Of Snowflakes And Spacetime.

Physics student, by the name of Christophe. The devolution of Christopher, very rare and can often be found around pool tables.

[mirai-e-jump]

[brianstowell]

Acadia National Park, Maine

Surprisingly, I was the only car in the parking lot at the peak of Cadillac Mountain for this “sunset” a couple nights ago. A little rain scared all the tourists away and I had it all to myself. Looks like just home.

Instagram

[thegoodvybe]

[quantizedweird]

The derivative of velociraptor is acceleraptor

[faronmckenzie]

STEPHEN HAWKING 1942 - 2018

Neil deGrasse Tyson

“His passing has left an intellectual vacuum in his wake. But it’s not empty. Think of it as a kind of vacuum energy permeating the fabric of spacetime that defies measure.”

[webeducationsciences]

physics formulas

[justbadpuns]

The only thing flat-earthers fear is sphere itself

[mathprofessorquotes]

It’s just sexier to refer to a single electron on a single atom.

Grumpy postdoc  (via mathprofessorquotes)

[chris-tophe]

I like this loading screen for Pokemon Go.

[quantanaut]

What we know about dark energy:

All of the matter in the universe, such as atoms, electrons, and dark matter (an unrelated subject), take up only about 32% of all the energy in the current observable universe. The other 68% goes to dark energy; a mysterious force that fills up all of space, and is driving the expansion of the universe.

When Einstein wrote his theories of relativity, he believed we lived in a perfectly static world; it never began, it will never end, and it will always stay the same size. In order to make this work mathematically, he introduced a mechanism that would balance out the force of gravity: the cosmological constant. However, when Hubble discovered that the universe was expanding, Einstein threw out this idea, calling it his “greatest blunder.”

At the time, people expected that the expansion of the universe would be slowing down, since gravity pulls things together, but it seemed as if the expansion was actually speeding up! Not only were distant galaxies receding away from each other, but they were receding away faster and faster, against the known laws of gravitation. The only way we can explain this without sacrificing Einstein’s laws of gravitation was to again reintroduce the cosmological constant, but altering it slightly to beat out gravity instead of just balancing it.

So, what exactly does the cosmological constant mean? Essentially, it means that empty space actually has some energy in it, inflating it like the surface of a balloon. Since this energy comes from space itself, it acts as a feedback loop; dark energy creates more space, more space creates more dark energy, which means even more space, and so on. And yes, this does mean that energy is not conserved, which is actually allowed in general relativity. Still, you can’t use this energy in any useful way.

While the cosmological constant is the most likely source of dark energy, it’s not the only candidate. Other theories, such as quintessence and moduli, are similar to the cosmological constant, but are allowed to change throughout space and time. Because these theories would look so similar, it’s difficult to tell which one is correct. But whatever dark energy is, it determines the ultimate fate of our universe.

[garadinervi]

Proof Without Words: Cubes and Squares, by J. Barry Love. Originally appeared as: Love, J. Barry, Proof Without Words: Cubes and Squares, Mathematics Magazine, vol. 50, no. 2 (March 1977), p. 74

/ Fermat’s Library /

[quantummechanics]

Time doesn't exist, clocks do

[astrophysics-official]

Euler’s Identity//e^(i*π)=-1 PROOF

I’ve received several requests for the proof for eπ*i= -1, also known as Euler’s Identity, so here it is. If you have not taken calculus, you’ll have to trust me on a few parts, but you’ll definitely be able to understand. If you have any questions or I didn’t explain something right, let me know! The first part is a little confusing, so bear with me, but once we get past it, it’s significantly easier to get.

Before I do the proof, it’s important to explain what Taylor polynomials are. Taylor polynomials are polynomials used to approximate//estimate values for functions we can’t calculate by hand, such as sin and cos functions. Its general form looks like this (it’s intimidating, i know, but don’t worry):

where f’ is the first derivative, and Xo is the “starting point” (usually 0) and X is the point you’re trying to find a value for. Basically, each term is the nth derivative divided by n factorial, times x^n, and the Taylor Polynomial is all of these terms added together. This function goes on forever, or until you want to stop. The more terms you add, the more accurate your function is.

If you haven’t taken calculus, don’t understand, or don’t like math, you don’t need to worry about the formula or what it means, just that Taylor polynomials approximate functions.

The Taylor polynomials for e^x, sin(x), and cos(x) look like this:

meaning, these polynomials can approximate the functions above. We’ll need all of these for the proof.

If you don’t understand the above math, all you’ll need to know is the Taylor polynomials for e, sin, and cos, and that they are equal to those functions.

Now we’re going to do the actual proof. For this, we’re going to take the Taylor polynomial for eix and expand it:

Now, remember these powers of i:

since i^2=-1, we can substitute that value in every time we see an i^2, every time we see an i^3 we evaluate it and write -i, etc. Basically, we’re simplifying all the values of i. This leaves us with some terms having i in it, and other terms not having an i. We can group these terms separately, with terms not having i in one group, and terms having i in the other:

We can factor out an i from the terms on the right, since they all have an i:

Take a look at the two sets of terms we have remaining. The one on the left looks like the cos Taylor polynomial, and the one on the right looks like the sin Taylor polynomial:

because of this, we can substitute in sin(x) and cos(x) into the equation:

This general form is called Euler’s Equation. Since we are trying to find e^(pi*i), we plug in pi for X:

cos(π)= -1, and sin(π)= 0, so we evaluate and get:

This proof is kinda mind blowing and feels like math magic, but it’s real and it’s pretty cool. You’ll use it in differential equations classes. I hope you thought it was interesting and were able to understand it. If any of you have any questions, be sure to let me know!!!

[watcheroftheskies1335]

[maxwellsequations]

Laplace transform table. Source. (I’m obsessed. <3 And figured y’all would like this one, too!)

[mathprofessorquotes]

The third derivative is called jerk. I met a lot of third derivatives on the road this morning.

Calculus professor (via stem-and-leaves)

[shitphysicspeoplesay]

My goal in life is to compute as few integrals as possible, and to make an even number of sign errors

quantum mechanics lecturer (via shitphysicspeoplesay)