4d Definition and 130 Threads

iam sorry if this is crackpottery,but is it true that a 4 dimensional figure*called the tesseract has been constructed,i came across this over the net.*kindly rebuke me if iam not abiding with the rules of pf.

Homework Statement Find the generators of the four dimensional irreducible representation of SO(3), such that J_3 is diagonal. The Attempt at a Solution I know how to get the rest if I know J_3, by using ladder operators. But what is J_3? For a 3d representation it's diagonal with 1,0-1, in 4d...

What is the name of the theory (or person who thought it up) that the universe is infinite in the 4th spatial dimension and that our big bang is only a local effect?

I am looking for a 4D angular coordinate system (radius and three angles) and its corresponding "hypervolume element". 2D: polar coordinates - dA = r dr dtheta 3D: spherical coordinates - dV = r^2 sin(phi) dphi dtheta dr 4D: ?

I've seen the statement repeated in many places that a stable knot comprising 1D curves cannot be created in 4D, since it's always possible to untie the knot by moving in the 4th dimension (whereas it is possible to create a stable knot in 4D using 2D surfaces). Can anyone point me to an...

Major paper by Fairbairn--a way to put matter into 4D quantum gravity I expect this paper will "raise the dead" in the sense of evoking a comment from John Baez :-). It develops some lines of research he was working on three years ago. It references work by Derek Wise, a Baez PhD----also...

Can a 4-dimensional manifold with the Schwarzschild metric be embedded into a flat manifold of 5 (or more if necessary) dimensions? In other words, are there functions of t,r,\theta , \phi and M such that if x_1 = f_1 (t,r,\theta ,\phi ,M) x_2 = f_2 (t,r,\theta ,\phi ,M) . . etc...

Lisa Randall said "string theory reproduces GR in 10 dimensions" Does string theory gravitons have 4D GR as its low energy limit? I know that its lowest mode vibrations corresponds to a massless spin-2 particle, the graviton. I know GR in 4D can be extended with susy. Does it reproduce...

Is there a way to get a local bosonic theory out of spin foam formalism? Xiao-Gang Wen's suggestion, first published 6 Jul 2004 http://arxiv.org/abs/cond-mat/0407140v2 Page 8 "Remarkably, it appears that the theory of loop quantum gravity can be reformulated in terms of a particular kind of...

this may seem quite stupid to many of you but i was wondering how it is possible to draw 4D objects. I have seen pictures of 4D objects such as the hyper-cube etc, but they are drawn in three dimensions. The picture of a hyper cube that i looked at seemed to me to just look like a cube with a...

http://arxiv.org/abs/hep-th/0611042 Hidden Quantum Gravity in 4d Feynman diagrams: Emergence of spin foams Aristide Baratin, Laurent Freidel 28 pages, 7 figures "We show how Feynman amplitudes of standard QFT on flat and homogeneous space can naturally be recast as the evaluation of...

Yo anyone, Could someone enlighten me as to why, if there is a 4th spatial dimension, we can't see 3D shadows of 4D objects? Lots of talented people built an amazing 3D shadow of a 4D object but I'm almost certain I've never seen one pop in and out of existence while on the way to the shops...

Any one can guide me to some good books about 4-dimentional electrodynamics? I don't want books that starts from electromagnetical theorems for maxwell, i want them to start from 4-dimentional systems and operations on them or tensors about them Thanks,,

Baez et al revised the title of their March 2006 paper to say "strings" instead of "loops" and reposted it http://arxiv.org/abs/gr-qc/0603085 Exotic Statistics for Strings in 4d BF Theory John C. Baez, Derek K. Wise, Alissa S. Crans 41 pages, many figures. New version has minor corrections and...

Well we start out with -\frac {d} {dt} \int_{V}^{} \sigma dV = \int_{\Pi}^{} \vec{J} \cdot d\vec{\Pi} Using the Gauss theorem \int_{V}^{} (\frac{ \partial {\sigma}}{ \partial {t}} + div \vec{J}) dV = 0 so \frac{ \partial {\sigma}}{ \partial {t}} + div \vec{J} = 0 and written in 4D...

To be science a theory must bet its life on the outcome of some future observation. That is what it means to predict something new and to be falsifiable. If the observation goes against the theory's prediction then the theory is wrong. so the theories of space time and matter that are currently...

I only learned the meaning of a manifold recently and in the most elementary terms but I thought that I might link it with this example. It seems that the universe is made out of 3D objects. So put all of them together (stars, black holes, galaxies etc) and you have the whole universe. It...

Please follow my deduction and tell me where am I wrong, or maybe I’m not? 1) the cosmological principle: "Viewed on sufficiently large distance scales, there are no preferred directions or preferred places in the Universe" it says that there is no center of the universe, or in other...

In 2D for example, warping it only makes sense in a 3D enviorment. In a 2D world, bending 2D would be meaningless. So in GR when we talk about bending 4D ST, is a fifth dimension needed to give ST something to "bend into"? If not, in what sense can we talk about warped ST? I suspect that...

Would forces act with the same symmetry in 4D as it does in 3D?

I know that gravity can be extended to 4D but the conclusion always seem to be unstable, is the reason why they come up with unstable orbits and atoms is because they take how gravity acts here in 3D physics and apply it the same way to 4D physics? How about modificating the model? but we just...

I'm an "on-my-own-free-time" arm-chair student of physics. Lol. So if this question is way off the mark my apologies. Feel free to let me know where I’m off base. Anyway... For me, a great visual example of the twin paradox was found at this site...

this poll refers to this other thread https://www.physicsforums.com/showthread.php?t=81295 when I first read the "sum over topologies" papers linked there, i was very optimistic. Loll and Westra have been able to make the CDT path integral in 2D sum over topological variation the...

Humans have full 4D spatial vision Consider this: 1) objects in motion show non-simultaneities along the direction of motion (the "temporal distance" between the endpoints is \gamma vl/c^2) 2) objects in motion show time dilation (the "temporal velocity" runs slow with a factor 1/\gamma)...

http://www.astronomycafe.net/qadir/q1940.html Is this true?

Okay, I understand that if you dedicate some motion to one dimension at a constant rate you consequently pull motion from another dimension. Like driving at an angle rather than a straight line traveling a longer distance to a said stopping line (traveling in two dimensions rather than one). I...

Suppose you have a piece of paper in the shape of a left shoe, on a flat surface. Suppose also that it can only stay in contact with the surface. No matter how you move it or rotate it in the 2D surface, it cannot become a right shoe. However, if you move it out of the 2D space, flip it and...

Can anyone explain 4D space-time in a simple form ? Some say the Hawking's expalanation is the simplest but I don't get it :biggrin:

Can you explain "Emergence of a 4D World"? Can anyone help explain the new paper "Emergence of a 4D World from Causal Quantum Gravity" by Ambjorn, Jurkiewicz, Loll? http://arxiv.org./hep-th/0404156 ten pages involves monte carlo simulations (computer experiments)

I hope my question makes some sense; if not, just post an "evil smiley" and ignore it :smile: So, my only "knowledge" about this is based on one of Hawking's books, wherein it is written: If space had four dimensions instead of three, gravitation would behave differently (I think it was...