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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)
Dec
3
comment Why is $\mathbb{R}^1$ different than Euclidean space $\mathbb{E}^1$? Roger Penrose road to reality
see en.wikipedia.org/wiki/Affine_space
Dec
2
answered Why is coordinate time frame dependent?
Nov
29
revised The relationship between the structure of spacetime and the existence of spinor field?
deleted 6 characters in body
Nov
29
answered The relationship between the structure of spacetime and the existence of spinor field?
Nov
28
awarded  Yearling
Nov
22
comment “Reality” of length contraction in SR
@Frank: sure, the analogy isn't perfect due to the non-Euclidean nature of Minkowski space, but the intuition you get from this isn't totally wrong; relativity of simultaneity, time dilation and length contraction are essentially about 'perspective'
Nov
22
comment “Reality” of length contraction in SR
Think of this way: if you tilt furniture so it fits through the door, did you really change its width?
Nov
22
comment “Reality” of length contraction in SR
@Frank: the clock shows accumulated time, but a rod doesn't accumulate anything; the different observers in relative motion could compare the (apparent) length of the path they took, though, and then they'll end up with different values; you can construct 'paradoxes' that way (think about adding stationary distance markers along the way travelled by a meter stick - basically a variant of the ladder paradox)
Nov
22
comment “Reality” of length contraction in SR
@Frank: the length of the rod only depends on the instantaneous relative velocity and is independent of the path taken
Nov
22
comment Needed small explanation of the notation in this paper
@Fluctuations: Right (modulo a factor of $1/2$ depending on the chosen convention)
Nov
22
comment Needed small explanation of the notation in this paper
@Fluctuations: $\delta_{jk}$ is the Kronecker-delta (a rank-2 tensor), but you only anti-symmetrize over one of its indices, leaving $k$ fixed
Nov
22
awarded  Custodian
Nov
22
reviewed Edit Needed small explanation of the notation in this paper