Recent content by Petr Matas

Hello Greg, I was not even asked for the Google password (nor my confirmation), because I was already logged in. Logging out from Google solved the problem. Maybe something went wrong two weeks ago when I tried to log in using an unassociated Google account and reset my PF password just after that.

I am trying to associate my PF account with my Google account. At .../connected-accounts/google/ I am entering the same password I use to login to PF (verified by logging out), but I am getting the following error: Oops! We ran into some problems. Your existing password is not correct. Can we...

Some alpha or beta decays produce an excited daughter nucleus, which typically immediately emits one or more gama rays to reach a ground state. This is the case for beta decay of Co-60 or Na-24 for example. While the table of cobalt isotopes on Wikipedia mentions the gamma emission, the one for...

@hilbert2: Thank you for your clear explanation. Oh yes, that did not come to my mind. And any system is always entangled with its environment. Is it even possible to prepare a single atom with a 100% probability of it being in its ground state then? ΔE⋅Δt ≥ ½ħ comes to my mind as well, so...

Because at extremely low temperatures the energy of individual atoms and thus their momentum is also extremely low and therefore very precisely specified. This should result in high uncertainty of their position. Shoudn't this lead to the crystal becoming liquid? However, from another point of...

Is it theoretically possible to cool a macroscopic crystal (for example NaCl 1×1×1 cm) to an extremely low temperature, like 1 nK? Will it retain its microscopic structure? Why? Does it have anything to do with zero point energy (I mean something like the lowest energy level of a quantum...

In an attempt to falsify your statement, I tried to show that a photon sent into the black hole to chase an infalling object can reach the object before crossing the event horizon, reflect off the object and return from the black hole, although extremely delayed and red-shifted. Using the...

Aside from that, your post explains things a lot, so thanks for it, Chronos.

A static black hole's radius is rs = 3M/MSun km, so if the mass of the Sun shrunk to the radius of 1.2 km, as you have written, it would be a black hole. Neutron star radii are about 10 times larger, let us say 12 km. That would result in a spin rate f = 1500 s-1, still about twice as fast as...

The rotation period is proportional to the radius squared (ignoring relativistic effects). If it were proportional to just the first power of radius (as you have written), the surface speed would be unchanged by the collapse (it was 5.75 times the speed of light before the collapse as well, see...

I have obtained a different result: $${v \over c} = {1 \over \sqrt{{c^2 \over J^2} + 1}}$$ Anyway, v/c < 1 for any value of J or L or r.

That is interesting. Does any of these frames belong to an observer, which never falls into any black hole? Can you provide an example, please?

Consideration of special relativity requires ##m## to be replaced with ##γm_0##, where ##m_0## is the rest mass, and the Lorentz factor $$γ = {1 \over \sqrt{1 - {v^2 \over c^2}}}.$$ Unfortunately this factor depends on speed and therefore on position inside the body. A simplifying assumption...

You're welcome. However, doesn't the collapse increase the surface speed? How can the initial super-luminal become post-collapse sub-luminal then?

The moment of inertia of a solid homogeneous sphere is $$I = {2 \over 5} mr^2.$$ Its angular momentum is $$L = Iω = I{v \over r} = {2 \over 5} mrv,$$ which has to be conserved, i.e. $$L = L_0$$ $${2 \over 5} mrv = {2 \over 5} mr_0v_0$$ $$rv = r_0v_0.$$