Minkowski Space

The title is nothing more than Euclidean space merged with the dimension of time. In other words, your familiar three physical dimensions and one time dimension. I realized something with this space (maybe it's true) just now. You CANNOT have physical degeneracy since the dimension of time lifts any sort of degeneracy you might see in statics. By physical degeneracy I mean one cannot have the same physical value for one instant and another instant.

Consider something traveling on a ring. If we set this ring in Euclidean space (x,y,z), say on the x-y plane and start our something object at (x=R, y=0), where the radius of the ring is R, then if we think about the points in this 3D space where our something will can be, then we are (in this case) stuck on the ring. So, our something can start at (x=R, y=0) and rotate about the ring and be back where it started even after tracing out the shape of the ring. Physically, our something doesn't know the difference between the cylindrical coordinates (an inbreed from Euclidean space, instead of (x,y,z) defining a point in space we use (s,@,z) where z is equivalent to the z in Euclidean space, s is the distance from the z axis, and @ gives us the rotation about the z axis...really @ is denoted by the Greek letter theta, but I don't have a theta key or option) (s=R,@=0,z=0) and (s=R,@=360E,z=0) (E being degrees). With the help of cylindrical coordinates, we can see that we've made a full rotation, but we're in the same spot! This causes the degeneracy of our physical space. But in the Minkowski space, we have time to consider. Our coordinate in this space is denoted by (x,y,z,t). At the beginning of our something's rotation, it's at (x=R,y=0,z=0,t=0), but after making a full rotation, we now have (x=R,y=0,z=0,t=T). Clearly, these two state coordinates are not equivalent, and thus there is no more degeneracy. In other words, our something was someplace, then some time passed. During this time, our something could move or stay put, but it's state is always unique!

This is really somewhat of a trivial bit of information, but it was fun to think about since I just read that Minkowski space is Euclidean space tensored with the time dimension. Also, this degeneracy business is really fascinating when applied to other systems and spaces.

Biophys talk

I attended a talk tonight by Dr. Robert Austin prof of physics at Princeton. It was an entertaining talk on biology and physics and how the two fields have entangled over the last century and what biophysics may turn into in the future. His main points were on how his attempt at describing the physics of a single cell was extremely complicated and led him no where, whereas he had more success with looking at many cells at once, a many-body problem ,in physics terms. He also talked about evolution and how he's using microstructure enclosures connected by nanocannals to show that bacteria are social. What he has done is injected a food source in one of the ten enclosures and watched the bacteria congregate in various enclosures. Over time, the bacteria migrate from enclosure to enclosure and eventually exist in each block after about 5 days of having only one enclosure getting food. I don't recall where his physics was, but it was neat to watch. He also gave off the vibe that he has been a trouble-rouser over his entire career...calling various people idiots and insulting many biologists. At least it was entertaining.

Degeneracy and Orthogonality

I HATE language!

I won't rot in hell if you just say so. I mean, come on, life really isn't that big of a deal. We just make it into an awesome fabrication of a roller coaster ride with all the sweet ups and downs and twists and turns. Which, if you think about it is just a degenerate cliche. All you need is vertical and horizontal and you're golden. But if all you would do is say everything will be okay, then sweet, I can get behind that and there's no problem, right? Wrong. Climbing to the stars doesn't happen overnight, or wherever there is no hell. In fact, why say we live in hell when all there really is is vertical and horizontal. Why don't we just say, I'm more negative vertical, or some sort of 1984 BS form? If you think about it, if heaven were up and hell were down, then all you'd need is vertical. There'd be no need of the horizontal. And THEN, what about the forward setting? I'm not a cartoon character on a page am I? Absolutely, probably! Now back to the real question of heaven and hell being in-line, if hell is just the negative of heaven, then what's the point in having both. All you need is vertical to get both. That's annoyingly degenerate! However, the two are still polar opposites, or so I'd think. If that's so, then wouldn't one of them be horizontal? What does that mean?! I won't say, because I don't want to. However, let's just note that heaven and hell shouldn't be under the same axis. With this, I could say I'm so much vertically in heaven with this much of a horizontal in hell to still go around. But what happens if I have negative vertical? That is, negative heaven! So I contradict myself and we're back to heaven and hell being degenerate from vertical...or horizontal...or forward....whatever, pick one. I'm going to pick vertical since that's less confusing in my reared mind. Now, there's got to be something about the vertical that will allow me to exclude heaven from hell since we've agreed they're polar opposites. RIGHT?! So all I'm sayinsisthat whatever happened to the horizontal and forward? Is life just a one state collage of degenerate bull shit? Does heaven and hell ever change over the years? over the seconds you read this? Ask yourself if you believe the bull shit you grew up with. Do you believe it's bull shit? Or should I have asked you if you believe in the mirage you ran into and you saw in it a reflection of yourself? If so, does that make you a skewed image of reality that you cannot see? Are you what you think you are? Or have you made it out of the mirage stage and are looking at the beautiful creature that you really are...you wouldn't think you're truly ugly at the core would you? I'm a fucking bad ass and I can prove it. Did I lose my train of thought? NO! I made you think.

It is time

to go to bed. Perhaps I'll unload the good ole thoughts of my physics here. Get ready people; you're gonna like this. I promise...in a mix state where you'll like it and you won't. Read this, and it'll change your perspective. That I can promise with certainty.

you might search (wikipedia sort of covers this):
collapse of the wave packet
superposition amplitude