Our world may be a giant hologram

[sol invictus]

The expansion part is clear, what isn't is the no center and no edge on the 3D version.

You see that a circle (the boundary of a disk) has no center and no boundary, right? You see that a sphere (the boundary of a ball) has no center and no boundary, right? All you have to do is move up one more dimension...

Or if you like math, it's easy to prove that the boundary of a boundary is empty (i.e. doesn't exist). Since a 3-sphere is the boundary of a 4-ball, it has no boundary. And it cannot have a center because it is a homogeneous space - all points are equivalent.

 

[Skeptic Ginger]

The sphere has a center and an edge. I get the concept. I currently maintain the hypothesis (ignorant as it may be) that the past is the center and the edge is the future (spacetime). But this is unsatisfactory because I cannot conceptualize the 3 spatial dimensions having no center or edge.....

But thinking about this now, perhaps the Universe is more flat than we realize. That would eliminate the center. The Universe would have to curl back on itself. But the edges would be the past and the future and this hologram hypothesis becomes more interesting.


Hmmmm.......[contemplates contentedly, if only briefly]

 

[Viper Daimao]

Plank length side topic notwithstanding, can anyone go into anymore depth about the holographic theorem? Any models to better understand? What would this mean for cosmology going forward? The many jokes I read elsewhere about God using Visa, us being in a holodeck, or even just being a simulation on a computer while funny, leave me wanting more.

 

[sol invictus]

The sphere has a center and an edge.

Precisely the contrary. Please re-read my post above.

I get the concept.

Hmmm...

I currently maintain the hypothesis (ignorant as it may be) that the past is the center and the edge is the future (spacetime).

If you want to include time, the 4D manifold at small time is a bit like a cusp or the tip of a cone (the tip being the big bang, t=0). Would you call the tip of a cone its center?

Or if by past you meant any time before the present, calling that the "center" makes even less sense - a center is a point, but the past is a 4D manifold.

But this is unsatisfactory because I cannot conceptualize the 3 spatial dimensions having no center or edge.....

Please re-read my post above. If you can understand 1- and 2-spheres, you can understand a lot about 3-spheres.

 

[Third Eye Open]

Physics is a mathematical science. If you don't understand the math you can't truly understand the physics. But you can sometimes get an idea of it from analogies, and that's what the 2-sphere (that's the surface of a ball) is for - to help you gain some intuition about what a 3-sphere is.

As an example, on a 2-sphere if you draw a circle (a 1-sphere) around a point (the north pole, say) and then make the circle expand, after a while it reaches a maximum circumference (the equator). If you keep going it contracts down onto the antipodal point (the south pole) from the one you started at. Exactly the same goes from a 0-sphere (which is two points) on a 1-sphere.

Given that, it's pretty clear (and it's true) that on a 3-sphere, if you start with a 2-sphere centered on a point and expand it, after a while it reaches a maximum size, and if you keep going it contracts again onto a different point. Understand that fully and you've understood a lot of what there is to know about 3-spheres.

Thanks Sol! I always like reading your posts. I'm pretty sure I will have to settle for not understanding most of this stuff until I learn math, but that post clicked something in my brain, thanks.

As for the Planck length and time, I will probably have to give up on that too

It seems to me that at the Planck scale, the only measurable speed is the speed of light. (one Planck length per Planck time, if I understand correctly)

If I were to move my finger (or whatever) one Planck length, my measured speed would be the speed of light, because even if it 'really' took me 50 Plank times to move 1 Planck length (just making up numbers here) I would be measured as 'just sitting there' for 49 of them, and then moving at the speed of light for the last one.

Is any of this making sense?

So, if we are all moving around at the speed of light, with pauses in between Planck lengths, how does time-dilation figure in?

 

[INRM]

Is it possible to draw a 3 Sphere?

If the universe is unbounded doesn't that mean it's either infinite or like that game Asteroids where if you go off the end of the screen you appear on the other?

 

[Third Eye Open]

Is it possible to draw a 3 Sphere?

If the universe is unbounded doesn't that mean it's either infinite or like that game Asteroids where if you go off the end of the screen you appear on the other?

Well, since you can make a 2 dimensional representation of a 3 dimensional object, such as drawing a cube or sphere on paper, perhaps someone could figure out how to make a 3 dimensional representation of a 4d object.

 

[Ziggurat]

Is it possible to draw a 3 Sphere?

Yes, but it's not terribly useful to do so, because you have to abstract it too much to really get the feel for it. It's easier to draw a 4D cube, but even there it's fairly abstract.

If the universe is unbounded doesn't that mean it's either infinite or like that game Asteroids where if you go off the end of the screen you appear on the other?

Unbounded means infinite. If it wraps back on itself (ala Asteroids), it's bounded.

 

[sol invictus]

Is it possible to draw a 3 Sphere?

A 2-sphere projected onto a plane is a disk. As you move the sphere towards or away from the plane, the disk gets bigger or smaller (but with a maximum size where the plane cuts the sphere along an equator). A 3-sphere projected (in 4D) onto flat 3D space is a ball. As you move the 3D space towards or away from the 3-sphere, the ball gets bigger or smaller, and again with a maximum.

If the universe is unbounded doesn't that mean it's either infinite or like that game Asteroids where if you go off the end of the screen you appear on the other?

Asteroids is a 2-torus, not a 2-sphere (otherwise things would get all warped in parts of the screen). A 3-torus is a possible topology for the universe, but not a very likely one.

 

[INRM]

A 3 Torus is shaped like a tire or inner tube right?

 

[recursive prophet]

@Plumjam: I just nominated your 'sitting on the fence' line as the quote of the month. You are often clever, but this was one of your best.

Glad I looked in on this thread; interesting subject. It also gave me an opportunity to find myself agreeing with sol invictus. To transfer the maths of physics we must deal in analogies, and as with all transfers something will be lost in the process. Of course, mathematics itself is a form of metaphor. A fractal of the hologram?

 

[recursive prophet]

Sorry about the double post. Is there no way to delete?

 

[sol invictus]

A 3 Torus is shaped like a tire or inner tube right?

A 2-torus is, yes. If you cut open a tire and spread it out, it would be a rectangle or square (depending on how skinny it is). Gluing it back together means identifying opposite edges in pairs, just like in Asteroids.

A 3-torus is a flat 3D space with 3 pairs of planes identified.

 

[INRM]

The holographic universe theory would be completely deterministic, correct?


INRM

 

[Asm]

The holographic universe theory would be completely deterministic, correct?

How did you arrive at that conclusion?

 

[INRM]

Asm,

Instinct

 

[Skeptic Ginger]

Precisely the contrary. Please re-read my post above.



Hmmm...



If you want to include time, the 4D manifold at small time is a bit like a cusp or the tip of a cone (the tip being the big bang, t=0). Would you call the tip of a cone its center?

Or if by past you meant any time before the present, calling that the "center" makes even less sense - a center is a point, but the past is a 4D manifold.



Please re-read my post above. If you can understand 1- and 2-spheres, you can understand a lot about 3-spheres.

I understand the concept, sol and re-reading your post will not help. I don't like the concept of the Universe as it is currently theoretically accepted. I realize I am unqualified to disagree with any physicist or cosmologist on this subject, but I cannot help it. I have contemplated and contemplated and my concept of the Universe is what it is.


Here's the problem. (You'll just have to accept I don't know what I am talking about and leave it at that. ) If one were to freeze spacetime and consider the Universe as it is in a single moment of time, either it comes back around on itself like the 2D surface of a balloon or maybe even the 1D surface of a mobius strip, OR, it has a center.

And I cannot conceptualize a 3D balloon surface. No one can draw one either. Any drawings or models cannot be made that represent the Universe in 3D with no center and no edge.

As for the center being past time, that comes from the fact one looks in any direction and your 'cone' model occurs. But one cannot make a 3D model of cones in all directions. Now that cone, I can conceptualize. But in my concept, the center was the smaller and smaller place the Universe expanded out from. That is how I see past time as the center, the singularity, not the last moment in time. You are looking toward the center when you look at the light from the past reaching your eyes.


But I have an issue with the time dimension. If one froze the Universe in time and traveled across it, what would the model look like?

I'll have to continue this later. It's a hard topic to discuss when one is falling asleep.


But I do want to add, this hologram model blends with mine as much as I currently understand it. (Which is not saying I understand it.)

 

[Almo]

Yes, but it's not terribly useful to do so, because you have to abstract it too much to really get the feel for it. It's easier to draw a 4D cube, but even there it's fairly abstract.

That one guy's avatar on this forum is a 4D cube rotating displayed in 3D. That's a good one. The thing to remember is that in 4D, every angle at every vertex is always 90 degrees. If you can begin to imagine that, you're on your way to visualizing 4 dimensions.

I wish I could find a post by him...

 

[Deneb]

The Wiki page on tesseracts has it.

A good exercise for anyone having issues grasping 4D mathematically would be to try drawing some of the tesseracts on this page. I personally like the representation of a cube inside a larger cube with each corresponding summit linked by vertices, once you figure out that both cubes are really the same size and that the connecting volumes are also cubes, it becomes a bit easier to grasp.

 

[alfaniner]

That one guy's avatar on this forum is a 4D cube rotating displayed in 3D. That's a good one. The thing to remember is that in 4D, every angle at every vertex is always 90 degrees. If you can begin to imagine that, you're on your way to visualizing 4 dimensions.

I wish I could find a post by him...

That would be Paulhoff. Although he seems to have changed it to a more advanced, yet less elegant version than the one he used for quite some time.

(OK, I'm just jealous. The original, non-rotating one is one of the most striking things I've ever seen, and me, I picked a carefree, bounding blue alien...)