February 26, 2009
The past months I’ve been studying the mathematics involved in understanding Maxwell’s equations, and Einstein’s work. A few nights back I was sitting in the kitchen, and was thinking about this:
Stand a certain distance in your backyard, away from a tree. Imagine this tree is about 50 meters away from you.
Walk toward the tree, touch it, and walk back. You’ve traversed a “space” of 50 meters, and possibly 30 seconds to a minute worth of “time”.
Now let’s change a physics parameter. We all know that the only reason we see the tree is because light from the sun (or moon) bounces off of it and travels to your eyes. Instead of light traveling from the tree to your eyes almost instantly, let’s say light takes much much longer – insanely longer – 10 years to travel across the distance of your backyard. You stand the same distance away. You then walk toward the tree. If you’re carrying a pocket watch with you, you still get to the tree in the same amount of time, and it takes the same amount of time to get back (on your watch), but if you watch the environment, you’ll see 10 years pass as you approach the tree, then watch those 10 years “rewind” as you walk back to where you started.
As light’s speed becomes slower and slower, each step of yours traverses more and more “environment” time.
Also, isn’t there “space” that existed for each of those moments in time? Using the slow-light experiment (10 years for light to cross yard), say you walk half-way to the tree and stop. When you spin around in a circle and look around you, it would seem that you could walk forward at that “time”. Each moment in “time” there was a backyard (“space”) for you to walk around in, wasn’t there?
By the time you’ve walked half-way to the tree, and stop, you would’ve seen 5 years worth of “back yard time” go by. You would’ve seen five winters, five springs, five summers, five falls, and all the changes in weather. You’d see rain, sunny days, the breeze blowing the leaves, little kids running around playing sports, birds flying, daytimes, night-times, etc. When you stop, since light is moving slowly, you’d watch all this “play” very slowly. You’d watch it all in super slow motion. When you move toward the tree, it’d be like you hit fast forward. For the sake of this example, let’s say all the kids, animals, trees, weather, etc., were slowed down to match the speed of light. (If they weren’t, God knows how to birds would know how to fly around, or the kids know how to play sports with one another!) They don’t notice that light’s been slowed down, because everything is slowed down to match it (at least to them). Even though it’s weird to think of, let’s just let that be our assumption, for now.
[ Note: You can see we’re already starting off with a weird assumption. It gets weird because WE’RE ASSUMING LIGHT’S VELOCITY IS DIFFERENT FOR DIFFERENT OBSERVERS! In reality, light’s speed is always constant, no matter the observer. People think that’s a weird assumption, but when I think about it, the weird assumption is to say it varies from observer to observer, as we’ll soon see!]
So let’s start the weirdness. One of the weirdest things to me is that when you take a step forward, you cannot get to the “space” next to you during that “time”. You end up mostly traversing time. You take a baby step forward and two weeks pass. In order to stay at that same moment in time (relative to those in the “normal” world), you’d have to walk in concentric rings around the tree, along “time” contours.
This already is a strange thing. If I was to go outside and walk around my backyard right now, the environment stays relatively constant throughout the entire process, so when I walk, I feel like the environment stayed the same, and I traversed an “absolute” kind of space. As for time, my intuition tells me it has passed by in a tick-tock-tick-tock fashion. Time and space seem separate. But they’re not, as we can see. When we changed light’s speed and made things a bit more extreme to illustrate what’s going on, we’re seeing a much tighter relationship between space and time.
Another weird question: How would you (this super faster than light mover) appear to those kids in the back yard watching?
The kids would only see you once the light bounced off of you, and back to them. If you didn’t give it much thought, you’d think you could “out-run” the light, and tap the little kid on the shoulder BEFORE the light even made it him. How the physics of this would even work baffles me, but we’ll try to assume it could be done. You stand in front of the kid, light slowly crawls up to you, reflects off of you, and makes its way toward the kid. You take a few steps the side, make your way behind the kid, then tap him on the shoulder, and wait for the light to make it to him. Sounds like you could do this, right? No, not quite. Here comes the problems.
When we, the “super faster than light” mover take a step forward we end up traversing massive amounts of time, remember? The kid has a bedtime, and has to go to school the next day. He’s not going to stand still out there for a month! Wait, I thought we were moving super fast? Or are we now moving EXTREMELY SLOW, and the kid’s moving extremely fast? Oh my gosh, how confusing is all of this? We mess around with light, and look what happens!
The reason this is all confusing is because we’re making several wrong assumptions. But let’s keep compounding the difficulties. I find it kind of fun and interesting.
Assuming you’re walking along a time contour near them, all kinds of light would hit you, and bounce off of you as you’re traveling along the ring and reflect almost like a strung out ribbon along the time contour. Light just wouldn’t hit you where you’re “standing”, it would hit you in all kinds of locations in space, and would reflect back toward them from all kinds of angles. They’d see this weird blur streak appear almost instantaneously, then disappear. (I guess?) I’ll have to think on that one more.
You could wreak havok on these people’s world just by walking back and forth to the tree, and doing zig-zag patterns across the yard. Light from all kinds of different times would be bouncing off of you, and reflecting back to people at different “environment times”. Talk about confusing! What would that look like? What would people see? Does that even make sense? I don’t think so. As you move toward the tree, you travel into some sort of quasi present/future… I don’t know what it’d be. And as you walked back, you’d go back into the past. But since we made that weird assumption in the beginning that things remained “normal” to everyone but us, the super-fast faster than light mover, we’re modifying both the past, then traveling toward some “environmental present” (which is our “future”), then when we turn around, running back into the “environmental past”, and modifying the environment this whole time, as we walk around. This is absolute chaos!
When we take a step, we push our foot off of the Earth and use that to propel us forward. What kind of “super-steps” are these? A force in physics modifies objects accelerations, but man oh man are these “super steps” weird! Super man! Six months in a single stride! But turn around, and this same force propels us into the past! One helluva force!
How would you ever get to a certain part of the backyard during a particular “time”? Say we’re not even picky. We just want to make it to the other side of the backyard, during the same day. Like we used to do, before we were “super fast”. It’d be complicated. Taking a step forward “fast-forwards” too much time. You’d have to find a way to really “slow down” your steps, but what does that mean? You’re still walking the same “speed” as you were before, traveling toward the tree across your backyard, it’s only light’s speed that we’ve modified.
We really face a similar problem in everyday life. We see an environment (“space”) in front of us. We take a step forward, but when we move (or even if we don’t move), time goes by. Is it possible to be at two places at the same time?
This is super confusing stuff, but a lot of fun. The more I think on it all, the more I see why space and time are treated as a single entity, because there is such a tight relationship between the two. Fully understanding all of this will come down to taking a a lot of time, and thinking on this more, and representing everything in mathematics, like Einstein did. The Lorentz transformation is the key to understanding the thought experiment I just gave. It relates all the variables needed to solve the puzzle. I’ve read Einstein’s papers on relativity several times, but I still need to work on it. These are not simple concepts.
I still get confused between various notions. I have a tendency to think of “absolute space”, versus “subjective space”, but I’m quite sure this is wrong thinking. If you were following this thought experiment, and in the beginning, thought what we were talking about “made sense”, then you too were confused about this same set of ideas. Like for instance in this experiment, I tend to think of an “absolute” backyard, where there is a tree, and there is an absolute distance between me and the tree of 50 meters. I think to myself, “No matter what the speed of light is, that’s just an optical illusion. Sure it’d look weird, walking across the backyard and this illusory ‘time’ flying by as I walk to the tree and back, but that’s just because light waves are carrying old dated information, and moves really slow. It’s like an alien receiving radio waves we sent out hundreds of years ago in space. These light-waves represent old information, like stars we see in the sky late at night, which have already burned out a long long time ago.”
But when I think about it, when do we REALLY see things as they are? Immanuel Kant’s entire book, “Critique of Pure Reason” was about whether we know things as are they are in and of themselves, or only how they appear? When I see anything, I only see its “light coat”. Light gives the object shape, color, and depth. When you look at a lovely woman, you’re seeing light waves bounce off of her. As you speed up, her shape will distort and scew, her movements will speed up or slow down, and even the color of her eyes and skin will move across the color spectrum, all based on the speed you’re moving and at what angles you fly by her. What really is this woman, then? Relating all possible images of her by mathematical physics relationships is the closest thing I can think of!
If the tree in the yard is scewing and bending based on how I move relative to it, then what is this “absolute” space? There is no such thing. You might think, like George Berkeley, that though the eyes work on the basis of perspective and objects change based on the distance you are away from them (and adding a slight corrective, speed you’re moving), you can rely more solely on the sense of touch, because the size of objects never changes to the sense of touch. Yet if we speed up to high speeds, how would you ever verify this assumption?
Touch is impossible to imagine at high speeds. Let’s say you’re wanting to touch this beautiful woman we were just talking about. At near light speed velocities, you’d have so much kinetic energy you’d be more dangerous than any bullet, and you’d tear her apart just by nipping her. Mass increases as you approach light speed, so depending on how fast you’re going, the more massive you’d be! As for the rest of the senses, hearing is based on air vibrations, and eventually the vibrations would become too rapid to make any audible sound we know of. Your ear drums wouldn’t last anyway. Taste would involve a collision of the tongue, so you’d do some serious damage trying to lick her as you fly by. Smell is out of the question too, because the air’s moving too quickly. In fact, your entire body would be torn to shreds by collisions with the air, far before you reached anywhere near light speed.
Let’s go to incorrect assumption two: the belief in “subjective space”. For instance, when we made it half-way across my backyard, stopped, then looked around us, we talked about seeing a 3D space at a particular time. It was confusing because it was both our present, and the environment’s past, at the same time. Moving faster than light almost gives us a time machine, like Doctor Who, and we’re warping around the space/time fabric of the backyard. Light waves travel through space. They have to travel across space, because light waves MOVE across something. But they also carry a form of “space” with them as well. This “space” light carries seemed less real though.
The space light carried is like those optical illusion tricks people do on sidewalks sometimes. You see a camera take a picture of a painting on a sidewalk, and it looks like a 3D person standing there, but then the camera rotates and you can see that there was no 3D space there at all. It was a 2D painting, but your brain THOUGHT it was 3D. One of those fancy light tricks.
I don’t claim to fully understand the solution to all of this. Once I see the physicists explanations of what’s going on, the mathematics gets reather intense, which is why I’ve been spending months cranking on nothing but math. It seems the answer lies in a more firm understanding of the core forces involved, such as electro-magnetism, energy, etc. Understanding energy, electro-magnetic waves, etc., and very clearly dissecting this problem with a scalpel is the answer. I will say a few of my current thoughts though, just for fun, as this is my own journal after all. I don’t really value these comments I’m about to say though, because I think the real solution to the problems will only be found in rather complex mathematics related to physics, forces, and electro-magnetism, energy, and quantum physics (possibly).
I think there’s a large degree of truth that space is a notion created in our minds by our brains. A very complex form of comparison, based on the colors of the images we see. I noticed when I was flying around using a computer simulator “Real Time Realtivity” where you can fly around an environment at speeds near that of light, the images our eyes would perceive (if that were even possible) aren’t really helpful at navigating the world. I remember getting at like 99.998% light speed and I had no idea what was going on. The images created by the simulator were so distorted I couldn’t tell what was going on, where I was in the environment, or anything.
I think space comes from some sort of complex evolutionary survival thing when our brains developed. It helps us exist for the short time we’re alive. When I play 3D video games, this point always hit me at home even harder. I play a 3D racing game, and the Playstation creates all kinds of images on the TV, and I think there’s a 3D world I’m driving around in, but there is no such “space”. I see a bunch of colored images and think it’s 3D because my brain tells me so. If, by sheer chance, they made some film, which was nothing but fast moving 2D slides that shown on the screen, showing me the same pictures that I saw while playing the game, I would’ve thought I was immersed in a 3D world, playing the game, just the same.
Time is heavily tied up in our brains too. Time seems to require memory, and possibly a combination of our imagination. If it wasn’t for physics and science, nobody would have the faintest idea how “old” the Earth, or the universe is. History is unknown to us, outside of what was written down. Whether or not any of it’s true is up for debate. After all, the winners write the historical accounts, and always want to make themselves look good, and their opponents bad. The Catholic church used to go around burning libraries all over the world. Even the little history we do have, a great deal of that was destroyed by superstitious beliefs. I don’t even know what’s going on in the present half the time, as the news networks are constantly lying to us, having their own agendas.
Time seems to exist only because we remember there was a state of existence before the one we currently see. The universe would probably go on, even if nobody was there to watch it, but I’m just saying we wouldn’t be conscious of “time”.
Time by itself is a meaningless word. Think of an empty black void. If there is no change, there is no time. Tick-tock-tick-tock requires a mind which does the ticking, and that ticking is the movement of the brain’s little gears. Time presupposes that SOMETHING HAS CHANGED. Even in the movies, when they try to show someone has died, the screen goes black, and the person talks to himself or herself, mumbling speech into the void. What they’re missing is that thought comes from movements of energy in the brain, and if the brain is no longer functioning, I don’t know what kind of speech or conversation they think is going on. They’re inferring some sort of existence of a “spirit” or something, which continues to survive, and apparently can operate without the brain or sensory stimulation. I suppose it’s possible, but there’s no evidence to support such a claim. In fact, evidence points to the contrary. Rational thought processes take place soley in the brain, and if the brain is injured, rational thought becomes impaired.
Since time presupposes a change of something, what kind of change do we see? The kinds of change we see are the objects which we call “matter”, and the various phases and states we find those objects in.
And how do we become conscious of matter? Assuming the only sense organ we have is our eyes, light waves. (and at high speeds, this is the only sense organ we have available). Knowing this shows why time is going to be heavily tied in with light, especially when we’re moving at high speeds. In order to get time started we have to first see an object, then we must be conscious of a change in that object. You can’t have time without objects which you see. Also, without objects, you can have no space. If you had nothing to see, there would be no space. You’d have a flat, 2D black plane, which you’d call the void. Whether a TV screen showing a solid black image is showing you a black painted wall, or an infinite vast 3D open space, is really up to your imagination. Light has to bounce off of something, and hit your eyes, then you see objects. The light makes sure the objects seem spaced apart, and that’s how it all gets rolling. You can’t have space without time, nor time without space, and you can’t have either space nor time without matter. They’re the inseperable trio.
Speaking of objects appearing “spaced” apart, this brings up my final thoughts, before I close down this entry.
Before I got busy trying to make money, I used to write 3D graphics engines for fun. That was one of my favorite things to do. There’s a lesson we could learn about space, from how computers emulate a 3D environment.
In the old video game Doom, the enemies you fight are 2D sprites. One of the things I found interesting when studying how to write 3D game engines is the use of what they call the “Z-Buffer”. Whenever you get into 3D gaming, and start drawing the walls, bad-guys, environmental objects, etc., onto the screen, you first rotate them all using a matrix to line them up relative to the player’s camera position (the players “eyes”). Then, each object’s coordinates are calculated as to how far they are away from the player’s position.
Imagine two bad guys are in front of you, with one quite a ways in the distance, and one right up next to you. The way computer graphics engines draw the environment correctly is for each “bad guy” it draws on the screen, each pixel is assigned a “Z” coordinate. The engine just starts drawing each bad guy to the screen, in no particular order. Now when each bad guy is drawn to the screen, pixel by pixel, if the bad guy’s pixel’s z-coordinate is less than what was previously there (whatever that may be), it gets drawn, but if it’s Z coordinate is greater, that pixel of the bad guy is ignored. The net effect is that objects which are up front “draw over top of” objects which are behind them, and we get the feeling of depth perception.
That’s interesting to me, and shows the flaws in the old physics ideas before relativity, where they thought objects were seen instantly. If objects are seen “instantly”, and light does not have to travel from the object to the person’s eyes in order to see it, then there is no way for “the world” to know which order to draw things to our eyes. There’d be no such thing as one object being in front of another. No such things as doorways, or walls. Everything would be drawn to our eyes in one big mess. Reality has no Z-Buffer, and no rotation matrix making sure objects are drawn to our eyes correctly. “Light” in a very complex fashion is reality’s Z-Buffer.
If light moved instantly, what would it mean for light to collide and bounce off of something, or refract when passing through various materials? “When” did it collide with the object? It doesn’t make sense.
In reality, if one object is in front of another, portions of the light get blocked by the object in front, whereas the rest of the light makes it to the observer from the object behind. Whatever light makes it to the observer’s eyes, determines depth, and which objects we think are in front of the others. Space that we see with our eyes requires light to work like this.
Though many mathematicians seem to give a strong sense of “reality” to points in space, I think such points come from the extremeties of an object’s light coat. Which makes me wonder about a further question:
In order for an object to have such “points”, requires our eyes to focus light to points. I have very poor vision, and have to wear contacts. Sometimes I’m wearing my glasses, and when I’m riding with my parents, I take off my glasses and look out the window. Everything is blurry splotches. Such things seem to tell me that there’s more to geometry than the stuff I’m learning in these math books. When I’m calculating the “volume” and “area” of these shapes and containers, I don’t really know exactly what that means.
If you draw a line on a chalkboard, and I sit half-way across the class-room, looking at the board with my glasses I see a thin chalk line. Take off my glasses, and I see a big thick smudge, and even the definitions of the “extremeties” of the chalk line lose focus. Optics and how the eyes work and focus light is very core to understanding geometry, because focusing the light seems to me to be just as important.
I need to get to work, and finish my studies for the day. I’m fascinated with light, and optics, and have to figure all of this out.