What Is Energy: Physical Reality or Mathematical Construct?

[Phrak]

That is incorrect. Maxwell's equations http://farside.ph.utexas.edu/teaching/em/lectures/node89.html" in general, the specific details of how you pulse your laser beam don't matter.

Please post a rigorous derivation if you believe otherwise.

okay

 

[Phrak]

That is incorrect. Maxwell's equations http://farside.ph.utexas.edu/teaching/em/lectures/node89.html" in general, the specific details of how you pulse your laser beam don't matter.

Please post a rigorous derivation if you believe otherwise.

Yeah, you're right. The momentum of a particle tends to zero, the frequency and energy remain constant; the invariant mass changes.

 

[Dale]

Sorry, I don't follow. Are you talking about a massive particle as v->0 or about two photons interfering with each other or a Maxwell description of the laser or what?

 

[Phrak]

Sorry, I don't follow. Are you talking about a massive particle as v->0 or about two photons interfering with each other or a Maxwell description of the laser or what?

I don't know, Dale. The truth is, I haven't sorted this all out. Every consideration brings up something unexpected. A simple scenario is a one dimensional reflected light wave,

$$\Phi = \phi \: cos(kt - \omega t) - \phi \: cos (kx + \omega t)$$

The frequency is constant. The particle count doubles. I suppose the energy doubles, and so is conserved.

 

[ryuunoseika]

I've been throwing this term energy around for a while now, and thinking about it I have absolutely no idea what it is. Is it something that actually exists in the universe, or just a construct that we use to simplify problems?

Terms like kinetic energy, and even gravitational potential energy (from a Newtonian standpoint) are a little bit easier to understand because they are exist in everyday life, but when you get E&M (I've only studied classical E&M) you have this idea of a field, the field has energy and you need to calculate it? How does a field have energy?

Consider a conducting bar, moving on rails with a large resistor at one end bathed in a strong, uniform magnetic field. As the bar moves, the magnetic flux increases, inducing a current in the circuit and thus energy is lost in the resistor as heat, so the bar must be slowing down (it never actually stops even though it moves a finite distance, as I've calculated). I can ascertain what happens in this situation because I know about E&M, but it bothers me that I don't feel like I understand what is actually happening. If you showed me that and I didn't know physics, I would say the bar moves an infinite distance. How can some invisible field (with energy) stop a real, moving object? This is the whole idea of transfer of this energy which I don't know what it is?

Is there a good model of a physical interpretation of this phenomenon? Is it just a mathematical construct?

An electromagnetic field, like a gravitational or other field, only has energy when it acts upon something. You could think of energy as a mental/mathematical mechanism for understanding a series of interchangeable phenomenon in our universe, but consider this: according to E=MC2, Energy has mass (relativistic mass), thus it has gravitational pull. It even has momentum. Enough light concentrated in one direction can open a door. Energy has it measurable affects on reality, like mass, so in my mind it's real.