A Challenging Question about an Infinite Universe.

[Eratosthenes (Peter)]

Originally Posted by sjastro

I have made it clear in the past that I don't accept String Theory as is not falsifiable.

I see.

And yet you make this statement concerning the Casimir effect and bosonic strings

Rather than being a mathematical trick, renormalization has a physical significance and is related to the Casimir effect where there has been a shift in the ground energy state of the bosonic string.

(incidentally, I don't accept String Theory as a science. It's a concept more akin to a Mathematical Philosophy. This of course can change, should experimental evidence emerge that supports the predictions that String Theory claims.)

Cheers

[sjastro]

Originally Posted by Eratosthenes

I see.

And yet you make this statement concerning the Casimir effect and bosonic strings

Rather than being a mathematical trick, renormalization has a physical significance and is related to the Casimir effect where there has been a shift in the ground energy state of the bosonic string.

(incidentally, I don't accept String Theory as a science. It's a concept more akin to a Mathematical Philosophy. This of course can change, should experimental evidence emerge that supports the predictions that String Theory claims.)

Cheers

Argument by repetition.
I addressed this point in my last post.
Do you actually bother to read posts or do you simply want to be argumentative.

[Eratosthenes (Peter)]

Originally Posted by sjastro

Argument by repetition.
I addressed this point in my last post.
Do you actually bother to read posts or do you simply want to be argumentative.

[N1 (Mirko)]

Steven,

Originally Posted by sjastro

We live on a (near) spherical surface.

We only know that because we can rise above it (in both theory and practice), but by doing that, we are introducing an external system of reference.

Originally Posted by sjastro

We can travel around along a great arc on the Earth's surface and end up in the same spot we departed. Clearly this is not possible if the surface is infinite.

But we could keep going indefinitely, couldn't we? We'd only

Originally Posted by sjastro

end up in the same spot we departed.

because we, not physical constraints, have decided to "end" our journey there.

By nominating a departure point, and by further stating that we could only be there once, we, not "the Universe" have defined the limits.

Originally Posted by sjastro

Cosmologists have used a similar principle to test if the Universe in finite and spherical. A photon emitted could traverse a spherical Universe and end up near the same spot of emission.
Since the anisotropic regions of the cosmic radiation background can now be well resolved, double images in the background would indicate this phenomena.

Just because this hasn't been observed doesn't mean it' not happening, since "well resolved" is clearly less than 100% resolved.

Edit: I might add that the further a photon travels, the less likely it is to maintain its original direction due to gravitational and other factors along the way. It would not seem unreasonable to think that given enough spacetime, a photon would eventually be turned back onto its origin, if not somehow rendered non existant in the process. As a result, perhaps the question of infinity is irrelevant because all possible trajectories of our photon are interlinked loops between which it can change. That way, it could avoid returning to the keen observer for a very long time but still be in a loop at any given time.

[sjastro]

Mirko,

I said.
We live on a (near) spherical surface.

Your response
We only know that because we can rise above it (in both theory and practice), but by doing that, we are introducing an external system of reference.

Our frame of reference is the same as the Earth's.
In this case it is in spherical coordinates defined by a polar and azimuthal angle which also locates our position on the surface.

I said.
We can travel around along a great arc on the Earth's surface and end up in the same spot we departed. Clearly this is not possible if the surface is infinite.

Your response.
But we could keep going indefinitely, couldn't we? We'd only because we, not physical constraints, have decided to "end" our journey there.

By nominating a departure point, and by further stating that we could only be there once, we, not "the Universe" have defined the limits.

The pathway is defined by the circle inscribed on the sphere. There are no limits. It doesn't matter how many times we travel around this circle, the radius of the circle remains the same. By calculating the radius through the circumferential distance travelled, we can find the surface area of the sphere which is finite.

I said.
Cosmologists have used a similar principle to test if the Universe in finite and spherical. A photon emitted could traverse a spherical Universe and end up near the same spot of emission.
Since the anisotropic regions of the cosmic radiation background can now be well resolved, double images in the background would indicate this phenomena.

Your response.
Just because this hasn't been observed doesn't mean it' not happening, since "well resolved" is clearly less than 100% resolved.

Edit: I might add that the further a photon travels, the less likely it is to maintain its original direction due to gravitational and other factors along the way. It would not seem unreasonable to think that given enough spacetime, a photon would eventually be turned back onto its origin, if not somehow rendered non existant in the process. As a result, perhaps the question of infinity is irrelevant because all possible trajectories of our photon are interlinked loops between which it can change. That way, it could avoid returning to the keen observer for a very long time but still be in a loop at any given time.

When I mean resolved, I'm referring to the angular resolution of the anisotropic detail in the cosmic radiation background.
There has been a progressive increase in detail from COBE to WMAP to the Planck probe.
Since the detail is now well resolved, cosmologists are able to measure the angular size of individual structures with greater precision.

The measurements are consistent with a flat univese.

Steven

[xelasnave]

I can't help it.
I find in my imagination the Universe as a ball and I am on the outside, without though as to what this outside is and the dimension is infinite.
I find it funny that there is no outside.
It is a wise man who can imagine a stick with no ends.
Steven I bet you have a formula for a stick with no ends.

[xelasnave]

I can't help it.
I find in my imagination the Universe as a ball and I am on the outside, without though as to what this outside is and the dimension is infinite.
I find it funny that there is no outside.
It is a wise man who can imagine a stick with no ends.
Steven I bet you have a formula for a stick with no ends.

[xelasnave]

I have just returned from a very stressful week in sydney.
Nine hour drive after mowing the lawns with gammy legs before I left.
I back on my mountain and got in some viewing thru the 80 mm binnos.
Came in somehow calmed..I could not see any outside.
Great to be home.

[Eratosthenes (Peter)]

...a stick with only one end....

[xelasnave]

Well you start with one of those.

I have been outside imaging what my stick passes ..

[Eratosthenes (Peter)]

What sort of shadow does a one ended stick cast?

.....can shadows move at speeds greater than the speed of light?

[julianh72 (Julian)]

Originally Posted by Eratosthenes

...a stick with only one end....

A Hula Hoop?

[xelasnave]

The shadow would be all over the place depending on the environment of that part of the stick.
The answer is complex.
A hoop qualifies.
But it must be a straight stick.

[sjastro]

Originally Posted by xelasnave

I can't help it.
I find in my imagination the Universe as a ball and I am on the outside, without though as to what this outside is and the dimension is infinite.
I find it funny that there is no outside.
It is a wise man who can imagine a stick with no ends.
Steven I bet you have a formula for a stick with no ends.

Alex,

The best I can do is to give the topological edge equation of a one sided sheet of paper.

If you are on the outside of this Universe you must be at a higher dimension than this Universe. An analogy is the surface of a ball embedded in 3-D space.
If the observer however exists in the same dimension as the Universe, in your example the surface of the ball, there is no outside.

Steven

[Eratosthenes (Peter)]

Originally Posted by julianh72

A Hula Hoop?

I just had a ridiculous idea float by.

What if a stick falls into a black hole whereby, one end of the stick has breached the event horizon and the other is still "outside" the event horizon? How many ends does this stick have?

In we consider a very long stick that spans the distance between two black holes, and the ends of the stick breach the event horizons of the two black holes, the question must be asked "does this stick have any ends"?

[xelasnave]

There will be only one end and that is the absolute destruction of all the stick.

[xelasnave]

If a hoop was huge one standing on it would not be able to notice any curvature, the stick would appear straight. So we can have a straight stick and a hoop.

[Eratosthenes (Peter)]

Originally Posted by xelasnave

There will be only one end and that is the absolute destruction of all the stick.

what if two black holes are placed at the ends of a very long stick?

Is this a stick with no ends?




(a flexible stretchy sort of stick)

[xelasnave]

I think one may find tidal forces would start demolition of the stick well before it could approach the event horizon, unless it was an imaginary stick.
And so we could observe the ends of a stick as it's ends are eaten away...it would be dust that would pass the event horizon.

[xelasnave]

It would be dust well before the event horizon gravity does not start at the event horizon.