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14h
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'
14h
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?
15h
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)
15h
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
18h
comment Needed small explanation of the notation in this paper
@Fluctuations: Right (modulo a factor of $1/2$ depending on the chosen convention)
18h
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
18h
comment Needed small explanation of the notation in this paper
see en.wikipedia.org/wiki/Antisymmetric_tensor#Notation
1d
comment Can all fundamental forces be fictitious forces?
but also keep in mind that there are classical forces corresponding to quantum YM fields (cf Wong's equations) - they just aren't terribly useful
1d
comment Can all fundamental forces be fictitious forces?
wouldn't a link to something about Kaluza-Klein theory be more appropriate instead of classical YM?
Nov
17
comment How, in practice, could instantaneous signalling violate causality?
note that any superluminal signal comes with a critical frame where is appears instantaneous; for an explicit example of how superluminal signals violate causality, see en.wikipedia.org/wiki/…
Nov
16
comment Physical meaning of the angular momentum
@DavidHammen: but just choosing a different point of reference will not affect linear momentum - in contrast to angular momentum, you need to introduce relative motion for that to happen; that aside, your point is of course a valid one
Nov
15
comment Is a photon really massless?
@kstb: a photon indeed has no rest mass; if you chose to do so (I do not), you could assign a relativistic mass that depends on the photon's frequency
Nov
15
comment Is a photon really massless?
@kstb: $E=mc^2$ is incomplete if $m$ denotes rest mass; the general formula is $E^2=m^2c^4+p^2c^2$ with special cases $E=\gamma mc^2$ for massive and $E=h\nu$ for massless particles; in principle, you could assign a 'relativistic mass' of $m_r=h\nu/c^2$ to photons, but personally, I wouldn't recommend doing so
Nov
3
comment What is a rocket engine thrusting against in space?
the rocket doesn't push against empty space, but against its exhaust gas
Oct
19
comment How quickly does gravity extend from created mass?
@LDC3: it's a theoretical prediction consistent with the orbital decay of binary pulsars, most famously PSR 1913+16 (cf Nobel price 1993, arXiv:1011.0718)
Oct
16
comment Are Lockheed Martin nuclear fusion claims realistic?
see also en.wikipedia.org/wiki/Magnetic_mirror
Oct
16
comment What is divergence?
The divergence of a vector field is the infinitesimal relative change in volume when transporting a volume element along its flow. The abstract definition in terms of Lie derivative and volume form is quite intuitive here.
Aug
10
comment QM without complex numbers
@Problemania: $U(n)=Sp(2n,\mathbb R)\cap O(2n)\cap GL(n,\mathbb C)$; however, the intersection of any 2 of the groups on the RHS is sufficient, and in particular $U(n)=Sp(2n,\mathbb R)\cap O(2n)$; complexity arises naturally when we deal with compatible symplectic and orthogonal structures; of course it's equally valid to say that symplectic structures arise naturally from compatible orthogonal and complex structures or orthogonal ones from compatible symplectic and complex ones; but complex structures are arguably less well motivated from a physical (or perhaps 'philosophical') point of view
Aug
3
comment Why can't we do some basic algebra in tensor calculus?
assuming a background in basic linear algebra, think in terms of matrices (which are rank-2 tensors): not all matrices are invertible, and those that are generally aren't orthogonal (ie $A^t\not=A^{-1}$)
Jul
31
comment Which function denotes the energy of thermal motion within a system?
$\frac32 NkT$ for translational motion as well as appropriately weighted multiples of $NkT$ for vibrational and rotational motion as long as quantum effects can be neglegted (ie the spacing of the discrete energy levels is much smaller than $kT$)