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Is our universe merely a hologram?
- stepryan
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- Red Giant
I have a conflict in my mind.
The article refers to pixelation of spacetime - ie there's an assumption of quantization. In other words there exists a scale beneath which distance cannot be be broken into smaller parts.
Take a chessboard and consider each square to be unit size (of length one).
Take the diagonal of one of the squares - it's going to be of length square root of two (sqrt( 1^2 + 1^2)). Now square root of two is an irrational number. That means one can't find integer values for p and q such that square root of two is equal to p/q. This means there is no integer size for which the diagonal is a multiple of it. That is, two dimensional euclidean space forbids quantization (and as three dimensional space comprises two orthogonal two-dimensional planes it is precluded in 3D space also).
For history of discovery and links to some proofs of irrationality see
en.wikipedia.org/wiki/Irrational_number
But these are very bright minds and I can't help feeling uncomfortable contradicting them in any shape or form - but the pixelization of spacetime is an equally uncomfortable thought.
Just my sqrt(2) cents...
Mark C.
i think what they may be talking about is planck length:
en.wikipedia.org/wiki/Planck_length
and planck time:
en.wikipedia.org/wiki/Planck_time
i think basically they are implying that there is a lower limit to how small a unit of space can be and how time it takes to cross this lower limit of space. if you read the book fabric of the cosmos by brian greene it goes into that a little bit. on the squares thing i would not imagine it being a problem seeing that most theories imply space is curved. i would imagine that instead of it being 1 x 1 it could be 1.1 x 1 or something as space itself it not completely flat. also M theory implies 10 space dimensions would it not have to apply all ten dimesions similtaneously ie. 1x1x1x1x1x1x1x1x1 even if you do not include time as a dimesion.
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- Seanie_Morris
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: blink:
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- dave_lillis
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Now imagine that you keep repeating the experiment but each successive time you reduce the amount you change your POV by. I think the suggestion is that there is a finite lower limit that you can change your POV by and still see a different slice of universe. i.e there is a finite number of these slices.
well, wouldnt the magnitude of the differance you see be proportional to the magnitude of the change in your POV, be it however big or small it is and that the smallest thing/size/change you can measure apparently would be the size of the plank constant, that this is where the quantisation comes in?
This seems to me to be more of a problem with the measuring system rather then the universe itself?
I would have thought that the universes dimensions were analogue, I dont like infinities.....
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- mjc
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You make one very good point which blows my original posting out of the water.
Assuming curvature of space then this cannot be neglected. Whatever the shape of the universe is (saddle, doughnut or whatever) it is also a manifold (which I am led to believe) means that when you consider any finite area on it and decrease this area it becomes increasingly euclidean. I made the mistake of assuming that it *was* euclidean. While it is as near as darn it on the scale of human direct experience (I don't think we've measured to be curved yet - I think the curvature is predicted by general relativity) it isn't going to be exact no matter how small one goes.
Thank you for that reminder.
Dave G.
With respect to the underlying geometric shape: I feel that we have to consider a square rather than some other polygon because each dimension (axis) must be orthogonal to each other dimension or axis to be independent (though these guys maybe saying something different for the third - hence the holographic reference).
None the less my original post is moot due to curved space.
However, I'm still uncomfortable with pixelated space.
Thanks guys.
Mark C.
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- johnomahony
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NOW my head really hurts...
: blink:
I think it would be easier to just read the Book of Genesis, its easier on the brain :silly: Oh for those Newtonian days...life was so simple then.
A seriously interesting topic though, my undergrad physics courses are coming back to me now.
The Lord giveth, the Revenue taketh away. (John 1:16)
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- stepryan
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Seanie_Morris wrote:
NOW my head really hurts...
: blink:
I think it would be easier to just read the Book of Genesis, its easier on the brain :silly: Oh for those Newtonian days...life was so simple then.
A seriously interesting topic though, my undergrad physics courses are coming back to me now.
it's elephant's all the way down, and epicycles on top i tells ya ! . the newtonian view is perfectly ok most of the time. it is just at the extremes of the universe ( extremely large or small) that is does not work.
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