Understanding Special Relativity

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No. Nothing within the universe can travel faster than C. This does not effect the velocity of the expansion of the universe itself. The galaxies are not speeding away from each other rather the space they are in is expanding. The classic explanation of this is drawing dots on a balloon then inflating the balloon. The dots move away from each other due to the expansion, they do not move freely on the balloons surface. Also on a further note about Einstein, people often think of E=MC2 as being the work of an old man, he was 26 when he wrote his paper containing this Equation, and was far from insane.

Eric, I understand where Einstein was coming from, IE Given Michelson and Morley if taken as an axiom Maxwells equations meant that time was not absolute. He was looking for something that everyone could agree upon no matter their frame of reference, and this is how he came up with spacetime. What I do not understand is that C is seen as invariant to all observers when clearly it is not.

I think maybe my question has been written badly. Better put it is;

How does C in a vacuum being invariant relate to events that are not in a vacuum.

Actually, what happens is that the electrons are immediately decelerated to the speed of light in water, and the energy of their lost velocity is immediately converted to visible light. Thus, the sudden deceleration of charged particles is the cause that produces the effect known as Cherenkov radiation.

A similar effect can be seen when relativistic charged particles change direction. The effect is known as Cyclotron Radiation.

More exactly, nothing with mass can be accelerated to or past the speed of light. That does not keep two points in the universe from moving apart faster than the speed of light as a result of the space itself expanding. The points might appear to be accelerated, but both are in their own innertial reference frame.



But it is invariant to all observers in innertial reference frames. 'c' is the speed of light in a vacuum. The speed of light in something not a vacuum would be a fraction of c. For example, in water the speed of light is approximately 0.75 c. 'c' is still the speed of light in a vacuum and only in a vacuum.

This is pretty much completely off topic, but I once read a science fiction story about a special glass in which the speed of light was so slow that it would take ten years for light to traverse the glass. So the result was that companies would make house windows of the glass and set them out in various places for ten years and then sell to homeowners so that for ten years the homeowner would have a ten year delayed view of some great scenery such as mountains, wilderness, beach, ... . Pretty neat basis for the story, but of course, not at all workable. I don't remember the plot of the story itself -- I think it had something to do with a crime in front of the window that was finally able to be observed ten years after the fact.

By the way, I've read about Einstein making a short film about baseball in his later life in which he played all positions. I've never been able to verify that he really made such a film.

That's close. It's actually the water molecules that release the photons.

The speed of light in a vacuum is the limiting speed, not the speed of light in water. Remember that electromagnetic fields propagate at the speed of light. If in water, they propagate at the speed of light in water.

The moving electron creates an electromagnetic field. As I understand it, when the moving electron enters the water, its electromagnetic field propagates more slowly even before the electron is slowed down by the water. The result is a kind of shock wave in the electromagnetic field that excites the water molecules. They then emit a photon of a particular blue wavelength when they return to normal.

I don't think there are objects on the surface of the universe. How about another analogy. Think of the air molecules inside the balloon as galaxies. Now, pop the balloon. Space would then be expanding into a medium of less density. Perhaps into nothing at all, where there are no speed limits.

The analogy with the balloon is intended to make it easier to see by reducing three spatial dimensions to just two. The points on the surface of a balloon are in 2 dimensional space and see only in 2 dimensional space. They cannot see across the balloon to the other side or anything like that. However, by making clever measurements over a large enough area, 2 dimensional beings in a 2 dimensional space like that of a balloon could determine that their space is not flat -- for one thing, the sum of the angles of a triangle would be less than 180 degrees. The sum of the angles of a triangle being equal to 180 degrees only applies to flat spaces.

Anyway, as far as the points on the balloon know in the analogy is that they see each other moving away from them and increasing speeds. When the two points are sufficiently far away from each other, each would see each the other going away at the speed of light and then disappear as they continue to travel faster and faster. This is possible because the space itself is expanding. At no point is one applying energy to one or both points to move them away from each other -- it is all due to the expansion of the space.

In the real word, of course, we have a three dimensional space plus a dimension of time. Since man is a three dimensional being and cannot see in four dimensions, it is difficult to picture a three dimensional space embedded in a four dimensional space even if it is trivial to deal with mathematically. To make it a bit more complicated, with time it is a four dimensional space embedded in a five (or more?) dimensional space.

There is no place in the analogy for popping a balloon. That would be like a massive fragmentation of the spacetime and there is no indication that such a thing would be possible.

This makes no sense.

Expanding space is an elegant solution to the discrepancy between the alleged age of the universe and its diameter, but does it really add up? A 14 billion year old universe, 93 billion light years in diameter, made possible by an incredible fast superluminal expanding non-measurable nothing? Sounds like religion to me.

if the universe is expanding rapidly how are the constellations still the same as thousands of years ago.

You are seeing light emitted from those stars from eons ago. Those stars may not currently exist in our universe as stars anymore. However, the light is still traveling to reach us, so we will not know until the light reaches us from the point that they change. Unless you are trying to see stars at the edge of the universe (too faint for our eyes to see, nor even some of the best equipment we have), the effects of the expanding universe on said stars is negligible to us as observers on Earth. Only those developing on the edge would be warped by the expansion directly.


Something to ponder about: (age of the universe is estimated at 13.8 billion years old, but the radius of the universe is much larger than if light traveled at constant c that amount of time from the big bang)

http://www.space.com/24073-how-big-is-the-universe.html

Within galaxies, gravitation holds keeps the galaxy together.

And, for what it's worth, the constellations are not precisely the same. Over thousands of years, there are changes as the stars move around in the galaxy.

1) they are not, just similar
2) the distances are so extreme, some stars in the same constellation being 100's of lightyears apart already, that the relative movement seems small (percents per year)

As far as I know, the constellations are changing due to galactic dynamics.

Actually, strictly speaking, Einstein did not know about the Michelson-Morly experiment until later. The reason why he formulated special relativity is because he realised that Maxwell's theory of electromagnetism was inconsistent with classical Newtonian mechanics. So he reformulated classical mechanics into what we now know as special relativity as opposed to what everyone else was trying to, which was to reformulate electromagnetism by assuming the existence of a medium, namely the ether, in which light and electromagnetic influences was supposed to travel in. Special relativity made the ether unnecessary by making light (in vacuum) travel at the same speed in all reference frames. It was another physicist, Hendrik Lorenz, who used the results from the Michelson-Morley experiment to derive the same transformation equations that Einstein found, though he discovered them independently.

I had never heard this claimed before (that I recollect) so I did a quick search for information about this. From On the role of the Michelson-Morley experiment: Einstein in Chicago by Jeroen van Dongen, http://philsci-archive.pitt.edu/4778/1/Einstein_Chicago_Web2.pdf:

Of course, it is quite possible that in doing his original work on Special Relativity, Einstein didn't actually use that knowledge.

OK so back to the question. Could someone please explain to this maths challenged seeker of knowledge, how it is that the speed C in a vacuum allows for spacetime events to be observed invariantly by all observers?

Not invariantly, but in certain predictable ways. Also, it applies to observers in an innertial reference frame, that is, one that is not accelerated. What is invariant is the speed of light.