My previous post was a description of the shape of spacetime around the Earth. I framed the discussion by asking what happens when I drop a ball from rest above the surface of the Earth. Spacetime is curved. And the ball takes the straightest possible path through spacetime. So what does that look like? Last time I generated a representation of the spacetime to illustrate. However, I generated some confusion by claiming that it “should be obvious” that the straightest possible path is curved towards or away from the Earth. When a textbook author says “the proof is trivial”

# Geometry

##### Geometry / Physics / Relativity / etc.

# Our Local Spacetime

General relativity tells us that mass (and energy) bend spacetime. And when people visualize the effect of a planet on spacetime, they usually imagine something like in figure 1, where the planet creates a “dip” in spacetime much like a “gravitational well.” But today I’m going to show you what spacetime actually looks like near a planet… and it doesn’t look anything like the common picture. This is the fifth part in my many-part series on general relativity. Here are the first four parts: Galileo almost discovered general relativity General relativity is the dynamics of distance General relativity is

##### Geometry / Mathematics / Physics / etc.

# General Relativity is the Curvature of Spacetime

Figure 1 shows light from a distant blue galaxy that is distorted into a so-called Einstein ring by the curvature of spacetime around a red galaxy. This is called gravitational lensing and today we’ll learn how it works. This is part three of my many-part series on general relativity. Last time, I told you how general relativity is the dynamics of distance, which we know is a consequence of the fact that gravity is the same as acceleration. This time, I describe the consequences of the fact gravity warps distance. And in the process, we’ll learn precisely why gravity

##### Astrophysics / Geometry / Mathematics / etc.

# Speculative Sunday: Can a Black Hole Explode?

Nothing can escape the gravitational pull of a black hole, not even light. That’s why they’re, well, black. (Of course, as I’ve described before, black holes can glow very brightly, thanks to all the in-falling matter. Sometimes they even produce gamma rays. I’m also ignoring the negligible amount of Hawking radiation that black holes theoretically produce.) Once you pass the event horizon of a black hole, you cannot ever escape. Escape is simply forbidden by the laws of physics. That is, of course…if there actually is an event horizon, not just something that looks like one. Carlo Rovelli ,

##### Electronics / Geometry / Mathematics / etc.

# Lightning Detection

Since I’ve been very busy lately my good friend Michael Schmidt agreed to do another guest post! Mike has a masters degree in physics from the University of Colorado at Boulder. You can check out Mike’s own blog at duality.io or his personal website Mike’s Personal Website. Without further ado, here’s Mike: Lightning Detection Currently, in the mid-west of the United States the first thunderstorms of the year have begun. Because I am a giant geek, I love lightning and I think tracking lightning is quite interesting. My personal favorite site is LightningMaps. On LightningMaps website youâ€™ll see

##### cosmology / Discrete Math / Geometry / etc.

# Quantum Geometry: Causal Dynamical Triangulations

A “quantum gravity expert” is presumably someone well acquainted with the details of our immense ignorance of the subject. I suppose I count. ~John Baez I long ago promised that I would discuss some of my own research. Here’s the first post that makes good on that promise. Today I’ll discuss a theory of quantum gravity. Why Quantum Gravity? Without a doubt, the two greatest advances in physics in the last 120 years were the advent of general relativity and quantum mechanics. These two amazing theories have totally changed the way we see the world. Quantum mechanics describes the

##### cosmology / Geometry / Mathematics / etc.

# A Mess of Cosmic Coincidences: Problems With the Big Bang Theory

The furthest bodies To which man sends his Speculation, Beyond which God is; The cosmic motes Of yawning lenses. ~Robert Frost, I Will Sing You One-0 I apologize for the long time of silence! I graduated from the University of Colorado about a month ago and was immediately assaulted by a huge amount of family affairs… and then caught up in moving. Sorry about this, everyone! My regular Sunday update schedule should resume next week. Last time, I described the theory of the Big Bang. I gave some history of the theory, and some reasons for why we believe

##### Geometry / Mathematics / Physics / etc.

# An Update On Kaluza-Klein Theory

I recently posted an article on Kaluza-Klein theory. This was partly because I was working a paper on it as a final project in my second semester of general relativity. The paper is finished, and I thought I’d upload it for the more mathematically inclined of my readers. If you’re interested, you can find it here.

##### Geometry / Mathematics / Physics / etc.

# Stuff From Shape — Kaluza-Klein Theory

There is geometry in the humming of the strings. There is music in the spacing of the spheres. ~Pythagoras When Albert Einstein and David Hilbert published the theory of general relativity, they weren’t just proposing a new theory of gravity. They were proposing a new way of thinking. In general relativity, gravity isn’t a force. Instead, it’s a natural consequence of the shape of the universe. Force comes from stuff. Matter pushes and pulls on other matter. A proton may need to use its electric field to attract an electron, but the field is a property of the proton.

##### cosmology / Geometry / Mathematics / etc.

# Receding Horizons: Dark Energy and the Expanding Universe

Astronomy compels the soul to look upwards and lead us from this world to another. ~Plato The history of astronomy is a history of receding horizons. ~Edwin Powell Hubble Last week, I discussed the possible shapes our universe could take. I offhandedly mentioned that not only is the universe expanding, but that that expansion is accelerating. We attribute this expansion to a mysterious phenomenon we call dark energy. This week, I want to explore the history of this idea and the beautiful experiments that tell us all is not as it seems. The Static Universe and Einstein’s Greatest Blunder