http://www.shadycrypt.com/(adsbygoogle = window.adsbygoogle || []).push({});

After equation (27) it says:

"Keep in mind that we are not talking about the kinetic energy of the entire apparatus – only the kinetic energy of the mass associated with the pair of light rays that were measured. Since the moving observer measureshigherradiated energy, the associated component of that apparatus's Kinetic energy must have beenreducedby the same amount (conservation of energy). The only conclusion that follows from equation (27) is that if the apparatus gives off energy [itex]E_0[/itex], its mass must decrease by a corresponding amount as a result."

I think the first bit is saying that the total energy of the two light rays (travelling in opposite directions) in the (instantaneous comoving) rest frame of the spaceship is greater than their total energy in the rest frame of the apparatus.

[tex]\gamma E_0 = E_0 + K.E. > E_0[/tex]

I've just added subscript zeros, for clarity, to the notation used at the site. But what does it mean by "the associated component of that apparatus's Kinetic energy must have been reduced by the same amount (conservation of energy)"? The apparatus, i.e. the pair of light rays, hasnokinetic energy in its own rest frame, as its entire energy is accounted for by [itex]E_0[/tex], the rest energy, so how can it be that K.E. is reduced from nothing (in the rest frame of the apparatus) to less than nothing (in the rest frame of the spaceship)? It must mean "reduced" in some other sense, given off, I suppose, even though the total energy is constant in either frame.

I don't understand this point:

"So the stationary observer measures [itex]E_0[/itex] energy for a given pair of light rays, and the moving observer measures [itex]\gamma E_0[/itex] energy for the exact same rays. But energy is energy. One can't measure different values of energy in different frames of reference or conservation of energy would be violated; unless there is something else going on related to energy in the different frames. And there is. In the stationary frame, the apparatus has no kinetic energy relative to the stationary observer. But the apparatus does have kinetic energy according to the observer in the moving frame."

The total energy is greater in the spaceship's frame, and the K.E. is greater in the spaceship's frame, so how can it say that both frames must have the same value for either kind of energy. I thought conservation of energy meant that kinetic energy plus potential energy is constant in any frame you choose to measure them in, rather than that a particular value of kinetic energy plus rest mass must be unchanged by a change of frame; how can it be unchanged, given that it's a sum of kinetic energy and rest mass, and kinetic energy is frame-dependent while rest mass is frame-invariant? And how can we draw any conclusions about whether energy is conserved when no mention is made of potential energy?

Or maybe conservation of energy means (as Taylor and Wheeler say inSpacetime Physics) that total relativistic energy, [itex]\gamma E_0 = E_0 + K.E.[/itex], is conserved. Still no mention of frame-imvariance, and indeed the gamma factor tells us that it's not frame-invariant. (I wonder how the concept of potential energy relates to these relativistic definitions.)

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Shady Crypt Observatory E=mc^2 derivation

Loading...

Similar Threads - Shady Crypt Observatory | Date |
---|---|

Testing gravitational wave observatories | Jul 31, 2014 |

**Physics Forums - The Fusion of Science and Community**