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Flat out in 3 or 4 Dimensions…

August23

How many dimensions are there in our universe?
space_time
From 2009 (http://phys.org/news/2009-02-fourth-dimension.html):

“Creating a unified theory of quantum gravitation is often considered to be the “Holy Grail” of modern science.
danielDaniel Grumiller (left) from the Institute of Theoretical Physics, Vienna University of Technology, Austria, can now at least unravel some of the mysteries of quantum gravitation.

We perceive the space around us as three-dimensional. According to Einstein, time and space are inseparabely linked. Adding the time axis to our three-dimensional space makes our space-time-continuum four-dimensional. For decades, scientists have been wondering about the existence of additional dimensions so far hidden to our senses. Grumiller and his colleagues are trying the opposite approach: Instead of postulating additional dimensions, they believe that our universe could in fact be described by less than four dimensions.

“A hologram, as you find it on bank notes or credit cards, appears to show a three-dimensional picture, even though in fact it is just two-dimensional”, Grumiller explains. In such a case, reality has fewer dimensions than we would thinkit appears to have. This “holographic principle” plays an important role in the physics of space time. Instead of creating a theory of gravity in all the time and space dimensions, one can formulate a new quantum theory with one fewer spatial dimension. That way, a 3D theory of gravitation turns into a 2D quantum theory, in which gravity does not appear any more. Still, this quantum theory correctly predicts phenomena like black holes or gravitational waves.

2015 Update (from http://phys.org/news/2015-04-universe-hologram.html)

Everybody knows holograms from credit cards or banknotes. They are two dimensional, but to us they appear three dimensional. Our universe could behave quite similarly:

“In 1997, the physicist Juan Maldacena (pictured here) proposed the idea that there is a correspondence between Juangravitational theories in curved anti-de-sitter spaces on the one hand and quantum field theories in spaces with one fewer dimension on the other”, says Daniel Grumiller.

Gravitational phenomena are described in a theory with three spatial dimensions, the behaviour of quantum particles is calculated in a theory with just two spatial dimensions – and the results of both calculations can be mapped onto each other. Such a correspondence is quite surprising. It is like finding out that equations from an astronomy textbook can also be used to repair a CD-player. But this method has proven to be very successful. More than ten thousand scientific papers about Maldacena’s “correspondence” have been published to date.

Correspondence Even in Flat Spaces

For theoretical physics, this is extremely important, but it does not seem to have much to do with our own universe. Apparently, we do not live in such an anti-de-sitter-space. These spaces have quite peculiar properties. They are negatively curved, any object thrown away on a straight line will eventually return. “Our universe, in contrast, is quite flat – and on astronomic distances, it has positive curvature”, says Daniel Grumiller.

However, Grumiller has suspected for quite some time that a correspondence principle could also hold true for our real universe. Now Grumiller and colleagues from India and Japan have published an article in the journal Physical Review Letters, confirming the validity of the correspondence principle in a flat universe…This however, does not yet prove that we are indeed living in a hologram.
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NCEA Level 2 Algebra Problem. Using the information given, the shaded area = 9, that is:
y(y-8) = 9 –> y.y – 8y – 9 =0
–> (y-9)(y+1) = 0, therefore y = 9 (can’t have a distance of – 1 for the other solution for y)
Using the top and bottom of the rectangle,
x = (y-8)(y+2) = (9-8)(9+2) = 11
but, the left side = (x-4) = 11-4 = 7, but rhs = y+? = 9+?, which is greater than the value of the opp. side??
[I think that the left had side was a mistake and should have read (x+4)?]

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