Recent content by Orodruin

The previous reply is excellent, so I will just add that the role of physics as an empirical science is to describe how things work, not to provide some underlying truth. You can always search for more detailed models, but physics will never describe what

I’ll try to offer yet another perspective. The function ##f## describes the shape of the wave. We can consider a point on the wave with a particular constant value of ##f##, call it ##f_0##. Now consider how the point (or more generally, points) with this value are moving with time. We have...

Because it was never there to start with. The position vector in cylinder coordinates is ##\vec r = \rho \hat \rho + z \hat k##, there is no ##\phi \hat \phi## term.

Thank you everyone who voted for me and others! Not sure I deserved it this year considering how inactive I have been over the last 12 months, but still grateful. Almost instant mentorship and subsequent disqualification from member award polls? 😂

Yes, they would, but this would be attributed to the spaceship accelerating rather than the light following a curved path.

If neutrinos collide they would undergo a regular weak interaction. This can either be elastic or inelastic depending on energy. An elastic scatter would not be very noticable. The cross section of interaction would increase manifold if the com energy approaches the weak scale.

… shortly put: if it is infinite today, it was infinite then. But with a smaller scale factor.

Not only is a Master’s degree helpful, it is often a prerequisite to be eligible for a European PhD program. (Local variations apply depending on country)

Planes, I agree, but not with a single ball, which was my understanding from the discussion.

I believe that is intrinsically applying the Levi-Civita connection as the geodesics of the Levi-Civita connection are the paths that extremise path lengths. More generally, for an arbitrary connection you could define the surface of the ball as the set of points reached from the center after...

Not only why, but ”you cannot”. It is impossible to do it without parallel transport - or at least without parallel transport being defined - as curvature is a property of the affine connection that defines what parallel means. OP’s misunderstanding that parallel transport requires embedding is...

Free-streaming means that the (average) density of matter is so small that the mean-free path exceeds the size of the Universe. The Universe is pretty low density after all.

I mean, it is a two-dimensional gyroscope, i.e., one where the gyroscope is only free to rotate around one axis ... :wink: I'd like to add some additional structure to this: In a Euclidean space - such as the flat plane - it is clear what "the same direction" means between points (precisely...

The FW transport in GR is the correct thing to use for gyroscopes precisely because we are talking about its frame describing spacelike directions orthogonal to the timelike tangent of the world line. In the Riemannian setting, consider for example a gyroscope in regular Euclidean space, which...

Compare to the density of the Sun's photosphere. The number density of hydrogen there is about ##10^{24}## per cubic meter. But of course the Sun is rather small in comparison to the Universe and we must remember what we mean by the light in the early Universe not being free-streaming - it means...