# Mid physics crisis

1. Apr 3, 2005

### T@P

i kinda lost 'faith' in gravity. can you clear this up?

supposedin you take two point masses, m1 and m2. the attraction between them is Gm1m2/r^2, right?

now what happens when r goes to 0? does the attraction really go to 0? that would mean that when two anythings get really close, you cant pull them apart because the *gravitational* force is almost infinite. where did i go wrong? (oh and same with point charges, the other similar law)

thanks

2. Apr 3, 2005

### Icebreaker

Theoretically, yes. But for all practical purposes, r will never reach zero.

3. Apr 3, 2005

### locke

Uncertainty principle would forbid this from happening. If you had some way of knowing the particles had 0 seperation, they would then need infinite momentum.

4. Apr 3, 2005

### Integral

Staff Emeritus
That formula can only be applied when the 2 objects are a good approximations to a point. This means that r must be large with respect to any dimension of either of the bodies. If this is not the case you must use other methods to compute the gravitational force.

5. Apr 3, 2005

### Danger

Gravity is measured from the centres of the masses involved. For the separation to be '0', they would have to be superposed. The Pauli exclusion principle would have something to say about that.

6. Apr 3, 2005

### gijsbert2002

My classical mechanics teacher put it this way: "The r is an arbitrary unit and must have a length of a minimum of one." In essence it is only valid if r is larger than one in any unit. That means that it is possible to be as small as anything, because you can choose your unit freely, but it can't be zero.

7. Apr 4, 2005

### Andrew Mason

What you describe would occur if the mass were concentrated in a volume smaller than the Schwarzschild radius:

$$R_{Schwarzschild} = \frac{2GM}{c^2}$$

This would be a black hole, and the gravitational attraction would indeed be almost infinite. But for normal matter, you just can't get those kinds of densities so you never have that much matter that close together.

AM

8. Apr 4, 2005

### T@P

oh so it does go to infinity but it cant happen because its not an ideal 'point mass'... i see
I suppose nothing like this can happen with two opposite charges, because once they touch they neutralize...
also, is there anything that gravity cant affect? like i heard somewhere that even light bends near the sun (massive object). is there anything it wont touch?

9. Apr 4, 2005

### Danger

Gravity doesn't exactly bend light. The light is going in what is to itself a straight line. The space that it's moving through is distorted, though, so an outside observer sees it as bending. It's roughly equivalent to you walking 'straight' home from school. To you it's straight; to someone in orbit you're following the curvature of the Earth.

10. Apr 4, 2005

### Galileo

The answers to the question posted in this thread still do not tell us how classical mechanics solves this problem. Newton knew nothing of Heisenberg, Pauli or black holes.
He did make a remark on this, but I can't remember .

11. Apr 4, 2005

### dextercioby

Coulomb force and gravity force have the same mathematical structure and both have a singularity at zero distance.While for the Coulomb potential this matter is dealt with by QED and its renormalization,unfortunately/fortunately this thing has not been done with gravity (namely graviton loops (unlike gluon ones) are not renormalizable).

Daniel.

12. Apr 4, 2005

### Andrew Mason

Classically it can be done with electric charges because the electron is treated as a point charge. The issue arises with an electron and a positron. The energy released (or work done by) by a positron and electron moving closer to each other keeps increasing - but only to a point. One can never get an electron and a positron arbitrarily close to each other. They both annihilate due to weak interaction at a finite distance.

But mass is a different story. There is no such thing as a point mass, so you cannot put one mass arbitrarily close to another. So the energy is limited - they don't have to destroy each other in order to avoid infinite energy being released.

AM

13. Apr 5, 2005

### T@P

seems a pity that the gravitational force cant go to infinity, it would be so much easier for things to stay in place :)

actually, doesnt this have any influence in the 'debate' over wether space is continuous or just made up of a bunch of little pieces? it seems that since you cant have two object be with distance 0 from their center of masses, then maybe space is not continuous? just a thought.

14. Apr 5, 2005

### Andrew Mason

The smallest particle with rest mass (apart, perhaps, from a neutrino) is the electron. The smallest meaningful size would be its Schwartzschild radius, which is $2Gm_e/c^2$. That works out to:

$$2Gm_e/c^2 = 2*6.67 \times 10^{-11}9.1\times 10^{-31}/9\times 10^16 = 1.35\times 10^{-56}$$m.

Unfortunately, you can't get two electron masses that close (eg. positron and electron) so we can't tell what would happen if you could.

AM

15. Apr 6, 2005

### T@P

:( i feel sad now. oh well, i guess lunch will cheer me up