TLE to something useful?

Hello bloggers! How are you all doing today? I’m a little bit frustrated. Right now I’m trying to experiment with what I’ve been learning in diff geo. What I want to do is take statelier reentry data and make it into a curve of its position and platitude with respect to time. That way I can get its equation. You see, when a satellite or comet falls towards Earth it’s free falling and the only force excreted on it is gravity (if we ignore winds, which we can do if we go high enough in the atmosphere). And according to general relativity gravity isn’t a force at all but a shape. The gravity around earth is shaped a certain way and that makes things like balls and satellites travel towards the earth. I’ve included a picture of what I think the gravity around Earth looks like (this is only a slice). I’m managed to secure some satellite reentry data but it’s come in the form of a two line element (TLE) which I guess is standard for NASA. But I want longitude, latitude and altitude from this data. I’m having an impossibly hard time making the jump from Right Ascension to a longitude and altitude or whatever it supposed to be. Does anyone know how to do that? Or know anyone who would know?

Back in Black!

Wow. So my little world counter up there in the right corner has exploded with little red dots, so I think it might be beneficial for me to start this thing up again! Since I left the blog I've been hard at work trying to unravel the secrets of the universe. I've spent most of this summer teaching myself differential geometry. (The study of diff geo actually starts in kindergarten. Basically it's all about shapes, but the formal version is more concerned with their equations rather than their names.) And I have made a sincere effort to teach myself general relativity as well, but that hasn't gone so well, mainly because every time I start to read it all I want to do is throw the book across the room! General relativity (GR) is about the least formal, least elegant physical theory I have ever laid eyes on! I like the concepts: mass bending space, acceleration and gravity being the same thing, light bending, black holes and all that good stuff; but the math is positively atrocious! After reading all the formalized elegant diff geo it just makes me want to go throw up. Honestly I feel like GR needs to be redone! Now a question for you: has anyone ever tried to reformulate GR into a more mathematically elegant setup? If not I'm very tempted to try it!

With Regrets

Hello Bloggers. Hohenheim here with some unfortunate news. My health has been acting up lately and I (and my health advisor) have decided that it would be best to temporarily discontinue the blog. Hopefully by summer I'll be in better condition and will be able to pick it back up again. Thanks for all the support.

Cosmo 101 (a bit of math included)

Oh here is another interesting property of Hubble’s law that I don’t think I talked about last time. You can use it to set a minimum on the age of the universe. So to review, Hubble discovered that the universe is expanding and he found that the rate at which stuff (stars nebula etc.) is moving away from us is proportional to the distance they are away from us. The further they are away the fast they are receding. And then he graphed his results and found a line. The equation goes something like this: (the speed at which something is moving away from us) = (the Hubble parameter) X (the distance from us to them). This Hubble parameter is sometimes called the Hubble constant but it’s not really constant. It changes with time, that’s why we use the word parameter. There is another really cool aspect of the Hubble parameter, we can use it to tell how old the universe it.

(the Hubble parameter)= (the speed at which something is moving away from us)/ (the distance from us to them)

In math terms this is

H=S/d so if we invert this we get

1/H=d/S

and if you take any distance (say the distance that a car has travel) and you divide it by the speed that it went at they you know the time it took to get there. So from the inverse of the Hubble parameter give you the time that it took the stuff (stars nebula etc.) to get where is at, thus putting a minimum on the age of the universe. The current accepted value for H is 70.8 ± 4.0 (km/s)/Mpc which give the age of the universe to be 13.8 billion years.

Suggestions?

Hello Bloggers! Well since we only have class on Monday, Wednesday and Friday we still haven't learned anything new this week so I still have nothing to report. But I do have a question for you all. We have to do a project and a presentation for the final exam in this class. So I was wondering if you guys have any suggestions? What do you want to know more about? What deep questions have to been staying up at night trying to solve?

GOD! ?

So we had a test today....I think it went well for the most part. But consequentially we didn't learn anything new so here is a GOD!? post.

So first up we have an Onion article with an interview from God:

http://www.theonion.com/content/node/28151

Next we have an entire website dedicated to the question: Does God Exist?

http://www.doesgodexist.org/

And look there, I added a video!

Cosmo 101 Cepheid Variables

Hey bloggers! We’ve now made the transition to cosmology! And I have a test on General relativity tomorrow oh no! Anyway we’ve already gone over a lot of the stuff that we are talking about in class but I noticed that while I talked about Hubbles law and all (you can read about it here), I didn’t mention Cepheid variable stars. These stars a very interesting in that they blink. Their luminosity literally varies periodically like a lighthouse. But the cool thing is that there is a very linear relationship between it’s period (how fast it’s gets light and then light again) and it’s luminosity (how bright it is). I’ve included a graph to show this relationship. The cool part is the since we know this, if we look out into the sky and see a variable star we can tell how far away it is. How? Well we can see measure it’s period and see how bright it comes across to us. If we know (from the graph) how bright it’s really suppose to be we can calculate how far it. Yay! You may have heard of these stars before but usually they are referred to as standerd candles.

lolfox?

I don't think I have anything to write about today. So I'm not going to write about anything. Here, have an lolcat...errr....fox.

Cosmo 101 Olber's Paradox

Hello bloggers! How are you all doing this fine day? Well I’m doing wonderfully. You know why? Because in my cosmology class we will actually start talking about cosmology and not just gravitation! (I will warn you now, some of this stuff we’ve already gone over in the background section of this blog). So first we’ve started off with Olber’s paradox. People before the 20^th century believed that the universe was infinite and static. And a consequence of an infinite universe was that if you looked out into the night sky any were you look you would see a star. So instead of being black and blotchy the night sky would be a uniform brightness. Like in the picture. But this is obviously not true. Why not? Well there are 3 main reasons quoted. Firstly is the finite speed of light. Secondly is the finite age of universe. Third is the fact that space expands. The first and second ones go together. If the universe was created a certain finite time ago then the light from the far away stars hasn’t reached us yet. The third one only adds to this effect because as the universe expands the light from really far away objects gets red-shifted into a wavelength we can’t see. So from all this we can concluded that the universe isn’t static or infinite.

Cosmo 101 Orbits (for that good clean feeling, no matter what)

Ok so what do general relativity orbits have to do with our solar system? Well for a long time the orbit of Mercury was a bit mystery. It doesn’t quite follow the prediction of Kepler’s laws. It is just a tad bit off. This issue was first observed in 1859. Scientist tried to account for it but they couldn’t figure it out. And then all of the sudden there was this other theory of gravity! So plugged all the numbers in for the orbit of Mercury and low and behold it explained the difference. And if you look at the graphs from yesterday you can see why. The Newtonian graph the Einsteinian graphs are rather different. And this accounts for the difference we see in the Mercury’s orbit. This was the first definitive test of the theory of relativity, and of course it came out positive. The moral of the story is that all of the gravity stuff we’ve been talking about doesn’t only apply to imaginary alien races that live on the surface of a black hole. It applies to our own solar system too.

Cosmo 101 Orbits (for that good clean feeling, no matter what)

Ok now that I’ve gotten that out of my system, back to black holes. There are a lot of different equations that I’ve not talked about here. They can get very complicated very fast and if I shared then it would be super confusing. But when you get an understanding of a certain number of equations it turns out that you can predict orbits around a black hole. And not just a black hole, one of the most famous applications of general relativity was an orbital prediction in our own solar system. Or bits in our own solar system?! you say. No! We already know those from Kepler and Newton, you say. But no! They are not quite right. I have a graphs here with two curved lines. They are both potential energy lines. Reading them is easy if you think about it right way. If you imagine putting a marble at the intersection of the straight line (the amount of energy in the system) and the potential energy curve and then letting it go then it’s going to go back and forth like a pendulum. But if we look at the horizontal axis we see that it is something corresponding to an orbital radius. From this we get a familiar looking orbit (the last picture). Now the first curve is what Newton and Kepler came up with, and the second curve is what general relativity predicts. You will notice there is a slight difference. When we get near the vertical axis the Newtonian curve just keeps going up. But when we get near the vertical axis in the general relativity curve we see that there is this sharp slope and the object falls off into the black hole. But the thing is that it doesn’t have to be a black hole. It can be any planet or star, including our own. Now, you say, what does this have to do with our own solar system? Well I shall explain that tomorrow!

a rant

Please forgive me in this post for it is a rant and nothing but a rant. I hate Ockham’s razor with a hatred that cannot be described in English. Perhaps in Russian Mat but not in English. It’s like the catholic school teacher’s ruler against the dreamer’s knuckles. I suppose this is a strange thing for me to say considering that most physicists swear by it. But just think about it for a moment. Going with the simplest, least contrived answer kills one’s imagination and deadens the soul. Very much akin to Ockham’s razor is the set of philosophical ‘rules’ that debaters and intellects have used for centuries. We treat philosophical arguments like mathematical proofs. I like mathematical proofs; they are challenging and intriguing puzzles that one can solve in an afternoon’s time. But I hardly think the deepest mysteries of the universe should be treated so flippantly. We view the wonders of the universe and the questions which our mind raises in response to those, why, we treat the very existence of God as things to be tackles. We have no reverence or respect. We are out to conquer. And this disgusts me to no end. This is why I dislike philosophers so much! I cannot stand their arrogance and their brutal treatment of things like truth and self awareness. It’s as if they have been handed a new born child and after pondering it and examining it for a bit, declare that they have understood the miracle of life and promptly disregard the babe. And these people are regarded as intellectual giants. On the other hand those that do not hold to Ockham’s razor, those that do not abide by the rules of the philosophical world, those that would have the universe and the human mind be infinitely more complicated and beautiful than we could begin to grasp, those that ponder possibilities far outside of the ‘normal’ realm of possibility, those either keep their speculations to themselves or are labeled new age spiritualist or crackpots. How this makes my soul cringe. Why does everything have to be intellectually conquered? Why does everything have to straight forward? We assume we have the universe under out thumbs but in my opinion we understand a mere speck of the actual knowledge there is to behold and, also in my opinion, if this history has shown how the human race treats knowledge, we don’t deserve to get any more.

Why I haven't been on.

Hey bloggers. You may have noticed that I have not been on since Tuesday. Well at the university I'm currently 'attending' we were informed that Westboro Baptist Church was going to come an protest our homosexual community. Don't go to their website, go to the Wikipedia article here. So we have been very busy organizing and planning in order to counter their efforts. My biggest part in all of this has been pointing out that Christians don't acctually believe this. Christians believe that God loves everyone and sent Jesus to die for everyone. Emphasis on the word 'everyone.' But anyway that's why I have written. Hopefully I'll be able to pick up on the blog again tonight.

Cosmo 101

Hey! Sorry I didn’t post yesterday. I said to myself, I said, “Self you gotta remember to post on the blog!” But then I started watching the finals for Olympics ice dancing. And they just got so exciting and I got so wrapped up in them that before I knew it, it was midnight and I hadn’t done any work! But I’m at a bit of a loss as to what to write about. In my class right now we are mainly doing a lot of calculations concerning the alterations one needs to make in order to compensate for the presence of a massive body such as a black hole. But I doubt these calculations are very interesting and in my opinion say very little about the concepts behind general relativity. So instead I think I’ll talk about the philosophical implications (and the implications to physics as a whole) of general relativity for a couple of entries. So let’s see, now we’ve done away with gravity and replaced it with a structural change in spacetime. What we’ve essential done is replaced gravity as one of the four fundamental forces. Now all we have left is magnetism /electricity, the weak force and the strong force. We have done away with gravity as a force and we have messed with time and space. They have become distorted. If we were to take a look out from out distorted place in the universe what do we see. We see things through a circus mirror. To me it feel like we have to question the way we see everything! It changes the whole playing field.

Cosmo 101

We interrupt the regularly scheduled programming to bring you the bigger picture. So we’ve been talking all about gravity, and we’ve been talking about it from the perspective of general relativity. In other words we’ve been looking at gravity as simply a bending in spacetime. It’s not a real force or anything it’s just a warping to the playing field. But there is a very different view on gravity that we haven’t talked about yet. It’s the particle view and it says that gravity is a force that is carried by a massless partial called the graviton. Yes I am aware that these two views are totally and completely in contradiction to one another. And everybody else knows it too. This is one of the great challenges facing physicists today. We have tried and tried again to fit two together. But we don’t have a straightforward answer yet. In fact string theory is one of the leading theories that people are trying to use to solve this conundrum. But if any of you young people out there (or old people for that matter) would like to give physics a go this could be an area you might check you.

GOD! ?

Hello there readers! I wanted to do a GOD!? entry today but I didn't want to just do pictures today. So to start things of here is the first paragraph of Wikipeida's entry on God:

God is a deity in theistic and deistic religions and other belief systems, representing either the sole deity in monotheism, or a principal deity inpolytheism.[1] God is most often conceived of as the supernatural creator and overseer of the universe. Theologians have ascribed a variety of attributes to the many different conceptions of God. The most common among these include omniscience, omnipotence, omnipresence, omnibenevolence (perfectgoodness), divine simplicity, and eternal and necessary existence. God has also been conceived as being incorporeal, a personal being, the source of all moral obligation, and the "greatest conceivable existent".[1] These attributes were all supported to varying degrees by the early Jewish,Christian and Muslim theologian philosophers, including Maimonides,[2] Augustine of Hippo,[2] and Al-Ghazali,[3] respectively. Many notablemedieval philosophers and modern philosophers developed arguments for the existence of God.[3] Many notable philosophers and intellectuals have, by contrast, developed arguments against the existence of God.

I have also been looking out for pop cultural views and references to God and have discovered that while American society isn't always interested in God there is a large interest in the supernatureal. So I googled that and the picture up top is the gist of the first 20 pages or so.

The last thing I've included for today is a picture of one of the most beautiful and moving buildings I have ever been in, the Hagia Sophia. It was originally a church (this is when I visited it), then it became a masque and now it is a museum but it is very closely associated with God (and it's just gosh darn pretty) so I thought I'd include a picture of it.

Cosmo 101 The Schwarzschild metric

Ok so here are two more strange effects of the Schwarzschild metric. One is the time. Let’s say we are attending the interstellar Olympics being held on our black hole alien friends home ‘planet.’ But a dispute arises with the speed skating. The fans in the stands measure the winning speed skater to have competed the required number of laps in 34 seconds. But the fans orbiting the planet from further out measure on 1.5 seconds. But there is no discrepancy. The time is warped by the curvature of spacetime alone. I think I’m going to leave the next item for tomorrow and got get some sleep. I’ve had a lot going on and I wouldn’t mind a bit of a break.

Cosmo 101 The Schwarzschild metric

Ok so equation 4 from yesterday is the Schwarzschild metric but we won’t use all of it. That last term, the one with r^2 and phi, has to do with angles so we don’t use it much. We mostly use the first two terms. The first term describes how time changes and the second term describes how space changes. You remember that alien race that thrives around black holes. Well they are used to this and know how to measure things around a black hole. And because this is so strange to us they give us an example. Let’s say we are very close to a 5,000 meter (that’s the mass) black hole. Let’s say we start out right above the horizon (which is at 2M or 10,000 meters) and want to measure 1 meter. Now we need more information than this. There are two viewpoints we could take with this measurement. We could take the viewpoint of someone outside the influence of the black hole or we look at this from the perspective of someone right here next to the horizon. Let’s say we want to measure one meter from the viewpoint of someone outside the influence of the black hole. Now what would that one meter look like from the perspective of someone right here next to the horizon? Well if you use just the second term of the metric you calculate a distance of about 83 meters! Quite strange. Ok this is all I have time to do tonight but I’ll see if I can’t explain this more tomorrow.

Cosmo 101 The Schwarzschild metric (math included)

Now I would like to take a moment to talk about the actual Schwarzschild metric. Now there will be a bit of math involved in this but hopefully it will be well worth it. First let’s talk about units again. In general relativity we like for things to be as simple as possible, so we make time and length have the same units. In my book we use meters. Well how do you make time go from seconds to meter? Well you multiply by the speed of light, c. So, now that we have everything in meters things will be pretty easy. We’ve seen the first equation up top (1). It’s the equation for the distance one travels. We’ve also seen the equation right below it (2). It tells us the distance one has traveled in spacetime. But the thing about equation 2 is that it only works for flat spacetime. But now we are dealing with a curved spacetime and we will have to change equation 2. What Schwarzschild discovered is that you can alter this equation to get a distance that works for curved space. But first we have to do some more unit changing. Now we are dealing with gravity and that means we have to deal with masses. Masses normally come in units of kg’s but now we want them in meters as well. So we multiply any mass we get by Newton’s gravitational constant, G, and then dividing it by the speed of light squared. This is in equation 3. Now our new equation for distance will look nice and neat. And there it is, equation 4. There is a lot more to talk about but I think I’ve given you enough already. We’ll talk about all that tomorrow.

Cosmo 101

I may not have a really sound answer to the question of why all this stuff is so strange but I do have a bit of an illustration that might help us think about it. Have you ever heard of the book flatland? Well it’s about this group of shapes that live in a 2D plane. Our protagonist is a fellow by the name of square. These shapes live in a 2D plane and have never experienced 3D. Now if our square were to travel into a vicinity of very high mass, as in the picture, he would dip down in be warped under the strange warped space. Strange things would happen. He would get distorted. Lengths and time would be distorted. And it would freak him out! Just like we do when we encounter strange things like this. He can’t imagine or see his space being twisted, just as we can’t see 4D spacetime being bent and twisted. But it is and that’s why all those strange things happen. It’s very hard to picture but I hope my illustration has given you a little bit of a better understanding of what is going on.

Cosmo 101 The Schwarzschild metric

We had some homework to do on the Schwarzschild metric. Now as we were staying yesterday, when one calculates a radius near a heavy object you have to be careful how you calculate it. There is the normal radius which is measured directly from the center of the object out, and there is what we call the reduced circumference (which is actually a radius and not a circumference) and it is what we calculate from knowing the circumference. But these, as we said yesterday, are different. It turns out that when you get very close to the black hole these things get very different. In fact as you approach the black hole the difference between these two gets larger and larger till it goes to infinity. Until of course you get sucked into that black hole. Quite a strange concept. But why does this happen. Well I asked the professor and he said just because the spacetime ‘fabric’ around that object is so distorted. I know it is very hard to comprehend something like that but that’s the answer he gave us. Now I’m not saying that’s a bad answer but it’s not the most satisfying of answers. It’s like being hungry and someone giving you a wafer. I don’t really like wafers but I do like big Macs! I would like a big Mac answer to the question but I’m afraid that is not something that will come easily. But if any of you have some clues or thoughts please comment!

Cosmo 101 The Schwarzschild metric

Ok so here is where things start to get weird. Last night I introduced the Schwarzschild metric, but now allow me to explain why it’s necessary. We are use to a world that is basically flat. If you have a circle and you measure the circumference then divide by 2 time pi you get the radius. If you measure from the center of the circle to the edge of it you get the same number for the radius. Duh! But now I shall show you an example in which this is not true. Ok so now take a look at the picture that I’ve included. The black thing in the center is a really heavy black hole. Now let’s say there is an alien race that flourishes around black holes. So what they do is big these big platforms all around the black hole. The purple and red dashed lines are 2 different platforms that our alien race has built. Not what the scientists of our alien race (they need a name) want to measure the distance from their platforms to the center of the black hole. So what would we suggest they do? We would suggest they measure the circumference of the platform and divide by 2 times pi (in light blue), and then do the same with the other platform (in dark blue). Our alien friends are a bit skeptical so we suggest that as a check they subtract these 2 radii and that should be the distance between the platforms (in orange). They do as we suggest and find something amazingly peculiar. Their outer radius subtracted from their inner radius does not equal the distance between the platforms! The human scientists are astonished, embarrassed and confused, but the alien scientists are quick to explain. Because of the heavy influence of gravity near the black hole our normal geometry (which we call Euclidian geometry) simply doesn’t work. It just doesn’t work. In this instance, our alien friends explain, we have to use the Schwarzschild metric.

Cosmo 101 The Schwarzschild metric

So we’ve recently been looking at one metric in particular, the Schwarzschild metric. There is an interesting history to this one. So Einstein published some of his finding concerning general relativity in 1915. This same year a man by the name of Karl Schwarzschild was serving in the German army and thinking about these same sorts of things. He came up with some equations that are now the Schwarzschild metric. And then he died only a couple of month later. Einstein didn’t think it was even possible to come up with these sorts of equations. It makes you wonder what he would have come up if his life hadn’t been cut short. Anyway, these equations, like any metric, describe a world and the way physics works around this world. Formally we say these equations describe the spacetime geometry for a certain situation. Well the Schwarzschild metric describes the world around a spherical non-rotating mass. The most famous examples are black holes! Yes, that’s right, we get to talk about black holes! Perhaps I should do a bit of an introduction. Most black holes arise from a star finally giving in to gravity and collapsing in on its self. At this point all of that matter is compresses so much that it sort of tears spacetime and creates the mysterious black hole. But anyway if you were to stand right outside a black hole your spacetime and hence the laws of physics will be governed by the Schwarzschild metric. It’s a very twisted spacetime that I don’t really understand completely but I think I shall have more information for you tomorrow.

GOD! ?

Oh my! I had forgotten how hard homework was and how long it took! All we did today was math. So today I think I’m going to put a God post up.

Cosmo 101

Forgive the lack of a post last night I was at a wedding and it took much longer than initially anticipated. But I have come to a decision. With this class and all of the other things I am doing. I think I’m going to only write a post once during the weekend (Friday- Sunday). Ok if figured out how we do velocity. If we are just trying to find the velocity of a thing we us normal (or coordinate) time. So now I think it’s time to discuss some interesting properties of gravity. Ok so let’s say we are characters in a sci-fi movie and we are going to visit a black hole. To our horror one of our androids slip over the edge of the observation deck of our spaceship and falls towards the black hole. As much as that android was useful, helpful and part of the team, this mishap provides us with a scientific opportunity. We watch the poor little android as he is sucked further towards the back hole and see a confirmation of general relativity. You remember the experiment with the gobstoppers when we feel towards the earth. The same thing happens to the android. As he falls gravity pulls on his feet more than on his head and he gets stretched. Also gravity pushes him inward and his arms get compressed. This goes on until he gets stretched into a thin string and finally sucked beyond the event horizon. This event has one of the coolest names in science; we say the android underwent spaghettification. Also, and I won’t provide an example for this just take my word for it, the curvature of spacetime messes with the lengths of things and the wavelengths of light. These effects are not due to special relativity, they are not associated with time dilation or length dilation, they are solely due to the curvature of spacetime. But I don’t know why. Perhaps I will have more information on Monday.

Cosmo 101 (a bit of math included)

Well…I was gonna talk about tidal effects and the Schwarzschild metric but I think I would like to talk about our homework more. I know that sounds weird but…it is, my homework, I mean. We are currently working with special relativity and it is just really weird. I’ve always known, well since 1687 (Newton’s year), which feels like forever, I’ve always known that gravity is a force and that v=d/t and that t is the same for everybody that hasn’t even been a concern, but now it is and I don’t really know how to handle it. Now all of the equations that I’ve always fallen back on are not valid anymore and I don’t know which ones are and aren’t. For example there are two (or possible more) types of time in relativity. There is measured time which we represent with a normal t and there is wristwatch (or proper) time, which is designated with the greek letter tau. Now which of those do you use if you want to find the velocity? And for example if you have people traveling at different speeds they will see different times for different events. In other words not everyone agrees on the time separation, delta t, between two events. And not everyone agrees on the spacing either. But there is hope (haha I sound like a public service announcement) there are some values that are the same for everybody, tau is the same no matter who you are or how fast you are going. The equation to calculate tau is tao^2=t^2-s^2. Here s is the displacement in space. It’s the same as the r we used a couple weeks ago.

Cosmo 101

Ok so hop back into your glass elevator we’re gonna need it again. So let’s get some more goobstopers and do a little experiment. The experiment is to toss one lightly up into the air and see what happens. First let’s start out on earth. You’re just sitting there in the chocolate factory and you throw the goobstoper up into the air. What does it do? It goes up and slows down, then comes to a stop and falls back down. Ok after you record the results you take off into space and find a nice little spot away from any gravitational fields. You cut the power and drift along at a nice constant velocity. Now you try the experiment again. You throw the goobstoper up but this time it just keeps going until it hits the ceiling. Hmm…interesting. Now you turn your power back on and set the controls to accelerate you at 9.8 meters per second per second (the ‘acceleration of gravity’ felt on earth) and you do the experiment again. This time the goobstoper goes up and comes back now just the way it would on earth. Very peculiar. Well now you go back towards earth and let yourself free fall down towards the earth. Now we repeat the experiment one more time. This time when you throw the goobstoper up it keeps going just as it did when you at constant velocity in deep space. This set of thought experiments is called the Equivalence Principle and, more succinctly, look like this:

A lab on earth = an accelerating lab in deep space

And a non-accelerating lab in deep space = a feel-fall lab on/near earth

Now there is one distinction that must be made. When I say earth what I really mean is a uniform gravitational field (remember the experiment from last night), but on earth’s surface it’s very close to uniform. You know what, I think I’ve been spelling goobstoper wrong…by George I have! It’s spelled gobstopper. Oh well, you knew what I meant.

Cosmo 101

Ok time for some more really cool introductory concepts. Proper time. I and the author of the book we will be reading like to call it wristwatch time and it has to do with moving clocks…or watches as the case may be. So let’s go back to wolverine and deadpool in their epic battle. Let’s say that in the computer chips inside deadpool’s head he has a clock. Now this clock measures the time when the battle starts, the first event and let’s say that deadpool himself is present when the call to the army is made, event two. If that were the case then the clock inside deadpool’s head would measure wristwatch time, or proper time. Right now it’s just a vocab term but latter it will mean something more. I also wanted to tell you about the reading we did for tomorrow. It was all about gravity. So you know in high school physics how they say that gravity exerts a force on you when you fall…well all the time…but it hurts you when you fall. Well turns out that there is really no force at all…we are accelerating towards the earth due to the fact that the space around the earth is curved by it’s gravity. Here’s an experiment to illustrate. Let’s say you have working replica of Willy Wonka’s glass elevator. Now first you take it way into deep space where there are no planets or anything with a very strong gravitational pull. Now you have 4 everlasting goobstopers and you set one near the ceiling, 2 in the center one on the left and one on the right, and one near the bottom of the elevator. As you sit there in space your goobstoper don’t move, not one iota. Now let’s say you come back to earth and let yourself free fall through the atmosphere and plummet towards the earth. Now you are experiencing the same sort of weightless feeling you did in deep space so you decide to try the goobstoper experiment again. You put the goobstopers in the exact same places and watch them. The funny thing is that they do move but only very slightly. The top one inches toward the ceiling the center ones move more towards the center and the bottom one goes towards the floor. Again this effect is very small but if you were to fall for quite a long time (and not die in a giant fireball upon impact with the earth’s surface) you would see the goobstopers move! And they are moving because of gravity. Cool experiment right? Now all I need is a glass elevator and some goobstopers…

Cosmo 101

So I went to my first cosmology class today and it was amazing. I am very much looking forward to walking through all of this with you. And guess what! All of the things we’ve been talking about up to now have been almost a perfect introduction to where we started off in class today. But there are some things I didn’t mention, so I would like to take today and explain what an inertial reference frame is. Ok so whenever I think of this topic I always picture people in bubbles floating around in spacetime and it always makes me think of this commercial. But anyway inertial means that the bubbles aren’t accelerating, they’re just floating along at a constant velocity looking at events that take place. The other thing I wanted to cover today way the units that I couldn’t remember from before. So when dealing with spacetime in any sort of relativistic way you have to make a choice. Both time and distance either have to be in meters or in seconds. The book we are using picks meters. So whenever you have a time 12 seconds for example you multiply by the speed of light, 3x10^8 m/s and you get an answer in meters. The units of everything else change too, for example velocity is unitless, it’s just a number.

in the interim

No real post tonight. I'm getting ready for school. Oh that was fun to say. But I shall report the happenings of our class back to you and I might even get some of my classmates in on it. Oh I'm so excited! In the meantime here have an lolcat...err...loltiger!

General Relativity

Ok so I’m getting the general sense that I’m in over my head, with this stuff. But I have terrific news! I’ve been enrolled in a cosmology class! Imagine me an old man in a class with a bunch of young college students. But I hope to learn so much! And I shall report it all to you. But I think I need to finish up this discussion of time and metrics first. So when Minkowski came up with his space time, Einstein had a new setting for trying to figure out gravity. So what he decided (and it took him quite some time to figure it out too) he decided that gravity warped space, it sort of bends the metric. Where there was a straight line now that line has been bent by the object that has been placed there. Just like in the picture. This is what creates gravity. This is why we feel pulled towards the sun. We aren’t actually pulled towards the sun we are falling into it. And that is the basis of general relativity.

Metrics 2

So the first spacetime I would like to talk about is the Minkowski spacetime. It was first invented by the German mathematician Hermann Minkowski soon after Einstein came out with special relativity. Minkowski came up with it to supplement Einstein’s theory. It’s a 4D space consisting of 3 spatial dimensions and 1 time dimensions. A lot of rules that we are used to in 3D space apply but there are some differences. And they are very important differences. But the problem is that these difference only make sense if you know a good deal of linear algebra and differential equations and in all honesty I don’t understand all of it. So I’m not really sure who to proceed from here. I guess to make it very simple when you take a 4D vector in Minkowski space and multiply or add it to another one it doesn’t work the same way as another sort of space. It sorta has magic math. I know, that sounded stupid. Oh well. I guess that’s all I can say…like I said I don’t really understand it either so, yeah.

Metrics

There are more relationships like this one but I won’t take the time to explain them all…mainly cause I don’t really understand them all/don’t care that much. Let’s move on to bigger and better things, The Metric. Now we know about the metric system, right? You know that thing that America reuses to use with meters and kilometers? Well that is a metric of sorts. In math a metric is a sort of…well it’s like Middle Earth. It a place that has its own set of rules and laws. You can do magic there. And there are elves. It’s a lot different from here. And that’s what a metric is. It’s a space that exists outside our own, like scifi, with its own set of rules and laws and things like that. So for LOTR we would call it Tolkien’s metric. Other metrics you might be familiar with include Rowling’s metric (Harry Potter), Roddenberry’s metric (Star Trek) and the Blizzard Entertainment metric (WOW). Some which you may not be familiar with but which we will be using include the Riemannian metric, the Euclidian metric and the Minkowski metric. And we will talk more about those tomorrow.

Time 10 warning math included (but it's not that bad)

So now we get to deal with the classic sci-fi topic of causality. Now let’s pick two events and since we are dealing with sci-fi and I recently watched the movie I pick wolverine and deadpool causing the meltdown of the three-mile island reactor. Ok, I know that didn’t really happen but let’s say it did. So we have two distinct events wolverine fighting deadpool (we’ll say the instant that they start fighting) and the reactor meltdown (we’ll say they instant that the people monitoring it call the military). Now these two events are separated by a time-like interval. Because we know this and that one event causes the other, we know the above equation applies. What it says is that the square of the spatial distance between the events must be less than the speed of light multiplied by the time between the two events. The second equation therefore says that the spacetime interval (or ‘distance) between the two events must be greater than zero. All this says if that if the instant wolverine took a step forward to fight deadpool a light sensitive trigger went off, tripping, by electrical signal the phone that was to call the military it would take at least as much time as a beam of light to be shot from the warehouse opening to the phone. I know it really doesn’t tell you anything important does it. Well I suppose the most important thing is that wolverine won.

GOD! ?

ok so i continued reading the wikipedia article on spacetime and i am currently feeling like penny in the presents of sheldon. so i'm gonna try again tomorrow night. but in the mean time have some pictures of god, gods and the like. the last one is called a flower for god if that helps.

Time 9 warning math included

Ok I ended up not seeing him today but when I do see him I’ll get back with you on that stuff. So everyone know that the shortest distance between two points in space is a straight line. In math that straight line is designated the distance between the two objects and we use a lovely little formula to derive it which I’ve included in figure one it’s the first equation, it’s sort of the extension of the Pythagorean theorem(I’m really gonna have to find another way to write equations in there, any ideas???) but in space time this equations changes to the second equation where c is the speed of light and t is time. I think since this post has some math in in…as will most the consecutive posts on time, I’ll make it a little shorter and go at a slower rate.

Time 8

Wow. Yesterday’s post was really long wasn’t it? Sorry. Anyway so hopefully today we can start getting at some of the detail’s of time and in particular the physical approach used by most physicist today with regard to time. In other words, spacetime. Ok first some vocabulary. A worldline is a path or line type thing in 4-D space that specifies the path of an object. I’ve included a picture that is much like the one from yesterday but has a worldline mapped out on it, the one of your hoverboard perhaps. If it is a ‘straight’ line, unlike the one in the picture, it is sometimes called a geodesic. And now for the units physicists use when talking about spacetime. Oh…wait…I don’t think I really understand these. I know we express velocities as a percentage of the speed of light. But even that doesn’t really make sense. But you know what I think I’ll be visiting one of my professor friends tomorrow and I’ll ask about that and report back.

Time 7

Before Einstein and the theory of relativity time was considered the one constant in the universe. It was absolute and everybody measured it the same way. So when Newton used the analogy of a giant clock for the universe, he met a very accurate consistent clock. But with Einstein that is not so. For Einstein the thing that is the same for everyone is the speed of light. It doesn’t matter where you are (save perhaps parallel universes or something like that) or how fast you are going if you measure the speed of light it is always the same. And now I would like to spend a few days on spacetime. We’ve already went over that briefly in past posts but I would like to go a bit more in depth. And we shall start with the horrible little picture I’ve included. It’s a 2-D picture that looks like it’s in 3-D and represents a 4-D phenomena. It starts by locating your point in space. That’s the arrow that points to the origin and says observer. Now let’s say on this hypersphere of the present, the observer arrow happens to find you in a very dark place for example a very large cavern. A very large cavern. And let’s say you have a flashlight. Now if you were to stand in that one spot and turn your flashlight on then you would produce a cone of light not unlike the one in the picture. You like would be moving away from your location in the hypersphere of the present as fast as is physically possible, and any action you do, say hop on your super-jet-powered-hoverboard and follow your flashlight’s light, would have to take place inside that cone of light. Now, but what does this tell us about you or more importantly how you are going to get out of the cavern in time to see tomorrows football game? Nothing it tells you nothing. That’s why it’s a horrible little graph. But it is a good way to think about the present and the past and the future and to incorporate time into the picture.

Time 6

The trick to measuring time is to find something repetitive that always takes the same amount of time. We just guessed at first. we said hey I think that the sun is there for the same amount of time each day so we used that to tell time with. Of course it wasn’t’. then we used the stars. And of course they weren’t quite right either, now the second is defined by the radiation emitted by caesium atoms. Which in another hundred years or so we will discover is not quite right either. To be more precise Now the SI (the people who define these sorts of things) has declared that a second is 9,192,631,770…well let me explain exactly what the periodic thing that caesium does is. Ok first you have all the electrons right? And they are in their little orbital. Have I ever explained about spin? Well it’s a property of electrons and protons and stuff BUT they don’t really spin. This confused me for a long time. Anyway electrons only have two ‘spins’. They can either spin up or spin down. And if you take a ceasium atom and look at the electrons on its lowest energy level you will it (they?) flip spin in a very period way. In fact 9,192,631,770 flips occur in our traditional second. So now this is what we use to define a second.

lolcat!

so i have bronchitis...which won't be so bad except that i am apparently allergic to antibiotic they gave me (you would think that wouldn't happen to an alchemist who specialized in medicine). anyway no real post today. but here have an lolcat. i don't have time to explain this...it's about quarks...but they're really cute so it's ok.

Time 5

As much as I don’t like philosophers I think it might be helpful to hear what they have to say about the subject. The first view is that time is a real tangible thing that is part of the fundamental structure of the universe. It’s pictured like a film strip where each cell is a moment and if you string all the cells together they form the reality that we are used to. So basically time makes up just another dimension. This is the point of view that physics holds (or at least the majority of physicists).The second view says basically the opposite thing, that time is not a physical think and can’t really be measured. Instead, it says that time is part of a fundamental intellectual structure that humans operate out of. To dumb this view-point down, it’s all in our heads. If I were to come to any conclusions on this one I would side with the physicists. But I do think there is something big we must be missing in the nature of time. Whenever I’m looking at something I can’t figure out it’s usually because I’m not looking at it in the right way. Unusually if I look at it from a different perspective then I can see the answer right away. I’m hoping this is the case with time. We’re just not looking at it from the right perspective. Once we figure out how to look at it, what it is will become clear.

Time 4

100th post!!!!

If you hadn’t noticed, the pop physics excerpt played in with our current theme, time. Now we’ll take a more fundamental look at it. What is time? According to Wikipedia,

“Time is part of the measuring system used to sequence events, to compare the durations of events and the intervals between them, and to quantify the motions of objects.”

The first definition (of 19) that Merriam-Webster is the same as Wikipedia’s. In other words it’s a really really hard thing to define. If I were to be asked to give a definition of it I would be a smart-ass and something like time is velocity times distance. But of course I can’t do that because in physics time is considered a fundamental unit from which we derive all other units, such as force or speed. Physics has 7 fundamental units: kilogram, meter, candela, second, ampere, kelvin, and mole. These correspond to mass, length, luminosity, time, current, temperature and a specific (6.22X10^23) number of atoms/molecules of something. All other units and quantities in physics can be broken down into a combination of these units.

Pop physics

You remember the pop physics think I started to do, well here’s another one: The Space-Time Continuum! (insert sci-fi music here) Now this is strictly my interpretation and my spin on it, this isn’t necessarily accurate. I imagine space-time like a graph (I’ve included a homemade copy). At one end of the continuum we have light, which is the fastest thing in the universe and doesn’t experience time. And at the other end we have something that is not moving (relative to some universal standard, I’m not sure how one would get this…but oh well). The person who is not moving experiences time the quickest. For them time is much faster than it is here on earth and they would grow old faster and everything. But for someone near the other end of the line (near light) time is experienced very slowly and it would seem like earth is on fast forward. And that’s how it works. If you increase your speed, time slows down for you and if you decrease your speed your time speeds up. And now you know what to do to get time to speed up and snow down. But good luck increasing your speed by 20% the speed of light during a business meeting.

Time 3

Why do I know this? Well, believe it or not I’ve worked on a physics experiment before, not cosmology but still. It was a particle physics experiment. And I chiefly worked on electronics. But we had a problem (well we had a lot of problems but this was a big one). The timing was off. We were trying to synchronize the computer and the electronics, but they were off by a couple of milliseconds. We can’t (at least I can) imagine what a millisecond feels like. But it was a big problem. We were getting different amounts of data in different sets. This threw the whole experiment off. And it was just a matter of milliseconds. That is way all this crazy timing stuff in important, it’s really important. And I know for a fact that there are other experiments where the timing counts even more and even smaller. Nanoseconds matter, they really do!

Time 2

I say it is arbitrary because, like all other forms of measurement we define it. We say, ok here, this is a second. For a long time (far beyond what my lifetime should have been) everybody knew time was arbitrary. Only in big cities did anybody have any right to say their time was right. Most of us, myself included had no way of measuring the time outside of the church bells. I once knew a man who claimed that the Babylonians were far more intelligent about their time system and so he followed theirs. Instead of 24 parts he divided the day up into 60 and I daresay he was never on time for anything (even his own funeral, but don’t ask how that happened). But we had absolutely NO concept of what a second was. Now everybody knows what a second is. Oh don’t worry I’m not going to start lecturing; I’m old enough to know that nobody ever listens. In fact I do see a need for things to speed up. The definition of a second (and you know, I keep waiting for somebody to change the second and make time run on intervals of 10 just like meters and liters) may be arbitrary, but it is also very necessary. Physics, at very least, needs it.

Time 1

Hey! I’m not dead (yet). But like I said our internet got messed up and then we had more snow and it got even more messed up. But this time it took a while to fix it. Yes, I could have gone to the library, but hey what can I say, I’m old. Anyway my posting should be regular again. And I think I’ve found a new topic. That tangent I went on during the Randall series got me thinking about time again. It’s always been something I’d hoped to study so I checked out a book about it. It’s a book called “Faster” by James Gleick. It was in with the other science books but from what I’ve read there’s a lot besides science in it. For example in the first chapter he records his visit to the Directorate of Time. Yes, there is such a place and it’s part of the United States Government under the Department of Defense. They make time. Well, I should say they set it. They, along with the time input from other nations set the global time. They have this system of atomic clocks (don’t they have those in watches now?), and they consult each other and form a consensus and send that time to the global time … place, just outside of pairs, and then the input from other places comes in and they form a consensus and that’s the time. It’s amazingly arbitrary.

GOD! ?

sorry i didn't post yesterday there was a lot of snow the internet was in and out. well i'm done with Randall's maze so now you guys have got to tell me what you want me to talk about any suggestions. anybody? anybody at all???? in the meantime here are some more pictures. have fun!

Randall's maze rapup

Ok so after that pathetic excuse for a post yesterday let’s see if I can come up with something more intelligent to say today. And today’s topic is superstring theory. Oh boy. Ok so instead of particles looking like little pool balls we say they are tiny strings. And let’s say they can oscillate in different ways, just like a guitar (or for a more accurate analogy and a way cooler interment, the one stringed Chinese Duxianqin) to make different notes. Each of these notes turns into a different fundamental particle such as a quark or an electron. So superstring theory says that the whole world is made out of nothing but strings. If you think about it this way all the issues with bringing together quantum mechanics and general relativity, which is notoriously hard to do. Extra dimensions come in when you look at the math. The theory doesn’t really make sense if you only have 3 spatial dimensions but the math works out perfectly if you have for example, 10. This may sound like a crackpot theory but only time and some more investigation will be able to say.

Randall's maze rapup

And now for our second set of applications, Large extra dimensions and the Randall–Sundrum model. Both of these theories attempt to explain the weakness of gravity in comparison with the other forces, but I think I shall summarize them separately. So first let’s look at Large extra dimensions, which is apparently also known as the ADD model. It goes something like this: all the normal laws of the weak force, the strong force and electromagnetism only work in the normal 3 spatial dimensions. But gravity works in more than that I’m not sure how many but more. As for the Randall–Sundrum model, I haven’t the faintest clue what any of this means so I think I shall take the cheap way out and just quote Wikipedia. "In physics, Randall–Sundrum models (also called 5-dimensional warped geometry theory) imagine that the real world is a higher-dimensional Universe described by warped geometry. More concretely, our Universe is a five-dimensional anti de Sitter space and the elementary particles except for the graviton are localized on a (3 + 1)-dimensional brane or branes.” Yeah…I’ve got no clue what that means, but there you have it.

Randall's maze rapup

First Kaluza-Klein theory. There’s a lot of stuff I don’t understand at all but I will try to explain it best I can. It’s a theoretical model that Theodor Kaluza came up with in the early 20th century. It was meant to take the new model of gravity (Einstein’s general relativity rather than Newton’s model) and combine it with electromagnetism (electronic fields and magnetic fields and light and the like). Kaluza, who was German, figure that if you have 4 spatial dimensions you combine gravity and electromagnetism by looking at electric fields and magnetic fields differently. Just like gravity is curved in the 3 normal spatial dimensions, the fields are a result of curving in the extra dimension. I have no idea how this allows one to combine gravity and electromagnetism but whatever. People had some problems with this extra dimensions stuff and so along came the Swedish physicist Oskar Klein who said that we hadn’t know about the extra dimension was because it was very small and curled up really tight. This (then very ) weird theory fell out of favor but of course when string theory came along it was looked at again and is now seen as a sort of predecessor of string theory.