# The influence of Gravity on particles

• B
• Fadicando
In summary, gravity has a minimal influence on an electron beam due to the small mass of the electron. This is demonstrated by the cancellation of the mass term in the equation for acceleration. However, in extreme gravitational fields, such as on the surface of a neutron star, the effects of gravity cannot be neglected. In these cases, a quantum-mechanical treatment is necessary to accurately describe the particles' behavior. f

#### Fadicando

How does gravity influence an electron beam? And how does it influence the other particles?

It makes it go down. Just like everything else.

mfb
It makes it go down. Just like everything else.

But how it happens mathematically? Because I thought that as the mass of the electrons is insignificant, the influence of gravity wouldn't do any difference.

Fadicando said:
I thought that as the mass of the electrons is insignificant, the influence of gravity wouldn't do any difference.
Have you studied Galileo's Leaning Tower of Pisa experiment? If so, what does it teach us?

Electrons don't feel a large force but they also don't have much mass that would need large forces.

Anyway: For realistic setups other forces on the electrons are far larger. Gravity is always negligible. You can calculate the electric field strength needed to provide a force as large as gravity.

But how it happens mathematically? Because I thought that as the mass of the electrons is insignificant, the influence of gravity wouldn't do any difference.
Do you understand the difference between "a very small amount" and "none" ?

But how it happens mathematically? Because I thought that as the mass of the electrons is insignificant, the influence of gravity wouldn't do any difference.

The force is very, very small, but so is the mass of the electron. If you look at the equation for acceleration, ##A=F/M## and put the equation for gravitational force in for ##F##, you'll find that the mass cancels out entirely. The acceleration of the smaller object is independent of its mass.

lomidrevo, Fadicando and Kremmellin
The force is very, very small, but so is the mass of the electron. If you look at the equation for acceleration, ##A=F/M## and put the equation for gravitational force in for ##F##, you'll find that the mass cancels out entirely. The acceleration of the smaller object is independent of its mass.

Thank u so much!

How does gravity influence an electron beam? And how does it influence the other particles?

It depends on the strength of gravitational field where you observe the particles. Physicists living here on the Earth's surface can safely neglect any gravitational influence on particles in their colliders. However, hypothetical physicist, let's say living on a surface of a neutron star (*) couldn't afford such luxury, ie. to neglect effects due to gravity.

(*) please ignore for while that such hypothetical beings couldn't survive in such conditions ;-)

If you mean particles in the gravitational field around the Earth a non-relativistic treatment is sufficient. Of course if you deal with single particles a quantum-mechanical treatment is more appropriate than a classical treatment. The most accurate test that the standard quantum mechanical treatment for particles in the homogeneous gravitational field of the Earth (i.e., the usual "free-fall setup") leads to the correct result to my knowledge is a measurement on neutrons subject to the gravitational field of the Earth and a "horizontal mirror on the bottom":

https://www.nature.com/articles/415297a

https://journals.aps.org/prd/abstract/10.1103/PhysRevD.67.102002
https://arxiv.org/abs/hep-ph/0306198

lomidrevo