Is energy always positive and dependent on observer's frame of reference?

[qbslug]

I was under the impression that energy had to be positive. Yet it seems we are still forced to use negative energies since we set the potential to be 0 at an infinite distance away. And the only reason we don't set the potential energy to zero at the origin of the source is because there is a singularity there? Is that correct?

 

[Born2bwire]

Sometimes, sometimes the potential at infinity will be infinite. Since most applications focus on the potential difference, how we set the reference potential is mainly defined by the physics we wish the potential to demonstrate and what is convenient to use as a reference. In addition, setting infinity to be our zero reference does not guarantee negative potentials. In electrodynamics, the potential from a charge will have different signs depending on the sign of the charge.

 

[Bob_for_short]

And the only reason we don't set the potential energy to zero at the origin of the source is because there is a singularity there? Is that correct?

Yes, that's right. When the potential at the origin is finite, it is usually set to zero.

 

[Dale]

I was under the impression that energy had to be positive.

Potential energy does not need to be positive. Where you choose your reference point and the potential energy value that you assign at your reference point has no physical significance whatsoever. Only potential differences are physically meaningful.

Kinetic energy does need to be positive (because the speed is always positive). Perhaps that is what you are thinking about.

 

[qbslug]

thanks for clearing that up.
So absolute kinetic energy by itself has physical meaning but only potential energy difference have physical meaning? I thought there would be some conceptual symmetry between the two.
Doesn't kinetic energy of an object also depend on the speed of the observer though according to relativity?
So we can say potential energy depends where we set potential to 0 and kinetic energy depends on the velocity of observer (where we set velocity to 0)?

 

[Cleonis]

thanks for clearing that up.
So absolute kinetic energy by itself has physical meaning but only potential energy difference have physical meaning? I thought there would be some conceptual symmetry between the two.
Doesn't kinetic energy of an object also depend on the speed of the observer though according to relativity?
So we can say potential energy depends where we set potential to 0 and kinetic energy depends on the velocity of observer (where we set velocity to 0)?

There is a particular case where kinetic energy and potential energy are in a rather symmetrical relation to each other: the physics of liquid mirror telescopes (or more generally the shape of the surface of a rotating liquid.)

In the case of a liquid mirror telescope the liquid is usually mercury, as it reflects so well. The first attempts at making a mercury mirror used a bowl filled with mercury, positioned on a turntable that was spinning as uniformly as possible.

The surface of the liquid then assumes a shape with a parabolic cross section. For particles at the surface the following is valid:
- The kinetic energy is proportional to the square of the distance to the central axis of rotation.
- The potential energy is proportional to the square of the distance to the central axis of rotation.

In this case, if you define the lowest point, (the center point) as zero point of potential energy, then at each distance to the central axis of rotation kinetic energy and potential energy have the same value.

The parabolic shape is the shape with the property of that kinetic/potential energy equilibrium. For instance, when there is a sudden change in spinning rate the liquid will ripple and wobble, but if the spinning rate remains uniform the liquid will once again settle into an equilibrium state.

Cleonis

 

[Dale]

Doesn't kinetic energy of an object also depend on the speed of the observer though according to relativity?
So we can say potential energy depends where we set potential to 0 and kinetic energy depends on the velocity of observer (where we set velocity to 0)?

Yes, definitely.