# Why is gravity only an attractive force?

As per the universal law of attraction, any two bodies (having some mass) experience a force of 'attraction' which is proportionate to ...and ...inverse proportionate ....

Then comes my question: Why it should be force should be of type 'attraction' only ? Why it should not be repulsion / any other kind of force ?

• There was an article in New Scientist on this a while ago. It was describing research into how antimatter (presumed to have a negative mass) reacts under Earth's gravity. It is thought that antimatter (specifically anti-hydrogen, in this case) may rise instead of fall. – Beta Decay Jul 28 '17 at 12:41
• The aforementioned article – Beta Decay Jul 28 '17 at 12:42
• @BetaDecay I'm not sure what that article is talking about. No real predictions in physics suggest antiparticles have negative mass. From wikipedia: "A particle and its antiparticle have the same mass as one another, but opposite electric charge and other quantum numbers." – zephyr Jul 28 '17 at 15:24
• I think the question is stated in a manner that limits generalizatioon. I think the larger question is if gravity is a manifestation of some larger theory under certain boundary conditions. Newton's theory of gravity is based on "ordinary observations" and works very well for most human considerations. Calculations based on Newton's theory got men to the moon and back. However for the orbit of Mercury and timing of GPS then relativistic considerations need to be taken into account. So back to what should be the question? Given that "dark energy" is causing the universe to expand faster and fas – MaxW Jul 29 '17 at 2:15
• Same question on the physics board. physics.stackexchange.com/questions/11542/… You can look up Spin 1 and Spin 2 particles for some explanations, but until gravity is actually understood, all the answers are pretty much hypothesis. Some related answers here as well: quora.com/… – userLTK Jan 27 '18 at 1:11

### Because mass is positive

To expand your quote concerning the gravitational force into an equation:

$$F_G = -\frac{Gm_1m_2}{r^2}$$

The force of gravity, $F_G$ is proportional to the product of the masses and inversely proportional to the distance, $r$, squared. Let's break this down and see what might cause $F_G$ to be positive.

In this equation, $r$ cannot be negative because it's a distance between two locations. Two locations cannot be a negative distance apart. And even if they somehow were, the squared would take care of that anyway.

$G$ is the universal constant and always positive. You might argue that it could possibly be negative, but that's not possible. $G$ actually doesn't really exist. It doesn't describe anything fundamental to the physics of the universe. $G$ is simply a bookkeeping constant that allows us to get the right answer for the force based on any choice of units for mass and distance. Technically, if one uses the "correct" units for mass and distance (e.g., the Planck units), then $G=1$ and effectively doesn't exist. Since $G$ is just a scaling factor that depends on the choice of units, it will only be a positive number.

That leaves us with the masses. These are the only things which could possibly be negative. Of course, to get a positive, repulsive force, one mass would have to be positive and the other negative. But what exactly is a negative mass? Mass is the metric which describes "how much" of something there is. How can you have less than nothing of something?

### Why can mass not be negative?

If you want to look at this another way, you can show that if mass could be negative, you'd get nonsensical results! Assuming of course, all other aspects of physics were the same. Recall from Newton's second law that

$$F = ma$$

Let's say there are two blocks sitting on a table. One block has a mass $m_1>0$ which is positive and the other has a mass $m_2<0$ which is negative. Ignore all other forces on these two blocks for the moment.

I go up to $m_1$ and I apply a force to push this mass forward. The acceleration that is induced is: $a = F/m_1$. Necessarily, the direction in which $m_1$ moves is the same direction in which I'm pushing. That's all well and good.

Now I go over to $m_2$ and I apply the same force, attempting to push it forward on the table. The acceleration induced on $m_2$ will be: $a = -F/|m_2|$. Note I made $m_2$ positive and pulled out the negative sign. You can see that if my force is forward, the direction the mass moves will be backwards! But here's the problem, my hand is in the way because it's trying to push to mass. As the mass tries to move backwards into my hand, it will be applying a force back on my hand, which by Newton's third law, necessarily mean's my hand is applying more force on the block, which then applies more force on my hand, ... and suddenly infinite forces are being applied or equivalently, these objects are infinitely accelerating. This is described by the concept of Runaway Motion.

If this seems strange to you, that's because it is. If negative masses existed, we'd live in a very weird universe. Fortunately, we live in a universe where physics makes sense, mass is positive, and by extension gravity is always attractive.

• As convincing as this explanation seems, electrical charge follows the inverse square law and charge can be positive or negative. I see no reason why mass couldn't theoretically behave the same way. I believe it's actually a "fundamental mystery" as to why gravity is the only one of the four known forces that acts only to attract and never to repel. The other 3 fundamental forces can do either. – user21 Jul 28 '17 at 15:33
• @barrycarter I thought about addressing this in my answer. I guess I should have. The catch here is that Newton's second law is not $F=ea$, it's $F=ma$. You can't apply the argument above to negative electric charges for that reason. The reason mass can't behave in the same way is for the reason I outlined above. It isn't a mystery. If Newton's second law instead was $F=ea$, then electric charge could not be negative. – zephyr Jul 28 '17 at 15:48
• The second law describes inertial mass, not (necessarily) gravitational mass though. – adrianmcmenamin Jul 28 '17 at 16:24
• @adrianmcmenamin But all evidence suggests the two are equivalent. In fact, their equivalence is a major component of GR and there has been no evidence so far showing this part of GR is wrong. I described the answer for the universe we appear to live in (aside from the potentiality for negative mass). If you want to throw in all sorts of other complications, that's outside the scope of my answer. – zephyr Jul 28 '17 at 16:32
• Interestingly, the force of gravity would be negative if the distance was imaginary! So just imagine some mass at a particular distance from you and it will repel you. – zephyr Jul 28 '17 at 16:55

Why is gravity only an attractive force?

TL;DR
Because mass is always positive.

There are different notions of mass, but they're equivalent.
There are two distinct notions of mass: gravitational and inertial. The masses in Newton's law of gravitation, $F = \frac{Gm_1m_2}{r^2}$, are gravitational masses. The mass in Newton's second law of motion, $F=ma$, is inertial mass. Gravitational and inertial mass are implicitly assumed to be the same in Newtonian mechanics. General relativity makes this assumption explicit in the equivalence principle.

But what if they're not equivalent?

Unlike mathematics, where one can simply make an assumption and see where it leads, assumptions in physics need to be validated. This assumption has been tested with many kinds of materials, both on the ground and in space. Variations on the Cavendish experiment using different kinds of materials have been made. Within the limits of the rather lousy accuracy of the gravitational constant (one part per ten thousand, at best), every one of these is consistent with the null hypothesis (gravitational and inertial mass are the same) and inconsistent with the hypothesis that different materials have measurably different gravitational and inertial masses.

The Earth's Moon, with its very different near-side and far-side, provides an even better mechanism for testing this equivalence. Rather than the one part per ten thousand (at best) accuracy available to Cavendish-style experiments, the Moon shows that gravitational and inertial mass for sodium and iron are equivalent to within about one part per ten trillion.

So much for ordinary matter, but what about antimatter?

That an ordinary matter particle and its antimatter equivalent have the same (positive) inertial mass has been tested over and over in particle colliders around the world. Whether the equivalence principle also applies to antimatter remains a somewhat open question. While there are many reasons to think that the equivalence principle applies to antimatter as well as normal matter, testing that this is the case is very hard. The best results to date are from the ALPHA experiment, which tests whether neutral antihydrogen (a antiproton and an positron) falls up or down. The results are that antihydrogen's gravitational mass lies somewhere between -65 and 120 times its inertial mass. This is not anywhere close to conclusive, but it does lean towards antimatter having a positive gravitational mass, consistent with the equivalence principle.

Along the same lines with previous answers suggesting "mass cannot be negative," I'd like to add an insight for why that might probably be the case. If Higgs field and particles' varying degrees of interaction with the field is what gives rise to what we call mass, then the theory suggests that photons don't have mass (and constitute the velocity limit through space) because they don't interact with the field at all. I don't think the framework allows for negative interaction with the field or an "anti-Higgs" field.

Theoretically, gravity can be "attractive" in the sense that objects move towards you when pushed. This can occur from negative mass (doesn't seem to make sense, but theoretically possible). Peter Engels and others have written a paper about it here and it's an interesting idea.

The idea is that by cooling the atoms to almost absolute zero, they create a Bose-Einstein condensate and act likes waves in the realm of quantum dynamics.

• That paper in no way suggests that gravity can be reversed. The paper says that atoms within a Bose-Einstein condensate can, under certain conditions involving 1-D expansion of the BEC, "accelerate against the applied force, realizing a negative effective mass related to a negative curvature of the underlying dispersion relation." In other words, the positive-mass rubidium-87 atoms briefly behave as if they had negative mass. The equivalence of inertial and gravitational forces remains uncertain at quantum level, so you can't use this result to argue for "negative" gravity. – Chappo Hasn't Forgotten Monica Aug 12 '17 at 7:23