation E=mc^2 when it is manipulated in a more complex manner.

16. Aug 22, 2006

### ZapperZ

Staff Emeritus
But look at the Dirac equation. What are the "energies" of the "positive electrons"?

Zz.

17. Aug 22, 2006

### Hurkyl

Staff Emeritus
I thought it was rather straightforward -- look at the electric field the anti-particle generates.

Again, I thought it straightforward! A particular charge may be either attracted or repelled to other charges. A particular mass may only be attracted to other masses.

18. Aug 22, 2006

### Andrew Mason

The field of the antiparticle is measured by the force it exerts. If negative mass accelerates in a direction opposite to the force, a negative mass with the same charge behaves the same as a positive mass with an opposite charge. How do you distinguish the two?

If it is attracted to another charge is it because it has opposite charge or because it has negative mass (same charge) and accelerates in the opposite direction to the force?

AM

19. Aug 22, 2006

### Andrew Mason

I don't see why that should follow. Negative matter would have inertia - it would require energy to change its speed. It is just that the direction of the acceleration is opposite to the direction of the force.

So the annihilation of normal matter or negative matter causes loss of inertia to occur. If energy is a measure of the inertia of an object, the loss of negative mass should result in energy being released.

AM

20. Aug 23, 2006

### Hurkyl

Staff Emeritus
So? I use the same test-charge to measure the electric field generated by my particle and its antiparticle. If the test-charge reacts in the same way to each field, then the particle and its antiparticle have the same charge. If the test-charge reacts in opposite ways, then they have opposite charges.

Even more explicitly:

If Z repels the test charge, and anti-Z attracts the test charge, they must have opposite charges.
If Z repels the test charge, and anti-Z repels the test charge, they must have the same charge.
If Z attracts the test charge, and anti-Z repels the test charge, they must have opposite charges.
If Z attracts the test charge, and anti-Z attracts the test charge, they must have the same charge.

Observational evidence shows that electric forces can either repel or attract, and gravitational forces can only attract. Furthermore, any particular charge can be observed to be attracted by some charges and repelled by other charges.

How you are going to get this behavior (what happens, happens, and what doesn't happen, doesn't happen) using only positive charges and both positive and negative masses?

Last edited: Aug 23, 2006
21. Aug 23, 2006

### rbj

only from

$$E = m c^2$$ .

since $c^2$ is decidedly positive, then if $m < 0$ so also must $E < 0$.

just a simple thought.

nonetheless, i'm still pretty confident (as was John Baez in first informing me about it) that a negative mass object repels everything (gravitationally) and a postive mass object attracts everything. a small negative mass falls to the Earth at an acceleration of 9.8 m/s2 just like any other amount of mass. it's not a step function (like the sgn() function) where the acceleration is -9.8 m/s2 and suddenly becomes +9.8 m/s2 when the small mass crosses over from positive to negative.

and two masses of equal size and opposite sign can be put together to make a perpetual motion machine. the negative mass will keep chasing the positive mass which will keep moving away from it. i think they would even accelerate along the axial line that connects the two masses.

22. Aug 23, 2006

### WhyIsItSo

Could explain why there isn't any negative mass known.

If negative mass repels itself gravitationally, it would never coalesce into larger forms (clouds or bodies). Since the expansion of positive matter from origin is slowed due to gravitational attraction, and expansion of negative matter would be increased from origin, it follows that negative matter, if it exists, would be the farthest material from origin and in atomic form. Such would make it virtually impossible to detect from here.

23. Aug 23, 2006

### rbj

yeah, but it's attracted to positive mass (just like anything else is attracted to positive mass). that's where this is so self-contradictory (which i think bodes poorly for the existence of the stuff).

if there is a lot more positive mass in the universe (or in some local region) than there is negative mass, the attraction of the positive mass will exceed the repulsion of the negative mass and the negative mass will fall inward along with the positive, although the positive mass would feel a small repelling force from the negative mass.

the big contradiction happens in the hypothetical situation of two masses of equal size and opposite sign separated by some not very large distance. such a scenario would have pretty impossible consequences.

24. Aug 23, 2006

### robphy

American Journal of Physics
March 1993 -- Volume 61, Issue 3, pp. 216-217

Negative mass can be positively amusing
Richard H. Price

Last edited by a moderator: May 2, 2017
25. Aug 23, 2006

### rbj

but not for the price they want. and i can't find the paper for free online anywhere.