Recent content by PeroK

It's a spectacular image, but it's essentially fake. It's not what the crew saw. This raises the question of what is allowable as enhancement or alteration before you have to declare something as "synthetic".

I would say that a black hole is about 4D geometry. There is no global "time" axis. In many ways, you need to free your mind of the simple concepts of classical motion. It might be helpful to realise that a black hole means two different things: 1) The Schwarzschild Black Hole is a...

Plenty of grist for the conspiracy mill!

I agree. Knowledge of this type always has some value. That said, Taylor is a comprehensive and somewhat advanced book. It's a big book to buy just for a few chapters. Instead, you could look for a free pdf from a legitimate source (probably a university professor) on Analytic Mechanics. And...

Following this principle, you could apply the Navier-Stokes equations and replace the molecular physics of water with continuous fluid flow. You can't do this because the continuum model breaks down at some appropriately small scale. Given, therefore, that the continuum model is an...

You have several misconceptions about entanglement. First, entanglement is often a result of conservation laws and any number of particles or subsystems can be entangled. For example, if you know the total energy of a system and you measure the energy of part of the system, then you know the...

You can do the paradox without acceleration. Ultimately, therefore, it is about the difference in paths through spacetime. And not "something funny happens when you accelerate".

Note that we can get a similar paradox by considering a length of elastic material that stretches out until instantaneously it has a certain rest-mass density ##\rho(x)## and a velocity profile ##v(x)##. Nominally, the instantaneous energy of the expanding material is: $$E = \int_0^L...

You can, but perhaps you can't meaningfully have the boundary of the dust cloud moving at ##c##. In one sense you can, because the boundary has zero mass and zero energy. This thread is trying to make sense of the consequences of that.

Dust is not a continuous distribution of matter.

There's an ambiguity over which limit to take first. Even if the physical model is not valid, there's a question over the validity of the mathematics. That said, a more sophisticated physical model might lead to a different integral and no ambiguity in the result.

Sure, if you do the integral first and then take the limit as the velocity tends to ##c##. But, if you consider the construction of the integral for velocity tending to ##c## (i.e. swapping the order you take the limits), then the definite integral does not converge.

A one-dimensional ring is fundamentally unphysical. Integration involves the limit of finite rings or annuluses, which is where the problem lies. If you deconstruct the integral as such a limit, then the problem is clear.

Consider the outer portion of the disk. For each ##n##, consider the annulus with inner radius ##r_n = R(\frac {n-1}n)##. The mass of that annulus is: $$m_n = M (1 - \frac{(n-1)^2}{n^2}) = M(\frac{2n -1}n)$$Now approximate the speed of that annulus by the speed at the inner radius (assuming the...

See also the recent thread about the electric field of an infinite, uniformly charged plate.