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.

 

[sardar]

I would like to clarify that the concept of pushing an object with a Lorentz contracting stick is not physically possible. The Lorentz contraction is a phenomenon that occurs at extremely high speeds and is a result of the theory of relativity. It describes the apparent shortening of an object's length as it moves at high speeds relative to an observer. Therefore, using a Lorentz contracting stick to push an object would require the stick to also be moving at high speeds, which is not possible in this scenario.

Assuming that the stick is not actually contracting due to high speeds, but is a regular stick being used to push the object, the concept of energy and conservation of energy still applies. The force applied by the hand and the distance the object is pushed are both important factors in determining the energy used. However, the statement that the distance that the object is pushed is less than the distance the hand is pushing is incorrect. In this scenario, the object is being pushed in the same direction as the hand, so the distance pushed by the hand and the object would be the same.

In terms of conservation of energy, it is important to note that energy cannot be created or destroyed, it can only be transferred from one form to another. So, in this scenario, the energy used to push the object is transferred from the hand to the object. As long as the total energy remains constant, conservation of energy is not violated.

In conclusion, the concept of pushing an object with a Lorentz contracting stick is not physically possible and the statement about the distance pushed is incorrect. However, the concept of energy and conservation of energy still applies in this scenario.