Keep on keepin' on...

Keep on keepin' on...
I now want to turn to momentum, velocity and the speed of light.

A useful metaphore may not be perfect, but it should help one to visualize many properties of a system. Our slice-time worm metaphore has allowed us to perceive a 4D universe and how time can be expressed as a space dimension, which lead to visualizing time travel... not bad! There are many things about our existance that do not have very good explanations, so our attempts to visualize them do not really leave us any worse off then we were at the beginning! Like gravity, momentum is exactly such a phenomanon. We have been able to describe the properties of momentum for a long time, but what "causes" it? Why should something at rest tend to stay at rest and something in motion tend to stay in motion?

Lets see how our Worm motif can help us visualize momentum. Remember when we talked about fixed points in the future and how we can be predestined without limiting us in the present? Well, you will need to exercise that thought a bit now. We have practiced visualizing our rib-slice-worm (RSW) in time. And practiced thinking of the RSW already existing in the future and possibly being able to move in the past. Lets play with that image a bit. Visualize yourself running down a straight section of trail and then see your RSW extending through time over that frame. Your RSW is sort of tilted in the direction that you ran and is fairly straight. Imagine the RSW being flexible, but somewhat stiff. Once you bend it in the direction down the trail, you are actually bending it in the future. Once it is bent you do not need to apply more force to make it "move", so you can just let time pass and it will express itself as moving forward through time.

Of course, we can not actually expect our RSW to float down the trail without some effort, because we still need to hold ourself up by moving our legs under us, overcoming wind resistance, avoiding obsticals and etc. However, if I was running on ice and then suddenly stopped running, I would continue to move forward until the reduced friction of the ice finally slowed me down. I can visualize the bent worm as being the means of creating the tendancy to keep moving and I can visualize my interaction with all of the surrounding worms as being the means of slowing me down... as I bend my worm into the future I must displace a lot of other future worms and I have limited energy to do that. Eventually the interaction with the other worms will cause me to "slow down" because I will then stop pushing the other worms around.

The other worms are exibiting the other property of momentum... they want to stay at rest because if they move they must push a bunch of other worms around... see? Moving through them into the future forces them to be displaced, which takes energy. If I stop appying energy, as when I stopped running, I eventually slow until my motion matches the motion of all the other worms around me. The concept of actually being "at rest" is sort of silly when you think about it... am I not on the surface of the earth spinning around 24,000 miles a day (1,000 mph)? Am I not circling the earth's orbit every year? Am I not moving with the solar system around the center of the Milky Way Galixie? What is "still"? Basically, we think of ourselves being at rest when we are matching our motion to the motion of all the other worms near us - see? If we ever find ourself in open space, with relatively few other worms around us, then we would expect to bend our worm and then sit back and move along into the future with almost no further expendature of energy. Of course we would surely find ourselves caught in some cometary eliptical orbit destined to return right back to the starting place! Can you see that creating a huge spiral racing across slice-time? At this point in my musing, I tend to think about the future "narrow gate" I need to pass through as a destination that is narrow, but accessible from anywhere in my 3D brane rather than as being some actual 3D locatiion. I can only visualize that in 4D space.

Now suppose we keep putting in more and more energy so that we go faster and faster. What will that look like? To me, I see my high velocity worm bending flatter and flatter to my "now" time surface. That means that for each slice, the next slice has to be displaced farther as I stack them up. It makes sense to me that there would be some limit to how far I could displace the slices, and that it would take more and more energy to accomplish that displacement. (Stay tuned for the next post when we will follow a single atom through time.) When we were thinking about time travel we visualized bending our RSW into an S shape in time. At the top and bottom bends of the S the direction of movement is flat, so that might cause a contradiction to the limitation of velocity except that the actual length of level travel is vanishingly small. It is like the moment in Calculus where the slope is 0, but it is exactly 0 for 0 time, so it does not actually violate the law! I love Calculus!

We will turn to the meaning of mass in the next posts and why it might be that mass increases with velocity. For now, just think about accelerating a particle. As velocity increases, the particle's mass increases, it shrinks and it takes more and more energy to accelerate it. I have read that one way to visualize the limitation of the speed of light is to imagine it taking more and more energy to accomplish the acceleration until it takes all of the energy in the universe to accelerate the tiniest particle to the speed of light. Like a nuclear reaction converting mass into energy, I would need to convert all of the mass in the universe into energy to accelerate that one particle... which would own that energy as mass but have vanishingly small length! Wow! If you packed all of that mass-energy into a single point and then it exploded, that would be a really Big Bang... ya'think?

It is sort of like the old saying that we know more and more about less and less until finally we know absoutely everything about nothing, at which point we also know absoutely nothing about everything!

(Hummm... So, why can light travel at the speed of light?)
Nois