Hilbert Space

I'm a physics nerd, posting random physics-y stuff here. :D :D :D

[17blcak]

Reblog if I can go on your page and write stupid things in your ask box whenever I'd like to.

[nerdynoir]

Shut Up and Calculate

David Mermin

That's a one line summary of the Copenhagen Interpretation of Quantum Mechanics. It saves a lot of heartburn. :P

[shitphysicspeoplesay]

we share a common goal, friend. always strive to be a better physics

manifestlycovariant (via shitphysicspeoplesay)

[shitphysicspeoplesay]

A solution of Laplace’s equation which satisfies appropriate boundary conditions is unique. That is to say, there is one and only one such solution, so that if we solve a problem by guesswork and skullduggery, and someone else solves it with refined and elegant mathematical techniques, the two solutions, in spite of their disparate pedigrees, must be the same.

Div, Grad, Curl, and All That, H. M. Schey (via shitphysicspeoplesay)

The Uniqueness Theorem <3 <3 <3

[zerostatereflex]

Neutron Stars Rip Each Other Apart to Form Black Hole

"This supercomputer simulation shows one of the most violent events in the universe: a pair of neutron stars colliding, merging and forming a black hole. A neutron star is the compressed core left behind when a star born with between eight and 30 times the sun’s mass explodes as a supernova. Neutron stars pack about 1.5 times the mass of the sun — equivalent to about half a million Earths — into a ball just 12 miles (20 km) across.”

Funny how the Universe is either epically violent or absolutely nothing happens. 

[shitphysicspeoplesay]

Is money a scalar or a vector? … Yeah, that’s right, it’s a scalar, although you have to ignore the fact that it always moves to the top one percent of the world’s population…

First year physics lecturer (via shitphysicspeoplesay)

[nerdynoir]

:D :3 Sharing the process and inventing little games helps me stay motivated.

[nerdynoir]

Stokes' Theorem

Now, this is a very popular result from vector calculus that is commonly referred to as Stokes’ Theorem by physics and engineering students. It is actually a special case of a generalized result and is also called the curl theorem. Now, you all know that it’s a handy way of relating the surface integral of the curl of a vector field over a surface S (say) to the line integral of the same vector field over the boundary C of the surface. We frequently encounter this in electromagnetism and you have to admit it: it’s a really neat tool. Also two of four Maxwell’s equation (Ampere’s Law and Faraday’s Law of Induction) involves curls of 3-D vector fields and their differential and integral forms are related through this result. By the way, the proof of this result is pretty daunting (or is it just me?!)

Now you have probably heard all this! I want to share with you a bit of it’s history. This theorem has really obscure origins. It is said that a “similar technique” was first used by Ampere himself in solving a few special problems. Probably, the theorem was first stated properly by Lord Kelvin in a letter to Stokes without proof in around 1850. Now Stokes gave this problem (i.e., the problem to find the proof of the curl theorem) as a question in the Smith Prize Examination of 1854. It is a prize awarded to two research scholars in theoretical physics annually by the University of Cambridge even today.

A bright young fellow of 23 did prove the theorem during the examination and eventually won the prize. Can you guess who it was? Well, it was none other than James Clark Maxwell himself! :D

Reference: “Calculus on Manifolds” by Michael Spivak (Preface, page no. viii) (Publisher: Addison Wesley)

[fouriestseries]

Chaos and the Double Pendulum

A chaotic system is one in which infinitesimal differences in the starting conditions lead to drastically different results as the system evolves.

Summarized by mathematician Edward Lorenz, ”Chaos [is] when the present determines the future, but the approximate present does not approximately determine the future.”

There’s an important distinction to make between a chaotic system and a random system. Given the starting conditions, a chaotic system is entirely deterministic. A random system, on the other hand, is entirely non-deterministic, even when the starting conditions are known. That is, with enough information, the evolution of a chaotic system is entirely predictable, but in a random system there’s no amount of information that would be enough to predict the system’s evolution.

The simulations above show two slightly different initial conditions for a double pendulum — an example of a chaotic system. In the left animation both pendulums begin horizontally, and in the right animation the red pendulum begins horizontally and the blue is rotated by 0.1 radians (≈ 5.73°) above the positive x-axis. In both simulations, all of the pendulums begin from rest.

Mathematica code posted here.

[For more information on how to solve for the motion of a double pendulum, check out my video here.]

[nerdynoir]

I can stare at this all day and not get bored! :D :D

http://scienceworld.wolfram.com/physics/DoublePendulum.html

[nerdynoir]

A mathematician named Klein Thought the Möbius band was divine. Said he: "If you glue The edges of two, You'll get a weird bottle like mine

http://mathworld.wolfram.com/KleinBottle.html

[schmidt-cassegrain]

Supernova SN 2014J, NASA/ESA

[caseybloomquist]

Interference

[nerdynoir]

Young's Double Slit Experiment sure looks trippy....

[birdfox]

Calvin and Hobbes - 09-01-1995

[nerdynoir]

Is that Dothraki?

[scientificphilosopher]

Given enough time, hydrogen starts to wonder where it came from, and where it is going.

Edward R. Harrison (via scientificphilosopher)

We are starsuff, wondering about the stars... :3

[nerdynoir]

Can Asimov be more awesome! 

[nerdynoir]

These keep popping up everywhere!

[humanoidhistory]

On January 24, 2015, the Hubble Space Telescope photographed three of Jupiter’s moons in transit across the face of the gas giant. This time-lapse imagery condenses 42 minutes, showing the progression of the moons Io (right), Callisto (center), and Europa (left). Each moon’s orbital velocity varies, proportionally slower with greater distance from Jupiter.

(HubbleSite)

[itsokaytobesmart]

Just caught myself staring at this Jovian splendor for three full minutes (which is a long time to stare at a GIF)

Here’s hoping that we get to see Europa up close in my lifetime. Like “from the surface” close.