I haven't made any firm conclusions about the philosophical part of the time discussion, but hopefully I can clear up some of the physics. Specifically, the "time is a dimension" thing and "can time have momentum?"
The reason they call time a dimension is because you can get some very nice results (meaning that you can predict the motions of particles, etc., reasonably well) if you TREAT time as a dimension. (Note to philosophers: that doesn't mean it IS a dimensions, just that this is a good way of describing it.)
OK, let's start in 3 dimensions first. We write the position of a particle as (x,y,z) relative to some origin. Say the origin is the southwest corner of the room, and you are 1.67 metres tall, and you are standing 1 metre from the west wall and 3 metres from the south wall. The position of your head in (x,y,z) coordinates would be (1,3,1.67). The x-axis in this case runs west to east, and the y-axis runs south to north, and z from ground to sky. The group of three coordinates is called a
position vector and is usually symbolized by
r. You can transform position vectors and get velocity, acceleration, and other useful physical quantities.
Now, it turns out that if you make your position vector four components long, instead of three, where the fourth component is time, some useful properties fall out. To do this, choose a "zero" for time as well, just as you arbtrarily chose the zero for your spatial coordinate system (I mean, it could have been in the middle of the room, on the ceiling, in the northwest corner, but I chose southwest corner). Imagine yourself zeroing a timer at a given moment, and call that "zero" for this purpose. As long as you are using the same coordinate system to describe two events happening at two times t1 and t2 at positions
r1 and
r2, the 4-vector DISTANCE between these two events is always the same. Say you sneeze and your brother across the room claps his hands. You can describe these events using a four-vector, which includes a component describing WHEN the stuff happened.
Distance: in 3-d space, distance between two points
r1 and
r2 is gotten by calculating sqrt((x2-x1)^2+(y2-y1)^2+(z2-z1)^2). In other words, subtract the components of the two vectors, then square those numbers, add them up, and square root the result.
If you're thinking in 4-D now, your vector looks like this:
r=(x, y, z, ict). The time is
t and you need the i (square root of -1, I know it doesn't exist in real life but it's a very useful way (again) of describing things) and the c (speed of light) to make the units work out right. Follow the same procedure to get distance between two EVENTS: the formula would be sqrt((x2-x1)^2+(y2-y1)^2+(z2-z1)^2-(ct2-ct1)^2). You just square the difference between the two time components and treat it the same as the spatial components. As long as you always remember to write in the
ic part, this four-vector is a very convenient tool.
NOW, we can get to momentum. You can get velocity if you take the derivative of your position four-vector with respect to "proper time". Proper time has to do with how fast you're going and allows you to convert time between yourself and a stationary observer, which is not the same thing for very large speeds, although in our everyday life those speeds are never achieved. For those who don't do calculus, the derivative is the rate of change of something. So, you take the position vector, measure the rate of change of the position vector, and you have velocity. (Makes sense, right? Imagine a car on the highway, measure its position at time t1, measure it again at time t2, the change in position divided by the change in time between t1 and t2 gives you the velocity.) Okay, then momentum is just defined as the mass of the object multiplied by the velocity; there is a scaling factor but it is the mass-velocity thing which is important. It turns out that the fourth component, which was equal to time in the position vector, becomes the speed of light in the velocity vector, and then when you calculate momentum using the velocity vector, that fourth component gives you the expression for the ENERGY of the particle, and you've all heard this one: it's equal to mc^2!
So, can time have momentum? I guess not. The four-vector describes a particle, or a point in space, and time is just one of the four components used to describe WHERE it is in space and time. You can't say that its x-component has momentum either, it's just a component. Time is no more special than the spatial coordinates (x, y, z) in this interpretation. It's just another piece of info to describe where a particle is. It's the particle itself that has momentum.
By the way, making general relativity (far more complicated than the above) and quantum mechanics to jibe is the one thing which physicists are searching for. Relativity works well on large scales, when there is lots of mass involved, and quantum mechanics works well on small scales, but during the Big Bang, you had large gravitational forces as well as very small distances...which would obviously require those two theories to co-operate. Which, as far as I know, right now isn't quite true. But hey, they're working as fast as they can, because they all want to figure it out too!
Oh my. I guess this will be my only post today. Sorry if I've bored anyone who (a) hates physics or (b) already knows all this.
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