# How to prove that two electron exerts gravity on each other

1. Dec 20, 2008

### loup

How to prove that two electrons exert gravity on each other?

I know electrons get mass, and according to the equation F=k (m1 + m2)/r^2,

there should be gravity between the two. But how to prove? I mean, what is the experiment?

2. Dec 20, 2008

### Staff: Mentor

As far as I know, there is no experiment that measures the gravitational force between two individual electrons, which would be extremely small.

However, consider the gravitational force between a typical object and the earth. About 1/2000 of the masses is in their electrons. If the electrons in the object and the earth did not exert gravitational forces on each other, the weight of the object would be smaller by about 1/4000000. Can we measure weight to that accuracy?

3. Dec 20, 2008

### D H

Staff Emeritus
Is this a real or rhetorical question? I don't want to give what would appear to be a snarky answer to a rhetorical question.

4. Dec 20, 2008

### Staff: Mentor

Now that I'm fully awake, I realize that changing two masses each by a factor of 1/2000 changes their product (and the gravitational force between them) not by 1/4000000 (the square of 1/2000) but by about 1/1000 (2 * 1/2000). We can certainly detect that!

5. Dec 20, 2008

### jambaugh

The problem though is that while we may detect such a difference, the gravitational constant itself is determined by such measurements. The absence of electron-electron gravitational force would result in our using the "wrong" G value.

What would be required would be precise measurements of the gravitational acceleration for masses of distinct stable isotopes of some element, the lighter the better (say lithium-6 vs lithium-7). These will have distinct mass/electron-mass ratios and should if the hypothesis is correct accelerate at different rates.

6. Dec 20, 2008

### D H

Staff Emeritus
Now I'm going to have to disagree. Either the electrons contribute to the mass affected by gravity, or they do not. The contribution of electrons to gravitational effects won't just suddenly turn off. In other words, there is no baseline against which one can compare measurements. To experimentally determine whether electrons attract electrons gravitationally one will need to isolate the effects.

Doing this directly is going to be a challenge. The effect is just too small. However, both the weak and strong equivalence principle have been verified experimentally to an extremely high degree of precision. That the electron has a specific intrinsic mass has also been verified experimentally to a fairly high degree of precision. What rationale would lead someone to think that somehow electrons, which do have mass, do not contribute to gravitational attraction?

7. Dec 20, 2008

### Staff: Mentor

You're right. I was thinking that we can measure mass independently of gravity; but we can't measure G independently of gravity, so we have to eliminate G from the analysis by comparing substances with different percentages of electron-mass.

8. Dec 20, 2008

Staff Emeritus
Exactly.

First, trying to measure it directly between two electrons is hopeless, as the electrostatic repulsion is 10^40 times larger. But once can look for a composition dependent gravitational force, and one is not observed. Because these are looking at electrically neutral atoms, it's more sensitive to the difference in gravitational attraction of a neutron and a proton+electron combination than an electron and a proton.

9. Dec 21, 2008

### loup

So the conclusion is, we can measure the gravity between two electrons using the neutral atoms?

Is that there is gravity between two electrons already proved?

10. Dec 21, 2008

### Staff: Mentor

Well how 'bout the sun vs earth (Jupiter and Saturn too...)? Do electrons account for the same fraction of their mass?

11. Dec 21, 2008

Staff Emeritus
Russ, it's not quite so simple. We can look for composition-dependent gravitational anomalies, and these are very small: people have claimed a precision of 10-11. However, since everything is electrically neutral, all this really tells you is that the proton+electron combination has the same gravitational coupling as the neutron. One could imagine a slightly perverse model where the electron has no gravitational coupling and the proton's is just slightly larger than the neutrons, in just such a way as to appear that all three have the same coupling.

Fortunately, we have a handle on this: neutrons and protons have slightly different bindings in different nuclei, so they have slightly different contributions to the mass. So while my slightly perverse model would allow an accidental cancellation for a single proton/neutron mass ratio, it can't explain why this would work over a wide variety of nuclei. My guess is that this degrades the measurement by three or four orders of magnitude, and if one takes 10-8 or 10-8 as a typical sensitivity (rather than the best case of 10-11) it's probably the case that electrons are known to gravitate like everything else at the 10-5 or 10-6 level.

12. Dec 21, 2008

### D H

Staff Emeritus
And that perverse model would of course violate even the weak equivalence principle.

I intended to post some links regarding experimental verification of the equivalence principle in my prior post. Seeing that that post is devoid of references, some articles:

From http://physicsworld.com/cws/article/news/20870
Equivalence principle passes atomic test
Sebastian Fray and colleagues compared two isotopes of rubidium in the Earth's gravitational field. As expected the atoms accelerated at the same rate.​
Also see www.arXiv.org/abs/physics/0411052.

From http://physicsworld.com/cws/article/print/21148
Relativity at the centenary
Gravitational physics has become a truly experimental science as tests of the special and general theories of relativity reach new levels of precision.​

Those "new levels of precision" might make particle physicists suffer from 'gravitational physics envy'. From the article, "The bottom line of these experiments is that bodies fall with the same acceleration to a few parts in 1013."

Last edited by a moderator: Apr 24, 2017
13. Dec 21, 2008

Staff Emeritus
Of course it would. That's sort of the premise of this thread - could the weak equivalence principle be violated by electrons? (And the answer is "no" - or at least "not by anything larger than a miniscule amount)

10-13 is quite impressive.

14. Dec 22, 2008

### spaceboy033

Is it not enough to show that electrons participate in gravitational attraction, perhaps some simple F=qE=mg levitating electron in electric field Millikan-like experiment? You now know electrons feel gravity, so they should feel each other.

Directly measuring a single electron-electron gravitational interaction? hmmm