Quantum vs. Classical Mechanics in Differential Element Analysis

[Meet Gandhi]

When we take a differential element for analysis why don't we consider quantum effects and only consider classical mechanics to solve the problem?

 

[scottdave]

Can you elaborate, perhaps with an example, of what you are asking about with differential elements. I would rather not speculate.

 

[Meet Gandhi]

Can you elaborate, perhaps with an example, of what you are asking about with differential elements. I would rather not speculate.

When we derive the heat diffusion equation which is a differential equation, we consider a differential element and the apply energy conservation.
In this conservation equation, we take energy coming in and going out, energy generated and change in energy stored.
Here the element is assumed to be infinitesimally small then why don't we consider quantum effects and include quantum energy terms?
Hope this suffice.

 

[scottdave]

Maybe not the exact answer you are looking for, but maybe this will help.

Since the effect that you are interested in is at the macroscopic level, I don’t think that making quantum level calculations will provide any advantage.

I don’t recall about heat transfer, when I took the advanced Physics class, which involved quantum calculations. But we did do some calculations which had to do with motion. One in particular, that I can recall, had to do with a satellite orbiting Earth hundreds of km above the surface.

We had to calculate the next energy level up or down for the satellite, using quantum calculations. It turned out the difference in energy levels was on the order of nanometers, I think. It was small enough, that we could say that standard Newtonian mechanics and quantum mechanics produce the same result, when looking at macroscopic events.