# The mass of sunlight

1. Aug 31, 2010

### RenasontsMan

Thought experiment:

Our sun burns hydrogen at a prodigious rate, billions of kilograms per second.

Let m = the mass of the sun at t=0.

Inside the imaginary sphere expanding exactly with the velocity of light emanating from the sun, the total mass cannot change.

After sixty seconds, the amount of mass lost by the sun is 60 x 6.3x10^11th kilograms, or
3.78 x 10^13th kilograms. This is the precise mass of the sunlight contained in the sphere surrounding the sun which is 60 light seconds larger than the sun, but excludes the sun itself.

It is often claimed with a presumption of scientific authority that light has "no rest mass," but light is never "at rest." You may slow it down, but stopping light converts it into something that is no longer light.

Anyone wish to claim that 3.78 x 10^13 kilograms of mass has vanished into photons, and is now weightless?

I don't see this happening.

This thought experiment is quite similar to the compelling argument that when you burn combustible materials inside a sealed chamber, the total mass of the chamber does not change, i.e. it doesn't become "lighter" because the wood, paper, or other material consumed has oxidized into ash.

2. Aug 31, 2010

### Staff: Mentor

Sure it can. After 8 minutes you would expect it to suddenly increase by the mass of the earth. You need to introduce the concept of mass flux across your boundary.

I would talk about the mass flux across a single stationary surface, but yes that is the mass of the sunlight.

A photon is indeed massless. A system of two or more photons has mass (unless the photons in the system all have the exact same momentum).

3. Aug 31, 2010

### pallidin

Uh, that's not possible. Expanding mass can not do that.

4. Sep 1, 2010

### RenasontsMan

Uh, pay attention.
This is a THOUGHT experiment

See, nobody can begin to build a shell that happens to be just beyond the sun.

We'd like run out of whatever you wish to use to build it.
Secondly, it would already be vaporized.
Thirdly, it could not expand AT ALL, much less at c.

So, uh, none of this is "possible." That's why I said "THOUGHT" experiment.

5. Sep 1, 2010

The trouble is that this thought experiment is non-physical and is thus not useful. Sometimes you can invent a hypothetical situation and gleam useful information out of it. But if you invent a non-physical, impossible thought experiment then you can conclude absolutely nothing from it.

As for the topic, remember that the sun puts out more than just light - it puts out massive particles as well. Also, alot of mass is converted into light. I believe that most of the lost mass is converted to light, but Im not sure what the ratio really is.

6. Sep 1, 2010

### martix

Here's a thought:
E=mc2

Which means - yes, the mass has vanished and is now all energy in the form of weightless photons. So I claim that to be true.

Next thing... furnace example - what part of that process involves any sort of change in binding energy? Mind that it is very different from bond energy. One is related to the strong nuclear force, the other to the weak nuclear force.

Just for information, fusion of H-Fe releases energy, fusion of Co and heavier requires energy, vice versa for fission.

7. Sep 2, 2010

### RenasontsMan

Perhaps you have heard of Albert Einstein? He originated his work with precisely such thought experiments.

Perhaps YOU "gleam" absolutely nothing from it, but others here are a bit more thoughtful and creative than that.

The massive particles are contained in the IMAGINARY, expanding sphere. So the thought experiment remains entirely valid and quite useful.

8. Sep 2, 2010

### the_house

I don't know, I think sometimes these questions can be useful for better understanding special relativity.

Imagine an object like the sun, except it only loses energy by radiating light (i.e., photons). When you understand exactly how all of the following statements are true, you will have a better understanding of relativity.

1) If you consider the total system of the sun plus any photons it emits as a single system, and assign it a mass, it will be exactly the same before and after the photons are emitted (although I'm not sure it's ever really useful to consider all of it as a single object)

2) The mass of the sun by itself is smaller after it has emitted radiation.

3) Each single photon has zero (rest) mass.

4) This is all related to the "equivalence" of mass and energy, but can be confusing since

5) A single photon has non-zero energy and momentum (yet number 3 is true at the same time).

6) All of this is very well-defined and consistent, even if there seem to be contradictions.

9. Sep 2, 2010

### Staff: Mentor

The proper term for what most introductory treatments of relativity call "rest mass" is "invariant mass." It's defined by the equation $E^2 = (pc)^2 + (mc^2)^2$. For light, E = pc (this is true in classical electrodynamics, too, by the way, where there is no notion of photons) which makes m = 0.

The invariant mass of the system of sun plus photons can be calculated using the equation I gave above, using the total energy and the total momentum of the sun and the photons it has emitted. It is the same as the invariant mass of the sun before emitting the photons.

If you prefer to think in terms of "relativistic mass", then you have to assign each photon a mass equal to $E/c^2$. Energy is conserved, so the "relativistic mass" of the system of sun plus photons after emission equals the "relativistic mass" of the sun before emission.

So, no matter which definition of "mass" you use, its value for the system is conserved or invariant (same before and after emission).

The difference between invariant mass and "relativistic mass" is that in general, the invariant mass of a system does not equal the sum of the invariant masses of the particles that it contains.

10. Sep 2, 2010

### TheRealTL

The problem with this thought experiment comes with some people will try to understand it using math and some with physics. By definition light has no mass. Problem solved.

However, you must ask yourself what actually happens in the process of converting mass into a lightWAVE. What effect is gravity having on the massive system relative the observation of the system. You are absolutely right that the light is still part of the measurable system.

Without being too insightful. I would point out that mass is one way of observing time, a light wave is another as relativity was attempting to teach us. Remember how a system is observed changes with how it is being dilated. Gravity in this case is dilating the system and changing your observation.

And never stop posing questions like this. Dumb or smart is something people with egos worry about, questions are something physicists never stop asking.

11. Sep 2, 2010

### RenasontsMan

Definitions are constructs of human beings.
Human beings are fallible.
I seem to recall Albert Einstein lecturing George LeMaitre on LeMaitre's Primordial Atom
theory. Said Einstein, "Your math is correct but your physics is abominable."

Einstein, and virtually the entire world community of scientists, were all wrong.
They had an ax to grind. They didn't want the universe to have a beginning. Alas it did.
They were wrong from the get-go.

There is no "problem" with respect to my thought experiment. I merely attempted to show how illogical it is to pretend that trillions of tons of mass simple evaporate because of some "definition" as you cite.

The countless stars of the universe continue to burn out, losing mass.
Likewise, the universe is dying a heat death. We must conclude that in the process of losing heat AND mass simultaneously, energy and mass are NOT conserved at all.

12. Sep 2, 2010

### RonL

With that said and the mention of E=mc2, a question (thought experiment) popped into my head as I am trying to develop a full understanding of the Carnot Cycle, the lowest limit of Zero degrees is stated to be impossible to reach, but I don't see an upper limit of pressure and temperature stated to be impossible, so my mind cannot yet grasp the restrictions between Max Carnot efficiency and 100%.
Since we are in thought mode and anything is possible and our parts can be indestructible, lets build a perfect cylinder, sealed at the bottom and a perfect piston in full contact (nothing between) with that bottom, then would the full energy of E=mc2 if possible to apply, be able to pull the piston away and form a below zero condition (a sub atomic vacuum) ?

I hope this is not too far removed from the OP.

Ron

13. Sep 2, 2010

### the_house

If that was your goal, then indeed it was not a useful thought experiment. Special relativity is not in any way illogical and requires no "pretending". It is completely internally consistent, and moreover is extremely well tested. I had assumed your goal was to better understand the theory, which can certainly appear contradictory if you only have a partial understanding.

In fact that is not the correct conclusion. There is no conflict with local conservation of energy and momentum, while we know that mass is most certainly not conserved. If you are interested in better understanding why, this forum can probably help you, but that does not appear to be the case at the moment.

14. Sep 2, 2010

### Staff: Mentor

Can you provide an example of this? The sun is certainly not an example as I pointed out above.

The four-momentum of a system is conserved and therefore energy (timelike component), momentum (spacelike component) and mass (Minkowski norm) are all conserved. Please see the comments above by myself and jtbell.

15. Sep 2, 2010

### TheRealTL

I was supporting your assertion. The math we currently use doesn't describe the total of the physics that is going on in any give system. You seem to be a little too excited, because I just described to you that there may be a link between mass and a wave of energy. That they in fact are not different, but the same thing with only the observation being the variable.

"Einstein, and virtually the entire world community of scientists, were all wrong.
They had an ax to grind. They didn't want the universe to have a beginning. Alas it did.
They were wrong from the get-go.
"

This is a textbook example of defining something. As far as anyone is concerned the universe began when you were born. The very act of attempting to define the beginning of the universe as you see it only seeks to take away from the reality. Attempting to define the undefinable is a Fools' Errand.

16. Sep 2, 2010