Time and space

[Niflmir]

Poincaré and Lorentz, in attempting to explain the null result of the Michelson-Morley experiment, got some of the right answers but for the wrong reasons. They were still clinging to the notion of the luminiferous aether as the medium for light transmission, and when your conceptual foundation is that flawed, you don't get credit for the results. It was Einstein who showed that the aether wasn't necessary in his 1905 paper describing Special Relativity, and Hermann Minkowski who cast it into the geometrical form that was crucial to the development of the General Theory of Relativity in Einstein's 1916 paper.

There's no legitimate question of plagiarism here. Everybody read everybody else's papers and built on each others' work and cited each other in their own publications.

That is the ultimate claim that a Physicist that wants to cling to the godlike image of Einstein will settle upon. The point is that in Science, we refer to other peoples results, thus showing that we know about them. There are all sorts of suspicious details about Einstein and special relativity. Such as the fact that all of the major results of the special theory of relativity were developed before he came along. It was even being called the special theory of relativity. It was already believed to describe all matter. The luminiferous aether that Lorentz and Poincare "clung" to, is nothing other than what we now refer to as the spacetime manifold. Even in quantum field theory, photons are seen as excitations of the vacuum, so the idea of an aether is quite sound, just not the aether as people believed it to be before Poincare and Lorentz came along. If you read Whittaker's book, all of those details will be outlined, minus the modern notions of vacuum excitations. So, if you must you can attribute to Einstein the notion of the spacetime manifold as being distinct from the aether and the photon vacuum, but you cannot claim that he created the tools of special relativity. Tools which bear the names of their true creators: The Lorentz Contraction, Lorentzian metrics, the Poincare group, and minkowski space.

I may be able to download a copy of it for you if you wish. I will check, and if you are curious and I can acquire an electronic copy, I can send it to you for academic purposes.

 

[s_lone]

Yes, the expansion of the big bang is a source of confusion for many people. The best analogy is one of a balloon. Get yourself a balloon and tape some pennies to it. Then blow up the balloon. You will see that the distance between any two pennies is expanding but there is no real centre to the expansion. For a more flat model of the same idea, you can take any picture on your computer and zoom in on it. The pixels will seem to expand and non neighbouring pixels will get further and further away from each other, but there is no real centre to the expansion.

I apologize if I used too much math. I have a lot of faith in my fellow man, I am sure if you had the time and the motivation, that you could learn all of the things that I am talking about. So I try to throw out the names of the mathematical ideas just in case some day you have both the time and the motivation. In the meantime, I can always try to restrict my explanations to a less mathematical nature.

Don't apologize for using lots of math. We need to call things by their names and as you said, giving me the appropriate terms will help me if I want to do some research. That being said, I always appreciate some vulgarization. (The balloon example being an example of vulgarization.)

I think I understand what you mean that there is no central point of expansion if you only consider the surface of the balloon itself and not the "vacuum" and "emptyness" inside the balloon. But what about the inside of the balloon? What about the inside of the universe? Is the universe a sphere or a circle with a vacuum inside?

 

[Niflmir]

Don't apologize for using lots of math. We need to call things by their names and as you said, giving me the appropriate terms will help me if I want to do some research. That being said, I always appreciate some vulgarization. (The balloon example being an example of vulgarization.)

I think I understand what you mean that there is no central point of expansion if you only consider the surface of the balloon itself and not the "vacuum" and "emptyness" inside the balloon. But what about the inside of the balloon? What about the inside of the universe? Is the universe a sphere or a circle with a vacuum inside?

So that is actually an interesting question. When we talk about the Universe as being a three sphere or a three dimensional hyperboloid, we generally talk about it in terms of Riemannian geometry. That is a fancy way of saying that we project ourselves into the space and can't see the space the universe is embedded in, that is, we talk about the intrinsic geometry. However, before Riemann came along, Gauss did a lot of work talking about geometry from the point of view of objects embedded in normal space. So from the Gaussian perspective, there is a natural centre to the three sphere, it is the point in the embedding space that all points on the 3-sphere are equidistant to. The problem is, that centre does not lay in our universe. Just like we can never walk through the centre of the earth, trapped as we are on its surface, no one in the universe could walk through the center of the universe, trapped as we are on its hyper-surface. Because of that, we physicists would call the centre of the universe "unphysical", and promptly ignore it. Of course, flat space would have no anologue, seeing as it is infinite in its expanse. Hyperbolic space is confusing as it doesn't have any three dimensional analogue, except a local one, I am not sure at present whether you could say it has a centre or not, but if it did, it would be just as unphysical in that you could never be at the point which you could call the centre.

 

[s_lone]

The problem is, that centre does not lay in our universe. Just like we can never walk through the centre of the earth, trapped as we are on its surface, no one in the universe could walk through the center of the universe, trapped as we are on its hyper-surface. Because of that, we physicists would call the centre of the universe "unphysical", and promptly ignore it. .

But isn't it against the very essence of scientific thought to consider something unphysical? Or do you simply mean that at that point physicists say "our specialization stops here." There must be some scientists who have something to say about the supposedly unphysical "space" in which our universe seems to exist. Right?

 

[Dexter Sinister]

I may be able to download a copy of it for you if you wish. I will check, and if you are curious and I can acquire an electronic copy, I can send it to you for academic purposes.

Thanks, I'd be most interested in seeing it, if that turns out to be possible. I've never heard of it before.

I see from your public profile that you're a graduate student in physics. It's been a lot of years since I studied that stuff. I'm retired now, and never worked in a field that required me to keep up with things like Riemannian geometry, so a lot of my youthful mathematical skills are gone. Or maybe it's just my brain ossifying with age. In any event, your knowledge is clearly more current than and superior to mine.

 

[Niflmir]

Thanks, I'd be most interested in seeing it, if that turns out to be possible. I've never heard of it before.

I see from your public profile that you're a graduate student in physics. It's been a lot of years since I studied that stuff. I'm retired now, and never worked in a field that required me to keep up with things like Riemannian geometry, so a lot of my youthful mathematical skills are gone. Or maybe it's just my brain ossifying with age. In any event, your knowledge is clearly more current than and superior to mine.

As it turns out, what I thought was an online copy of the book turned out to be a review of the book. I couldn't tell before looking at it because of JSTOR's poor abstracts. But if you are near any university libraries of any size, I can probably get you the reference to it and you would be able to read it in the library no problem. Here is an Amazon link: http://www.amazon.com/History-Theories-Aether-Electricity-Classical/dp/0883185237

As to being a graduate student in physics, General Relativity is my area of specialization, and requires me to learn these things. I struggled with it at first (I didn't take any classes on differential geometry, I taught myself from the book the class used) and used it poorly before I learned it. The hardest part for me was conceptualizing the covariant derivative. But if you start with the differential geometry, and work through problems, you can learn it in no time... I assume you know multivariate calculus and some basic vector calculus. Then we can get you a good book on GR and you will be a pro in no time. If you are interested I can refer you to some books that helped me.

First differential geometry:
Differential Geometry: Curves-Surfaces-Manifolds
Next, a good intro to GR:
Gravity: An introduction to Einstein's General Relativity
If you want to do graduate research you need more than Hartle gives you, but you will see most of it all in that book. Otherwise, you will have to look up Wald. Have a good night guys.

 

[Dexter Sinister]

Are you saying the universe appears to have the shape of a relatively thick surface of a sphere? Would that mean that theoretically, you could leave in a space-ship in one direction, follow the curve of the sphere and eventually come back to your point of origin?

No, that's not really what I'm saying; visualizations break down at this point, all we're left with is analogies based on our ability to perceive three dimensions, and sometimes they're pretty lame as a guide to understanding. You really have to be able to do the math like Niflmir can, and I used to be able to do some of, to get it. You're right though, that you would be able to take off in one direction and eventually get back to your starting point without turning around, same as you can on the surface of the earth.

Simple and common example of the difficulties here: what do you suppose a cube in 4 dimensions would look like? We can't visualize it directly, but we can figure out its geometric properties analytically. First consider an ordinary 3-d cube with sides of length one unit. Doesn't matter what unit, feet, inches, parsecs, whatever, it just simplifies things. Every corner can be specified by three numbers, its x, y, and z coordinates, and each number will be either a 0 or a 1. So how many corners are there? Three numbers in a row, either of which can have one of two values, means there must be 8 corners. Similarly with the 4-d cube, each corner is specified by four numbers, so there are 16 of them. A little vector algebra will enable you to figure out the relationships among the edges and how many edges there are. I'll spare you the details, but what the thing turns out to look like in 3-d space is a cube inside a larger cube with all the corners joined by an edge. Actually it's a well enough known shape that it has a name: tesseract. But that isn't really a 4-d cube, it's a projection into 3-d space, a shadow if you prefer, of a 4-d cube. You can't visualize the 4-d cube, you'll just get a headache trying.

 

[Dexter Sinister]

If you want to do graduate research... .

I'm long past the point of wanting to do graduate research, I'm 57, but thanks for your interest and assistance. As it happens I am close to a university library and an alumnus of two other universities that are fairly close, as Canadians reckon distances, so I'm certainly going to track down that book of Whittaker's that Tonington referred to. My interest in science has always been the science itself, not the politics of it, but if Einstein doesn't really deserve the credit for special relativity, I'd like to know more about it.

 

[Niflmir]

But isn't it against the very essence of scientific thought to consider something unphysical? Or do you simply mean that at that point physicists say "our specialization stops here." There must be some scientists who have something to say about the supposedly unphysical "space" in which our universe seems to exist. Right?

In physics it is generally seen as unscientific to invent something which can never be measured and to talk about it at length. That is what I mean when I say unphysical. It is like the invisible, pink unicorn that walks around with me wherever I go. The fact that the entity is unmeasurable makes it equivelant to nonexistant. If we could somehow pull off of normal spacetime and travel through the 84 dimensions that you would need to embed it in, then we could travel to some point that you could call the center of the universe. However, to everyone's knowledge, its impossible. So we say that it is unphysical, because current physical theories currently describe it as being unmeasurable.

 

[El Barto]

I don't know, but you can't have one without the other.

like beer and chips , the quantum dimension to it would be the salsa dip....