Looking Again at the Balloon Analogy

[liometopum]

Sure it is. .

and

Substituting earlier calculations, we get R0=1/2πR0.

Hi Bandersnatch:
In the case of a circle with area pi*r^2, and a radius of one unit, the distance from center to edge is one unit. A sphere with surface area (4*pi*r^2) has a "hyper-radius" of 1/2. That is, the distance from the center to surface is 1/2. We agree on that.

In the remodeling of the surface area, the observer that was in the center of the circle stays on the surface of the sphere. His distance has not changed.

 

[liometopum]

Any flat map of the Earth is a distortion of some aspect of the original spherical surface.

And maybe the universe is a distortion of 3D space? This was never my thought, but it applies.

Now look at your numbers. You've got a radius of the hypersphere that produces circumference that doesn't match the radius of the observable universe.

I am not sure what that is saying. But with that aside, they are different objects, yes.

Anyway, the whole thing being in conflict with observation, means this whole discussion is unnecessary. That you so easily dismiss the ultimate objection says a lot about what we can expect.

What observational conflict? There is no conflict. We take what we can see, and then calculate a volume. Then, we ask "how big would a 4D sphere be whose surface area matches what we see". That is it. There is no measurement conflict.

All it's going to be about is you defending your exercise in numerology, and us telling you you've been chasing a red herring.

What I see, and what I would like you to see, is that this pseudo-hyperverse gives us the exact numbers we would expect to find for the universe, if the universe were indeed the 3D surface volume of a 4D hypersphere. Exactly the numbers. You can blow it off, or take it as an insight. There are people who will find this interesting, and hopefully, valuable in there own pursuits. Let them decide if it numerology or not. But if you cannot explain it, then maybe you should be the one to let it go.

And let me say too, that I actually appreciate your input and challenges!

 

[liometopum]

Yes, but as more than one respondent have indicated, demonstrably based on an unphysical definition of R_H. The observable universe can be seen as a surface patch (radius some 46 Glyr) on a larger hypersphere with observed radius anywhere from 200 Glyr (the lower bound) to an imaginary number (negative curvature geometry), including "infinity" for a flat geometry.

It is not clear to me what your variant of the balloon analogy is to achieve.

Welcome Jorrie:

Yes, I agree the 'observable hyperverse" is a patch. No doubt, and I knew it from the start. But the results are noteworthy and should be on the table for others to see.

What does it achieve? I will give you something, but I have to go now. I will be in touch shortly.

 

[Chalnoth]

But the results are noteworthy and should be on the table for others to see.

I don't see how. It's a bunch of equations that don't (and can't) say anything about reality. How can that be "noteworthy"?

 

[Drakkith]

I think this thread has run its course. We get claims similar to yours all the time and they never lead anywhere. I recommend leaving the advancement of science to the trained scientists and not chasing a red herring just because something "looks interesting". In any case, PF rules prohibit speculation such as this. Thread locked.