If you've grokked what I've written so far, you may have noticed something. Without a particle, without mass, without a "thing" the property of "velocity" can be attached to, velocity becomes kind of difficult to reconcile with the universe as we observe it. What is motion? How can what is, basically, a wrinkle in spacetime be said to meaningfully "move"? As it turns out, we already have the answer in relativity.
Lorentz Contraction is the phenomenon in relativity in which objects contract along their axis of motion relative to the direction of motion. It isn't just the objects themselves, either; everything contracts, even the objects' own gravitational fields. By "contract", I mean that they get flatter, from an outside observer's perspective, along the direction of motion, as a proportion of lightspeed; an object somehow moving at the speed of light would appear as a perfectly flattened object.
At first, this might appear to be a product of subjectivity, rather than something that is "really" true. The trick in understanding Lorentz Contraction is to notice two things: First, that the gravitational field is also contracted, and second, that this means the density of spacetime is being distorted. Which is to say, the object isn't "really" flattening, but rather it is occupying a space that is bigger lengthwise (where length is parallel to the direction of motion) than the surrounding space.
And it isn't symmetric lengthwise; the space forward of the origin is slightly denser than the backwards section. Which is to say, space is denser forward of the ship than behind it. If you'll recall how gravity moves things, this is the same principle. We typically think of Lorentz Contraction as being a property of motion, but it is equally valid to think of motion as a property of Lorentz Contraction. And once you notice this, the notion of motion causing Lorentz Contraction becomes unnecessary; they're the same phenomenon, with Lorentz Contraction being the more basic.
Once we start thinking in these terms, we can start to redefine "motion" as a wave distortion in spacetime, or more specifically a wave distortion in the wave that is mass. This is a useful concept, but we aren't quite done yet; we need a mechanism of imparting this wave distortion on our mass-wave.
It's already been invented. I mean, I figured it out, but somebody figured it out long before I did, so I can't claim any credit. When objects are accelerating, they get an additional kind of distortion applied to them, which looks - not without accident - exactly like gravity. This phenomenon is called "Rindler Coordinates".
Now, I just made a massive leap, so let's take a quick step backwards. Let's try to figure out what gravity looks like to an object in it's influence, and what acceleration looks like.
Imagine two point masses in space. We'll simplify our mass wave to a single gauge, gravity. Point A, Point B, and us an observer at Point C. From Point C, the region between the two masses is denser. No surprise there. The interesting thing happens when we only examine the gravitational field of one of the two points, completely ignoring the other. Let's say we are looking at Point B.
Because the density between the two points is higher, this means that, from our outside perspective, the nice neat even distribution of spacial density, cleanly increasing as you approach Point B, no longer applies. It is flattened on the side facing Point A, because on that side, it has further to go, so weakens more quickly. More importantly, on its own, without any consideration of Point B's own gravity now, spacial density on the side facing Point B rises more quickly as we approach Point B. That is, even if we removed Point A entirely at this point, Point B's own gravitational field is already distorted such that it will pull -itself- towards Point A, through the simple expedient of moving through time and the side facing Point A being denser and thus more distance. (We are, for now, going to take motion through time as a given. It is the only motion we take for a given. Everything else arises from this single motion.)
Acceleration, and Rindler Coordinates, look exactly the same. Flattened more on the side oriented toward motion. This makes sense, if you think in terms of the speed of light; if you had reaction-less acceleration, that is, you weren't throwing particles out the back end of the ship, you'd get the same shape, just because the lightspeed "update" to the gravitational field takes time to propagate, such that, from an outside perspective, the forward region of fiethe gravitational field is always slightly behind, time-wise, the backward gravitational field. It takes time for light to reach things.
Of course, that is reaction-less acceleration; it presumes acceleration through some other mechanism causes this effect. I think this is slightly backwards; acceleration doesn't cause this shape, this shape is the phenomenon we call açceleration. This distortion is temporary, caused by the interaction of fields, such as gravity. But to explain this, we need to look at collisions, and more generally acceleration that isn't reaction-less. We haven't discovered reaction-less acceleration anyways, and this may help to illustrate why.
Collisions will require us to expand our gauge to include the repulsive phase of the wave just below gravity; gravity pulls things in, this phase pushes them away. Just as the attractive phase distorts the mass wave to be shorter on the near side, the repulsive phase distorts the mass wave to be longer, the opposite distortion, imparting acceleration.
If the two objects are approaching each other at speed, they'll get that much closer before the velocity is reversed, and have that much more time to accelerate away; greater velocity coming in means greater velocity going out, all things being equal.
Now, this acceleration has an interesting property that distinguishes it in relativity from Newtonian acceleration - it is relative.
No comments:
Post a Comment