Balance of Forces - Electrostatic Force vs. Gravitational Force

1. Sep 25, 2010

TheSicilianSa

Assume that you have two protons accelerated in opposite directions within a cyclotron. As they approach the speed of light their masses increase. At what proportion of the speed of light will their gravitational attraction (due to their increased mass) equal their electrostatic repulsion ?

2. Sep 25, 2010

ZapperZ

Staff Emeritus
Back up a bit.

Can you show, first of all, the physics where the gravitational force from a body is a function of the "relativistic mass" rather than the invariant mass?

Zz.

3. Sep 25, 2010

Drakkith

Staff Emeritus
I found this reference off of wikipedia's page on Mass in General Relativity.

http://arxiv.org/PS_cache/gr-qc/pdf/9909/9909014v1.pdf

He states at the end that: "We can thus tell our students with confidence that kinetic energy has weight, not just as a theoretical expectation, but as an experimental fact." (In the framework of general relativity)

4. Sep 25, 2010

ZapperZ

Staff Emeritus
You should not simply quote passages without understanding the physics here.

I can do even better. I can show you how, in many condensed matter system, the effective mass can increase 200 times the bare mass. Does this mean that these quasiparticles how have larger gravity?

The issue isn't that KE has a "weight" equivalent. The issue is to show a direct connection between such "relativistic mass" and gravity.

Zz.

5. Sep 25, 2010

TheSicilianSa

- Let's assume that this question were the bases for an experiment to show whether or not gravity was a function of "relativistic mass" - what would be the answer ?

6. Sep 25, 2010

pervect

Staff Emeritus
If you believe Olson, D.W.; Guarino, R. C. (1985). ""Measuring the active gravitational mass of a moving object"". American Journal of Physics 53: 661, it increases even faster than that, if you use a "flyby" approach to measure the mass. Which seems to be what you're doing. http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=AJPIAS000053000007000661000001&idtype=cvips&gifs=yes&ref=no" [Broken]

It's not terribly clear what happens if you have two oppositely moving massive objects - the paper above doesn't analyze that case. It's also unfortunately not readily available.

However, it's really incorrect to think of mass as generating gravity in general relativity. Mass is what generates gravity in Newtonian theory. In GR, gravity is generated not by mass, but by the stress-energy tensor.

It's also interesting to note that both the gravitational field (to the extent that that can be defined) and the electric field of an ultra-relativistic particle will be an "impulsive plane wave". See

"Aichelburg-Sexl boost of an isolated source in general relativity", Phys. Rev. D 64, 044022 (2001)

This on is on arxiv http://arxiv.org/abs/gr-qc/0110032

Most people don't seem to be familiar with the electromagnetic result, and naively expect radial symmetry.

Last edited by a moderator: May 4, 2017
7. Sep 25, 2010

Drakkith

Staff Emeritus
Perhaps you could explain to me why something that has more weight due to kinetic energy doesn't show a relation between relativistic mass and gravity? I thought it made sense, but I guess I was wrong.

8. Sep 25, 2010

ZapperZ

Staff Emeritus
This is because the concept of "relativistic mass" is misleading. There are considerable effort to not evoke such a term, because it leads to faulty ideas exactly as demonstrated in the original question. For example, why can't the energy in motion (KE) be lumped into the momentum part of the energy equation, rather than to the mass? After all,

$$E^2 = (pc)^2 + (mc^2)^2$$.

Lev Okun has written a very good paper on this issue. See L.B. Okun Am. J. Phys. v.77, p.430 (2009). In fact, there are historical account that even Einstein stopped using the term "relativistic mass" after 1906. See, for example, E. Hecht, Am. J. Phys. v.77, p.799 (2009).

So again, where exactly is the "relativistic mass" comes into play in the physics that connects it to "gravitational field"?

Zz.

9. Sep 25, 2010

ZapperZ

Staff Emeritus
Then you might as well ask if pain would cause rain.

Zz.

10. Sep 25, 2010

TheSicilianSa

If you can't answer the question, simply say so.
I'll make the question simpler for you: How massive would a two protons have to be so that it their attractive froce due to gravity would cancel the repulsive force between them ?

Last edited: Sep 25, 2010
11. Sep 25, 2010

Naty1

I don't want to butt in on the original post, but why not just change the question from

to
This begins to maybe better address what I think the OP was addressing(??) :

.

So mass (invariant if you wish), energy, and pressure....affect gravitational attraction....the curvature of spacetime.....I'd be interested to know if the answer depends on separation....distance between the charges....Newtonian gravity and electrostatic forces vary as 1/r2 but relativistically things may get more complicated...as spaceTIME is involved????

12. Sep 25, 2010

ZapperZ

Staff Emeritus
One cannot answer a question based on a false premise. That was what I was trying to illustrate.

If you simply put two identical masses with mass m separated at a distance r, with a Coulombic repulsive force, then this becomes a simple first year intro physics problem, does it not? Simply vary m until both the Coulombic forces and the gravitational forces cancels out. But this is no longer a "relativity" question, but rather belongs in the Classical Physics forum.

Zz.

13. Sep 25, 2010

TheSicilianSa

So, if it's so elementary, what's the answer ? - in kgs.

14. Sep 25, 2010

ZapperZ

Staff Emeritus
$$\frac{kq^2}{r^2}=\frac{Gm^2}{r^2}$$

Work that one out yourself. At some point, the spoon-feeding has to stop, and we have reached that point.

Zz.

15. Sep 25, 2010

TheSicilianSa

Just as I thought.
And before you go off on a diatribe about relativity, I suggest that you first define the difference between mass and inertia. - And where did you think that the measured mass comes from ? - pixie dust?

16. Sep 25, 2010

Staff: Mentor

That remains one of the big unsolved questions in modern physics.

However that is not really relevant to the question at hand. ZapperZ and pervect have made the key points. You cannot get a relativistic theory of gravity simply by plugging relativistic mass into Newtonian gravity equations. Mass (whether relativistic or invariant) is not the source of gravity in GR, the stress-energy tensor is. Only one component of 10 is the energy, and if you have relativistically moving particles then several of the other 10 become significant.

Last edited: Sep 25, 2010
17. Sep 25, 2010

ZapperZ

Staff Emeritus
Measured "mass" is different between "invariant mass" and "relativistic mass". Many things are based on the invariant mass. That is why I asked you what physics are you using to claim that relativistic mass generates the SAME type of gravitational effects as invariant mass. I mean, if you are DEAD SURE that the effect is the same, then I'd appreciate a reference to the actual physics.

Again, I cited the example of effective mass that's measured in condensed matter system (which, btw, is analogous the the Higgs mechanism!). There are zero claims that such a mass increase corresponds to an increase in gravitational field!

Zz.

18. Sep 25, 2010

pervect

Staff Emeritus
One of the other things that would need to be analyzed to answer the question properly are the magnetic effects. The counter-rotating beams will certainly have magnetic forces between them as well as the coulomb forces. So, you'll have an increased electromagnetic repulsive force over what you'd expect if you ignore the magnetic forces.

Something similar will happen with gravity as well - we can say this with some confidence because it's known that the coulomb force law is not Lorentz invariant. We have some experimental evidence for the reality of these effects now that gravity probe B has confirmed frame-dragging, another name for the same effect. I'd have to think about the sign of the gravitational effect though.

Last edited: Sep 25, 2010
19. Sep 26, 2010

Naty1

Dalespam posted
which is a much nicer way of explaining what I was at the end of my post #11....

kq2/r2 = Gm2/r2....can't be right can it??? surely a relativistic approach is required here isn't it???