Our world may be a giant hologram

[Ziggurat]

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.

Or it's infinite. Where is the center of an infinite plane? It doesn't have one.

You are looking toward the center when you look at the light from the past reaching your eyes.

And if you see light from the past reaching your eyes from all directions (which we do), what then?

 

[Skeptic Ginger]

Or it's infinite. Where is the center of an infinite plane? It doesn't have one.



And if you see light from the past reaching your eyes from all directions (which we do), what then?

Infinite makes sense until you try to conceptualize the singularity. Hard to see a single point as infinite.

And as for the light reaching us from all directions, what's the problem? My brain does not require the 'past is the center' concept to be exactly like a 3D center because actually, it is a space-time or 4D center.

Perhaps it is too simple to be a useful concept. You'd have to retrace my years of contemplating the Universe to understand how I got there.

The two things that bother me about current cosmologists' concepts of no center and no edge is 1) it doesn't seem to smoothly take into consideration the shape of the Universe at a single fixed point in time (IE is it finite, infinite, or is it a 3D version of a balloon surface), and 2) if the concept is correct then why do we need a 2D stand-in to model the 3D shape of the Universe?

 

[Ziggurat]

Infinite makes sense until you try to conceptualize the singularity. Hard to see a single point as infinite.

That's a problem with our intuition, not with the model. It should not be terribly surprising or disturbing that we have a hard time wrapping our brains around the structure of the universe. That's not what we evolved to think about.

The two things that bother me about current cosmologists' concepts of no center and no edge is 1) it doesn't seem to smoothly take into consideration the shape of the Universe at a single fixed point in time (IE is it finite, infinite, or is it a 3D version of a balloon surface)

Oh, but it does take that into account. You listed three choices, but your first and last are actually the same. Our models allow for either possibility, but the universe is either one or the other - which one is something that must be determined experimentally. But whichever it is, it can't switch back and forth.

2) if the concept is correct then why do we need a 2D stand-in to model the 3D shape of the Universe?

It is often useful for explaining and visualizing what's going on for those new to the field, and because such reduced dimensionality models still capture many of the non-Euclidean features of the full model. Just like how intro physics classes frequently start discussing kinematics in 1D, even though at the end of the day, we're usually interested in 3D motion.

The actual cosmological models in use can be developed in full 3D (well, 4D, really) from start to finish, so the fact that it's often explained in lower dimensions is actually irrelevant to the full models.

 

[sol invictus]

The two things that bother me about current cosmologists' concepts of no center and no edge is 1) it doesn't seem to smoothly take into consideration the shape of the Universe at a single fixed point in time (IE is it finite, infinite, or is it a 3D version of a balloon surface)

As Zig says, those are taken "into consideration". Given the 4D manifold, you can just check what the shape is at any given time (although that's a much trickier question than I think you realize - it's like asking "what's the cross section of a lumpy potato 3 inches in from the skin").
Of course we aren't sure what the 4D manifold is, because we can only see part of it, but there are only a three possibilities that are at all likely. Two are infinite (at fixed time), and one is finite.

2) if the concept is correct then why do we need a 2D stand-in to model the 3D shape of the Universe?

To explain it to people that don't understand curved 3 or 4D manifolds.

 

[martu]

THERE HAS TO BE STRUCTURE. IF THERE IS STRUCTURE, WE SHOULD BE ABLE TO MAKE A MODEL OF IT, not a substitute model like a 2D surface for a 3D surface.

I WANT PICTURES! I WANT A MODEL!

You, me and everyone not a physicist using the equations everyday want this, I do not know how many times I have been corrected on this forum because my visualisation of phenomena after reading a pop science book is off. I think the only answer is to study the physics and I really wish I had the time to do that.

Here is how I picture it and I’d wait until all my misconceptions are corrected, which could very well be all of it, before believing a word of it.

To picture what 4D is to 3D just pop down a dimension and consider what 3D is to someone living in 2D. Us 3D creatures can see many 2D ‘worlds’ at one time, that is we can see depth that, to the 2D denizens, does not exist and is, indeed, nonsensical. So picture lots of 2D ‘worlds’ all stacked on top of each other as panes (or areas of space), for 2D creatures they only can experience one but for us we see and can experience many.

Now move this up to 4D; 4D creatures must be able to experience\see many layers of 3D solids (volumes) all at one time, like we 3D creatures can experience many 2D planes. So what you may say, we can see many solids at one time what are you on about? Well the ‘depth’ one could see in 4D is time not a distance, that is one could see many volumes of space all stacked on each other and each one was a slice of time. Us 3D creatures can only see/experience one slice of a time at a, erm, time but for 4D creatures they can see many.

As to the shape of this 4D space we can only draw projections of it onto 3D, like a 2D creature could see a shadow of a 3D object.

 

[orange31]

That's a great way to conceptualize it, thanks!

So for string therapy, we 'visualize' that out to 11D??!!
That's a lotta layers .

 

[INRM]

If you had a universe that was infinite and you had a net energy that was always zero (same amount of positive and negative energy), it sounds like the universe would instantly neutralize down to nothingness.


INRM

 

[martu]

That's a great way to conceptualize it, thanks!

So for string therapy, we 'visualize' that out to 11D??!!
That's a lotta layers .

Well you'd visualise it in to 11D (as opposed to 'out to'), most of those extra dimensions are wrapped up too small to 'see'.

 

[martu]

If you had a universe that was infinite and you had a net energy that was always zero (same amount of positive and negative energy), it sounds like the universe would instantly neutralize down to nothingness.


INRM

What do you mean by positive and negative energy? Energy is just, well, energy and all we really know about it for sure is it is conserved in a system.

 

[Third Eye Open]

For trying to imagine higher dimensions, watch this and read this.

 

[Skeptic Ginger]

You, me and everyone not a physicist using the equations everyday want this, I do not know how many times I have been corrected on this forum because my visualisation of phenomena after reading a pop science book is off. I think the only answer is to study the physics and I really wish I had the time to do that.

Here is how I picture it and I’d wait until all my misconceptions are corrected, which could very well be all of it, before believing a word of it.

To picture what 4D is to 3D just pop down a dimension and consider what 3D is to someone living in 2D. Us 3D creatures can see many 2D ‘worlds’ at one time, that is we can see depth that, to the 2D denizens, does not exist and is, indeed, nonsensical. So picture lots of 2D ‘worlds’ all stacked on top of each other as panes (or areas of space), for 2D creatures they only can experience one but for us we see and can experience many.

Now move this up to 4D; 4D creatures must be able to experience\see many layers of 3D solids (volumes) all at one time, like we 3D creatures can experience many 2D planes. So what you may say, we can see many solids at one time what are you on about? Well the ‘depth’ one could see in 4D is time not a distance, that is one could see many volumes of space all stacked on each other and each one was a slice of time. Us 3D creatures can only see/experience one slice of a time at a, erm, time but for 4D creatures they can see many.

As to the shape of this 4D space we can only draw projections of it onto 3D, like a 2D creature could see a shadow of a 3D object.

I've read Flatland. I get that concept just fine. It applies to the 11D world with missing gravitational force, not the shape of the Universe problem created with claims like "our brains didn't evolve to conceptualize the Universe". Yes, they did. The fact we can conceptualize a missing dimension or 10 demonstrates that.

4D refers to time. I can conceptualize the time dimension, no problem there. I can conceptualize an infinite universe. I can conceptualize hidden dimensions.

But what does our Universe look like in the 3 dimensions we exist in? The physicists/cosmologists have their mathematical models and they believe that translates into truth about the shape of a universe they have not really seen. I understand how and why they've drawn the conclusions they have. But I don't have to pretend to see the Emperors clothes unless I can see them.

 

[Ziggurat]

But I don't have to pretend to see the Emperors clothes unless I can see them.

But you shouldn't act like he's naked unless you can see his naughty bits either.

 

[sol invictus]

4D refers to time.

No, not always. For example, in trying to understand 3-spheres, it's useful to think of them as embedded in 4D (just as it's easy to understand 2-spheres embedded in 3D). That 4th dimension has nothing to do with time.

So at least one of the sources of your confusion is now apparent to me. I'll try one last time to clear it up, now that I see what it is - one of the possible cosmologies is a 3-sphere that expands with time. At any given time, the geometry is a 3-sphere with some radius. So forget about time - it's fixed - and try to understand that spatial 3-sphere.

But what does our Universe look like in the 3 dimensions we exist in?

We keep trying to explain that to you.

The physicists/cosmologists have their mathematical models and they believe that translates into truth about the shape of a universe they have not really seen. I understand how and why they've drawn the conclusions they have.

No, you obviously do not.

 

[martu]

I've read Flatland. I get that concept just fine. It applies to the 11D world with missing gravitational force, not the shape of the Universe problem created with claims like "our brains didn't evolve to conceptualize the Universe". Yes, they did. The fact we can conceptualize a missing dimension or 10 demonstrates that.

The one line I always feel is disappointing to read is ‘Why do you assume <insert phenomena here> is intuitive’. Well why not? Why can’t we assume everything can be modelled in such a way any bright person can pick it up? Maybe everything can make sense to us in a way all it takes is a genius or two to tell us how.

4D refers to time. I can conceptualize the time dimension, no problem there. I can conceptualize an infinite universe. I can conceptualize hidden dimensions.

But what does our Universe look like in the 3 dimensions we exist in? The physicists/cosmologists have their mathematical models and they believe that translates into truth about the shape of a universe they have not really seen. I understand how and why they've drawn the conclusions they have. But I don't have to pretend to see the Emperors clothes unless I can see them.

I think Emperor’s clothes is a bit harsh, the one thing you can say is that the maths works which at least gives the Emperor some underwear.

 

[martu]

No, not always. For example, in trying to understand 3-spheres, it's useful to think of them as embedded in 4D (just as it's easy to understand 2-spheres embedded in 3D). That 4th dimension has nothing to do with time.

So at least one of the sources of your confusion is now apparent to me. I'll try one last time to clear it up, now that I see what it is - one of the possible cosmologies is a 3-sphere that expands with time. At any given time, the geometry is a 3-sphere with some radius. So forget about time - it's fixed - and try to understand that spatial 3-sphere.

I think you are wrong about this, if the 4th dimension isn’t time what is it? And what do you mean by ‘time – it’s fixed’?

 

[Roboramma]

I think you are wrong about this, if the 4th dimension isn’t time what is it? And what do you mean by ‘time – it’s fixed’?

I don't think he means there is a 4th dimension, just that when thinking about 3 spheres it's useful to think about them as though there were. As though the 3 sphere is imbedded in a 4th dimension.

 

[Vorpal]

Yes: that four-dimensional space has no particular meaning beyond serving as a convenient and simple device for constructing a 3-sphere. It's a straightforward generalization--for spheres of radius r centered at the origin, in ordinary Cartesian coordinates:
0-sphere: x² = r², in E¹--a line
1-sphere: x²+y² = r², in E²--a plane
2-sphere: x²+y²+z² = r², in E³--'space'
3-sphere: w²+x²+y²+z² = r², in E⁴--etc.
The physical space of the universe would be the 3-sphere itself, which is 3-dimensional. Things outside of this surface have no physical meaning, at least from the point of view of GTR.

Time being 'fixed' just means we're taking only the spatial part of the universe, i.e., the time coordinate has some particular value. To put time back into this situation, just picture r being varying with t. (Caveat lector: the above is an oversimplification; issues of embeddings in GTR are generally quite complicated if not impossible; fortunately, they are also always optional.)

 

[Vorpal]

The one line I always feel is disappointing to read is ‘Why do you assume <insert phenomena here> is intuitive’. Well why not? Why can’t we assume everything can be modelled in such a way any bright person can pick it up?

I disagree. While I do think that whatever the field, the bar for following along the simpler cases isn't that high at all (and this is definitely one of those), and within the capability of any reasonably bright person, what one finds intuitive largely depends on experience. Thus, it's simply not reasonable to expect that any fairly bright person would find things intuitive without experience in background concepts.

What we have in this thread is a good example, actually--someone proficient in high-school coordinate geometry should have absolutely no trouble of making the intuitive leap to a 3-sphere once it is described to them, and in hindsight would actually regard it as more or less a trivial step. On the flip-side, I wouldn't be at all surprised that someone that avoids mathematics finds it absolutely mind-boggling, regardless of intellectual ability in other areas of life.

In other words, intuition generally adapts fairly well if you just do the homework, but expecting things to be intuitive without such work is just plain silly.

 

[martu]

Yes: that four-dimensional space has no particular meaning beyond serving as a convenient and simple device for constructing a 3-sphere. It's a straightforward generalization--for spheres of radius r centered at the origin, in ordinary Cartesian coordinates:
0-sphere: x² = r², in E¹--a line
1-sphere: x²+y² = r², in E²--a plane
2-sphere: x²+y²+z² = r², in E³--'space'
3-sphere: w²+x²+y²+z² = r², in E⁴--etc.
The physical space of the universe would be the 3-sphere itself, which is 3-dimensional. Things outside of this surface have no physical meaning, at least from the point of view of GTR.

Time being 'fixed' just means we're taking only the spatial part of the universe, i.e., the time coordinate has some particular value. To put time back into this situation, just picture r being varying with t. (Caveat lector: the above is an oversimplification; issues of embeddings in GTR are generally quite complicated if not impossible; fortunately, they are also always optional.)

Do you mean that things aren't accelerating? Because if they are then time has to be taken into account.

 

[martu]

I don't think he means there is a 4th dimension, just that when thinking about 3 spheres it's useful to think about them as though there were. As though the 3 sphere is imbedded in a 4th dimension.

Why would one think their wasn't a 4th dimension?