Is Energy Conserved When an Object Approaches Light Speed?

[ChrisPhy]

Basic question I'm sure but...please help...

If there is an object of some mass accelerating toward some other massive object, I can see that total energy of system is same regardless of time as potential energy from gravity well is being lost as kinetic energy of object increases. It would appear that total energy in system is unchanged.

1) Am I correct in this understanding ?

2) If the object in question was say moving at the speed of light to start with, as the object gets closer to other massive object, isn't the gravity potential still being reduced over time ?

3) But object cannot gain any more kinetic energy (already at top speed) so I am thinking the total energy of this system is reducing as object gets closer to massive object ? But this cannot be the case...

I know I am missing a piece of the equation here, what is happening in this situation ?

 

[PeterDonis]

If there is an object of some mass accelerating toward some other massive object, I can see that total energy of system is same regardless of time as potential energy from gravity well is being lost as kinetic energy of object increases. It would appear that total energy in system is unchanged.

1) Am I correct in this understanding ?

In this particular case, yes, you can view things this way. In the general case, it is not always possible to define a "total energy" for the system that remains constant. For example, there is no good way to define a "total energy" for the universe as a whole that works this way.

2) If the object in question was say moving at the speed of light to start with, as the object gets closer to other massive object, isn't the gravity potential still being reduced over time ?

A terminology note: the word "object" is normally not used to refer to light, or anything that moves with the speed of light. Particularly since you used the phrase "object of some mass", and objects with mass cannot move at the speed of light. So I'll interpret your question as asking what happens when light "falls" in the gravitational field of a massive object.

3) But object cannot gain any more kinetic energy (already at top speed) so I am thinking the total energy of this system is reducing as object gets closer to massive object ?

No, it still stays constant, because light can still change its kinetic energy even though it can't change its speed, and it does so when "falling" in a gravitational field. This is called "gravitational redshift" or "gravitational blueshift" depending on whether the light is rising (redshift) or falling (blueshift), and it has been observed experimentally:

http://en.wikipedia.org/wiki/Pound–Rebka_experiment

So you can view the light as gaining or losing kinetic energy to balance the change in its potential energy, the same as an object with mass does.

 

[ChrisPhy]

In this particular case, yes, you can view things this way. In the general case, it is not always possible to define a "total energy" for the system that remains constant. For example, there is no good way to define a "total energy" for the universe as a whole that works this way.



A terminology note: the word "object" is normally not used to refer to light, or anything that moves with the speed of light. Particularly since you used the phrase "object of some mass", and objects with mass cannot move at the speed of light. So I'll interpret your question as asking what happens when light "falls" in the gravitational field of a massive object.



No, it still stays constant, because light can still change its kinetic energy even though it can't change its speed, and it does so when "falling" in a gravitational field. This is called "gravitational redshift" or "gravitational blueshift" depending on whether the light is rising (redshift) or falling (blueshift), and it has been observed experimentally:

http://en.wikipedia.org/wiki/Pound–Rebka_experiment

So you can view the light as gaining or losing kinetic energy to balance the change in its potential energy, the same as an object with mass does.

Thank you for reply. I think I understand. I didn't know that about objects with mass can not go to full C speed. Thanks...

 

[georgir]

Well, it probably is not appropriate to call electromagnetic energy "kinetic", but yes, it does change along with gravitational potential.
Also, I'd think potential energy for the whole system can be defined the same way as in classical physics, a sum of the potential energies between each pair of objects, as long as there are a finite number of objects... and from that total energy is also easy to define. Not sure why Peter thinks otherwise.