4d Definition and 116 Threads

For this problem and solution, I'm confused by part (c) and (d). I don't understand how the Lorentz formula ##ct' = \gamma (ct - \frac{v}{c}x)## can be used to find the ##ct'## axis. This is because they found the ##ct = \frac{v}{c}x## which is in terms of ##x## not ##x'##. Does anybody...

Let’s dubiously assume that these 4D atoms would have the same radius as 3D atoms. Let’s further dubiously assume that a 4D HyperEarth has the same number of atoms as 3D Earth. Then the diameter of HyperEarth would be less than a kilometer. Four dimensional Earth is much more compact. Wouldn’t...

This is probably a stupid question but, ## \frac{d\partial_p}{d\partial_c}=\delta^p_c ## For the notation of a 4D integral it is ##d^4x=dx^{\nu}##, so if I consider a total derivative: ##\int\limits^{x_f}_{x_i} \partial_{\mu} (\phi) d^4 x = \phi \mid^{x_f}_{x_i} ## why is there no...

A 4D planet has no axis of rotation. Nothing special about planets, all freely rotating 4D bodies have two perpendicular planes of rigid rotation. (Clifford proved this in the 19th century.) Now there is nothing stopping us from thinking of planes of rotation here in 3D Universe. It's the...

Hello everyone, I am struggling to get insight into a certain set in 4D space. Given is a closed path in 4D-space with constant Euclidean norm $$\vec{\gamma} (\theta):[0,2\pi]\to\mathbb{R}^4, \ \ \vec{\gamma}(0)=\vec{\gamma}(2\pi), \ \ ||\vec{\gamma}(\theta)||_2 = \mathrm{const.}$$ I am looking...

Assume a TV screen or a book page represents 2D information viewable within our 3D world. From our 3D world, we see the entirety of the 2d world...all of it. Now imagine if somehow we lived within the 2D TV or book page. From our 2D world, we would be incapable of viewing, interacting or...

Q. Calculate the linearised metric of a spherically symmetric body ##\epsilon M## at the origin. The energy momentum tensor is ##T_{ab} = \epsilon M \delta(\mathbf{r}) u_a u_b##. In the harmonic (de Donder) gauge ##\square \bar{h}_{ab} = -16\pi G \epsilon^{-1} T_{ab}## (proved in previous...

Suppose I have two intersecting planes in a four dimensional space. It seems to me that there are two angles between these planes. If the two planes intersect in a line then one of those angles is zero. If the two angles are non-zero then the planes intersect in a point. If one plane is the...

Why doesn't it repel things... or just pass through and leave distance unchanged?

Given the parameters ##n## and ##m##, I'd like to initialize a ##n \times n ## 4D array where each entry is an ##m \times m ## matrix, and where each column of the matrix is an array of type numpy.linspace(0,1,m). Furthermore, I'd only like to have entries on the diagonal and above it, or only...

Hi, so the four-dimensional generalization of $$\vec{B}=\mu\vec{H}$$ is $$F_{\lambda \mu}u_{\nu} + F_{\mu \nu}u_{\lambda} + F_{\nu \lambda}u_{\mu} = \mu (H_{\lambda \mu}u_{\nu} + H_{\mu \nu}u_{\lambda} + H_{\nu \lambda}u_{\mu})$$ From these four-tensors and four-vector I should be able to...

Is the intersection of a 4D line segment and a 3D polyhedron in 4D a point in 4D, if they at all intersect? Intuitively, it looks like so. But I am not sure about it and how to prove it.

Can someone simply explain to me what are the time crystals? What are they built from (matter, do they have mass)? I cannot find a clear explanation of them. I just know that ordinary crystals are 3d, time crystals - 4d.

I am uncertain if this belongs in the differential geometry thread because I don't know what area of mathematics my question belongs into begin with, but of the math threads on physics forums, this one seems like the most likely to be relevant. I recently watched a video by PBS infinite series...

I have a 4D array of dimension ##100\text{x}100\text{x}3\text{x}3##. I am working with `Python Numpy. This 4D array is used since I want to manipulate 2D array of dimensions ##100\text{x}100## for the following equation (it allows to compute the ##(i,j)## element ##F_{ij}## of Fisher matrix) ...

I'm a beginner in QFT and I'm always hearing people say that QFT is undefined in 3+1 dimensions or that the Hamiltonian cannot be rigorously defined, what do these statements mean exactly? In particular I'd like to know what makes the 3+1D case that much worse than non-relativistic QFTs like the...

Hey, i can't see actual space in tesseract. Like in 3 dimensional cube, you have squares as faces and between them there is a space. But in tesseract where you have 8 cubes as faces, this leaves 0 space for actual space inside, i can see only 8 faces and nothing between them. I first thought it...

I have just simple Knowledge, but recently a question came To my mind. An Entity Living in 2d Space cannot Directly Observe a sphere, but rather a Circle Changing its Size when a sphere is traversing trough the observable 2d plane. Similar, a 4d sphere would Appear To us as 3d sphere Changing...

Is it possible that our 3D universe is just a shadow in 3D space of 4D or higher dimensional reality? And we are limited in our perception of it by our 3-dimensionality. In other words like Flatlanders would just see s square of a cube sitting on the plane or passing through the plane...

I see that this has been discussed before, but the old threads are closed. As Carl Brans and others note, it seems too big a coincidence to ignore. Why is exotic smoothness "good" (in the sense that it permits richer physics or something like that)? Exotic Smoothness and Physics,arXiv "there...

I have a surface defined by the quadratic relation:$$0=\phi^2t^4-x^2-y^2-z^2$$Where ##\phi## is a constant with units of ##km## ##s^{-2}##, ##t## is units of ##s## (time) and x, y and z are units of ##km## (space). The surface looks like this: Since the formula depends on the absolute value of...

Hi all, Clarification question: I've read that string theory is manifestly Lorentz invariant - however, I'm confused about this being true in 4D spacetime or in the full 10D setting of the theory (well, one version anyway). At some point I'd also read in a paper that 4D Lorentz invariance...

Can many worldlines occur in 4D spacetime where observers in each worldline think they're the "real" worldine? Is there a mechanism preventing many worldlines from occurring in 4D spacetime. Einstein said this in his book Relativity: Look at this scenario. Event A occurs outside of the light...

So I know what these are 4 translation : ##\frac{\partial}{\partial_ x^{u}} = \partial_{x^u}## 3 boost: ##z\partial_y - y \partial_z## and similar for ##x,z## and ## y,x## 3 rotation: ##t\partial_x + x\partial_t ## and similar for ##y , z## however I want to do it by solving Killing equation...

I was just thinking about this randomly today. I feel like the answer is that it "does" and it "doesn't." A math teacher I had said that the 4th dimension is perpendicular to everything and anything in the 3rd, so does that mean that it can't be displaced, or is the answer more complicated than...

can string theory reproduce hawking radiation in non-extremel black holes in 4D? i.e physically realistic black holes. do they exactly match hawking's calculations? what is the interpretation of hawking radiation in string theory?

...and what is the difference between true 4D and the minkowski space? To me, it would be much easier to see universe as a 4D and us humans just experiencing the dimension of time differently. In my mind i pictured the universe as a complete 4D structure which we humans experience in one...

From the perspective of a 4D observer would 3D infinity appear to exist? Why/why not?

Could anyone please recommend any papers that describe the path of a 4D ball through 3D space?

Using Ray D'Inverno's Introducing Einstein's Relativity. Ex 6.31 Pg 90. I am trying to calculate the purely covariant Riemann Tensor, Rabcd, for the metric gab=diag(ev,-eλ,-r2,-r2sin2θ) where v=v(t,r) and λ=λ(t,r). I have calculated the Christoffel Symbols and I am now attempting the...

I know how to solve systems, but the question asks to work backwards. "Create a 4-d system that has a solution (-2,5,-6,1)." How would i do this?

thus far the LHC has not seen any SUSY in run 2, with possible exception of the 750 scarlar boson which may disappear with further data. If LHC run 2 provides no BSM type physics, would either The New Minimal Standard Model Hooman Davoudiasl, Ryuichiro Kitano, Tianjun Li, Hitoshi Murayama...

"To visualize the standing waves (or orbitals) of electrons bound to a positively charged nucleus in three dimensions, we will need a four-dimensional plot of the wave function vs. x, y, and z." http://www.grandinetti.org/electron-orbital-shapes"The wavefunctions in the N=2 family are vectors in...

I've been wondering what spaces with an extra physical dimension would look like. That is, instead of our 3+1D space it would be a 4+1D space. In general, it can't be done. There is too much information for a human brain to handle. But some special cases can work. The main one I thought of...

Question outline: In the case of 5d Kaluza (Klein) GR with NO charge and NO gauge field we expect 5d to reduce to 4d GR exactly. So this should be a very simple useful sanity check.s the side and corner terms of Einstein, Ricci and Energy tensors are zero, then R would be the same in 4d or 5d...

An element of SU(2), such as for example the rotation around the x-axis generated by the first Pauli matrice can be written as U(x) = e^{ixT_1} = \left( \begin{array}{cc} \cos\frac{x}{2} & i\sin\frac{x}{2} \\ i\sin\frac{x}{2} & \cos\frac{x}{2} \\ \end{array} \right) = \left(...

Looks like my main pet GR project is about to enter something akin to maintenance mode, since it now does all I currently need it to. It's nothing earth-shattering at first glance, but is very concise (e.g. ~100 lines of Python for the simulator script) and should be easier to understand than...

this is the idea...

I've read the descriptions and watched the videos over and over that describe these shapes, and my skepticism has simply not gone away. Can anybody explain what I might be missing? Here is my reasoning: Physics supercedes, or at the very least, is parallel to math. Math is not something that...

Can a 4 spacially dimensional shape exist in our 3 spacially dimensional universe? Could one exist and we just cannot perceive like a 2D animal could think it lives on a flat plane yet it actually lives on a sphere or donut shape? And could our universe be a 4 spacially dimensional shaped?

Let’s imagine a moving point bound to a 2D plane. If we wrap this plane on a sphere within a 3D space the point would now eventually end up at the same position while moving in a seemingly fixed direction (it is actually not fixed in the 3D space). I am now wondering: Can a 3D hyperplane be...

The brains at the Perimeter Institute recently published a paper describing how our 3 dimensional universe could possibly exist as the event horizon of a 4 dimensional black hole in a 4 dimensional universe as the event horizons of black holes have one less dimension than the black hole itself...

This is a rather naive question concerning the dimension of the schrodinger equation. If the Schrodinger equation can be wrtiten in a three dimensional form using the laplacian operator can it be written in a 4d version. I understand that the schrodinger equation shows the development of the...

What is the relationship with the Mobius strip (or loop) and the 4 dimension? Is Mobius strip a four dimensional object?

Dear All, I am trying to calculate the Riemann tensor for a 4D sphere. In D'inverno's book, I have this equation R^{a}_{bcd}=\partial_{c}\Gamma^{a}_{bd}-\partial_{d}\Gamma^{a}_{bc}+\Gamma^{e}_{bd}\Gamma^{a}_{ec}-\Gamma^{e}_{bc}\Gamma^{a}_{ed} But the exercise asks me to calculate R_{abcd}. Do...

It is too new for me to know for sure but I think it probably is. The action has a new kind of momentum, consisting of tetrahedral volume flowing along an edge-network: a "one dimensional branched manifold" derived from a simplicial decomposition of the original 4d manifold. Wieland calls the...

Ansatz metric of the 4 dimensional spacetime: ds^2=a^2 g_{ij}dx^i dx^j + du^2 (1) where: Signature: - + + + Metric g_{ij} \equiv g_{ij} (x^i) describes 3 dimensional AdS spacetime i,j = 0,1,2 = 3 dimensional curved spacetime indices a(u)= warped factor u = x^D =...

Before I get down to business, I would like to note (you don't have to read this; feel free to skip to where it says "here are my questions") the following: ------------- Firstly, I am somewhat still new to posting in these forums, and as such, am not sure if this is the right place to put this...

I hope this is the right forum... In 3d space, a 2d plane can be specified by it's normal vector. In 4d space, is there a 3d plane, and will these planes be specifiable by a single vector?

Homework Statement Given N=1 SYM in 10 dimensions (all fields in the adjoint representation): \int d^{10}x\, Tr\,\left( F_{MN}F^{MN}+\Psi\Gamma^M D_M\Psi\right) D_M\Psi=\partial_M \Psi+i[A_M,\Psi] is the gauge covariant derivative. Reduce to 4 dimensions A_M=(A_\mu,\phi_i)...