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When light is propagating in glass or other medium, it isn't really true, pure light. It is what (you'll learn about this later) we call a quantum superposition of excited matter states and pure photons, and the latter always move at the speed of light $c$. You can think, for a rough mind picture, of light propagating through a medium as somewhat like a ...


10

A classical explanation to supplement Rod's excellent quantum mechanical one: If you make a Huygens construction of wave propagation (I assume you know how to do that) then every point on the wave front is treated as the source of a new wave of the same frequency and phase. How that wave propagates depends on the medium it encounters. So the Huygens ...


5

Energy conservation stems from Noether's theorem applied to time (i.e., time-invariance leads to energy conservation, similarly to how spatial-invariance leads to momentum conservation). Since the universe is expanding (and accelerating at that), the state of the universe today is different than it was yesterday and will be tomorrow, hence energy ...


2

The height $h$ is probably the vertical displacement pointing downwards. Therefore: $$ h = \left(-\mathbf{\hat j}\right)\cdot\mathbf s = -|\mathbf{\hat j}||\mathbf s|\cos\alpha = -s\cos\alpha $$ Now we can derive: $$ \frac{dh}{ds} = -\frac{d}{ds}\left(s\cos\alpha\right) = -\cos\alpha \quad\Longrightarrow\quad \frac{dh}{ds} = -\cos\alpha $$ Therefore, ...


2

You're making a mistake in assuming that there is any left. Heat and sound account for all of it. There is one exception, though. If it crashes into something, and that breaks or bends the object, then the potential energy of the molecules is higher. That's why cars end up smashed after a collision. The molecules of the metal or plastic or whatever have ...


1

Assuming that hands remain completely static, and the object do not breaks, then all of its energy can be considered to be converted into heat and sound (as you have already described).


1

What we like to call the energy, i.e., the total matter/energy content of space-time, might not be conserved. However, there is a lot of reason to suspect that fundamentally the universe is some big quantum system, and that space-time and particles and fields are emergent from this underlying idea. In that case, we expect there to be a Hamiltonian $H$ and ...



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