4d Definition and 116 Threads

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...

[FONT=Times New Roman]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...

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...