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Author Topic: Are relativity equations compliant with the energy/mass conservation principle?  (Read 1571 times)

Offline zordim

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Offline yor_on

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Offline a_dark_knight

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I'm not an expert but yes, I'm pretty sure it all works out perfectly. For example, let's say a spaceship is moving "near" the speed of light. Then you could measure its kinetic energy, using its apparant mass (or inertia) instead of its rest mass. This will tell you exactly how much work/energy has been put into moving the spaceship. If it weren't for relativity, the spaceship would be moving faster instead of "weighing" extra, but either way, the energy's the same. That's also exactly how much work/energy it would take to slow it down. So basically, none of the work is wasted. Please correct me if I'm wrong about this!
 

Offline Pmb

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I'm not an expert but yes, I'm pretty sure it all works out perfectly. For example, let's say a spaceship is moving "near" the speed of light. Then you could measure its kinetic energy, using its apparant mass (or inertia) instead of its rest mass. This will tell you exactly how much work/energy has been put into moving the spaceship. If it weren't for relativity, the spaceship would be moving faster instead of "weighing" extra, but either way, the energy's the same. That's also exactly how much work/energy it would take to slow it down. So basically, none of the work is wasted. Please correct me if I'm wrong about this!
Yes. Not only are alll the equations SR consistent with the conservation of energy and mass but they are so because we use conservation of mass-energy in deriving their relativistic form.
 

Offline zordim

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Dear Pmb,

Gravitational time dilation equation is:

d29afb73b4a6ea498446531b57da3f68.gif

We have a body with a mass 377b1a53b01e907138040867edc7cac2.gif. We observe some point which is at a distance  baf606802b02a2603db47ea634c06429.gif  from that body. The time equation at that point is

e406e87562895a36b34b1b5515bf704d.gif

If another body with a mass a4e435d4d078e7df1fa07e13d4a32ebb.gif comes (from very far away) at some distance 9968fc4470c99482a3c991158a8e9448.gif from the observed point, the time equation at that point becomes 

ddf86274a5e37462f501ae59515f2850.gif

So, 8d9c307cb7f3c4a32822a51922d1ceaa.gif bodies will produce the following time behavior at the observed point:

f42bcf2945fa4d526d24785ad246ff32.gif

af2593b49488f8bc44396795792c2d79.gif is the distance of the i-th body from the observed point

Hence, the superimposed time-behavior at some point which is equally distant from two or more objects will not be the same as the time-behavior produced at the same distance from one object with the mass equal to the mass-sum of those two or more objects:

6db47a4484e8c450a77b1afe335b6beb.gif

How does this fit with the continuity principle, that is, with the mass (energy) conservation principle?
« Last Edit: 11/12/2012 10:03:15 by zordim »
 

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