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A 5th dimension shape causes the expansion of the universe?





ocalhoun
Okay, suppose that our familiar 3D universe is the surface of a hypersphere in the 4th dimension.


Now, suppose our 4D hypersphere is a cross-section of a 5D hyper-hyper sphere. (hold on, this actually is going somewhere.)

The cross section is defined by the intersection of a plane with the 5D hyper-hyper sphere.

The plane moves in relation to the hyper-hyper sphere at a constant rate.

To a 4D observer, this would appear as a hypersphere that expands and contracts, depending on where the plane intersects at any given time, and what direction it is moving.

To a 3D observer on the 3D 'surface' of the hypersphere, it appears that our entire 3D space is expanding or contracting, depending on the motion and position of that 5th D plane.

So, at the time of the 'big bang', the plane was at the very edge of the hyper-hypersphere, so it intersected only in one point, therefore our entire universe was one single point. As the intersecting plane moved towards the center of the sphere, our universe expanded.

Actually, given that the rate of expansion seems to be increasing, the 5th dimensional shape that is intersected by the plane may not be spherical. Perhaps it is more like a cone with edges curved outwards. The actual shape of this hyper-hyper object would determine the future of our universe.



Not a correct theory perhaps, and maybe not fully formed yet, but it is very interesting, no?
Chris65536
Buh... Shocked

Ok, that's a little hard to wrap my head round. But I think I did it!

So the hyper-hyper shape can't be spherical because that would imply the rate of expansion was decreasing? If that's right, I've got it!

Although this does raise the further point of what the 5d shape is. The 4D shape is our Universe (or rather the surface is), but what on earth are we intersecting?
ocalhoun
Chris65536 wrote:

So the hyper-hyper shape can't be spherical because that would imply the rate of expansion was decreasing? If that's right, I've got it!

Looks like you managed to understand that mess! Very good.
Quote:

Although this does raise the further point of what the 5d shape is. The 4D shape is our Universe (or rather the surface is), but what on earth are we intersecting?

Since the expansion is getting faster, I guess that (at leas the part of it we are experiencing now) would have to be shaped like the end of a trumpet. (This is also assuming that our 4D universe is moving at a constant rate. If it was accelerating in its motion, then the 5D shape could be a simple cone.)
NeoDarkElf
Hmm, that all sounds about right to me. The verse' is composed of multiple planes transposed over each other with all sub-atomic particles shared between them. It's how I've interpreted everything to explain the weakness of gravity compared to the other forces. It's reasonable to imagine them moving around and through each other.

I like the idea of a doughnut shape universe, it allows for a lot of interesting sci-fi physics. The 3D observer would see a single doughnut while the 4D observer would see multiple doughnuts passing though each other within a larger doughnut shape. As they move around and through each other they pull on each other and push on the outer reaches. Each universe is expanding naturally in addition to being pulled on by counterparts; possibly compounding the expansion rate.

Everything I know about this I learned on the science channel :p so if I'm way off that's why. I see the universe being defined as everything we can see. Beyond that sphere of space are other spheres just as big, thus a multi-verse. This space all falls onto the surface of the doughnut shape.

As far as it being cone shaped, I could see that as what you would see if you actually observed the 4th D with enough perspective to see it smeared out across the ether as liner time would leave an imprint of the past behind it as it expanded into the future. Every time I imagine it I see a branching tree as the further time progresses the more variations are available, and as everything that can happen does happen more and more space would be expanded into. Perhaps that is the cone shape you're picturing. What I want to know is what happens when those curving sides of the cone start to bend back in and the future is forced to pass through the distant past.

Cheers to anyone who gets to the bottom here, I have coupons good for one free internets.
Bikerman
It is a scientific proposal (ie it can be tested).
It is perhaps a bit beyond us right now, but I can outline the method.
Basically you want a big triangle - the bigger the better. Each vertex of the triangle (probably a satellite) shines a laser at the one next (so that the lasers form the triable). Now measure the angles and see if you get 180 degrees. If you don't then spacetime is bent, innit!
NeoDarkElf
I've heard of that test being done recently, three satellites some millions of miles apart. It came up negative basically but I'm cretin their scale is far to small. here's a link to a story of it : http://www.telegraph.co.uk/science/space/7695994/Largest-scientific-instrument-ever-built-to-prove-Einsteins-theory-of-general-relativity.html
Radar
I hear you on this one, although it seems like that's a tad too simple an explanation, and not really the way that research is currently heading.

I do like the idea though. It's the kind of thing that could be a good basis for a science-fiction story.
Bikerman
No, it isn't science fiction. There are proposals to test it but we haven't realistically got the necessary technology yet. You need as big a baseline as possible - ideally light years along each edge of the triangle. Unless you can make the triangle really big then the normal measurement errors will swamp any actual angle difference. The longest baseline humans have managed up to now is about 9 billion miles or about 13 light hours (Voyager 1), and that can't be used because the craft doesn't have the necessary kit. We have some way to go before this question can be answered empirically.
ocalhoun
Bikerman wrote:
Unless you can make the triangle really big then the normal measurement errors will swamp any actual angle difference.


What if you make many, many measurements and average them statistically?

Perhaps then we could make due with a smaller baseline?
If your result was a bell curve, you could use the center of that curve as your measurement. It wouldn't be absolute proof, but it would be good evidence.
Bikerman
You can't average measurements where the experimental range of error is much greater than the value being sought to produce anything meaningful.
You would probably get something like a normal distribution centred around 180 degrees with the predicted reading so close to 180 that it would lie within a tiny percentile either way - which would show nothing worthwhile...
ocalhoun
Bikerman wrote:

You would probably get something like a normal distribution centred around 180 degrees with the predicted reading so close to 180 that it would lie within a tiny percentile either way - which would show nothing worthwhile...

Yes, the baseline would still have to be as large as possible...
But that tiny percentile difference would become more worthwhile with every test performed, as long as it stayed biased in one direction or the other.

We might start with a 1:2 chance that the deviation is mere chance, but more testing would reduce that ratio until it finally became somewhat meaningful... Enough to change 'we don't know' to 'looks like it might be _____'.

It wouldn't replace an astronomic-scale measurement, but it might allow us to use a somewhat smaller scale and still get meaningful results. (Or get more definitive results from the same large-scale test.)
Bikerman
Let's consider the figures:
let's say the universe is around 100 billion light years (give or take) and is curved into a 4-D 'sphere'.
100billion/360 = 280 million light years per degree.
Take a realistic present-day baseline - 5 light minutes = 1/12 light hour = approx 10^-5 light year.
So you are looking for an angle difference of around 3*10^-14 of a degree.

We don't have anything that could get close....in fact it isn't do-able since you are below the wavelength of the laser (typically around 400 nanometres)
ocalhoun
Bikerman wrote:

We don't have anything that could get close....in fact it isn't do-able since you are below the wavelength of the laser (typically around 400 nanometres)

Yes, I know we can't get close now... I'm just saying that we could use statistics to get an estimate more easily than we could get an exact measurement, making it somewhat closer to within reach, though still too far away.

(Come to think of it, we could use four measuring-probes rather than three, making a 3D pyramid shape, which would give four 2D triangles to measure, rather than just one, reducing the margin of error further.)

*Dammit* All these great ideas, and no warp-drive to make implementing them possible. *pout*
jetgirltaxi
ocalhoun wrote:
Okay, suppose that our familiar 3D universe is the surface of a hypersphere in the 4th dimension.


Now, suppose our 4D hypersphere is a cross-section of a 5D hyper-hyper sphere. (hold on, this actually is going somewhere.)

The cross section is defined by the intersection of a plane with the 5D hyper-hyper sphere.

The plane moves in relation to the hyper-hyper sphere at a constant rate.

To a 4D observer, this would appear as a hypersphere that expands and contracts, depending on where the plane intersects at any given time, and what direction it is moving.

To a 3D observer on the 3D 'surface' of the hypersphere, it appears that our entire 3D space is expanding or contracting, depending on the motion and position of that 5th D plane.

So, at the time of the 'big bang', the plane was at the very edge of the hyper-hypersphere, so it intersected only in one point, therefore our entire universe was one single point. As the intersecting plane moved towards the center of the sphere, our universe expanded.

Actually, given that the rate of expansion seems to be increasing, the 5th dimensional shape that is intersected by the plane may not be spherical. Perhaps it is more like a cone with edges curved outwards. The actual shape of this hyper-hyper object would determine the future of our universe.



Not a correct theory perhaps, and maybe not fully formed yet, but it is very interesting, no?


Very interesting indeed, and perhaps not such a new idea. Something similar was suggested by the writer HP Lovecraft in his short story, "Through the Gates of the Silver Key". Strangely enough some of it reminds me of things I've heard from modern physicists and cosmologists regarding the nature of time, space, and higher dimensions.

"...every figure of space is but the result of the intersection by a plane of some corresponding figure of one more dimension--as a square is cut from a cube, or a circle from a sphere. The cube and sphere, of three dimensions, are thus cut from corresponding forms of four dimensions, which men know only through guesses and dreams; and these in turn are cut from forms of five dimensions, and so on up to the dizzy and reachless heights of archetypal infinity."

"[Time] is motionless, and without beginning or end. That it has motion and is the cause of change is an illusion. Indeed, it is itself really an illusion, for except to the narrow sight of beings in limited dimensions there are no such things as past, present and future. Men think of time only because of what they call change, yet that too is illusion. All that was, and is, and is to be, exists simultaneously."

"...what the denizens of few-dimensioned zones call change is merely a function of their consciousness, which views the external world from various cosmic angles. As the Shapes produced by the cutting of a cone seem to vary with the angles of cutting--being circle, ellipse, parabola or hyperbola according to that angle, yet without any change in the cone itself--so do the local aspects of an unchanged--and endless reality seem to change with the cosmic angle of regarding."

Does any of this remind you a little of string theory or M-theory?
therimalaya
Although I'm from statistics, i'm not well acquainted with the n-dimensional geometry.. It is a bit hard to get into but it seems to be an interesting theory..
harrer
Seems like out 3D universe is part of another 3D entity.

Taking space in the x-y axis and time on z axis, we can assume that the universe is expanding along time.
emedeiros
Were these other dimensions also created by Jehovah (or maybe Zeus, or whaterver)? Because at the end of the day it's all just a big exercise of imagination based on imaginary concepts.
Ankhanu
emedeiros wrote:
Were these other dimensions also created by Jehovah (or maybe Zeus, or whaterver)? Because at the end of the day it's all just a big exercise of imagination based on imaginary concepts.

This is a science forum, please stick to it. What's the actual reason these concepts should be rejected?
emedeiros
Ankhanu wrote:
emedeiros wrote:
Were these other dimensions also created by Jehovah (or maybe Zeus, or whaterver)? Because at the end of the day it's all just a big exercise of imagination based on imaginary concepts.

This is a science forum, please stick to it. What's the actual reason these concepts should be rejected?

I'm not saying they should be rejected: I'm saying they're imaginary. There's no actual science here apart from some concepts of math, physics etc... that are used. It's cool, I love this kind of stuff, and it can actually help people to learn several scientific principles, but it's important to make it clear that it's an exercise of imagination.
emedeiros
I think my views on the subject that I'm addressing are valid and even interesting, but I should have created a topic in the "Science" section of the forum with this purpose (something like "How people relate to scientific knowledge and how does it influence their minds" or whatever).

My post in this topic doesn't follow the actual discussion, I'm sorry. It's just that I don't participate in forums for some months, and I got kind of superexcited and a bit loony; this phase is going to be over soon.
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