Recent content by cesiumfrog

(Reviving an old thread based on a recent request by "mr.smartass#1") A sophisticated answer has to do with the notion that symmetries give rise to conserved quantities. The mathematical expression of this relationship is named Noether's theorem. In this case, the fact that the laws of physics...

If I count n heads out of N tosses, based on my prior assumption that the bias (the true probability of heads) could equally be any value between zero and unity i.e. P(a≤r≤b)=\int_a^bdr, and noting the binomial distribution is the well-known likelihood of the observed result for a particular...

Well, ok, but can't you still do that with only one spatial dimension too? Just by taking a large enough detour in space (e.g. (0,0) → (0,10) → (1,1)) then a curve between the two events will be space-like.

Incnis, I don't follow. If two events in Minkowski space are connected by a null geodesic, I can't see any way of also connecting them with only space-like curves.[mistaken] Conversely, at the photon sphere of the Schwarzschild spacetime it is trivial to find a time-like curve between two events...

Ah, I see, so that formula involved an approximation that the ratio wasn't extreme. Is there a exact Bayesian approach, given a prior distributed uniformly over [0,1] for the population's ratio, to correctly determine the credible interval for the estimate of that ratio from the sample?

Hi, If I poll 10 people (with a yes/no question), and all of them respond with 'yes', should I report the rate of 'no' answers (in the greater population) is "zero plus or minus zero", or simply be confident that it is "less than one in five"? I ask because using the "margin of error" (or...

Hi, How can null geodesics be defined? Obviously the concept of parallel-transport, of the tangent to the curve, applies equally well to null curves as to time/space-like curves. Technically this is only the definition for an "auto-parallel", not for a "geodesic". For example in...

Thanks, lurflurf! So.. two questions.. If the branch cut is customarily at the negative real axis, which side does that axis itself fall on? (For example, if we were to trace a contour from -1 to +1, do we pass the origin on the south side of the complex plane? And if there wasn't just one...

Why does the incomplete gamma function have an imaginary component, when the exponential integral does not? \Gamma(0,z,\infty)\equiv\int^\infty_z \frac{e^{-t}}t dt Ei(z)\equiv-\int^\infty_{-z} \frac{e^{-t}}t dt Looking at how these integrals are usually defined I would have expected them to...

Ah. So some authors combine residual strong force with Pauli degeneracy pressure, expressing this as a difference between the strength of proton-neutron and same-same interactions, which makes shallower the potential well of whichever kind of nucleon is in excess. Others prefer just to say...

Perhaps may I ask slightly different questions: Why do nuclei with equal ratios of protons and neutrons (e.g., in elements lighter than calcium) tend to emit protons more easily than neutrons? Why is the proton-neutron force stronger than the proton-proton and neutron-neutron...

So let the iron marbles be able to turn to stone! Wouldn't you still predict the remaining portion of iron marbles to be the ones with the best chances of coming out of the cup? I can see how the weak nuclear force can directly determine whether or not a nucleus is stable to beta decay, but...

K^2, though I respect that this is supposedly much closer to your area of speciality than mine, I'm really having difficulty making sense of your reasoning (in context). For example, I don't see why the total energies would stay the same, nor why the difference between electrostatic potentials...

Thanks for the replies! So are Blatt & Weisskopf mistaken when, comparing protons to neutrons, they write "The protons are more strongly bound by the nuclear forces in order to compensate for the electric repulsion energy"...

Why is it that neutrons evaporate from nuclei more easily than protons do? Intuitively, since protons are electrostatically repelled (in addition to whatever nuclear forces they have in common with neutrons), one would expect protons to be ejected more readily than neutrons. (Maybe this is...