# Posts by celtschk

In special relativity, spacetime coordinates are normally given as $$(ct, x, y, z) \tag{S}$$ with the metric being either $$g = \operatorname{diag}(-1,1,1,1) \tag{+}$$ or $$g = \operatorname{d...

The major advantage of AC is that is can be easily transformed to different voltages. This is important because current transport is most efficient if the currents are low (because the losses are p...

In short: Yes. And there are standard ways to distinguish variables from units. Let me explain in detail. In physics, we deal with physical properties of objects and systems. Those quantities can ...

Inflation in cosmology refers to a phase of the early universe where the universe expanded extremely fast. And the universe expanding quite literally means the space getting bigger. As you noticed...

To understand this, it helps to look at a dimension less. Imagine, you're having a dispute with a flat-earther about whether the earth is a sphere or a flat plane. Moreover, there's a third person...

If you are accelerating while running on Earth, actually you are also accelerating Earth in the opposite direction. However for a given force, the acceleration is inversely proportional to mass, th...

Change in momentum is force times time. On the other hand, change in kinetic energy is force times distance (more accurately, the component of the force along the movement times distance; a force p...

In general, the only way to do it is to solve the equation of motion. In simple cases, that can be done analytically (that is, you can find an explicit formula, but in most cases (outside problems ...

Let's first remember how you check that you are at an extremum (minimum, maximum, saddle point) of a normal differentiable function. You do so by checking that the first derivative is zero (plus fu...

Your mistake is that you did a second derivative of $L$, taking the derivative according to both degrees of freedom together. Instead you need to make a separate equation for each degree of freedom...

To start with, black holes in the GR model don't radiate. At all. Even Hawking radiation isn't predicted by GR. Rather, it is predicted by doing quantum mechanics in curved spacetime. That is, you ...

As you probably know, one of the postulates Einstein's Special Relativity is based on is that all observers see light in vacuum go at the same speed $c$. Now consider a lamp at rest relative to Jo...

Yes, that would the obvious interpretation of that equation in one dimension. Note also that in that case, the divergence also reduces to the ordinary derivative. In other words, in one dimension,...