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Dec
6
comment Are Asimov's short duration spacetime “jumps” feasible?
note that my answer does go the speculative route and is light on physics, but more technical answers about energy conditions, CTCs, some details about time dilation and estimates about interstellar travel with relativitic rockets are possible...
Dec
6
comment Are Asimov's short duration spacetime “jumps” feasible?
@DavidZ: paraphrasing, the questions are (1) Will superluminal travel ever be possible? and (2) If not, does that mean humans can never venture beyond the solar system? These are perfectly fine questions in the context of mainstream physics. Just because they were inspired by reading sci-fi doesn't make them non-scientific. Also, they aren't mainly about engineering as they are concerned with limitations imposed by physical laws instead of specific implementations.
Dec
6
revised Do the number of possible microstates increase as temperature decreases?
more explanation
Dec
6
revised Do the number of possible microstates increase as temperature decreases?
added 149 characters in body
Dec
6
comment Relationship between Energy and Time
energy is the component of momentum in a time-like direction
Dec
6
revised Are Asimov's short duration spacetime “jumps” feasible?
no solar sails?
Dec
6
revised Are Asimov's short duration spacetime “jumps” feasible?
added 146 characters in body
Dec
6
answered Are Asimov's short duration spacetime “jumps” feasible?
Dec
6
answered Do the number of possible microstates increase as temperature decreases?
Dec
5
comment Is the metric-induced topology relevant at all in a (psuedo) Riemannian manifold?
also note that if $g$ is a solution of the Einstein field equations, it needs to be differentiable at least twice, and there's a pre-existing topology due to the diferential structure of the manifold, independent of any metric tensor; there are other kinds of topologies that might be of interest to physicist (Wikipedia lists two of them)
Dec
5
comment Is the metric-induced topology relevant at all in a (psuedo) Riemannian manifold?
a GR singularity is not necessarily topological: possibly, it's 'just' a metric degeneracy; @CristiStoica probably has something to say about that...
Dec
5
comment Physical observables and hermiticity
note that in the infinite-dimensional case, observables need to be self-adjoint, not necessarily Hermitian (eg position and momentum operators of the free particle aren't Hermitian); operators with continous or unbounded spectrum are a bit more complicated than most introductory courses on quantum mechanics suggest
Dec
3
comment How does quantum decoherence occur?
Can you give a mathematical explanation that is simple, precise, and easy to understand? No.
Dec
3
comment What is the Difference between a Lepton and a Fermion?
one more rather obvious example: nuclear spin
Dec
3
comment What is the Difference between a Lepton and a Fermion?
baryon resonances can have spin $3/2$ - not being in the most favourable spin configuration is where (all?) their additional mass comes from
Dec
3
comment Why is $\mathbb{R}^1$ different than Euclidean space $\mathbb{E}^1$? Roger Penrose road to reality
@David: exactly; after choice of origin (as well as a set of basis vectors), $\mathbb R^n$ can be used to label the points of the abstract affine space
Dec
3
revised Why is $\mathbb{R}^1$ different than Euclidean space $\mathbb{E}^1$? Roger Penrose road to reality
deleted 33 characters in body
Dec
3
answered Why is $\mathbb{R}^1$ different than Euclidean space $\mathbb{E}^1$? Roger Penrose road to reality
Dec
3
comment Why is $\mathbb{R}^1$ different than Euclidean space $\mathbb{E}^1$? Roger Penrose road to reality
You can use a vector space to represent an affine space - you just have to remember that you're not allowed to do addition or scalar multiplication. Consider dates: What's the result of adding March 13th to December 4th? That's nonsense. However, what you can do is add a duration to a date, which would be what is called 'displacement vector' in general. General relativity (or analytical mechanics) goes even farther than that: In curved spaces, finite displacements generally do not make sense, and you have to stick with infinitesimal ones (tangent vectors)
Dec
3
comment Why is $\mathbb{R}^1$ different than Euclidean space $\mathbb{E}^1$? Roger Penrose road to reality
Yes. Going by name, it's probably supposed to be an Euclidean space, which is an affine space with some additional structure, in particular angles (not terribly useful in the 1-dimensional case) and distances and corresponding motions (rotations and translations)