Recent content by tomprice

I think that learning about Grobner bases / Buchberger's algorithm will help you. There are algorithms based on these concepts for solving systems of polynomial equations.

false alarm Nevermind I got it.

I am confused about lebesgue measure. I have heard that the lebesgue outer measure of the rational numbers is 0. So could someone please give an example of a set of open intervals such that: a. The union of these intervals contains the rational numbers on [0, 1] b. The sum of lengths...

Alright thanks again robphy that answers it pretty well.

Ok so I begin by entertaining the following hypothesis: Suppose a number of points are selected in spacetime, and then all relationships between these points that are invariant under Lorentz transformations are recorded. Given only these relationships, one should be able to reproduce the...

Ok thanks loads for that

Could someone pleases either: a. Justify the notion that the Lorentz interval between two events is independent of the observer, without referring to the Lorentz transformations. b. Derive the Lorentz transformations without resorting to the notion that the space-time interval between two...

No, thanks to you, it was an interesting problem.

whoa that's weird... so complete photonic bandgap will not necessarily happen here because of the relative phase shift between reflection and transmission; could you please give an example of a situation in which it would happen? Thanks.

The forces acting on mass B are the force of gravity and the force of tension from the rope. The forces acting on mass A are the tension, gravity, and normal force, the last two of which cancel out. The horizontal component of the force on mass a is the same as the tension in the rope, since the...

Thanks for the link, it was interesting. So does this mean that, whenever you have an electrical current flowing through a wire, the wire gets a slight negative charge due to relativistic length contraction?

Thanks Sojourner I think I get that... So, if the two lasers, instead of being the exact same frequency, were of a very slightly different frequency, we would get both areas with nearly completely destructive constructive interference and with nearly completely destructive intereference (and...

Ok Sojourner, thanks for that answer, I think it's a little over my head though. First of all, could you please elaborate on what you mean by: a. "probability of interaction" - interaction with what? b. "Transfer its energy" - transfer energy to what? + A little off-topic point for dst...

Let's say that the electric field caused by a given laser at a distance d from the mirror is given by sin(d). Let's say that the electric field caused by the the other laser at a distance d from the mirror is given by sin(d + pi), which must be possible with correct positioning of the laser...

Ok let me clarify my question. If the magnet is stationary, no force will be exerted on the charged particle, supposing it stationary as well. (Let's ignore gravity, or suppose the magnet is massless, or something like that...) If the magnet is moving along the axis of infinite length, a...