Recent content by kg4pae

This follows from a math theorem that says for any vector A the following is true: \mathbf{\nabla} \cdot (\mathbf{\nabla} \times \mathbf{A})=0 So if \mathbf{\nabla} \cdot \mathbf{B}=0 then there must exist an A such that \mathbf{B}=\mathbf{\nabla} \times \mathbf{A}

The proof depends on the fact that \gamma^2=\frac{1}{1-\frac{v^2}{c^2}} which in this context is true. Implicitly we are assuming all the caveats of SR and (for this proof) m\ne 0 It is possible to relax the requirement that m\ne 0 by proceeding from a topological argument using the invariance...

Now that you mention it, I notice that Gentoo is missing too. - Moooo. :)

Obviously those websites are out of touch with reality. In my experience, most people who are geared toward education are unabashed Ubuntu devotees. Those who value stability and freedom from licenses tend to gravitate toward Fedora/Scientific Linux. Theose who favor a thin installation will do...

Aside from the fact that this question appears to have some built-in wrong assumptions, it is a bit like asking if it is possible to explain a circle with only lines. The answer to both is "not very well". At any rate, there is a good explanation of gyroscopes and precession at...

The easiest way to get involved is to join an astronomy club After that you might want to attend a star-party (usually listed online). Usually they have professional presenters there that can get you started on a project. Also look for astrophysics colloquia at the closest university with a...

Virtual particles are particles that seem to violate Heisenberg's Uncertainty Principle. That is because the distance over which they act is smaller than the wavelength corresponding to their momentum. As a result, they are particles that must exist due to the requirements of conservation laws...

The word "singularity" is a mathematical term that means that the function is non-analytic. Generally this comes about due to the fact that some law is applied where it is not defined. An example is the very singularity we are talking about: g[0,0]=-(1-Rs/r) where Rs=dthe Schwarzschild...

Yeah, everytime I hear it too, I find that the two extremes on the issue gear up for war. Perhaps I can shed some light on the issue. The formula E=mc2 comes from a more basic formula in SR, which is E^2=p2c2+m2c4 When p=momentum=0 then we get E=mc2. Thus the formula tells us the energy...

I think you're right on Pr(B)=3/4. Now to find Pr(A and B), consider that "A and B" means "3 balls in one cell and 1 ball in another cell". This has to be 3/64. It would be 1/(4^3)=1/64 if the balls were labeled as to their order, but apparently they are not, so Pr(A and B)=3/64. At least...

Actually I don't object. It's just that it wasn't specified in the original post. Your restriction that the muon exists such that it moves exactly one circle of the helix in its lifetime took some thinking for me to accept, considering that individually muons decay randomly. - But this is just...

The only objection I have with this is that the "T" in \omega=2\pi/T is the period around the helix, whereas the "T" in (cT,0,0,0) is the time to decay for the muon. Otherwise what you've said is right on.

Not quite. Let cos(\theta+\alpha)=1. That will give the maximum for 3 cos(\theta) - 2 sin(\theta) after it is multiplied by R. Since R is effectively a constant any maximum of cos(\theta+\alpha) will be proportionate to R cos(\theta+\alpha)=3 cos(\theta) - 2 sin(\theta).

No problem. A good start with LaTex is http://frodo.elon.edu/tutorial/tutorial/". Others can be found by Googling "latex tutorial". At any rate, take care, 73s and clear skies.

Note that cos(\theta+\alpha)=1 means that \theta=-\alpha. However, the pattern repeats every 360^o.