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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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Superstrings and supermembranes withouth the maximal spin constraint

Can supermembranes exist in higher dimensional superspaces if we admit higher spin fields?
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Cartesian coordinates and reality [on hold]

I'm not a physicist. I watched a great video in which someone described what passing a sphere through 2 dimensions would look like to a 2d being. First is anyone actually looking for higher ...
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Why do we say the three-dimensional space is flat (in Physics) although we have three dimensions? [closed]

This is quote from Hawking's book: The surface of the Earth is what is called a two-dimensional space. That is, you can move on the surface of the Earth in two directions at right angles to each ...
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Strange super script notation $^{(4)}R$ in the textbook Numerical Relativity

In Numerical Relativity by Thomas W. Baumgarte and Stuart L. Shapiro. There are bunch of superscript $(4)$ over $T,\Gamma, R$ i.e. $^{(4)}\Gamma^a_{bc}$ _ $^{(4)}R_{abcd}$ _ $^{(4)}R$ ... (...
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Would a 5-dimensional black hole actually break laws of physics?

I discovered a paper by, Figueras, Kunesch, and Tunyasuvunakool, "End Point of Black Ring Instabilities and the Weak Cosmic Censorship Conjecture." A Cambridge University press release is here. The ...
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1answer
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The action of Einstein Maxwell system for arbitrary dimensions

The question is as mentioned in the title. To write the action for the Einstein-Maxwell system in arbitrary dimension. Is it possible just to add them (The Lagrangian for gravity and for ...
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2answers
145 views

How many eyes are needed to see a four-dimensional world? [closed]

If a four-dimensional world were to exist, how many eyes would a creature minimally need to see it (in three dimensions)? Three? Four? (Bonus question: how should these eyes be spatially configured?)...
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2answers
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Are there any general results about the nodes of energy eigenfunctions in higher dimensions?

A well-known result of quantum mechanics is that for a single particle in one dimension in a bounding potential $V(x)$ that goes to $+\infty$ as $x \to \pm \infty$, the energy eigenfunctions are ...
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1answer
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Is there a higher-level reason why $\nabla\cdot(\hat{\bf r}/r^2) = 0$ in three dimensions but not two? [duplicate]

I am working through Griffiths, Introduction to Electrodynamics, and finding the divergence of the electric field generated by a single charge sitting at the origin. $$\mathbf{E}(\mathbf{r}) = \frac{\...
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1answer
50 views

What does a closed 3-brane look like?

A closed 2-brane looks like a donut, or in scientific terms, a torus. This is a three-dimensional object. I came across this diagram in a book, "The Little Book of String Theory". A torus is a three-...
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1answer
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How do we assign length to dimensions in string theory?

My current understanding of the variations of string theory includes the sentence "string theory needs (at least) 6 extra spatial dimensions to work, but because our observable universe consists of 3 ...
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1answer
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Shining a light on a brane

I am not entirely sure if this question is supposed to be posted on Physics SE, but I'm going to post it anyway. We have been told that shining a light on a three-dimensional object will always ...
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54 views

Can the space-time be a discrete lattice? [duplicate]

I would like to know how much conjectures about the space-time's being discrete are valid. There is a short article here: https://www.meta-religion.com/Physics/Quantum_physics/is_space.htm One ...
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0answers
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What should I learn to understand 6d (2,0) theory? [closed]

I'm a first-year graduate student, I heard that 6d (2,0) theories can provide various dualities between lower dimension field theories, and can give many beautiful results in mathematics. So I ...
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1answer
41 views

General question about dimensionality of the universe [duplicate]

I am a high school math teacher with some basic physic/lay person knowledge. Each year after the AP test, I show the movies Flatland and Sphereland to my calculus classes and talk about the ...
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2answers
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Are the units of energy the same in higher dimensions?

In 3 spatial dimensions, $$[E] = [ML^2 T^{-2}]$$ Would it change in higher dimensions? If yes, then what would be the dimensions for 4 spatial dimensions?
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2answers
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Distance between events at relativistic speeds

The problem: A spaceship is travelling between Mountain $A$ and Mountain $B$, both of which erupt simultaneously as recorded by a scientist on the ground. The mountains are $300 \; \text{km}$ apart on ...
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1answer
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Dilatations and action on derivatives of fields

How do derivatives of fields transform under dilatations? Specifically I am interested on what I misunderstand with the example: Consider a theory that has a field $A_\mu$ that transforms under ...
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2answers
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How can 0-dimensional particles or 1-dimensional strings be 3D matter? [closed]

According to the latest information we got String theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings....
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3answers
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Why does the LIGO observation disprove higher dimensions?

I recently read this article which claims that last year’s LIGO observation of gravitational waves is proof that, at least on massive scales, there cannot be more than three spatial dimensions. I ...
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3answers
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Kaluza-Klein theory metric

What are the physical dimensions of the $5\times 5$ Kaluza-Klein metric? (the metric should be dimensionless but doesn't look so with the inclusion of the four potential and the scalar field)
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Grassmann-odd extra dimensions and gravity

Take a world with $D=3+n$ space-time dimensions, where $n$ are extra space-like dimensions. With extra-dimensional newton gravity $$F=G_N(D)\dfrac{Mm}{r^{2+n}}$$ Can $n$ affect IF the extra ...
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Is simulating the interaction of multiple particles possible in $0$ spacelike and $3$ timelike dimensions?

In multiple time like dimensions it is possible for particles to effect it's own past, and two particles can both be effected by each others future. I tried to simulate the interaction of multiple ...
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1answer
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Why does only gravity leak into extra non-compact dimensions?

This article K. Pardo, et. al., Limits on the number of spacetime dimensions from GW170817, Journal of Cosmology and Astroparticle Physics, Vol. 2018, 2018. which was published recently in JCAP ...
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1answer
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Is it possible to test the physical reality of extra dimensions predicted by string theory?

I have no business asking this question since I am not a string scientist but I like to follow science news in phys.org and I read an article dated today Gravitational waves provide dose of reality ...
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Density of states as a function of dimension: what happens between 3D and 4D?

Consider a parabolic dispersion $\varepsilon_{\boldsymbol q} = \frac{\boldsymbol |q|^2}{2m}$. The two-particle density of states $\rho_2(\boldsymbol k, \varepsilon)$ is zero for $\varepsilon < \...
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1answer
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Why is there a maximum number of supersymmetries?

Where does the NO-GO theorem for a maximum number of supersymmetries come from? I read from here https://en.wikipedia.org/wiki/Supersymmetry that number is 32, and that fixes the number of spacetime ...
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1answer
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Does energy conservation take into account the dimension of time?

We know that there are only 3 spacial dimensions because if we light a light bulb, we are able to measure the energy at any point in the 3 spacial dimensions and we can see that no energy is leaking ...
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2answers
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Can you affect higher dimensions from lower ones?

To make it easier to explain, I'm going to use 2-D and 3-D. Imagine you have a stationary sphere in a 3-dimensional space crossing through a 2-dimensional space (meaning the 2-D perspective has a ...
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0answers
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3 generations as extra unconventional dimensions?

Kaluza-Klein resonances arise in theories with extra dimensions like superstrings or old KK models. Usually, extra dimensions and KK states provide regular spacing in the spectrum. Question: can some ...
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1answer
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Why can't our cognitive sense or five senses sense or fathom hyper-dimensional spaces? [duplicate]

Why can't our cognitive sense or five senses sense hyper-dimensional spaces? Is it because of the way our human body is built?
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What is the critical string?

What is the critical string? From wiki, I found the definition of non-Critical string wiki The non-critical string theory describes the relativistic string without enforcing the critical ...
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How to best describe wave behavior on even dimensions?

Main source: http://www.mathpages.com/home/kmath242/kmath242.htm On this article, as far as I understand, the author claims that wave behavior on even dimensions would give rise to many waves with ...
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1answer
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How can we be sure that there are only four dimensions? [duplicate]

Infants can only perceive in one dimension (closeness and farness). Young children can only perceive three dimensions (they can't plan or handle time). Teenagers and young adults can perceive 3+1 ...
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(2+2)-dimensional flat spacetime with neutral signature [duplicate]

Is there an example of (2+2)-dimensional flat spacetime with neutral signature (i.e. (+,+,-,-))? ...for example the metric $ds^2=(dt_1)^2+(dt_2)^2-(dx)^2-(dy)^2$, has been studied? Are there any ...
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1answer
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Is general relativity about Lorentzian manifolds only?

General relativity is often used in context of Lorentzian manifolds. But the texts which describe Einstein Field Equations discuss them in context of general pseudo-Riemannian manifolds. It seems ...
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1answer
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Spatial dimensions inside the event horizon

Consider a test particle falling radially to a black hole. The radial direction toward the singularity inside the black hole becomes a direction in time while the dimension that used to be time ...
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1answer
118 views

How to define *dynamical* dimensions?

I'm considering a simple toy model. The spacetime is flat with $d$ space dimensions. Using cartesian coordinates, the spacetime metric is Minkowskian : $$\tag{1} ds^2 = dt^2 - dx_1^2 - dx_2^2 - dx_3^...
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1answer
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Path integral in even number of spatial dimensions: does it exist?

The path integral formulation of Quantum Mechanics is related to Huygens principle, as stated by Feynman in his seminal article [1] and widely commented since then. However Huygens principle does not ...
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Lienard-Wiechert fields in D-dimentions

I tried to calculate Lienard-Wiechert fields in D-dimentions and got some expression with sums of derivatives, very ugly. Does anybody have "nice" expression for it?
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1answer
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Is time really a 1-dimensional object that we only traverse through? [duplicate]

Is time really a 1-dimensional object that we traverse || is it possible that time can also be traversed horizontally. I think the later would also put it on a 2 dimensional plane.
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3answers
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What generates the curvature which is necessary for curling-up extra dimensions?

To say it right away, I am not an expert in string theory, but I know well General Relativity. So I wonder how the curling up of extra-dimensions which is assumed in many "Kaluza-Klein" like theories (...
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Dimensions and superstring theory [duplicate]

While I was reading B. Greene 's "the fabric of the cosmos" , There he says that the theory of relativity and quantum mechanics are the two pillars on which modern physics stands, but these theories ...
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1answer
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Why do we assume that Gauss' law of gravitation to remain same even when there are extra spatial dimensions?

Every kid knows that the magnitude of the gravitational force between two point masses is inversely proportional to the square of the distance $r$ between them i.e., $F\sim r^{-2}$. But experimentally,...
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2answers
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A three rank Levi-Civita tensor in four dimensional spacetime

Is it possible to construct a Lorentz invariant, three rank Levi-Civita tensor in Minkowski Spacetime? If not, why so? I am talking about something like this $\epsilon_{\alpha\beta\gamma}$ or $\...
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1answer
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Is 3 spatial dimensions most suitable to life? [closed]

As we're 3 dimensional beings, it's easy to say that the 3rd dimension is the most suitable for life, because we have trillions of examples of 3 dimensional life and no examples for any other ...
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3answers
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How strict are the boundaries that divide dimensions? Is a single-layer sheet of graphene 2D or 3D? [closed]

I would like to know if there is any theory that describes a set of rules that define the boundaries of dimensions. For example, does a single layer sheet made of graphene considered a two or a three ...
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1answer
122 views

Spacetime dimension and the dimension of Clifford algebra

The dimension of the Clifford algebra $C_p$ generated by a vector space $V^p$ is given by $2^p$, where $p$ is the dimension of the vector space (T. Frankel, the geometry of physics). Based on the top-...
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Density of States General Formula

So I have this formula regarding the density of states in 3D and 2D respectively are given by a function of the dispersion relation: $N=\frac18 \frac{4\pi}{3}(V^{\frac13}\frac{k(\omega)}{\pi})^3$ $N=...
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Can Higgs mechanism happen in 1+1D?

How I understand the Higgs mechanism is that, although it is called “spontaneously breaking of the gauge symmetry”, the gauge symmetry is actually not broken in the higgs mechanism and it is the ...