# Does energy cause gravity?

1. Sep 14, 2006

### Elfie

This may be a dumb question as I am no expert on this matters but curiosity compells me to ask anyway. Does energy have the same kind of bending effect on spacetime that causes gravity that matter does? Does the E=mc^2 make them interchangable in this regard also? If we implode the earth ripping apart every atom into energy, but contain this energy in the same amount of space that the mass of the earth used to occupy does the bending effect the earths mass used to have on spacetime remain the same? If the answer is yes -does this mean a massless particle can have a weight?

2. Sep 14, 2006

### WhyIsItSo

I'm a "new born" in relativity, so highly likely I'm wrong, but I'm going to guess "no", because gravity is a phenomenon of mass.

It'll be interesting to see how badly I get mauled on this one :)

3. Sep 14, 2006

### chroot

Staff Emeritus
Indeed, energy has gravity, too.

A box full of light -- bouncing between mirrors, for example -- weighs slightly more than a similar empty box.

The difference in weight is extremely small, but real.

In general relativity, a theory which describes gravity, energy and mass are actually lumped together into the same term in the equations.

- Warren

4. Sep 14, 2006

### michael879

as far as I know mass is just energy that "takes up" space. It is interchangable with energy using E=mc^2 because it is just energy.

5. Sep 14, 2006

### rbj

that's because all of them photons bouncing around in the box are massless.

6. Sep 15, 2006

### pervect

Staff Emeritus
I would say "in spite of" rather than "because of". In spite of the fact that the individual photons are massless, the box of photons weighs more than an empty box.

There are some subtle points here, the first point is that one cannot find the invariant mass of an object by summing up the invariant masses of the parts. Rather, one computes the total energy and total momentum of the parts, and uses the relativistic mass formula to compute the invariant mass from the total energy and momentum.

See for instance http://en.wikipedia.org/wiki/Mass_in_special_relativity#The_mass_of_composite_systems

There's also what I consider to be a good discussion of the mass of a box containing a relativistic gas (which includes a box of photons) in

http://en.wikipedia.org/wiki/Mass_i...simple_examples_of_mass_in_general_relativity

but I may be biased, because I wrote much of it.

7. Sep 15, 2006

### DaveC426913

Would it be safe to say though that, fiddling with the equation to get $$m=\frac{E}{c^2}$$, you need a pretty hefty amount of energy to get it to produce a significant amount of gravity?

Like, say, take all the energy in an optimally exploded nuclear bomb (20kt), and squish it all into an energy>matter converter, which spits out 6.2kg of matter. (Wiki)

6kg of matter doesn't create a whole lot of gravity.

Last edited: Sep 15, 2006
8. Sep 15, 2006

### pervect

Staff Emeritus
I get 20kt (explosive yield of energy) = 1 gram, not 6.2kg. Otherwise, yes, it does takes a lot of energy to cause even a small gravitational field (even more than your post indicates).

9. Sep 15, 2006

### michael879

yea but this would probably make a significant difference in something like the sun. How much mass do you think is just from the mass of the atoms that make up the sun?

10. Sep 15, 2006

### chroot

Staff Emeritus
The Sun is approximately in steady-state -- the same amount of energy generated in its core per unit time also escapes its surface in the same period of time.

As a result, the Sun is not like some "bank" of pure energy. Even for the Sun, the internal radiation has very little gravitational contribution, when compared to that of its matter. The energy "contained" in the Sun is actually contained in the form of massive particles -- hydrogen nuclei.

When the Sun fuses hydrogen nuclei together into helium nuclei, the resulting helium nucleus has less mass than the hydrogen nuclei used in its production. The "missing mass" is converted into heat and radiation.

- Warren

11. Sep 15, 2006

### DaveC426913

Your numbers are surely better than mine. I just did some fancy footwork with Wiki and a calculator.

12. Sep 15, 2006

### chroot

Staff Emeritus
13. Sep 15, 2006

### michael879

o comon it has to make some significant difference. How many fusion reactions are there per second in the sun?

14. Sep 15, 2006

### chroot

Staff Emeritus
Does it? Why? Because you say so?

Can you do your own calculation? It should be easy to look up the energy output of the Sun, as well as the energy liberated by one p-p chain reaction.

- Warren

15. Sep 15, 2006

### chroot

Staff Emeritus
michael879,

By my calculation, assuming the energy liberated in the core of the Sun takes about a million years to reach its surface, the Sun contains about 1.3 × 1023 kilograms' worth of radiation energy.

That sounds like a lot, except when you compare it with the total mass of the Sun, and realize it's only about 67 parts per billion.

- Warren

Last edited: Sep 15, 2006
16. Sep 15, 2006

### michael879

lol ok sorry, Im completely wrong.

17. Sep 16, 2006

### WhyIsItSo

I have to ask this *gulp*

Reading this thread, I cannot seem to avoid wondering, despite knowing this is against an accepted "truth" about photons, that photons have some phenomenaly small mass, but mass nevertheless.

I keep hearing people say mass is energy is mass; they are the same. Well, obviously they are not. The are convertible, but not the same.

Yet, if a photon is truly massless, how can it have weight? Ok, I follow to a limited extent the relativistic arguments regarding momentum (of energy?), but I do not find I can easily accept that this also leads to light being capable of producing any gravitational effects whatsoever.

...Unless it has mass of some finite amount.

Other than shooting me to put me out of my misery, can anyone help out with this seeming conundrum? And folks, throwing math at me isn't likely to help...

18. Sep 16, 2006

### pervect

Staff Emeritus
It's possible that light has a very small mass, but by defintion, if its small, it won't make any difference to any expeirment that you can perform, so it can't be used to explain anything. Basically you're just "stuck" on an untrue idea. I don't know how to get you "unstuck" unfortunately, basically that's something you have to do yourself.

19. Sep 16, 2006

### chroot

Staff Emeritus
Seems like the best way to get yourself out of it, WhyIsItSo, would be to learn general relativity. Once you understand the model -- and accept how well it agrees with experiment -- you'll understand why energy and mass are treated similarly.

- Warren

20. Sep 16, 2006