Questions tagged [spacetime-dimensions]

Use this tag for dimensions of a manifold, typically the space-time. DO NOT USE THIS TAG for dimension of a physical quantity nor for the size of an object.

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Why does Misner, Thorne, and Wheeler’s Gravitation visualization technique breakdown in dimension $> 4$?

In this chapter we will introduce and discuss at length one of the ways that physicists sometimes visualize “nice” differential forms. In essence, we will be considering ways of visualizing one-forms, ...
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How does Einstein Field Equations (EFE) work with more than 4 infinitely large spacetime dimensions?

How does Einstein Field Equations (EFE) work with more than 4 infinitely large spacetime dimensions? But is gravity in Newtonian physics valid with more than 3 infinitely large spatial dimensions?
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Why exactly is reality 3 spatial dimensional? [duplicate]

Reality seems to be 3 dimensional. Not just as a result of our own subjective interpretation, but as a result too of what our machines sense and derive. It does appear as though, apart from in unusual ...
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Are there 4D spacetime not described by GR? [closed]

I heard the EFE is specifically for 4 spacetime dimensions. Does it mean whenever there are 4 spacetime dimensions, there is automatically GR? In other words, are there 4D worlds or spacetime that ...
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1answer
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Are dimensions of physical quantities and 1D/2D/3D/4D… spacetime dimensions the same?

Are the [L]/[M]/[T]... dimensions of length/mass/time... somehow related to 1/2/3/4D spacetime dimensions? If not; why are they called dimensions and what do they actually mean?
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Dimensionality of fluid flow

In some textbooks flow is classified as one, two, or three-dimensional depending on the number of space coordinates (i.e. x,y,z) required to specify the velocity field while according to some other ...
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79 views

Compactification of additional dimensions [duplicate]

The extra dimensions in string theory are supposed to close in on themselves to form circles. Are there other possibilities for compactification? For example a compactification in segment.
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2answers
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Can string theory be background independent?

Are there any models in string theory which are background independent? If there are, would this mean that these models could be built in any number of dimensions? (Instead of assuming a fixed number ...
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2answers
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What experimental techniques could be used to search for higher (macroscopically occurring) spatial dimensions?

We live in a a universe with 3 spatial dimensions and 1 time dimension. However, if we lived in a universe with 4 or more spatial dimensions, under the right conditions (such as a general lack of ...
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Heisenberg uncertainty principle fluctuations and dimensions less than 3+1

I've been looking at the 1+1 dimensional Dirac equation recently and am wondering if the Heisenberg uncertainty principle would allow application of said model to spin-1/2 fermions in 3+1 dimensions ...
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Why the force is inversly proportional to the square of distance? [duplicate]

Lesser the distance higher the force of attraction.but why it is the square of distance?And also the reason i guess for this force is the attraction force between atoms ( electrons of one atom and ...
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Is the space in which we live fundamentally 3D or is this just how we perceive it? [closed]

What troubles me is how "nothingness" can have any attributes. The way we perceive space has a lot to do with light moving in straight lines and that we see this. But is there some non-...
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1answer
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String theory assumes that strings are complex geometric objects

In string theory, a string is a one-dimensional space that can be closed on itself as a circle (closed string) or open as a linear interval (open string), but does a string have one real dimension or ...
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How does gravity leak to other dimensions, if extra dimensions existed?

There was research article that showed the gravitational waves and electromagnetic waves propagated through the universe the same way, loosing energy by the inverse square law. The researchers ...
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1answer
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Would extra dimensions really solve the hierarchy problem?

The hierarchy problem revolves around the fact that we don't have a way to explain why gravity is so much weaker than the other forces. It may just be a coincidence, but since physicists tend to ...
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1answer
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What sets the scale of a free Maxwell theory in $d\neq 4$?

The action for the free Maxwell theory is given by $$S=\int d^dx\sqrt{-g}\bigg(-\frac{1}{4}F^{\mu\nu}F_{\mu\nu}\bigg)$$ The theory is invariant under conformal transformations $g_{\mu\nu}\to\Omega^2(x)...
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Different symmetries or no symmetries in string theory?

I was reading the book "A Fortunate Universe" by Geraint Lewis and Luke Barnes and something caught my attention: At page 195 the authors say that universes with different symmetries could ...
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159 views

Block universe theory [closed]

How to make sense of change in static block universe if every event already exist in block? if you say it's an illusion created by brain even that requires forward evolution of patterns of information ...
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2answers
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Regarding the velocity of waves in even dimensions

A few years ago I asked on Reddit about the behavior of wave propagation in even and odd dimensions. I received this answer: "The answer lies in the solutions to the wave equations. Essentially, ...
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1answer
38 views

In what dimensions to the Navier-Stokes equations work?

I have only seen examples and references to the Navier-Stokes equations in two and three dimensions. Do we know if these equations work in one dimension or greater than three dimensions?
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The block universe theory

i watched a video on YouTube https://www.youtube.com/watch?v=_A7wk40AeiI regarding the block universe where brian greene seem to be saying we live "forever" (i am probably misinterpreting ...
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1answer
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Is the equivalence of axial vectors with skew symmetric tensors in 3 dimensions a coincidence?

We happen to live in the only number of (large space-like) dimensions that permits an equivalence between skew symmetric tensors, like the magnetic field, and vectors. Similarly (equivalently? not ...
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1answer
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Black rings in 4D gravity

In Introduction to Black Hole Physics by Valeri P. Frolov, Andrei Zelnikov there is a discussion of gravity solutions. They present some examples of solutions with non-spherical horizon topology: But ...
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Newtonian mechanics in higher dimensions [duplicate]

Once in a book ( I think title was Mathematical Physics, no idea who the author was) saw the proof of instability of planetary orbits in 4 dimensions, cant remember the details of derivations only the ...
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1answer
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Can there be a multiple dimension of time? [duplicate]

Multiple dimensions of space makes sense. We can understand multiple dimensions of space by lines ,planes,spaces etc. But what does a 2-D time,3-D time etc means. Visualizing time as a line makes ...
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3d solutions for 1d Schrödinger equation?

The general Schrödinger equation in 3d is $$i\hbar\frac{\partial\psi}{\partial t}(\mathbf r, t)=-\frac{\hbar^2}{2m}\nabla^2\psi(\mathbf r, t)+V(\mathbf r)\psi(\mathbf r, t).$$ Now consider that $$V(x, ...
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1answer
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How to draw all the Electric field vectors associated with an em wave?

This is a single ray of an electromagnetic wave propagating in one dimension. But we know an electromagnetic wave travels in three dimensions. So, I wish to draw the Electric field and magnetic field ...
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1answer
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Is there such a thing as negative dimensions? [duplicate]

From what I understand so far, we live in a 3rd dimension, and we see in the third dimension. We can imagine both the third, second, first, and even the zeroth dimension with thought. However, the ...
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SUSY and free Majorana field theory

Given a free Majorana field theory in $D$ spacetime dimension. Say $D=2$ to $10$. Question: Which $D$ spacetime dimension,do we have a free Majorana field theory with Majorana spinor in the real ...
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1answer
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Do EM waves live in the 4th dimension? [closed]

By an $n$-dimensional wave, I mean the wave is propagating in $n$ spatial dimensions. (Ripples on water are 2D waves.) The question is just the title. Below are my explanation and hypothesis. ...
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2answers
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Is there any way to prove that contrarly to a flat 3D space, a curved 3D space can only be constructed in a 4D manifold?

This question is a result of me trying to understand how this universe can be possibly infinite if it isn't infinitely old. So to compare with an area that is flat it can be constructed both in 2D and ...
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2answers
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Is a Schwarzschild solution possible in 3 space-time dimensions?

Reading the book "Supergravity" from Freedman & van Proeyen I stumbled over the assertion that in 3D GR the vacuum solution $R_{\mu\nu} =0$ leads to a vanishing 4-rank curvature tensor $...
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1answer
53 views

Why did Kaluza-Klein need an additional dimension? [closed]

Why did Kaluza-Klein need an additional dimension and not just treat the fourth dimension as a description of both time and space? Assume that you can exchange the time dimension to a space dimension ...
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1answer
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Solutions of non-linear equations in QFT and interpretation of particles

One of the simplest QFT model is $\lambda \phi^4$ theory. $$ S = \int dt d^dx\; \left(\frac{1}{2}(\partial_\mu \phi)^2 - \frac{1}{4!}\lambda \phi^4 \right) $$ Equation of motion: $$ \Box \phi = -\frac{...
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Time-reversal symmetry and the generalized special axes (eg: $y$) in any $D$ space dimension

In 3D space, it is common to choose the time-reversal symmetry acting on spin-1/2 doublet fermions as $$ T = i \sigma_y K = \begin{pmatrix} 0 & 1\\ -1& 0\end{pmatrix} $$ where $K$ is complex ...
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How to add extra space dimensions linked to time?

My understanding is that extra space dimensions are added in a way such that the line element in flat spacetime is calculated by the Pythagorean theorem: $$ds^2=-c^2dt^2+dx_1^2+dx_2^2+dx_3^2+dx_4^2+......
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Proof of Coulomb's law in two and higher dimensions

I have found that the Coulomb force in two dimension varies with $\frac 1 r$: \begin{equation}\tag{2}F=\frac{1}{2\pi\epsilon}\cdot\frac{q_1q_2}{r}\end{equation} But I was not able to prove it. I think ...
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1answer
47 views

Do energy levels ever appear at the peak of a cosine potential in higher dimensions?

I simulated a hyperspherically symmetric wavefunction for the case of $V=-\cos(r)$, in which $h=1$, and $m=1$ and the number of spatial dimensions is $4$. I charted the integral of the square of the ...
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55 views

Method of Images for $d$-Dimensional Sphere Derivation

The method of image for spherical boundary conditions relies on a fact that two point charges with opposite signs, $q1$ and $-q2$ with $q1 > q2 > 0$, form a sphere of zero electric potential $V =...
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Dimensional reduction with supermanifolds and gravity

When having compact dimensions (I guess it is not true with supermanifolds), the gravitacional constant gets diluted in extra dimensional space: $$G_N(4d)=G_N(Dd)/V(X)$$ However, I presume that the ...
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3answers
65 views

Can we represent 4D graphically? [closed]

Actually I know that axes are always perpendicular but after three axes we cannot draw any other axis that is perpendicular to all the other three axes. can any one say how can we draw another axes ...
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3answers
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Gravity bends space, so how can space have only 3 dimensions? [duplicate]

Due to the laws of gravity and electromagnetic attraction (decreases with $\frac{1}{r^2}$) we know that space should be limited to 3 dimensions. At the same time we know that gravity bends space. All ...
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48 views

Can time be just another spatial dimension which the universe travels through with a particular direction and constant velocity?

Is it possible that time is not a 'time-like' dimension, but a proper spatial dimension just like the others but we only have access to a 3D cross-section of it? I did some research about the internet ...
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2answers
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What does it mean to have a dimension of $1.5$?

Question. How do I explain to my dad what it means for some object to have a dimension of $1.5$? My attempt. I tried to tell him the definition for an object to have a dimension $D$: if we scale up ...
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1answer
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Are the fermions in 4D Euclidean $\mathcal{N}=4$ SYM Majorana? If not, what are they?

It is stated in this paper (as well as in many other) that the fermions of $4$D Euclidean $\mathcal{N}=4$ Super Yang-Mills (SYM) are Majorana fermions (see eq. (42) and (43)). However it is stated in ...
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Are fields projections in spacetime of higher dimesions?

I am initiating my learning on QFT and my question might be really basic, but I am having difficulties finding an answer, I would appreciate any help to find this in the literature. Here is my ...
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Because of the spacetime foam, we can't calculate a complete string, we can only calculate parts or ends, right? [closed]

What is the relationship between the vibration of the string and the uncertainty of space-time.Not seeing the string, but when doing calculations, some parts of the string are affected by spacetime ...
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1answer
120 views

How to count degrees of freedom in a symmetric $N \times N$ matrix?

I am reading Wayne Hu's short lecture on cosmology mathematical infrastructure (https://arxiv.org/abs/astro-ph/0402060), and have several questions. Some background for us lazy people that don't want ...
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1answer
61 views

Scalar fields and spinors in 0+1D

As part of learning about SUSY quantum mechanics, I am trying to get a grasp on the following Lagrnagians in 1 (temporal dimension): But since these early times the treatment and methods of field ...
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2answers
119 views

Are All Dimensions Infinite and 'Closed'? [closed]

I have formed a thread about loosely how a 'fluid', geometrically flat, N-space, that is 'curved', in infinity'. With flows of fluid, 'space', that can facilitate known forces in that flat space. In ...

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