Suppose we have a field in a curved spacetime, and we want to know how fast it is changing as you move in some direction in space or time. Because there is more than one possible direction to move in, … Continue reading
One of the things I've been trying to do on this blog is to explain Einstein's theories of relativity. Here are my previous posts on this subject: Time as the Fourth Dimension? The Ten Symmetries of Spacetime Fields Geometry is … Continue reading
I've told you so far that the gravitational field is encoded in a matrix known as the metric. Here it is, displayed as a nice table: There's 10 components because the matrix is symmetric when reflected diagonally. The 4 diagonal … Continue reading
In my last post about spacetime, I explained how the geometry of spacetime is determined at each spacetime point by a set of 10 numbers. These 10 numbers are packaged together into a matrix called the metric, which is written … Continue reading
In Time as the Fourth Dimension?, I explained how to calculate the distance (or duration) squared between any two points of spacetime, using a spin-off of the Pythagorean theorem: Then I explained the Ten Symmetries of Spacetime, i.e. ways to … Continue reading
There's been a huge kerfuffle in the quantum gravity community since this summer, when some people here at UCSB published a paper arguing that (old enough) black holes may actually be surrounded by a wall of fire which burns people … Continue reading
What is the world made out of? In the most usual formulations of our current best theories of physics, the answer is fields. What are those? Well, if you know what a function is, you're already most of the way … Continue reading
Previously, I described the main formula of Special Relativity: This formula tells us the amount of distance squared between two points (if ) or the amount of duration squared (if ). (By using some trigonometry we can also use this … Continue reading
You've probably heard that time is the fourth dimension. What does it mean? It should seem rather fishy that time should be the same sort of thing as a spatial dimension. We all know that you can only go in … Continue reading