Length Contraction in the Muon Experiment

AE used the example of a circle in a hypothetical two dimensional universe. If this universe was an infinite flat plane then any circle measured on it would have the ratio of its circumference/diameter equal to pi no matter how large. If the 2D universe was some other shape, then this would not hold. However, if the region measured was so small compared to the curvature of this universe then the inhabitants might well conclude they were in a "flat" universe.

Likewise, if one measures a sphere in our universe, the ratio of circumference/diameter in all three dimensions may always be pi on small scales. However, if you make the sphere big enough you may find that this isn't so.

Or something like that.

 

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James, the first part of my post was me just thinking with my keyboard. Nevertheless, the final conclusion was, all objects must go through an acceleration phase to be in a different frame of reference than the initial frame of reference from whence the universe exploded (big bang) (I wonder if there really was a noise if no one heard it

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).

Anyway, I'll comment on your last two statements:

Yes, but this "curvature" is an approximation just like the "resistance" is an approximation for an electron going through a resistor on a circuit. If the electron was lucky enough to follow the path of least resistance, well... you know.

Again, it goes back to your approximation assumption. Each path a photon takes through the universe will encounter different levels of curvature just like each path an electron takes through a resistor will encounter different levels of resistance.

 

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Are you saying spacetime is flattened by expansion? This doesn't seem like an unreasonable statement, but is it true? How does one factor in this effect?

 

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Assuming your "big enough" sphere came into the vicinity of some portion of spacetime with curvature, yes.

 

Not really.

I should have said rate of expansion. Mass curves spacetime one way by decreasing this rate, something ("dark energy") curves spacetime the other way by increasing it.

Damn, I'm not much good at explaining it, at this hour. Try Wikipedia, especially the bit about the Friedmann equations.

 

I think "rate of expansion" is inherent in the concept of "expansion" whether the rate is constant or increasing. Are you saying the variation in rate changes the curvature? I'll check the link out after asking questions

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OK, after a quick glance

here

and

here

I decided I am not in the mood to read anything right now. Explain conceptually without referencing authority. I really hate referencing authority.

 

Well, mass slows down the expansion of the universe, dark energy increases it. If there's too much mass, the expansion will slow down, reverse, and the universe will collapse. This is called a "closed" or "Big Crunch" universe. If there's too little mass, dark energy gets the upper hand, the expansion will accelerate forever, eventually to the point were spacetime is expanding do fast that even subatomic particles are ripped apart. This is called an "open" or "Big Rip" universe. The third possibility is on the edge of these two. If there's just the right mass, the expansion will slow down, but not quite halt except in the limit. This makes the scale factor of the observable universe finite, meaning that we will suffer "heat death" with the entire universe a homogenous (very thin) particle soup of uniform temperature, when entropy is maximal. This is called a "flat" universe.

These three universe models correspond to spacetimes with positive, negative, and zero curvature.

 

Thats all very nice and well... but "dark energy" has no known properties. It is just an invented idea to explain the expanding universe.


I'll be back to read the rest of your post.

 

OK - everything you posted is pure spectulation. There is no "actuality" in the definite sense of the concept you proposed. I've heard them all before.

 

And why shouldn't they since gravity analysis indicates you need (5) times as much Dark Matter as observable matter to account for observations.

Particularily since there are views which account for observation without any Dark Matter or Dark Energy. Of course that requires giving up on GR which you would not want to do.

Keeping in mind that the inverse functions of Dark Matter and Dark Energy require that each exist in specific regions cosmically to work just right makes the idea a bit suspicious. A bit AD HOC.

 

Eh?

To answer another question, yes, "dark energy" is just a term for something we don't yet understand, but the expansion is observed, as is the effects on spacetime by mass.

Well, it certainly didn't seem that you were familiar with the concepts.


Anyway, I'm not going to do your research for you. If you don't accept it, fine, but don't expect me to care.

 

I accept it as an explaination, but not as "fact". This is a point we differ on.

 

I don't think we are considering the same universe. Are you imagining the entire universe as a pebble type object in a wider picture? Because I am not. I am only considering the edges of the universe where "mass" occurs. Correct me if I am wrong, but curvature dies off with the distance from massive objects. So objects on the extreme opposite end of the universe do not have as much of an effect as objects on the arbitrarily chosen edge of the universe from which we started when the photon is at this arbitrary chosen edge.

 

OK - so the curvature is not based on the average density that you previously mentioned? Because that would be synonymous with you averaging the hills and mountains on Earth to find the average spherically radius and that is nonsense.

So what causes this overall curvature?

 

The analogy is not the same then. You were talking about walking on the surface and the path you take. We can imagine that the Earth is a hollow spaceship with the same topography, how does this change anything? (well, there is no matter which is NOT on the surface).

The analogy doesn't hold.

I think the overall curvature is the wider picture view of the universe I described previously - unless you can prove otherwise. A link may help.