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.
944 questions
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Can light exist in 4 spatial dimensions? [duplicate]
Light is electromagnetic radiation, according to what I have learned so far essentially a changing magnetic field inducing an electric field which induces a magnetic field and so on.
The equations for ...
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Paper on Dependent time coodinate in spacetime relation [closed]
I want to write a research paper on the topic mentioned above using a mathematical framework of my own (stil in progress).
Is this idea novel or already explored?
Are there gaps in my reasoning?
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What does Backward Time Factor mean physically?
I'm fresh in Photonic Time Crystal research, struggling with the physical origin of Time Reflection.
Like what would happen at a spatial boundary, where an initial beam split into reflected and ...
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Equivalence of Hawking Temperature Between Black Hole and its KK Reduction
Consider the following $2+1$ dimensional metric describing a stationary black hole:
$$ds^2 = g_{tt}dt^2+g_{rr}dr^2+g_{\theta t}d\theta dt+g_{\theta\theta}d\theta^2$$
Where $t$ is temporal coordinate, $...
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Multiple time dimensions and understanding ultrahyperbolic differential equations
On article "On the dimensionality of spacetime (https://space.mit.edu/home/tegmark/dimensions.pdf) Max Tegmark writes about ultrahyperbolic differential equations leading to unpredictability:
&...
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Is there a one-to-one relationship other than the T-duality between the winding number and the momentum along the compactified dimension?
I have a doubt related to compactifying a dimension leading to the concept of string winding.
Suppose we compactify a dimension, the momentum along this dimension makes the string move along this ...
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How does the lifetime and temperature of a black hole scale with mass in universe with more then 3 spacial dimensions?
I've tried to find out how the lifetime and temperature of a black hole scale with mass in a universe with more then 3 spatial dimensions. I've spent a while trying to look up an answer to this ...
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The relation between the Planck scales and the extra dimensions scale
In extra dimensions models like ADD model paper the relation between the extra dimensions Planck scale $M_{p_l(5)}$, the 4-dimensional Planck scale $M_{p_l}$, and the size of the extra dimension $R$ ...
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Is there any connection between the number of spacetime dimensions and the number of fundamental forces?(Non-string version)
This question is connected to the old post:
Is there a relation between the number of dimensions of space time and the number of fundamental forces?
Why doesn't the number of space dimensions ...
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Does the third spacial dimension exist,? [closed]
Our eyes see the World in two dimensions while we rely on our minds to create the visual perception of a third dimensional existence.
Why can't we visually experience the third dimension? Surely we ...
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Is it physically plausible for a universe to have global distance dilation/contraction relative to a parallel universe?
In the video game Minecraft, one can go through a portal from the overworld to the "parallel world" called the nether. If one starts at a point $A$ in the overworld, takes a portal to the ...
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Dimensions And dimensional Formula
I was recently studying about dimensions and I am stuck at a question that why Angles and exponents are dimensionless?
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If there's no outside space in the universe, is it going to be converged as a dot? [duplicate]
I am a junior high school student in Japan.
Today, while having dinner with my friends, we were talking about the edge of the universe. Then we thought that although it would be exciting to think ...
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Visualizing 10D
With 4D we can make a 1D array with 3D subplots to visualize time. With 10D I wonder if having 3D subplots that are 3D plus animation would be possible to utilize to visualize string theory, or is it ...
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Is there another way to reduce the many dimensions of string theory to the observed 4 dimensions?
I understand that string theory works best with many more dimensions than the 4 observed dimensions (1 time, 3 space). To reduce the visible dimensions, I always read that it could be that most of the ...
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Strings on group manifolds and critical dimension
In their work, Witten and Gepner in "Strings on group manifolds" have shown that the central charge of the theory is
\begin{equation}
c=\frac{kD}{c^{\vee}+k}+d=26,
\end{equation}
where $d$ ...
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Does the Laplace-Runge-Lenz vector generalize to higher dimensions?
The Kepler problem in three spatial dimensions has a non-obvious $\mathrm{SO}(4)$ symmetry that leads to the conservation of the Laplace-Runge-Lenz vector via Noether's theorem.
Does this only hold in ...
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A research about wormholes from higher dimension prespective [closed]
I want to write a research paper about higher dimension and wormholes, what could I research about? What could be the question, I have graduated from high school 1 years ago, and not recently joined ...
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Does the force of gravity equation include only one dimension?
Been in a debate with someone who is claiming the force of gravity equation describes three dimensions. I was under the impression there is only one dimension relevant in the equation, that being the ...
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Why does gravity obey an inverse square law? [duplicate]
I am reading Martin Rees' Just Six Numbers, and came across this paragraph, where the author explains why a three-dimensional universe implies an inverse square law.
I understand the argument, but my ...
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Baby monster group order and the hierarchy between Planck and top quark/Higgs in string theory
I was puzzling if there were anything trying to explain $M_p^2=NM(higgs)^2$ or $M_p^2=NM(top)^2$ and I found it that $N\sim N(BM)$, where $N(BM)$ is the order of the Baby Monster group, about $\sim 4\...
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In which dimensions is it possible to define supersymmetric actions?
Susy gauge theories only exist in dimensions 3,4,6,10. This is stated by Baez and Huerta as:
Nonabelian Yang-Mills fields minimally coupled to massless spinors are
supersymmetric if and only if the ...
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Goldberger-Wise Mechanism in Randall-Sundrum I Model
Can someone explain the Goldberger-Wise mechanism for radius stabilization in the Randall-Sundrum model? I am reading their original paper https://arxiv.org/abs/hep-ph/9907447, but I am a bit confused ...
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What physical argument to say that time is a dimension? [closed]
To demonstrate Lorentz transformations mathematically, we assume that time is a dimension (via linear transformations, etc.), what physical argument requires us to do this?
Details for the reason for ...
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Would the electroweak interaction be possible in a space of odd dimension?
In order to describe well the electroweak interaction, chiral particle states are necessary. This works well in 4D (Minkowski) space, but it seems that it is not possible in a space of odd dimension (...
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In equation (20) from lecture 10 in Leonard Susskind’s ‘Classical Mechanics’, why is there a summation involved?
Here is the equation
$$\{x_i,L_j\}=\sum\limits_{k}ϵ_{ijk} x_k.$$
Is this equation generalised for any number of dimensions? In which case, would the following example be correct assuming 4 dimensions?
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How do I know if a motion is 1 dimensional or 2 dimensional?
If an object is moving in a straight line with an angle with x axis (it may be vertical or horizontal) , is it 1 dimensional or 2 dimensional?
The question was asked by my teacher and he himself gave ...
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Question on spatiotemporal dimensionality about the contradictions of time being a dimension
We can axiomatically see that all spatial dimensions have a fundamental rule where they can either move back or forwards infinitely. However, the temporal dimension started when the universe began and ...
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What happens if we differentiate spacetime with respect to time? [closed]
Essentially, what would differentiating space-time with respect to time provide us with? What are the constraints associated with such operations? Is it possible to obtain a useful physical quantity ...
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Do the Komar/ADM mass equations also hold in 2+1D?
All definitions I have come across for the ADM mass require asymptotic flatness, which always is defined for 4 dimensional spacetimes. I was wondering if these formulae in 3+1D hold in 2+1D aswell?
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Multiple time dimensions in the eternal inflation model
From a lecture by Prof. Kaiser, I reckoned that according to the Eternal Inflation model, it is possible that all of the 10500 topologies posited by string theory could exist somewhere in the region ...
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Definition of the gravitational constant in 1+1 gravity
In this paper, the author formulates a $(1+1)$-dimensional theory of gravity by taking the trace of the Einstein equations
$$\left(1 - \frac{D}{2}\right)R = 8\pi G_D T,\tag{2}$$
(where $G_D$ is the ...
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Poincaré algebra and supersymmetric spaces
If i understand correctly, a supersymmetry algebra should contain as a subalgebra the Poincaré algebra, however for a supersymmetry algebra the corresponding supersymmetric (Minkowski) space has ...
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What does the superscript $3$ in $d^3x$ mean in an integral?
At the risk of seeming ignorant, please explain what does the superscript $3$ in $d^3x$ mean in the integrals 5.12, 5.13, 5.14, 5.15? Why 3? Why there is no such in the 5.10 integral?
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How does 1D Schrödinger equation arise out of the postulated 3D Schrödinger equation and solving 1D particle using 3D Schrödinger equation?
I've stumbled upon this question when I was trying to solve the Schrödinger equation for a particle confined to a 1D line with some given time independent potential $V(x)$.
The energy eigenstates ...
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How many dimensions are in string theory? [duplicate]
How many dimensions are in string theroy? I heard that there are 11 but to my understanding, there is an infinite, also can strings be on a 2D plane?
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Does the distance between two objects of mass not matter when measuring strength of gravity in one-dimensional space?
From all that I have heard about Newton's Law of Universal Gravity, one fact, which I find quite interesting, is that the distance between the two objects of mass is squared and not cubed due to our ...
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What are dimensions and how are they defined? [duplicate]
We all study dimensions as a topic in physics in which we are taught the dimensions of different physical quantities but I don't understand what is the connection between the things that we study ...
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Is there a true one-dimensional object? [closed]
I'm reviewing and expanding my knowledge of dimensions.
We live in three spatial dimensions but, apart from volume, we also have the concept of surface and curve. However, if you write a line on paper,...
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How to prove that the Brachistochrone problem could be reduced to finding a curve on a plane?
Given two points in space, the 2D Brachistochrone problem could be solved to give solution of a cycloid. I am wondering how could one prove that in arbitrary dimensions ($d\geq 3$) with a 1D uniform ...
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Can you naïvely reduce the dimensionality of a QFT?
I want to study a QFT, given by an action $S$ which is defined in $(2+1)$ dimensions, i.e.
$$
S=\int d^3x \mathcal{L}[\phi,\,\partial\phi].
$$
This QFT is invariant under rotations, i.e. in radial ...
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Relation between the number of curvature functions and dimensions in GR
I am reading Weinberg's Gravitation and Cosmology. On page 10, it reads
In $D$ dimensions there will be $D(D+1)/2$ independent metric functions $g_{ij}$, and our freedom to choose the $D$ coordinates ...
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Electromagnetism in 2+1 dimensions?
Consider the Lorentz group $SO(2,1)$ in 2+1 spacetime dimensions. It's little group for massless particles should be just "$SO(1)$", which is just a trivial group with an identity element. ...
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Mechanics/Statics: How to decide which statics problem can be modeled/solved in 2D or 3D? What are the steps to identify the dimension?
I am a first year mechanical engineering student. In statics we learn to solve/model different problems (free body diagram, sum of forces in $x/y$ etc...) in 2D and in 3D. But how to think about 2D? ...
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Action formalism of braneworld gravity and effective field equation on the brane
Is it possible to derive the effective gravitational field equation on the brane by simply varying the action?
Context: The popular way to derive that equation is by starting from Einstein's field ...
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Tensor densities in 1 dimensional space
When we consider a 1 dimensional manifold, is a scalar density with weight (-1) the same as a covector?
In particular, in a theory of gravity, if we consider $\sqrt{-g}$, with $g=\det(g_{\mu \nu})$, ...
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The Lebesgue covering dimension of the Cosmic String interval topology
Take the spacetime $(M,g)$ that satisfies Einstein's Field Equations exactly where $g$ is locally:
$$g= - c^2 dt^2 + d \rho^2 + (\kappa^2 \rho^2 - a^2) d \phi^2 - 2 ac d\phi dt + dz^2 \ $$
in the ...
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How small can we measure space? [closed]
I got this question after looking into transcendental numbers and I noticed how there are some distinctions that should be made from numbers and reality especially in measurement of length for example ...
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3D manifestation of a higher dimensional object
The starting points of this theorical exploration are the following.
I do believe we exist in a universe where 10 (or 11) dimensions do exist, but the ones beyond 3 spatial + 1 time are compactified.
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Scalar spherical harmonics in $S_n$
In the Kaluza klein reduction we can "decompose" the spacetime $M_n$ as $M_n = M_4 \otimes K_d$, in which $K_d$ is a compact spacetime. So, functions like a scalar $\phi(x,y)$ can be ...
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