Kinetic Energy Transfer in Relativity: A Puzzler

[Skwint]

I wasn't sure whether this question belonged in relativity or QM, or even just plain classic. This forum seemed the best bet, but I am not using speeds near C - mere Galilean relativity will suffice here.

I have two objects, A and B
A is moving with velocity V and thus has kinetic energy E
B is stationary and has no kinetic energy

But now I put my foot down and accelerate until I am moving with velocity V, or, put another way, A is now stationary and B is moving at -V. Thus, now A has no kinetic energy and B has kinetic energy E.

So, how did the energy move from object A to object B? I touched neither and they are separated by vacuum. I am forever being told that energy is "real" and not just a convenient conservation constant, and that we can convert it to and from matter should the conditions permit, but if it's location depends on the observers velocity I am having trouble understanding that...

 

[dx]

The energy did not move from A to B.

You could have observed A and B from a car moving with a speed 10V, and then the sum of the energies of A and B in that frame wouldn't add up to the total energy they had in the original frame of reference.

 

[Skwint]

Sure. It doesn't really answer the original question though? Does energy actually "exist"? The total energy in a system depends on who is looking at it - is it no more than a mathematically construct, or is it as tangible as, say, a particle?

 

[dx]

In a given frame of reference, you can always talk about energy as if it exists in space; for instance the energy in a given region of space only decreases by flowing out of the that region. But it is not actually a tangible substance, like water.

 

[Dale]

So, how did the energy move from object A to object B?

The energy didn't move from A to B. If A and B are different masses then their KE's for the same velocity are different, so there is no way even in principle to simply treat the energy as having moved from A to B.

In the starting inertial frame the energy was always in object A (your energy changed as you accelerated) and in the final inertial frame the energy always was in B (your energy changed as you accelerated).

 

[Dale]

Does energy actually "exist"?

What experiment do you propose to determine if something "actually exists"? Otherwise, can you even unambiguously define the meaning of "actually exist"?

 

[Bill_K]

In relativity, energy and momentum are parts of one object, the energy-momentum vector. When you change from one reference frame to another, part of your energy turns into momentum and part of your momentum turns into energy. In the original frame, A has energy and B has momentum. In the second frame, A has momentum and B has energy.

 

[Bill_K]

What experiment do you propose to determine if something "actually exists"? Otherwise, can you even unambiguously define the meaning of "actually exist"?

This is getting rather philosophical, but I believe what he meant by "actually exists" could be more accurately stated, "is a useful concept."

 

[1977ub]

In science-fiction one often encounters breathless exclamations that such-and-such a thing is "pure energy." It might be interesting to the OP to be informed / reminded that mass changes with one's frame. So there is rest mass, which is invariant by frame, and then there is the relativistic mass which depends upon the observers' relative velocity. So a similar question arises regarding how much mass "exists" for a particle or body.

 

[Bill_K]

Nowadays the only mass we use is the rest mass, which is independent of rest frame. The term "relativistic mass" is no longer used, being just 1/c² times the energy.

 

[HallsofIvy]

"Energy" is fundamentally a "bookkeeping" device. Historically, every time a situation has occurred in which it appeared that energy was NOT conserved, a new kind of energy was defined to account for it.

 

[1977ub]

"Energy" is fundamentally a "bookkeeping" device. Historically, every time a situation has occurred in which it appeared that energy was NOT conserved, a new kind of energy was defined to account for it.

I have been confused over the years when encountering energy in the context of relativity, when we see phrases such as "converting a body's mass entirely into energy."
http://www.pbs.org/wgbh/nova/einstein/tiny-nf.html

Can you describe how it is a bookkeeping device in this context? This type of discussion seems to treat it as a real "thing" like mass...

 

[Khashishi]

Energy is just part of a 4-momentum 4-vector. 4-vectors do transform when you change the frame of reference, but from a certain point of view, they are the "same" vector, simply looked at from a different point of view. Of course, this gets all philosophical. The point is that the vector transformation rules are clearly spelled out, and if you go back to the original frame of reference, you see that the 4-vectors transform back to the original state, and everything is conserved. In fact, the magnitude of the 4-vector is conserved, and the "4-direction" is only changed when you change your viewpoint.

As an analogy, suppose we have a rule that says that the length of a box is conserved. Yet you can rotate around a box to change a 2x4 box to a 4x2 box. But "really", it hasn't changed.

 

[1977ub]

It's conserved in this way regardless of whether it transforms to or from mass?

 

[Skwint]

I don't mind the answers becoming philosophical. I remember one of my professors laughing when I said energy was just book keeping and telling me it existed and has mass. It is interesting to see it circle round to where I started when I try to resolve that...