Dimensional perspective
There’s a lot to consider in physical dimensions. Let’s look, in turn at 1,2,3, and 4. Let’s do it as a being in each dimension.
So we’re a one dimensional being, we live on a line along with billions of other one dimensional beings. We know two of them. We’ll call them Left and Right. While we live on the line Left is always on one side of us and Right is on the other. That is the extent of our ability to measure our surroundings. We may be able to expand ourselves from one inch to one light year, but all we know of our surroundings is Left is on one side and Right is on the other. If the line curves in 2 dimensions Left is on one side and Right is on the other, our experience hasn’t changed at all. If the line coils in 3 dimensions Left is on one side and Right is on the other, our experience hasn’t changed at all. If the line hoop-di-doos, or whatever it does in 4 dimensions Left is on one side and Right is on the other, our experience hasn’t changed.
Now let’s be two dimensional and live in a plane. Now we have a much greater ability to measure the world around us. We can significantly change our experience by moving through our world, which we could not do in line. Ownership becomes relevant because we can own a large or small area of our plane. This is much like our experience on the surface or earth, or, perhaps more so, as a boat on the ocean where we’re limited to the surface. We can move around freely left, right, fore and back and can’t even imagine and up or down (unlike the boat on the ocean where down is a frightening thought). If our line had been like a piece of string that we could lie our straight or curved on our desktop, or wrap around our finger, then our plane is like a piece of cloth. If our plane lies flat then our experience is left, right, fore and back. If our plane hyperboles then our experience is still left, right, fore and back. If our plane is wrinkled our experience is still left, right, fore and back. We would be completely oblivious as we went on about our lives. But in our plane we can measure. So we take a line and we turn it back on itself, we put in a bunch of beings to take up a fixed area inside the bite, so now the line surrounds roughly a circle. We post a few beings where the line comes together to keep it pinched in, it looks kind of like the Mississippi near New Orleans. We can measure the amount of line around all these beings and mark the line off in feet. We start our measurement at 0 feet and go around the loop, where the line comes back to itself is 1000 feet and we have a fixed area inside of that 1000 feet perimeter. Now we pull the line. Something amazing happens. We still have the same, fixed area inside the loop but the marked off measurements are moving past our stationary observers where the line comes back to itself. Those inside the loop can measure out their area and it is the same. Those outside the loop can measure the area and it is the same. To those making measurements the line may have appeared to stretch, but only where it encloses this area not in the straight parts they’re pulling on. Perhaps the measurements at the observers are now 10 and 990, 0-10 is 10 feet and 990-1000 is ten feet, but 10-990 is a perimeter around an area that takes 1000 feet to encompass. As three dimensional observers we can see that the plane puckered. To do this experimentally at home take a plane (cloth) and run a line in a circle (weave a thread through in a circle) then pull the ends of the line (thread). This will approximate what happened in the two dimensional world. But generally the experience in the plane didn’t change, left, right, fore and back. There was an observed anomaly, which could be explained away as stretching, even though you and I know the line didn’t stretch, the world puckered.
Now let’s be a being in three dimensions. This one shouldn’t be too difficult to imagine, as we actually are beings in three dimensions. We have left, right, fore, back, up and down. We can measure, we get volume this time, or space. No matter what we do, our experience of left, right, fore, back, up and down are the same. Here’s where I need to interject. We’ve all seen the drawings of space being warped around a black hole. Looks like graph paper on LSD. But really, if we take a cube 10 light years on a side it contains a volume of 1000 cubic light years. If that cube is around “empty” space its volume is 1000 cubic light years. If that cube is around a star its volume is 1000 cubic light years. If that cube is around a black hole its volume is 1000 cubic light years. Those grid lines don’t mark off distance, they represent a gravity well. They deal with lines of trajectory of a particle (or photon) in free fall near an object with mass. Our measurements of space remain the same. These lines only describe what will happen to our travel through space. For all we know turning on the TV creates a field that warps our three dimensions, we just don’t see that warping because our left, right, fore, back, up and down are experienced the same way to us.
Now to instantaneous travel across warped dimensions.
If our one dimension warped around and touched itself we may be able to transfer to a new spot on the line. We’re going along like always, the line warps, we can’t tell, it warps more, we still can’t tell, it touches itself, nothing happens and we can’t tell, it wriggles, we can’t tell, then it touches itself again and suddenly we’re between Sam and Ted instead of Left and Right. Hello.!?
In our two dimensional world we could travel from point A to point B. We’d go by a route that had some distance and we’d travel at some speed which would mean it took an amount of time. If that world warped over and A touched B we could be at A one instant and then at B the next instant. Travel time of 0. The same amount of time it takes me to travel from here one instant to here the next instant. None. We would go point to point. No route. No speed. Technically not infinitely fast because, no route, no distance travelled. The distance between the points may be great, but still 0 meters travelled in 0 seconds. Some might want to say that is 0m/0s and it is division by 0 and therefore infinite speed, however my here to here in no time is the same and I am definitely not moving at infinite speed. This is also not travelling through a third dimension. We’re not being taken off the plane and placed back on it somewhere else. We never leave the plane, just go from one place on it to another, non-adjacent place. This will become important when we get to “Windows and wormholes” a little later. An important thing to remember is that, except for non-adjacent places touching each other making them the same place for an instant, the distance between those points is constant in the plane. They never get closer to one another except in a third, unknowable dimension.
Now we get to three dimensions again. There’s really not much to say now. You either get it or you don’t. Warping space could make two places closer in a fourth dimension, but not in these three. This may have application in wormhole technology. More on that in the next installment. Space warping back and touching itself may “open a window” between two points that we could step through. More on that in the next installment.
Sunday, February 24, 2008
Saturday, February 23, 2008
Educating Carlton: Part 2
Thinking outside the box
In part 1 I talked a bit about Boss-Einstein Matter. Producing it required temperatures on the scale of 1/1000th of a degree absolute, maybe even colder. In the box thinking says that to make something cold use something colder. If I want cold tea I start with tea at 78F and add ice at 20F and wind up with tea pretty close to 32F. In the northern latitudes this is easy. Put out water in winter, get ice. Making things colder than anything we have presents a problem for in-the-box minds. How do I get ice at the equator? Here we begin with those outside thinkers. Someone observed the cooling nature of evaporation. Water evaporating cooled some amount. Ammonia evaporating cooled more. An enclosed evaporating system was produced that could make ice at the equator. Be careful about leaks. But then we wanted something colder, and colder, and colder. We can produce a really cold artificial heat sink to draw heat off of our matter, but still can’t get to the necessary temperatures with evaporation. (notable: this has become inside the box thinking, but that’s only because it has become common.) To get even colder let’s break away and talk about sound. Let’s say we want it to be quiet. In-the-box thinking says we stop the sources of noise. If you’re driving in the car and need to talk on the phone, park the car. Thankfully, there are those outside thinkers. To make things quiet add sound. Not intuitively obvious. Noise cancelling technology adds in a sound that nullifies ambient noise. A brilliant application of wave theory. When an unwanted sound wave is producing a pressure on your eardrum have a speaker produce a sound wave that applies a negative pressure of the same magnitude. The net is zero pressure on the eardrum and virtual quiet, even though it’s really quite loud. To get colder than we can through evaporation we do the same thing. Except with lasers. And it’s cumulative. So I’d better break away again. We’ve all seen boxing. Boxers train. They use heavy bags. Heavy bags swing. So let’s say there’s a heavy bag swinging and you want to stop it. There’s a pendulum thing going on here, and you have a flexible rod. There’s only so much force you can apply with it, because it flexes. As the bag swings up toward you and gets almost to the top of its arc hit it with the rod. You just imparted a little bit of energy on the bag that acted to lessen it’s overall amount of energy. The bag’s backswing will now be a little less than it would have been, so will the next fore swing. Again, as it nears the top of it’s swing hit it. Keep doing this. The bag will come to a stop. Same bag, same initial energy. Without you hitting it with your little rod it will come to a stop – due to air resistance and friction in its chain – in, let’s say 100 swings. With you hitting it, at appropriate times so that the energy you add works against the system energy and has the effect of lessening it, the bag stops in 70 swings. So adding energy to a system, in the correct way, can cancel some of the system energy. Back to our lasers and cold. Temperature is a measure of the random motion in a system. In our really cold system that is atomic oscillations. Those oscillations are at a fixed frequency. Think cesium oscillations for an atomic clock. Using lasers tuned to the correct frequency we get photons striking the atoms at just the right time to dampen the oscillations. By dampening the oscillations we lessen the amount of random motion in the system. Temperature is driven down below the temperature of anything we have by adding energy to the system. We have achieved what is impossible to the in-the-box mind. Get out of the box. It is errant thinking to say “we can’t” based on “we haven’t.” Instead go with the truth: “we haven’t, yet” because “we haven’t, yet.”
In part 1 I talked a bit about Boss-Einstein Matter. Producing it required temperatures on the scale of 1/1000th of a degree absolute, maybe even colder. In the box thinking says that to make something cold use something colder. If I want cold tea I start with tea at 78F and add ice at 20F and wind up with tea pretty close to 32F. In the northern latitudes this is easy. Put out water in winter, get ice. Making things colder than anything we have presents a problem for in-the-box minds. How do I get ice at the equator? Here we begin with those outside thinkers. Someone observed the cooling nature of evaporation. Water evaporating cooled some amount. Ammonia evaporating cooled more. An enclosed evaporating system was produced that could make ice at the equator. Be careful about leaks. But then we wanted something colder, and colder, and colder. We can produce a really cold artificial heat sink to draw heat off of our matter, but still can’t get to the necessary temperatures with evaporation. (notable: this has become inside the box thinking, but that’s only because it has become common.) To get even colder let’s break away and talk about sound. Let’s say we want it to be quiet. In-the-box thinking says we stop the sources of noise. If you’re driving in the car and need to talk on the phone, park the car. Thankfully, there are those outside thinkers. To make things quiet add sound. Not intuitively obvious. Noise cancelling technology adds in a sound that nullifies ambient noise. A brilliant application of wave theory. When an unwanted sound wave is producing a pressure on your eardrum have a speaker produce a sound wave that applies a negative pressure of the same magnitude. The net is zero pressure on the eardrum and virtual quiet, even though it’s really quite loud. To get colder than we can through evaporation we do the same thing. Except with lasers. And it’s cumulative. So I’d better break away again. We’ve all seen boxing. Boxers train. They use heavy bags. Heavy bags swing. So let’s say there’s a heavy bag swinging and you want to stop it. There’s a pendulum thing going on here, and you have a flexible rod. There’s only so much force you can apply with it, because it flexes. As the bag swings up toward you and gets almost to the top of its arc hit it with the rod. You just imparted a little bit of energy on the bag that acted to lessen it’s overall amount of energy. The bag’s backswing will now be a little less than it would have been, so will the next fore swing. Again, as it nears the top of it’s swing hit it. Keep doing this. The bag will come to a stop. Same bag, same initial energy. Without you hitting it with your little rod it will come to a stop – due to air resistance and friction in its chain – in, let’s say 100 swings. With you hitting it, at appropriate times so that the energy you add works against the system energy and has the effect of lessening it, the bag stops in 70 swings. So adding energy to a system, in the correct way, can cancel some of the system energy. Back to our lasers and cold. Temperature is a measure of the random motion in a system. In our really cold system that is atomic oscillations. Those oscillations are at a fixed frequency. Think cesium oscillations for an atomic clock. Using lasers tuned to the correct frequency we get photons striking the atoms at just the right time to dampen the oscillations. By dampening the oscillations we lessen the amount of random motion in the system. Temperature is driven down below the temperature of anything we have by adding energy to the system. We have achieved what is impossible to the in-the-box mind. Get out of the box. It is errant thinking to say “we can’t” based on “we haven’t.” Instead go with the truth: “we haven’t, yet” because “we haven’t, yet.”
Educating Carlton: Part 1
Can we trust Einstein?
Boss-Einstein Matter
The best test of a theory is not whether it can describe what we already know, it is can it describe what we do not know. Einstein developed some theory. It described a lot of stuff we already knew and did a pretty good job of it. It also described a lot of stuff we didn’t know, and who can say how good a job it did there? Much of that unknown stuff is still unknown. However, … In the 1920’s (?) a theorist named Boss proposed a new state of matter. The nature of theoretical physics is this: It’s tough. Boss was visionary, but wasn’t scientist enough to confirm what he thought, even theoretically. That’s no slam on Boss. As I said, theoretical physics is tough. Probably harder than Mt. Everest. A lot of people can make theories about reaching the summit, few can actually do it. He did the reasonable thing, he sent his theory to Einstein. Einstein ran it through and proved it, theoretically. Big deal, lots of people can make a theory and who can say how good it is? Over 30 years later technology had advanced enough to produce, for a short time, the first (probably ever in the entire universe) BEM. It has now been produced using several different elements, enough to say that it is not anomalous. It has probably never occurred naturally because it only exists at extremely cold temperatures. So cold that wherever there has been matter to be converted to this state it has been too hot to do so. By “too hot” I mean 1/100th of a degree C absolute. Way hot. Make a mental note because I’m sure to come back to this for “Thinking outside the box,” a later installment. The important thing here is that Einstein’s theories predicted not just a reaction, but the existence of something that had never even been observed. Kudos to the scientists that came up with air conditioning. They theorized ways to produce cold air and make ice and, and, and. But they knew that cold air already existed. They had handled ice from nature before they manufactured it. Einstein’s theories predicted something that had never been and proved out to be correct. His theories may not be perfect, even he thought this, but they do pass muster. Einstein was able to work out those theories – such ability being a mixture of science, art and magic – to predict BEM. For this reason we can trust the theory. Others have those capabilities and have been able to work out the theory to predict plenty else. Because these predictions are legitimate resolutions of the same theories we can trust them as possible.
Boss-Einstein Matter
The best test of a theory is not whether it can describe what we already know, it is can it describe what we do not know. Einstein developed some theory. It described a lot of stuff we already knew and did a pretty good job of it. It also described a lot of stuff we didn’t know, and who can say how good a job it did there? Much of that unknown stuff is still unknown. However, … In the 1920’s (?) a theorist named Boss proposed a new state of matter. The nature of theoretical physics is this: It’s tough. Boss was visionary, but wasn’t scientist enough to confirm what he thought, even theoretically. That’s no slam on Boss. As I said, theoretical physics is tough. Probably harder than Mt. Everest. A lot of people can make theories about reaching the summit, few can actually do it. He did the reasonable thing, he sent his theory to Einstein. Einstein ran it through and proved it, theoretically. Big deal, lots of people can make a theory and who can say how good it is? Over 30 years later technology had advanced enough to produce, for a short time, the first (probably ever in the entire universe) BEM. It has now been produced using several different elements, enough to say that it is not anomalous. It has probably never occurred naturally because it only exists at extremely cold temperatures. So cold that wherever there has been matter to be converted to this state it has been too hot to do so. By “too hot” I mean 1/100th of a degree C absolute. Way hot. Make a mental note because I’m sure to come back to this for “Thinking outside the box,” a later installment. The important thing here is that Einstein’s theories predicted not just a reaction, but the existence of something that had never even been observed. Kudos to the scientists that came up with air conditioning. They theorized ways to produce cold air and make ice and, and, and. But they knew that cold air already existed. They had handled ice from nature before they manufactured it. Einstein’s theories predicted something that had never been and proved out to be correct. His theories may not be perfect, even he thought this, but they do pass muster. Einstein was able to work out those theories – such ability being a mixture of science, art and magic – to predict BEM. For this reason we can trust the theory. Others have those capabilities and have been able to work out the theory to predict plenty else. Because these predictions are legitimate resolutions of the same theories we can trust them as possible.
Friday, February 22, 2008
Educating Carlton: Preamble
Some time ago there was a news story about an astronomy feature that elicited quite a bit of chatter in the discussion that followed about Einstein’s theories. As is the nature of such public things, there was a lot of useless input from people who couldn’t possibly understand the ongoing discussion, so they couldn’t possibly have input, so they did what they could do, distract. There were, however, several people with meaningful input. Among that group is Carlton. Carlton is an amateur astronomer and seems pretty well versed in the down to earth, practical sciences. Of course the discussion deals with a lot of theoretical physics, which is anything but down to earth and practical, being theoretical and all. I thought it might be nice to set out some things that might bring people up to speed, if they are as interested and already knowledgeable as Carlton is. This is by no means a substitute for real instruction. I’ll treat things with broad strokes, so a lot of explanations won’t stand under scrutiny from someone who really knows this stuff. It’s not written for the instructor. I’ll use a lot of examples from more everyday life and hope that the lines are close enough to parallel to make sense of things. I don’t know how long this will take, nor how long between installments. I also don’t plan on staying up nights to make progress here, so if anyone is actually reading this and doesn’t think I’m posting fast enough, you can always get a podcast for a dozen or so courses on math, physics, astronomy, etc. and then once you’ve gotten a bit of mastery over the understood aspects, get some on theory, method, development. You’ll be better off going that route, I assure you.
Subscribe to:
Posts (Atom)