Recent content by Penn.6-5000

The Pauli exclusion principle tells us that two electrons can't occupy the same quantum state. To get S=1, both electrons would have to have a spin of +1/2, which is OK only when some other aspect of their state is different, e.g. they're in different orbitals. In this particular problem, those...

Volume three of the Feynman Lectures does an excellent job of explaining the intuitive underpinnings of quantum mechanics---what superpositions are, what the hamiltonian does, what changes of basis are, and so on. The downside is that Feynman takes his time in getting to how his explanations...

Try doing it without either equation. I have a checking account; the total value of this account is called "V." There are four ways to change the amount of money in my account: I can write someone a check, someone else can write me a check, I can withdraw cash at an ATM, and I can deposit cash...

Your college's registrar should tell you which classes are prerequisites for quantum mechanics classes. If you want to know what subjects you have to understand in order to follow quantum mechanics, here's a decent list: 1. Be comfortable manipulating complex numbers. 2. Understand linear...

Careful, there. While it's true that quantum mechanics is named after 'quantization,' it isn't quite true that everything is quantized. Mr. Khemist got it right three posts back when he remarked that the standard formulation of quantum mechanics requires you to be able to take a derivative with...

At what rate do you radiate heat? The maximum emitted power is the Stefan-Boltzmann constant (5.67*10^-8 Watts per square meter per Kelvin^4) times the surface area of your body (Wikipedia gives an average of 1.73 square meters) times your skin's absolute temperature raised to the fourth power...

Time isn't "undoubtedly" anything; there is not yet a scientific consensus on how to unite general relativity with quantum mechanics. The modern presentation of quantum electrodynamics regards time as continuous, but it isn't compatible with general relativity. The string theories assume that...

No, instantaneous acceleration never makes a difference, even when we take relativity into account. Only your instantaneous velocity will affect angle measurements.

That's clever, but it isn't enough. How do you compare two clocks that are in different places? There are two ways: 1. Look at them "at the same time" and compare the numbers on the front. But that means different observers will get different answers. 2. Move the clocks to the same position...

Some measurements don't have a consistent answer between observers. That's one of the rules you had to sign when you first agreed to live in a relativistic world. A person on the train *will* observe things that directly contradict an observer on the platform, and that's just life. It turns out...

An observer at the station will think the rear clock started first. But other observers will give different answers.

This question is usually discussed as the train paradox: lightning strikes the front and back of a train simultaneously, but not all observers think it's simultaneous. The resolution is to just leave it unresolved. If you observe events taking place simultaneously at two different points, some...

Think of it in terms of r's having to cancel. Work = Force * distance = Torque * theta. If Torque = Force*radius then theta must equal distance(around the circumference)/radius so that the radii cancel. Applied power = Force * momentum = Torque * angular velocity. If Torque = Force*radius then...

A note to Mr. Klimatos on what would happen if the hypothesis were correct: This idea has come up in astronomy as "Olbers' Paradox." The paradox is that if the universe were infinitely large (and it were old enough for light from everywhere to have reached the Earth), then there would be stars...

It does require some time to mix thoroughly and yes, the fact that it's moving will help it mix pretty quickly. What I meant was that the fact that the exact amount of time is of no consequence. There's no equation into which you can plug "1.5 seconds" to get a useful answer. But it's reasonable...