# Proton falling into a Black hole?

1. Jun 28, 2011

### cragar

I don't know if this is the right place to post this but would a proton falling into a black hole experience tidal forces. If the proton is like a wave could we stretch the wave out, that is probably really bad wording. Or does the quantum of energy move all together?

2. Jun 28, 2011

### bcrowell

Staff Emeritus
A proton is a composite object with quarks inside, and the proton has a size, about 1 fm=10^-15 m, which is essentially the typical distance between the quarks. In the frame of an observer hovering just outside the event horizon, the proton falls past at a velocity close to c, so that the de Broglie wavelength corresponding to its center-of-mass momentum is very short -- much shorter than the size of the proton itself. In a frame comoving with the proton, its de Broglie wavelength is infinite. Because a proton has a finite size, it would certainly experience tidal forces that would tend to distort its shape, i.e., cause the correlations among the quarks to change, probably giving it an ellipsoidal shape. However, tidal forces have less effect on smaller objects, and a proton is very small, so I think for any astrophysical black hole the effect would be much too small to measure.

3. Jun 28, 2011

### WannabeNewton

How would you quantify this tidal force in the framework of classical GR if at all since the equation of geodesic deviation is proportional to the four - velocity which is undefined for a photon?

EDIT: yeah...nevermind

Last edited: Jun 28, 2011
4. Jun 28, 2011

### PAllen

5. Jun 28, 2011

### WannabeNewton

Wow thats embarrassing. I read it as photon. Thats what happens when I don't drink coffee.

6. Jun 28, 2011

### cragar

No but it would be interesting to consider tidal forces on a photon.
@ bcrowell, How can you tell me a proton has a finite size if its wave.
If we can I would like to discuss how the tidal forces would effect the photon.

7. Jun 28, 2011

### bcrowell

Staff Emeritus
Mm...what's your level of background in quantum mechanics?

8. Jun 28, 2011

### cragar

I have self taught myself a little bit about QM out of Griffiths . I know what a momentum operator is, Quantum harmonic oscillator . Spin matrices . But still a very elementary understanding of it. But I know a little bit.

9. Jun 28, 2011

### bcrowell

Staff Emeritus
OK, that's plenty. The idea is that if you want to describe an n-body system in one dimension, you need n coordinates. Those coordinates don't have to be just the x coordinates of each particle. For example, if your system consists of three quarks, A, B, and C, then you might want to take one coordinate to be the position X of the center of mass, one to be xA, and the third to be xB. The advantage is that the behavior of X is fixed trivially by conservation of momentum, so that simplifies the problem. The wavefunction in terms of X is simply a sine wave. The momentum P associated with X is the momentum associated with the center of mass motion.

So for example if you ask why an elephant doesn't have observable wave properties, the answer is that P is on the order of 103 in SI units, so the wavelength is on the order of 10-33 meters. The wavelength is a gazillion times smaller than the elephant itself.

10. Jun 28, 2011

### cragar

ok , thanks for explaining that .

11. Jun 28, 2011

### bcrowell

Staff Emeritus
I thought a little more about the photon version, and I don't think it makes sense to analyze that one in terms of tidal stresses. It's not a bound system that can have internal stresses. And whereas in the case of the proton there is a natural frame of reference in which to measure its elongation (the comoving frame), there is no comoving frame in the case of the photon.

I think this is similar to a contrast that comes up in the case of cosmological redshifts. Photon wave-trains lengthen over cosmological time, and this can be interpreted in terms of the expansion of space itself as they travel through it. But protons, solar systems, etc., do not undergo any significant cosmological expansion.

Last edited: Jun 28, 2011