Recent content by PlanckShift

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Physicists Detect Elusive Orbiton By "Splitting" Electron "Condensed-matter physicists have managed to detect the third constituent of an electron — its 'orbiton'. Isolated electrons cannot be split into smaller components, earning them the designation of a fundamental particle. But in the...

So why is it that when you tilt the plates of a laser to different angles you see the different normal modes projected on the screen?

Anti-matter can be thought of as regular matter that's traveling backwards in time.

But ε2 = 0 remember? Think about it. How do you find the inverse of a+bε? Rationalize the expression using ε2 = 0. Then find where the resulting expression is undefined.

Definition of a field.

The real numbers are a field even though 0-1 doesn't exist. It's the same thing with this definition of complex numbers although elements along the "imaginary" line don't have inverses.

1/ε is undefined. It is so a field. It's closed under linear combinations. It's commutative and associative. It has an identity element: 1+ε0 and the inverse element which I've described already. It's distributive, too.

Some experiments are too advanced t conduct in one's basement. One also gets the advantage of bouncing ideas off others when working in with a group of people learning the same subject

What's the inverse of 0? The inverse of 1/(a+bε) can be found by rationalizing. 1/(a+bε) * (a-bε)/(a-bε) = (a-bε)/(a2-b2ε2) but ε2 = 0 so that last is (a-bε)/a2 = 1/a - b/a2 ε . The only problem comes with division by 0 which is undefined just as with real arithmetic.

There is a second delta function at the negative frequency. In addition, there's a phase shift of \pi/2.

Multiplication by i is an instruction to rotate your vector by 90_o counter-clockwise. Two successive rotations, or i^2, is an instruction to completely reverse your direction. Said another way, multiplication by i^2 is the same as multiplying by -1. Examples of creating your own...

Conservation of momentum = linear shift invariance.

Once you get Maxima you can use an editor like TeXmacs.

MMA isn't free but Maxima is.