Pushing with a lorentz contracting stick

[jartsa]

Let's say I'm pushing and accelerating an object using a long stick, like this:

H--------------O
-->

H is my hand, O is the object.

The force I use is F, the distance I push is s, the energy I use is Fs

The force pushing the object <= F
The distance that the object is pushed < s

So energy increase of the object < Fs

Is conservation of energy violated here?

 

[Dale]

No. Energy is different in different frames, but it is conserved in each. Conservation and invariance are separate concepts.

 

[jartsa]

No. Energy is different in different frames, but it is conserved in each. Conservation and invariance are separate concepts.

You answered some other question. This question was about energy at different ends of a stick. Energy of push.

We know a force meter shows a smaller reading at the other end of the stick, because an accelerometer shows smaller reading at the nose of an accelerating rocket.

And we know the hand moves a longer distance compared to the other end of the stick.

So force times distance is smaller at the object side of the stick.

 

[Dale]

You answered some other question. This question was about energy at different ends of a stick. Energy of push.

Oh, I misunderstood the question, apologies.

That is a much more difficult question to answer. Depending on the exact details of the motion and the material properties of the stick there are several things to consider. First, the pure kinematics makes it so that the KE is higher than you would get classically (i.e. in Newtonian physics the limit of KE as v→c is finite but in SR it is infinite). Second, the rod itself has KE. Third, the rod may be compressed by the push, in which case the rod also stores elastic PE.

If you carefully account for all the types of energy then you will get conservation.