(not sure if this has been posted yet....)

The Law of Conservation of Matter (Lavoisier) states that in a chemical change, matter can neither be created nor destroyed, but only changed from one form to another (or that the mass of the reactants equals the mass of the products). However, Einstein's mass-energy relationship dictates that matter and energy are interchangeable. I find these two conflicting, yet both are correct. How can this be?

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Hi %BlueSoulRobot%,

The Lavoisier law of conservation of matter was formulated in the 18th century (perhaps even the 19th century). The equivalence of matter and energy was formulated in the early 1900's and should be regarded as more correct than the conservation of matter (since basically it states that matter is not conserved and we know that this is the case).

However, the law of conservation of matter seems to apply in some cases, which is in low-energy (non-relativistic) systems where not enough energy is released to form new particles. You could formulate it as follows: the law of conservation of energy, together with E = mc² falls apart into conservation of energy and conservation of matter in low-energy systems. (Note that this is also the case in classical mechanics, where matter is conserved).

Bye!

Crisp

The matter conservation is one of those laws like Newtons that are basically correct but need fine print to be better.

The rule we have now is that
Rule 1) Energy is conserved.


No theory to explain Rule 1 just lots of experiments.

With Albert's E = MC^2 we can re-arange this to M = E/C^2. Since C is a constant this implies if no matter is converted from/to energy then Matter is also conserved. More formally we can also say that for a closed system the quantity TOT = E + MC^2. is conserved- here E stands for the energy not present as matter.

For a chemical reaction the amount of energy converted to or from matter is so low that we usually safely ignore it and claim that matter is conserved.

BTW. Rule 1 is very powerfull, add in a very few rules like E=hv, E=MV^2, E=MC^2 etc and nearly all of modern physics theories can be (mathematically) derived/proven. Hope this helps

That's great, thanks a lot, Crisp and allant!

%BlueSoulRobot%,

Another way of looking at it is to assume that energy is a form of matter.

Tom

Heeey..that's right, Prosoothus/Tom! Thanks!

actually, conservation of energy can be proved using the emperical statement that the universe is invariant under translations through time. in other words, physics works the same today as it did yesterday.

Of course, it is a matter of convenience what you want to choose as axiom, and what is a theorem, there still must be an axiom which is empreically verified. I just think that the invariance is a more natural choice, more intuitive, more easily observed. you can also get conservation of momentum from invariance of space, and conservation of angular momentum by invariance through rotation. note that in SR, space and time are the same, and so are momentum and energy. in both cases, they are just different components of a single vector, and can be intermingled with lorenz rotations.

Huh ? Lorentz Xform for Space -time I can handle, but not Momentum - Energy ? Can you give me some pointers please.

well, if you approach it classically, you treat space and time separately. the invariance of physics under translations through space yields the conservation of momentum, and the invariance under translations in time yields the conservation of energy.

conservation of energy and conservation of momentum are separate laws, and the quantities are conserved separately, in this case.

in a relativistic approach, we do not strictly distinguish between space and time. you create a 4-dimensional minkowski space, and populate it with 4-vectors that represent events in space time. lorentz transformations are rotations in minkowski space that intermingle the space components of your 4-vector with your time component, making it difficult to make a hard distinction between them.

physics is invariant under translations in space-time, which yields a law which we call the conservation of mass-energy. here, momentum and energy are just different components of the same 4-vector, so it is artificial to separate the laws of conservation of energy and the law of conservation of momentum.

NB: in any situation, whenever there is a invariant quantity, then there is always an associated conserved quantity. energy-time, momentum-space, etc

Thanks Lethe.

In case others have the same problem...

What I got from the Charcoal and Slate computer was. Using { for sum.

Started out using sums instead of Integrals as integrals are a PITA.

So { mv^2 is conserved for all t

Index is over hypercubes of delta L,
with the time "length" = Delta L / C

After add Lorenz and doing some dodgy chicken scratching I got

{ mvC is conserved over X (space).

and since C is a constant { mv is conserved.

I think I am safe in assuming the intergal would work out the same. The bit that threw me was the C in the { mvC