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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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A thought about extra dimensions [on hold]

Under dimensional reduction, for instance, we get a diluted gravitational constant: $$G_N(4D)=G_D/V_D $$ Usually, the argument of dimensional reduction compactifies extra dimension on torus or higher ...
3
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2answers
95 views

Is there a higher dimension analogue of Noether's theorem?

So I have recently read the proof of Noether's theorem from the book variation calculus by Gelfand. Basically, what I have already seen is that for any single integral functional, if we have a ...
2
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1answer
68 views

Interacting conformal field theories in spacetime dimensions higher 6?

Are there any papers which directly tackle the question of whether or not there exists interacting CFTs in spacetime dimensions higher than 6? It has been proven that there do not exist any ...
3
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2answers
83 views

Meaning of $n+1$ dimensions

Is there anything mathematically significant about studying a theory in $n$ dimensions or $m+1$ dimensions if $n=m+1$? For instance in the context of general relativity I hear people talk about the ...
4
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1answer
75 views

Nonrelativistic Quantum Mechanics Results Implying Analogous QFT Results?

One particularly fascinating example of this I have found is the following. The delta function potential has no effect in nonrelativistic quantum mechanics in spatial dimensions greater than or equal ...
3
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2answers
128 views

Triviality of Yang Mills in $d>4$?

It has been proved that the $\phi^4$ theory is trivial in spacetime dimensions $d>4$. By trivial I mean that the field $\phi$ is a generalized free field, or in other words, it's only nonzero ...
3
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2answers
69 views

Spatial and temporal dimensions orthogonality

It seems that the spatial dimensions are orthogonal: a particle can move along one axis without changing its position in relation to other two axes. It seems that the temporal dimension is somewhat ...
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1answer
48 views

Time difference between all particles and waves [closed]

Since all elementary particles and waves were created simultaneously in the big-bang (t0) would there be any time difference between any interacting elementary particles and/or waves after t0? I'm ...
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0answers
23 views

What is the simplest possible explanation of the String Theory? [duplicate]

I was recently reading through 'The Little Book of String Theory' by Steven S. Gubser, and found it too complicated. Now, some people may say that the string theory is meant to be complicated as even ...
2
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2answers
111 views

Relativity in 2+1 or 4+1 dimensions

Whereas we have experience of relativity working with 3 spacial dimensions and one of time would there be similar rules affecting a two dimensional space and one of time or even with a 4 space and 1 ...
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1answer
28 views

Respect to What Time is Calculated in Space

This may be the silly and stupid question but I have read that time appears to move slower near massive objects because the object's gravitational force bends space-time and the phenomenon is called ...
2
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0answers
56 views

Possible extra term in the Gauss-Bonnet Action

Is it possible to add a term like $\epsilon_{\alpha\beta\gamma\delta}R^{\alpha\beta}_{\enspace\mu\nu}R^{\mu\nu\gamma\delta}$ to the Gauss-Bonnet action in higher dimensional theories of gravity? Or ...
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2answers
102 views

Maxwell's equations in differential form in 2-space+1-time dimensions

How does one write maxwell's equation in 2+1 dimensions? It becomes particularly interesting as the components of 2 forms and 1 form are 3. Are there any sources for this?
2
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1answer
120 views

Problems with Twistor theory

Penrose developed a theory called "twistor theory" that tries to describe the universe using twistors. (https://en.wikipedia.org/wiki/Twistor_theory) From what I've read, there are a lot of papers ...
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1answer
48 views

Are the “extra dimensions” in string theory universal?

Are the extra (compactified) dimensions from string theory universal, in that any particle/field with a sufficiently small enough wavelength will be able to propagate through them? The reason I want ...
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0answers
26 views

What would be the Schwarzschild radius of an $n$-dimensional black hole? [duplicate]

The Schwarzschild radius of a 3 spatial dimensional black hole is 2GM/c^2. What would be the Schwarzschild radius of an n dimensional black hole according to Einstein's field equations having n x n ...
2
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0answers
58 views

Are there supersymmetry algebras with higher spinor representations?

The super-Poincare algebra contains supersymmetry generators $Q^I$ which satisfy fermionic anticommutation relations. By the higher-dimensional analogue of the spin-statistics theorem, they must ...
15
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1answer
285 views

What is the spin-statistics theorem in higher dimensions?

In $d = 3+1$ dimensions, the spin-statistics theorem states that fermionic particles have half-integer spin and bosonic particles have integer spin, in a well-behaved relativistic quantum field theory....
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0answers
44 views

What's the difference between internal spaces and extra dimensions?

From a geometrical perspective, we attach a copy of our gauge groups (e.g. $U(1)$ to each point in spacetime. Since Lie groups are manifolds we can, therefore, imagine that there is a little circle, ...
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2answers
71 views

Could we use experimental evidence of micro black holes to prove the existence of additional spatial dimensions?

They are planning to create a new particle accelerator that can smash particles together at a much higher energy than the LHC. If in the process we observe the decay of a micro black hole, would that ...
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0answers
22 views

Group velocity in different dimensions

I am given the following equation for the group velocity in one-dimension: $$v_g = \frac{d\omega}{dk}.$$ In solid state physics one has $-\pi/a \leq k \leq \pi/a$ for a one-dimensional lattice with ...
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0answers
49 views

Kaluza-Klein approach and Gauss-Cadazzi approach

Can you tell me the difference or physical application of Kaluza Klein approach and Gauss Codazzi approach? In Kaluza Klein theory, 5 dimensional theory can be dimensional reduced to 4 dimensional ...
6
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1answer
149 views

Spacetime has an infinite number of choices for differentiability. Coincidence?

Spacetime can be modelled using a four-dimensional topological manifold. Say we denote the manifold using $(M, \mathcal{O})$ where $\dim M =d$. The structure $(M,\mathcal{O})$ is not sufficient for ...
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1answer
29 views

How could we extend Kuramoto Model to Arbitrary Dimensions?

The generalised version of a theory describing synchronisation in an ensemble shows that coherence arises differently depending on whether the number of dimensions is even or odd. But how could you ...
2
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1answer
89 views

Gamma matrices in (2+1)

I am sure that is very well-known question and see on this site several similar questions but I would like to specify the answer 1) I know that in $(2+1)$-dimensions one can construct $\gamma$-...
1
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1answer
47 views

Is there a way to separate 2D from 3D? [closed]

When we see object around us in space, we can always interpret those in 2D, by considering them to pass through a plane, its only when we interact with those objects do we realise that it is 3D, is ...
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0answers
42 views

Bound on large extra dimensions using gravitational waves

Are there proposed observations using gravitational waves which put a bound on the size of large extra dimensions (say in the context of ADD model)? The claim in the ADD paper is that you cannot ...
2
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0answers
107 views

Why $\kappa = 8 \pi G$ in $D$ dimensional spacetimes?

Probably another question without an answer! ;-) In most books/papers I saw on General Relativity, everybody writes $\kappa = 8 \pi G_D$ in the right part of Einstein's equation, even for spacetimes ...
3
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0answers
46 views

Debye screening in $\mathbb{R^d}$

Consider the Poisson-Boltzmann equation $$ \nabla^2 V(r) = -\frac{1}{\epsilon_0}en\left(1 - e^{e V(r)/k_BT}\right) $$ which models the electrostatic potential in a spherically symmetric ideal gas of ...
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0answers
75 views

Natural classification of fundamental constants of Nature

I was wondering about the fundamental constants of Nature since several years, and still pondering on them. Of course, I have read a lot of papers on them, but never found any satisfying ...
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0answers
61 views

What would the periodic table look like in 2 spatial dimensions? [closed]

I looked at this question https://worldbuilding.stackexchange.com/q/13094/, and I think it answers part of my question about how atomic physics would work, but I'm not sure. How many orbitals would ...
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0answers
17 views

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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2answers
102 views

Why do we say the three-dimensional space is flat (in Physics)? [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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2answers
55 views

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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1answer
123 views

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 ...
2
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1answer
84 views

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
169 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 ...
2
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1answer
72 views

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
69 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-...
4
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1answer
78 views

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
43 views

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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0answers
59 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
48 views

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
45 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 ...
31
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2answers
3k views

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
73 views

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
41 views

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
113 views

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....
91
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3answers
9k views

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 ...