Recent content by closet mathemetician

You are right, that "moving through time" in, say, a two-dimensional spacetime is represented by a static line in the time direction that is not dynamic. I was playing loosely with the language. However, if I have velocity in space, then my worldline in spacetime has a slope between vertical and...

I think another weakness of the rubber sheet analogy is to picture a ball rolling along the sheet. A ball is an object with an existence separate from that of the sheet. So now you need something to hold the ball on the sheet. I like to think of it this way: take a deflated balloon and draw...

The way I think about this is that you can't have any knowledge of any event that happens anywhere until the light from that event reaches you. From your perspective, it doesn't "happen" until the light from the event reaches you. For all events that emit light at some time and at some position...

If everything is moving at the speed of light in the time direction all the time, Then how does the light from an event in the past ever catch up and reach me?

LukeD - Thank you. That is exactly the sort of answer I was looking for. I have no objections to moving the post to SR/GR.

What is the difference between the Algebra of Physical Space (APS) and the Spacetime Algebra (STA), and why do we need them both?

Hi Mahinda, I'm no expert on either subject, but I've had the same question. I'll attempt to answer it. I think tensor calculus and linear algebra are two different ways of looking at some similar subject matter. Tensor calculus is more like an extension of vector calculus. Calculating...

Quoting myself, Could this be the basis for quaternions, i.e., three complex planes? However, there is really only one imaginary dimension involved with all three planes.

I know that generally complex numbers are represented in a two-dimensional plane with one real and one imaginary dimension. I also know that we have the quaternions, consisting of one real number and three imaginary numbers. The imaginary axis is always perpendicular to the real axis. The...

Yes, I understand that, but they seem to both increase in the same direction. More entropy, more symmetry, less entropy, less symmetry. And the idea of the 2nd law of thermodynamics, that entropy increases over time seems to line up with the idea that the universe's symmetry has broken, but is...

In my opinion, dimensions are simply a theoretical degree of freedom. There is no reason why there shouldn't be an infinite number of possible degrees of freedom. However, actual geometrical structures don't generally have an infinite number of dimensions. They have some finite number of...

Twofish-quant, yes I know that my post is along the basic lines of cosmological thought. The thing that just occurred to me was the connection between symmetry and entropy. I hadn't put those two together before. Even though, based on the responses, I haven't got it exactly right, I believe...

Could the universe have been at one time near the time of the big bang, in a highly symmetrical state, like liquid water? Consider that water has maximal entropy, AND maximal symmetry. Then, the maybe the universe underwent a phase change and "froze". When water freezes it acquires rigid...

In the various pages I found in a Google search, i.e., Wikipedia, etc .. in defining weights they all specified that the weights must be non-negative. Suppose you are looking at the profit and loss statement of a foreign company over a period of time. You want to convert the foreign currency...

Why do weights in a weighted average have to be positive?