Randall's maze rapup

We’ve spent some time going though (to be painfully honest) the first chapter of Lisa Randall’s ‘Warped Passages.’ We’ve basically been talking about coordinate systems and how to conceptualize other dimensions. I looked over the rest of the book and it has some really good things to offer but I don’t have the time or energy to finish the book but I would like to go over some of her research and some ideas about more dimensions, so I think I shall be mostly consulting Wikipedia for most of my information. (oh by the way, my vacations over so I will hopefully be posting every day again.) So let’s take a looks. When consulting Wikipedia it aperies that there are 3 main ‘uses’ or applications for extra dimensions, Kaluza-Klein theory, Large extra dimensions and the Randall–Sundrum model (these apparently have to do with each other), and superstring theory. My next proposition is that we take a quick look at each of these applications and what they have to do with extra dimensions.

GOD! ?

here! have some more pictures and leave some comments!

Randall's maze 6

This brings me to a very interesting point (it’s totally a tangent from Randall’s book, but oh well). It has to do with God! So God’s supposed to be omnipresent, right? Everywhere at once? Well that would include extra dimensions. And if he created the universe then he must have created those extra dimension. He created time. This means he was not subject to it in the beginning. And he must exist outside of it! And like I was saying before we are 4-D (at least) creatures. So he must see us that way. So when God looks down at a person, say Einstein, he sees him as a holistic 4-D creature and not him as an old man (the way most of us are used to seeing him). It also means that whole thing about him knowing the future and us still being able to change it doesn’t even apply. When you think about it this way a whole host of interesting consequence pop out at us. I would really like to hear what you guys think about such a weird concept so send me a line!

Randall's maze 5

Now for another term. You know how I said that physicist and mathematicians put numbers onto our axes? Well this may seem like not that bit of a deal when we are just moving a string around a table, but when theorist make up new math these numbers become very very important, they even get their own name. They are called the metric of a system. If you’ve ever dabbled in relativity you will hear this work a lot, usually preceded by someone’s name. All they means is a specific system of units and measurements that goes along with the coordinate system they are talking about.

Now if I could I would like to take a moment to talk about time. Einstein declared it to be one more dimension and stated that we now had 4 dimensions. How does that fit into all of this? Well it is an extra dimension by not an extra spatial dimension (you know I just learned how to spell spatial…what a weird spelling). But how to picture this? Well…just like we normally would. Imagine yourself as a baby, a 5 year old, a 15 year old, a 20 year old and so forth to your current age. If you string these images together you get your 4-D projection. We are in all honesty 4-D creatures. We grow and change with time.

Randall's maze 4

All right now that you know what a vector is we can talk more about dimensions. In the exercise we did yesterday you were using a 3 dimensional coordinate system. There were 3 axes each corresponding to a different dimension. And we needed 3 different numbers, an x component, a y component and a z component, to specify exactly where your vector end was located. If you only had one dimension you would only need one component to tell where your vector end was located. And the same holds for five dimensions. You may not be able to draw a graph like that but you still only need 5 numbers or components to specify a location in 5-D space. I've included a picture of some objects in 2, 3 and 4 dimensions. String theory and now M-theory suggest 10 and 11 dimensions, respectively. Why so many?

Randall's maze 3

Hello!!! And Merry Christmas! I hope it was a good day for all. And now back to physics. So in order to more fully understand what Randall means by ‘dimensions’ we need to understand the concept of vectors. This took me two years to fully understand! It’s a weird concept for those who aren’t used to it, so take your time and think about it… So what is a vector? A vector is just a straight line. But when we say vector with regard to dimensions we’re talking about a straight line anchored at one point. (no one on the internet seems to have done this so I will go ahead and do it!) Here’s an exercise that should be helpful. Get a piece of string (or something like it). Now we are going to set up a 3 dimensional coordinate system. All you have to do is declare and origin (or zero point like in the picture), it could be the corner of a table or a book or anything. Next you need to declare an axis. The normal axis in math and physics are: left right or x, back and forth or y, and up and down or z. Next hold one end of the string against your origin. That is the anchor for your vector. Now pull the string taut in any direction. And there you have a vector. You can move the one end but not the one connected to the origin. Ok now pick a vector position. Take your finger and put it up to the end of your vector. Now drop it straight now onto the table. This is your vectors ‘projection’ onto the ‘x-y’ plain. Now if you run your finger straight over to one of you sides or axis you have that axis, say the x axis, ‘component’. The only thing that physicist and mathematicians to is put numbers on them. I hope this walk through was helpful. If it wasn’t let me know and I can change it.

Randall's maze 2

So why would be even bring such a crazy ideal up? We can only see 3 dimensions…why would there be more? Well why not? Why couldn’t there be more than 3 dimensions? Perhaps that could solve some of the weird problems we have in physics. And according to Randall, they do. There is one that I find fascinating that has to do with gravity. Have you ever thought about how weak gravity is? It’s really really weak. Even though you have the entire pull of the whole earth on you, you are still able to jump off the earth (it’s actually the electromagnetic force that allows you to do this). So in comparison to all the other forces gravity is really weak. Why is this? Randall and some of her colleagues say that it’s because the gravity is shared with the other dimensions. Fore some reason or another it’s stronger in those other dimensions than in ours and that’s why it seems so weak. Now, of course, that’s not all there is to her idea. There is a lot of super complicated math that I haven’t even looked into to go along with that general idea, but the point it extra dimensions are defiantly worth taking a look at.