Are relativity equations compliant with the energy/mass conservation principle?

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Offline yor_on

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"BOMB DISPOSAL EXPERT. If you see me running, try to keep up."

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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!

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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.

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Offline zordim

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Dear Pmb,

Gravitational time dilation equation is:

[tex]t(m,r) = t \cdot \sqrt{ 1- \frac{2 \cdot G \cdot m}{c^2 \cdot r}}[/tex]

We have a body with a mass [tex]m_1[/tex]. We observe some point which is at a distance  [tex]r_1[/tex]  from that body. The time equation at that point is

[tex]t_1 = t \cdot f(m_1, r_1)[/tex]

If another body with a mass [tex]m_2[/tex] comes (from very far away) at some distance [tex]r_2[/tex] from the observed point, the time equation at that point becomes 

[tex]t_2 = t_1 \cdot f(m_2, r_2) = t \cdot f(m_1, r_1) \cdot f(m_2, r_2)[/tex]

So, [tex]N[/tex] bodies will produce the following time behavior at the observed point:

[tex]\displaystyle \tau = t \cdot \prod_{i=1}^N f(m_i, r_i) \Rightarrow \frac{\tau}{t} = \prod_{i=1}^N f(m_i, r_i) = \prod_{i=1}^N \sqrt{1 - \frac{2 \cdot G \cdot m_i}{c^2 \cdot r_i}}[/tex]

[tex]r_i[/tex] 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:

[tex]\frac{\tau}{t} = \sqrt{1 - \frac{2 \cdot G \cdot \sum_{i=1}^N {m_i}}{c^2 \cdot r }} [/tex]

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 »