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[TR] US gov boffins achieve speeds FASTER THAN LIGHT - Page 8

post #71 of 101
This is old news with a new twist, Dr. Wang recorded light traveling 300x its speed through cäsium gas.
partners.nytimes.com/library/national/science/053000sci-physics-light.html

And hes not the only one
news.bbc.co.uk/2/hi/science/nature/841690.stm
Edited by Jim888 - 5/10/12 at 6:00am
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post #72 of 101
It's also possible to slow light down to 1mph using a Bose-Einstein Condensate. Yay for Science. biggrin.gifwheee.gif
post #73 of 101
Quote:
Originally Posted by mushroomboy View Post

When you bring math down to it, what is the basic operands? Addition, subtraction, multiplication, and division. Everything mathmatical is based off that, because that IS math. you may have different variables, but everything comes down to that. If you break it farther, multiplication is just addition. Now you might go into division, but division is just multiplication (if you change the equation) which ends up with addition AGAIN. What math doesn't use the basic principles of math, and then you think about it THAT IS MATH. You want to get real crazy, what does a computer do? It can't multiply or divide but it does every form of math imaginable (only addition and subtraction).
Now phycis, you have the standard theories like you just listed but those occupy a distinct set of rules outside of quantum physics. If you get down to it, there is only one set of physics, it's quantum physics. We just haven't really mapped that out enough to explain the non-sub atomic physics theories. That's the difference, you have a sub-atomic physics and then a "set" of physics that explains the non-sub atomic world. Two real main categories, one just branches off into the theories you listed.
http://www.ted.com/talks/aaron_o_connell_making_sense_of_a_visible_quantum_object.html
[edit] If you don't get my direction... Small phycis = quantum physics, large physics = the world around us. The world around us has several branches of physics now, but it's no longer a main category after Quantum Physics was created. Because it makes an entire NEW set of rules that none of physics in the "world around us" follow. Such as, two objects in the same place. Questions?
[edit2] Now technically Physics used to be multiple subjects, I'm just being a dick. However, math was always a single subject. When you can break an equation down to nothing but addition and subtraction, you really start to understand. Now I'm not saying it's practical, just that all math breaks down into those two operands. We use everything else as a form of short hand, which makes us create more complex theories. However they all follow the same rules if you broke them down.
[edit3] My bad, a processor only adds. it adds negative numbers for subtraction. Though since subtraction is the reverse of addition, it's essentially the same step. I still hold that addition and subtraction would be the root subject in Math. That is what Math is at it's base form, a singular function that can go both ways.

That's completely wrong. Unless you're talking about arithmetic - which isn't "all" of math. Mathematics begins with a set of axioms such as the existence of zero and builds up from there. To further prove my point, addition doesn't even exist in the arithmetic sense on a manifold. You can't add tangent vectors at different points together because not only is the result meaningless, but the resulting vector is no longer even on the manifold. Addition and multiplication (subtraction and division are the other side of the same coin) are only applicable when you're working with algebra over rings where addition and multiplication are defined. Not every space allows you to arbitrarily add things together.

I don't know where you're getting the idea that there are only two areas of physics. If you ever spoke to anyone studying in that area they would say that's completely wrong (including myself). Its not even worth arguing about because this is the first time I've ever seen someone say that and it doesn't surprise me when the same person also says that all of mathematics can be broken into addition and multiplication.
post #74 of 101
Quote:
Originally Posted by Sourtop View Post

That's completely wrong. Unless you're talking about arithmetic - which isn't "all" of math. Mathematics begins with a set of axioms such as the existence of zero and builds up from there. To further prove my point, addition doesn't even exist in the arithmetic sense on a manifold. You can't add tangent vectors at different points together because not only is the result meaningless, but the resulting vector is no longer even on the manifold. Addition and multiplication (subtraction and division are the other side of the same coin) are only applicable when you're working with algebra over rings where addition and multiplication are defined. Not every space allows you to arbitrarily add things together.
I don't know where you're getting the idea that there are only two areas of physics. If you ever spoke to anyone studying in that area they would say that's completely wrong (including myself). Its not even worth arguing about because this is the first time I've ever seen someone say that and it doesn't surprise me when the same person also says that all of mathematics can be broken into addition and multiplication.

Welcome to OCN, where everyone is right, even if they're just plain wrong. wink.gif
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post #75 of 101
^^Similar points to what I raised. biggrin.gif

Also whilst addition isn't a central part of all mathematics, all mathematics was derived from simple arithmetic.

As for adding tangent vectors, I'm not sure if they form a group but adding tangent vectors on a manifold wouldn't make sense if you simply added their n-dimensional vectors as you'd just get another random point as you said. However could you not find equidistant points on the manifold as an application of basic arithmetic in simple cases such as the manifold of a sphere? It's not exactly as much of a relevant example and arithmetic certainly isn't as prevalent in areas such as topology but it can crop up occasionally.

Either way I'm not sure he meant it was relevant in topology, it's a bit too complex for simple arithmetic and for me aswell. biggrin.gif
post #76 of 101
Quote:
Originally Posted by Paradigm84 View Post

^^Similar points to what I raised. biggrin.gif
Also whilst addition isn't a central part of all mathematics, all mathematics was derived from simple arithmetic.
As for adding tangent vectors, I'm not sure if they form a group but adding tangent vectors on a manifold wouldn't make sense if you simply added their n-dimensional vectors as you'd just get another random point as you said. However could you not find equidistant points on the manifold as an application of basic arithmetic in simple cases such as the manifold of a sphere? It's not exactly as much of a relevant example and arithmetic certainly isn't as prevalent in areas such as topology but it can crop up occasionally.
Either way I'm not sure he meant it was relevant in topology, it's a bit too complex for simple arithmetic and for me aswell. biggrin.gif

You'll be completely sick of the sphere after you do a course in differential geometery. biggrin.gif

You can only add vectors when they're elements of the same vector space. That's why you can only add tangent and cotangent vectors at the same point because at each point there is a different vector space. How to move from one of those spaces to the other is the subject of vector bundles though!

The sphere is pretty much the best example to illustrate all the reasons why differential geometry is awesome! Because of the curvature of the sphere you would have to use differential geometry to find those equidistant points. The reason why its so easy to find those points in regular R^n is because there is no curvature.
post #77 of 101
Quote:
Originally Posted by Sourtop View Post

You'll be completely sick of the sphere after you do a course in differential geometery. biggrin.gif
You can only add vectors when they're elements of the same vector space. That's why you can only add tangent and cotangent vectors at the same point because at each point there is a different vector space. How to move from one of those spaces to the other is the subject of vector bundles though!
The sphere is pretty much the best example to illustrate all the reasons why differential geometry is awesome! Because of the curvature of the sphere you would have to use differential geometry to find those equidistant points. The reason why its so easy to find those points in regular R^n is because there is no curvature.

Next year I have Vector Calculus and all that wonderful stuff. mad.gif

But yeah I get why it's more complicated on a sphere, I was thinking of it more along the line of wrapping a tennis ball in a sheet of paper and using the paper to find the equidistant points from a given point where the sheet of paper maps from a plane to a surface, but that is a little difficult for me to comprehend only being in my first year of the degree.

Speaking of which I should probably go and revise for my Advanced Calculus exam in two days. tongue.gif
post #78 of 101
Quote:
Originally Posted by Paradigm84 View Post

Next year I have Vector Calculus and all that wonderful stuff. mad.gif
But yeah I get why it's more complicated on a sphere, I was thinking of it more along the line of wrapping a tennis ball in a sheet of paper and using the paper to find the equidistant points from a given point where the sheet of paper maps from a plane to a surface, but that is a little difficult for me to comprehend only being in my first year of the degree.
Speaking of which I should probably go and revise for my Advanced Calculus exam in two days. tongue.gif

That's actually kind of what you do. That "paper" that wraps the tennis ball is the metric. It tells you what distances and angles are on the manifold.

Wow, you do vector calculus in your second year? That was a third year course for us. Second year was just linear algebra, statistics, and calculus III. Third year was ordinary differential equations, analysis, and vector calculus. Things get a hell of a lot more interesting once you get into those meaty subjects though. If you're really interested in mathematics and how its used in physics look up a book by Baez - "Gauge fields, loops, and gravity". The majority of the book is all intro to background math from the point of view of a physicist so its really easy to read and the author is amazing. It might be a bit advanced right now for you, but keep it in the back of your mind if you're ever curious!
post #79 of 101
So far I've done Vectors and Matrices, Calculus and Geometry, Numbers and Symmetries and Groups, Dynamics, Advanced Calculus and Discrete Mathematics. Most of it is horrendous. tongue.gif

I think I'd probably have to wait until I've done a bit more stuff until I even attempt to read something like that, it sounds to much like Group related stuff. biggrin.gif
post #80 of 101
Yep, lots of groups! The beginning is all about differential forms, vectors, tensors, and bundles though.

That's a hefty first year workload. I guess things are done a lot differently in England biggrin.gif. Everything gets easier as you go though. Your brain just starts to adapt to it and everything starts to fit together naturally. It wasn't until my third year that things became clear.
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