how can mass be converted into energy?

Question: how big is this "box", and what's it made out of?

 

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Before annihilation, the electron and positron each had .511 MeV of rest mass energy, which contributes to the total gravity produced by the box. After annihilation, your method was only measuring the difference in the momentum of two photons. Do you honestly think difference in measured momentum of the two photons will be 1.22 GeV of energy? The question is whether the 1.22 GeV energy of the two photons will contribute the same amount of gravity to the system total as when the energy was in the form of rest mass, the electron and the positron. Does rest mass and gravity reduce due to the annihilation even though total energy remains the same? If it does, E=Mc2 is not true when gravity is the property being measured.

 

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What?
The method simply measures the mass of the fox by seeing how hard the box is to accelerate. I note that that measurement is affected by the photons. I suspect, but haven't checked, that the difference will be the energy of the photons. I don't have time to do the sums.

And I haven't said a word about gravity, and don't intend to.

 

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You've missed an obvious objection to this thought experiment: if the box is small enough, there won't be any room for photons, so they won't be emitted. You'll have a potential or stationary state.

So this box is big enough for gamma photons to bounce around in? What's stopping them from producing a pair of particles?

 

"Obvious" perhaps, but wrong.

I did my Ph.D. using a Fabry Perot, FP, interferometer that had less than 1mm separation between the glass plates. I used an extended sodium lamp source to adjuste it (get the rings) which happen to be one I had used with a Mach-Zelnor (two separated paths with wave front division) year or so earlier to measure the length of the photons (When difference in length between the two paths exceeds the photon length there is no interference pattern as each photon interfers only with itself.) Those photons were about 30 cm long. Thus, when passing thru my FP interferometer to make the rings in transmission, the photons were folded back on themselfs at least 300 times.

Not important for the point I am making here, but just to tell why I used such a narrow gap FP:
I had a "shot noise" problem as I tried to measure the shape of lines coming from a dense transient plasma. I could thus not take high resolution slices of the line. Instead I had to "de-convolute" the line pass profile of the FP and use it in low resolution (for an FP) to avoid too much shot noise on my transient shock tube plasmas. To get low resolution out of a FP, the gap between the plates must be small. - why less than 1mm in my case. (My "spacers" were 3 tiny precision ball bearings that I slightly squeezed differentially as needed to make the plates parallel. The whole FP was inside a metal box with two windows - I adjusted the effective optical spacing to scan across the line profile by changing the pressure of the dry N2 inside the box. - The physical spacing remained constant. My plasms source was so higly reproducible that line intensity profiles vs time recored fell on top of each other form one shot to the next so each plasma gave a little part ot the line profile.

 

Hello Pete

Hehe, the photon bouncing off the back of the box will always have more momentum (smaller wavelength) than the photon bouncing off the front of the box (longer wavelength) as long as the box is in motion. Sounds like a good way to test for absolute motion.

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So there's an electron and a positron in this box, which isn't made out of anything in particular, but happens to be a perfectly reflecting surface, and it's an unknown size, but big enough for photons with a short wavelength?
Is it smaller than a planet? How about a toaster?

 

No that will not work if the speed is constant. - the effect on the cycles approaching the mirror is exaclty undone later when they are leaving. Only if the speed of the mirror is changing during the reflection (I.e. the mirror is accelerating) is there any net effect. There is no detector of "absolute motion" because "absolute motion" is a non-sense concept.

 

It is big enough for anylength photon - they do not mind folding up -read post 45's first paragraph. I have folded them more than 300 times back on themselves if you want to speak classically - I do not know what to say in a QM POV. Actually FP's have a characterization called "finesse" which is sort of the number of times the photon reflects with out losses and then starts to "pop out" of the FP. - Again this is a wrong classic POV. In that POV, I only folded them about 30 times (that was my FP's Fineses) and then the head was "poping out" on the far side while the tail section of the photon was still 90% yet to enter the FP.


Jame did not tell how the mirrors were made. I have been assuming they are non conductive dielectric multi layers like the anti-reflecting coating on a good camera lens but made to reflect as are the dielectric coating mirrors used with lasers.

If the mirrors are instead the inferior metal films then the story does change - read about the Casimir effect but it would need to be an extremely tiny box to not let an annhilation 0.511Mev gamma* fit inside and then the more realistic POV is that they just go thru the metal films and do not reflect at all - why I have tacitly been assuming dielectric mirrors. In principle they could reflect 0.511Mev gammas, I think.
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*It is not the 0.511Mev that makes them "short photons" but the fact that the electron/positron annhilation is so fast. - In the uncertainity principle this well defined time means the energy is ill defined, which means via Fourier analysis that there are not many cycles. or that the photons are short.

 

Hello Billy T

For any given frequency isn't the frequency seen by the mirror and hence reflected by the mirror solely dependent on the relative velocity between the source and the mirror?
Photon momentum is inversely proportional to the wave length of the photon. The wave length seen by the leading mirror is lengthened (red shifted) and the photon seen by the trailing mirror is shortened (blue shifted).

What equation describes this "exactly undone later" for mirrors?

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Mass and energy are the same thing. Your body is a swirling mass of electrons. Just another complex temporarily stable pattern in this freakish universe we've found ourselves inhabiting. Most of the matter in this universe is in the form of chaotic particles or plasma and that's what all mass will eventually end up as.

Nothing is permanent. Even the laws of physics aren't fixed. According to Steven Hawking we are living in a fluke state of affairs which won't last. If you think about it there are no real physical laws in this universe. There are always exceptions to these "laws" and that makes them invalid. At the quantum level the rules are completely different. At the macroscopic too when you meet singularities.

But we should be ok for a few trillion years. Hopefully.

 

I must go to bed so only read this and realized that you don't know that once the photon has left the source the source speed can do what it likes with no effect. The effect is only at the mirror during the reflection

by edit: think of it this way. (put your self on the mirror in its frame) The cycles (waves) yet to be reflected of the long string of cycles will be blue shifted in the frame of the mirror moving to met them. But those that are running away from the mirror in its frame are red shifted.

Hope that helps and I am not too sleepy to think straight. Good night.

 

Hello Billy T

Catch you tomorrow, but going by what you imply (if I understand it), if I take two spectroscopes and mount them back to back with one of them pointed at a source and the other pointed at a trailing mirror then there will be a difference between the two outputs of the spectroscopes that is proportional to the velocity of the assembly towards the light source.

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Here is an interesting link about the mass or lack thereof of light trapped in boxes:
Does light have mass

See also this section in the Wikipedia Photon article:
Contributions to the mass of a system

 

The cited article links to a cached version of the relativistic mass FAQ ("does mass change with velocity"). It's a good thing they link to a cached version: Somebody rewrote the usenet physics FAQ in favor of relativistic mass: http://math.ucr.edu/home/baez/physics/Relativity/SR/mass.html. Here is the old version: http://www2.corepower.com:8080/~relfaq/mass.html.

 

Thanks for the link. It states what my post 15 simple rule does, but here in their text below, which I made bold, there is a slight mistake, IMHO, but I may just be quibbling by pointing out that "thermal energy" is "kinetic energy" on an atomic scale summed up to a macro scale.

This is why I prefer my very simple rule:
"Energy is mass and makes gravity, IFF it is the same in all inertial frames."

From Pete's link above:
"... The definition of the invariant mass of an object is m = sqrt{E2/c4 - p2/c2}. By this definition a beam of light, is massless like the photons it is composed of. However, if light is trapped in a box with perfect mirrors so the photons are continually reflected back and forth in the box, then the total momentum is zero in the boxes frame of reference but the energy is not. Therefore the light adds a small contribution to the mass of the box. ... Relativistic mass is equivalent to energy so it is a redundant concept. In the modern view mass is not equivalent to energy. {Billy T insert: I agree 100% with that sentence as stated earlier.} It is just that part of the energy of a body which is not kinetic energy. Mass is independent of velocity whereas energy is not. ..."

But as an "old timer" I still like my "relativistic mass" when speaking about cyclotrons for reasons stated earlier (post 31) also. When I and a few others like me are gone, then Physic can get rid of "relativistic mass" entirely - As they say: "Phyiscs advance a little with the death of each physicist."

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Lets say we take Billy T and we take Billy T into a plasma chamber, we can convert all of Billy T's mass into plasma and thus energy...

 

That's just nasty. Who is Don Koks, and does John Baez know of this butchery?

 

I'll vote for that IFF Billy T has been dead for a day or if not conscious for a month. {I have instructed my childern how convert the second condition into the first, with no fear of being detected, but they do not want to talk about it. It is a minor conflict but I do not want what I have saved to go to keeping an unconscious body alive, when it could help my grand children etc.}

 

I just got around to reading this link. It states following, which in part I made bold, I think*, is "flat out wrong" but that is not rare in wiki from my limited experience with it.

From Pete's Wiki link:
"... Since photons contribute to the stress-energy tensor, they exert a gravitational attraction on other objects, according to the theory of general relativity. Conversely, photons are themselves affected by gravity; their normally straight trajectories may be bent by warped spacetime, as in gravitational lensing, and their frequencies may be lowered by moving to a higher gravitational potential, as in the Pound-Rebka experiment. ..."

That fails to distinguish between trapped photons and free ones. (Except for part I made bold, it is true, or at least a "defendable POV," for the free ones only, as your first link and my simple rule state.) Also, while it is true in simple POV that gravity "bends LIGHT PATHS, I think light only travels in straight lines in a vacuum, as even a definition of what is "straight" - I.e. the short in time path - the least "action" principle of physics, etc.**
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*Part of reason I think this is that the starry heavens look the same to both my eyes. If freely traveling photons made gravity and were attracted to each other by it, then the rays from very distant (many light years) "point sources," headed in a towards my up-turned face would have coalesced into very fine filaments during their long trip to me. Certainly these filaments would have diameters small compared to the space between my eyes. Thus the heavens seen by my right eye would differ from the heavens seen by my left eye. Last time I looked this was not the case.

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**Reason I take this POV is that if I were to allow that masses like the sun were exerting a gravitational force on photons (instead of "warping space") to actually bend their trajectories from the straight line (impossible with my POV as the vacuum path of them defines the straight line) then I would either need to admit that the free traveling photons do make gravity (to exert a "equal and opposite" force on the sun), or abandon Newton's 3 law. (I'd join him in his grave before doing that. -Too many "free lunches" if that is not true, like self accleration rocket that only throws mass around inside etc.)