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Conservation Laws 
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#1
May608, 12:06 AM

P: 4,512

Place equal amounts of matter and anitmatter in a box on a scale. It's a very good box; it's very reflective, and light doesn't get in or out. Allow all the stuff to annihilate to photons. The box floats away. Has a conservation law been violated?



#2
May608, 01:04 AM

P: 277

No, for lots of reasons.
First and foremost, the box will not float away. Oddly enough, although light is "massless," energy is not. To my understanding, if the energy is perfectly contained inside the box  then the box overall will still be massive and weighted down. Now, even if i'm wrong on that account > there is no such thing as conservation of mass (or gravity etc). So if the box does float away, then energy would still be conserved. Can anyone comment on the massivity of the box after annihilations? 


#3
May608, 04:20 AM

Sci Advisor
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#4
May608, 08:30 AM

P: 2,954

Conservation Laws
As far as the massivity of the box after annihilations, the mass is constant since the total mass will be the sum of the (relativistic/inertial) mass of each particle of the system. Since the energy of the system does not change then neither will the systems mass change. This holds even if you intrpret "mass" to mean "rest mass" since "rest mass" of a sytem equals "the systems energy as measured in the zero momentum frame"/c^{2}. Since energy and momentum is conserved then so too is the rest mass. Pete 


#5
May608, 08:46 AM

P: 92

lol First, after annilhilation, some will form back into matter and antimatter. After a while, it will establish equilibrium(like a chemical) with lights and matters. Lights and mass are different. Lights and mass are energy of different form. In my opinion, it will have less weight. It's contradicting to say that that box of heat weight the same as a box of mass (assuming heat and mass amount are equal in term of energy). It's like one have temperature and weight and one have only weight. It's unfair. :)
The question is it violate the conservation? I don't think it is. It's just like a helium ballon floating in air (assuming that initally box+matter density = surrounding gas density). Now one may ask but floating away means that's extra energy, where is it come from? I'm not sure. Use the helium ballon example on this one. I know that once it go out to vaccum, it's at constant speed and constant speed doesn't require any energy. 


#6
May608, 11:45 AM

P: 277

pmb_phy; you're a little off. Conservation of mass does not hold (look it up). It hasn't since SR and QM. Especially the rest mass, is not going to be the same. Very clearly.
Also, the collisions of the photons with the walls will be boltzmann like, and randomly distributed > therefore not exerting any net force in any direction (also necessitated by conservation of momentum  which is an actual conservation). Gravitational redshift is also going to have absolutely no appreciable effect (try looking at a flashlight pointed away from earth vs towards the earth). 


#7
May608, 11:55 AM

P: 869

If the box were truly perfectly sealed from emitting radiation (obviously impossible) then the mass of the box would be indistinguishable after the m/aam reaciton.



#8
May608, 01:04 PM

P: 3,967

[tex](Rest Mass Energy)^2 = (Total Energy)^2(Momentum Energy)^2[/tex]. In the example of the box containing matter and anti matter assume the initial momentum is zero. After anhilation the total momentum is still zero. Each anhilation pair creates a pair of photons moving in opposite directions conserving the (zero) momentum. The total energy of the system remains the same (No free lunch theorem). Therfore the rest mass of the box system remains the same before and after the anhilation process and therefore the created photons have rest mass when considered as a total system rather than individually. Mass, energy and momentum for a system is always conserved individually over time in the rest frame of the system, as long as the system is closed. Mass, energy and momentum are not conservered individually under transformation to a different reference frame but the energymomentum relationship of a system is conserved under transformation. Sometimes the relationship is complicated a little bit by pressure adding an effective mass component and tension providing a negative component according to the stressenergy tensor but overall, as far as I am aware, there are conservation rules that regulate the universe even in post Newtonian physics. 


#9
May608, 01:27 PM

P: 277

I dig kev; but i feel like mass is variant even in a nonrest reference frame (even without a transformation to that reference frame). At the same time, even though energy is always equivalent to mass  and energy is always conserved; there isn't always energy in mass form. Does that make any sense?



#10
May608, 02:49 PM

P: 3,967




#11
May608, 10:11 PM

P: 4,512

So if both 1)the box floats away and 2) the reaction is thermodynamically reversible, then the Earth and the box system imply a perpetual motion machine as the box would do work as it drops when containing the matter and antimatter. 


#12
May708, 06:22 AM

Mentor
P: 17,541

What Pete and Ich were describing can be summed up in the conservation of the fourmomentum for any isolated system. In one nice package the conservation of fourmomenum gives you the classical conservation of momentum, conservation of energy, and conservation of mass.
The relevant quote from the Wikipedia link: "Note that the mass of a system of particles may be more than the sum of the particles' rest masses, since kinetic energy in the system centerofmass frame counts as system mass. As an example, two particles with the fourmomentums {5 Gev, 4 Gev/c, 0, 0} and {5 Gev, 4 Gev/c, 0, 0} each have (rest) mass 3 Gev/c2 separately, but their total mass (the system mass) is 10 Gev/c2. If these particles were to collide and stick, the mass of the composite object would be 10 Gev/c2." 


#13
May708, 10:36 PM

P: 4,512

What would Hawking say of two merging, nonrotating, uncharged, black holes; one originating from collapsing matter, the other in collapsing antimatter?



#14
May808, 09:43 AM

P: 2,954

Pete 


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