Does Rest Mass Affect the Bending of Spacetime?

[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 Earth's mass used to have on spacetime remain the same? If the answer is yes -does this mean a massless particle can have a weight?

 

[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 :)

 

[chroot]

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

 

[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.

 

[rbj]

Indeed, energy has gravity, too.

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

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

 

[pervect]

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.

 

[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. (http://en.wikipedia.org/wiki/Plutonium" )

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

 

[pervect]

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).

 

[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?

 

[chroot]

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

 

[DaveC426913]

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).

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

 

[chroot]

http://www.google.com/search?hl=en&lr=&q=1+gram+*+c^2+/+(4.184+*+10^12+joules)&btnG=Search

1 gram = ~20 kilotons of TNT.

- Warren

 

[michael879]

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

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

 

[chroot]

o comon it has to make some significant difference.

Does it? Why? Because you say so?

How many fusion reactions are there per second in the sun?

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

 

[chroot]

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.

http://www.google.com/search?hl=en&...ion+years)+/+c^2)+/+(mass+of+sun)&btnG=Search

- Warren

 

[michael879]

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.

http://www.google.com/search?hl=en&...ion+years)+/+c^2)+/+(mass+of+sun)&btnG=Search

- Warren

lol ok sorry, I am completely wrong.

 

[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...

 

[pervect]

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.

 

[chroot]

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

 

[selfAdjoint]

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...

Einstein's equations say that gravity is not only produced by mass, but also by momentum and energy. That's just a hard fact about GR. Photons have both momentum and energy in spite of not having any mass (as far as we know). So photons gravitate. You don't have to learn the whole theory of GR to learn that.

 

[WhyIsItSo]

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

Well, there's some progress. You said "similarly", not "the same".

As to your solution, well, in case you haven't noticed, I've been asking a lot of questions to just that end. I've been given a lot of links to online resources, and I read an reread those links.

I'm sure you'll agree that a genuine "understanding" of either theory doesn't happen overnight.

And there is a lot of math to learn too, and I really don't have much time to dedicate to all this just now. It is frustratingly slow.

In the meantime, I read, and read, and read... whenever I can, and that includes this forum. When I see something that's not making sense to me, I ask. A lot of folk seem pleased to share what they know.

Of course, many have little patience with teaching, and that's ok.

I'm very inquisitive, and that should be ok too...

 

[pmb_phy]

Does the E=mc^2 make them interchangable in this regard also?

The source of gravity is mass which is described completely by the stress-energy-momentum tensor. Suppose you were to ask what the (relativistic) mass density at a point P in spacetime was. The answer would not be energy density. It would be mass density ~ energy + (3 x pressure/c^2)

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 Earth's mass used to have on spacetime remain the same? If the answer is yes -does this mean a massless particle can have a weight?

for something to have weight there must be a way of supporting it in a gravitational field. With light this is not possible. Then again Pound & Rebbca entitled one of the famous articles on an experimental data. The title was "The weight of a photon." so there's that.

Pete

 

[pervect]

The source of gravity is mass which is described completely by the stress-energy-momentum tensor. Suppose you were to ask what the (relativistic) mass density at a point P in spacetime was. The answer would not be energy density. It would be mass density ~ energy + (3 x pressure/c^2)

Warning:

Pete's explanation above is true only in the static case and only with his personal defintion of mass density.

On the bogosity meter scale, with 0 being 'straight from the standard textbook' and 5 being utter garbage, it rates about a 2 - well intentioned, for the most part, and not totally wrong, but not quite right, either.

[add]
For a reputable source which says something similar to what Pete says, but without the bogosity ('relativistic mass density') check out http://math.ucr.edu/home/baez/einstein/

Note that in spite of this warning note Pete is unlikely to change his views (he's a stubborn old coot), but the naieve reader does need to be warned about Pete's non-standard views.

[add^2]
Pete's "relativistic mass tensor" is not in any textbook I've checked (MTW, Wald, Schutz), while the stress-energy tensor is from Einstein himself and is in all of the above textbooks. It (the relativistic mass tensor) seems to be Pete's own invention.

As far as I can follow it, Pete's idea seems to be based on the incorrect computation of the amount of momentum in a ball of fluid of rest density rho_0 and rest pressure P_0 moving at velocity v. This non-isolated system can be shown to have a total 3-momentum p of (rho_0+P_0/c^2)*gamma*v per unit 3-volume via applying a Lorentz transform to the standard stress-energy tensor, gamma = 1/sqrt(1-(v/c)^2).

Probably we shouldn't discuss it here in more detail, unless we get a peer-reviewed reference that actually uses this approach.

 

[michael879]

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.

this isn't true is it? If light had some small mass, it would mean it didnt travel at exactly c. I know that the reason they knew neturinos had mass was because they had a half-life (anything traveling at c can't decay because it doesn't experience time). Are there any particles that dont have some type halflife? If so, wouldn't the fact that photons don't spontaneously become other particles suggest that theyre massless?

 

[pervect]

this isn't true is it? If light had some small mass, it would mean it didnt travel at exactly c. I know that the reason they knew neturinos had mass was because they had a half-life (anything traveling at c can't decay because it doesn't experience time). Are there any particles that dont have some type halflife? If so, wouldn't the fact that photons don't spontaneously become other particles suggest that theyre massless?

Electrons don't have any half-life as far as anyone knows, and the decay of the proton has been hypothesized but so far not observed. So there are particles that don't spontaneously decay besides the photon, which is also not expected to decay or change.

The sort of oscillation test you describe is probably one of the most senstive indicators of mass, it even shows the tiny mass of the neutrino.

However, even this test will eventually fail to detect a small enough mass with finite observational periods.

For other, less sensitve tests, a nonzero rest mass will make even less difference, which was my main point. For instance, in the ultra-relativistic limit, if we had a gas in which 99% of the total energy was due to kinetic energy, 99% of the gravitational effect of the gas would be due to its kinetic energy, and only 1% would be due to the rest mass.