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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72 views

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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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
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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
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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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1answer
49 views

World of 2-dimensional beings [closed]

In a world of two-dimensional beings, How would a two-dimensional (A) being view another two-dimensional (B) being as? Would they always perceive each other as a straight line?
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3answers
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Dimensions of Physical objects doesn't make sense [closed]

Can you show me a pure 1D or 2D object? A line and a plane have a thickness. A pure 1 D line is one with no width. But if its width is zero, it doesn't exist. Similarly, a 2D plane is perfectly ...
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3answers
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Why does GTR not need a higher dimension to describe the bending of spacetime?

I am a bit confused on how GTR uses intrinsic curvature instead of extrinsic curvature. Maybe it is just a misunderstanding, but I will do my best to describe my question: If we take an object of $n$ ...
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1answer
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The dimension of spacetime in GR [closed]

In SR the 4-divergence of the 4-position gives the dimension of spacetime. What is the dimension of spacetime in GR, i. e, The covariant divergence of the covariant position?
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2answers
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Interacting CFT in $d>6$

There's an expectation that there aren't interacting CFT in $d>6$. As I understand, main reason for this is due to the scaling dimension of ordinary scalar fields and Dirac fields. This lead to ...
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1answer
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Aren't Tesseract Illustrations incorrect as they give volume and surface in the same number of dimension?

From Wikipedia on how to create a tesseract: 0 – A point is a hypercube of dimension zero. 1 – If one moves this point one unit length, it will sweep out a line segment, which is a unit hypercube of ...
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2answers
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Is electric field like a dimension of space? [closed]

We all know the classical four-dimensions used to locate objects in space: Length, width, height and time. It occurred to me that electric field acts also like a kind of dimension does it not? ...
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Transformations in higher dimensions that lead to symmetry

I'm watching Sean Carroll's video on symmetry [relevant section at around 8:05] He talks about 120 degree rotations of triangles that leave them invariant. Then he proceeds to talk about flipping them ...
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Validity of Gauss Law [duplicate]

If the electric field due to a point charge varies as $r^{-2.5}$ instead of $r^{-2}$, then would the Gauss Law still be valid? I infer that the $r^{-2}$ term in the Electric field comes as a result ...
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A doubt regarding discrete spacetimes

Shorter version of a deleted post which hopefully is focused enough to not be closed. Basically, I'd like to ask: How is it that a discrete spacetime (Taking our universe as a basis, of course) can be ...
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Can many-particle wave functions be imagined in 3 dimensions - instead of $3N$ dimensions?

It is usually said that the wave function for $N$ particles cannot be imagined in 3 dimensions, but only in $3N$ dimensions. What is the exact argument? Is there a loophole? Schrödinger, Feynman and ...
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How does one determine the $R$-symmetry group?

As far as I understand it, the $R$-symmetry group is just the largest subgroup of the automorphism group of the supersymmetry (SUSY) algebra which commutes with the Lorentz group. I know for $\mathcal{...
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Does it make sense to say that something is almost infinite? If yes, then why?

I remember hearing someone say "almost infinite" in this YouTube video. At 1:23, he says that "almost infinite" pieces of vertical lines are placed along $X$ length. As someone who ...
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Why did cross product only exist for three and seven dimensions? [closed]

According to this wikipage, The cross product only exists in three and seven dimensions as one can always define a multiplication on a space of one higher dimension as above, and this space can be ...
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4answers
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Triviality of interacting QFT

In this Wikipedia article there are interesting statements: A quantum field theory is said to be trivial when the renormalized coupling, computed through its beta function, goes to zero when the ...
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2answers
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Is it possible for an object with more than 3 dimension to exist in a 3D space? [closed]

I understand that it is possible for 4D objects to exist in a 3-D space. I also speculate that 5D objects cannot exist in a 3D space? Is there a reason to this limitation (assuming there is a ...
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5answers
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If you live in a two-dimensional world, would it be possible to explain the angular momentum? [duplicate]

If you live in a two-dimensional world, would it be possible to explain the angular momentum?
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1answer
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Does the second law of thermodynamics apply to parallel universes or higher dimensional universes? [closed]

Does the second law of thermodynamics apply to parallel universes and universes of higher dimensions?
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2answers
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Limitations/breakdown of Mermin-Wagner Theorem

Mermin-Wagner theorem says that continuous symmetries cannot be spontaneously broken at finite temperature in systems with sufficiently short-range interactions in dimensions $d ≤ 2$. (this is ...
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4answers
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Is physics possible without spacetime dimensions?

One of the most central concepts in physics is energy. But on a deeper level energy is the same thing as information. Classically information about a system is given by spacetime coordinates and their ...
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1answer
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Lagrangian in $D$-dimensions in maximal supergravity

In the paper Dualisation of Dualities. I. By Cremmer,Julia, Lu and Pope they derive the $D$-dimensional lagrangian in terms of the generators $E_{i}^j$, $E_{ijk}$ and $D$, I believe $E_{i}^j$ is the ...
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Is one dimension the same as one space-time?

In this Cern article, https://home.cern/science/physics/extra-dimensions-gravitons-and-tiny-black-holes, it states: "In our everyday lives, we experience three spatial dimensions, and a fourth ...
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2answers
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Are there versions of String Theory formulated in $D$ spacetime dimensions or even in infinitely many dimensions?

There are a lot of different versions of string theory, and almost all of them differ in the number of dimensions. The most famous ones are formulated in 10, 11 or 26 dimensions. But are there any ...
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1answer
72 views

CFT in non-integer dimension

Is it possible to have CFT in non-integer dimension? At first sight, Wilson-Fisher fixed point in $4-\varepsilon$ gives such example. What is known about such theories?
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3answers
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Given that 1D space $\mathbb{R}$ and 3D space $\mathbb{R}^3$ are in bijection, why do we describe our physical world as 3D?

Mostly the reason given is that that three numbers are required to specify a point uniquely in our world. But this is utter nonsense! It has long been mathematically proven that $\mathbb{R}$ is in ...
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1answer
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Why the maximum number of supercharges in supergravity must be $Q=32$?

For a supergravity theory not to have particles with spin greater than 2, all books state that $Q\leq 32$, where $Q$ is the number of fermionic supercharges and for a given dimension $D$ it's related ...
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1answer
67 views

Einstein tensor in Schwarzschild spacetime

If we consider a metric in $n$-dimensional spacetime $$d s^2=-(1-f(r)) dt^2+(1-f(r))^{-1}d r^2+r^2 d\Omega_{n-2}^2,$$ what is the Einstein tensor, $G_{\mu\nu}=R_{\mu\nu}-R g_{\mu\nu}/2$, expressed in ...
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Anomaly inflow mechanism

I know very simple example of anomaly inflow. See section 4.4 in David Tong: Lectures on Gauge Theory. As I read, such mechanism have some applications in condensed matter and in quantum field theory, ...
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1answer
46 views

Relation between units , quantities and dimensions [closed]

If two quantities have the same dimensions, do they represent the same physical content then?
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1answer
43 views

Gravity creating other dimensions [duplicate]

It is a well known fact that gravity can bend space, kind of like a rock placed on a sheet of paper, bending the paper. But, doing this will make another third dimension, that the marble actually ...
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3answers
77 views

Are black holes 0 dimensional? [duplicate]

If black holes are mass of the star concentrated on a single point then how can it be moving through a 3-dimensional space? How can they spin?
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Does Birkhoff's theorem generalize to higher dimensions without additional assumptions?

In the Newtonian theory of gravity, the shell theorem says that the gravitational field inside a massive and spherically symmetric shell is zero. The conclusion is the same in general relativity, as ...
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Dimension of scale, or depth - does it exist?

Description of an object in 3 standard space dimensions seems not to be its full description. Say, the placement of a molecule is described by $x=2N$, $y=4N$, $z=7N$ measurement units in the Descartes ...
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Is there an equivalent of Kaluza-Klein for fermionic dimensions?

Taking GR in $D$ dimensions, one can use the process of compactification to turn this into GR in $D-1$ dimensions coupled to a Yang-Mills field. i.e. you start with spin-2 fields and you and up with ...
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Can one derive charged black hole solution of GR using Kaluza-Klein?

Kaluza-Klein showed that a 5 dimensional gravitional theory with one dimension on a circle, is equivalent in the limit to a 4 dimensional gravitational theory with electromagnetism. So for the ...
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Second dominate phenomenon to effect the speed of time? [closed]

Part of Einstein's Theory Of Relativity is that the faster an object and/or person moves through space, the slower they move through time. What other phenomenon could potentially effect the passage ...
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1answer
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What evidence exists to show that hyperdimensions are spacially perpindicular to the dimensions before it?

I've heard of a tesseract which is supposedly spacially perpendicular to the other 3 dimensions. Is there evidence this is possible in our universe or another?
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1answer
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Is there a theory that proposes the universe is a spacetime bubble within a higher dimensional reality? [closed]

I have heard that one proposal/interpretation of string theory is that, perhaps, extra dimensions exist at minuscule scales. I would conjecture that it is possible for the opposite to be true, akin to ...
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1answer
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Why is the normal argument for fermions/bosons wrong?

If we have a state $\psi(x_1,x_2)$ of two identical particles and an exchange operator $O$ which swaps the particles. Obviously the physics must be the same and hence $O$ can only introduce an ...
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1answer
51 views

Is the dimensionality of space considered a universal constant? [duplicate]

What if the dimensionality was something like 3.0001 or 2.999? Would we be able to tell the difference? I heard about fractional dimensionality in 3b1b and was wondering about its implications for ...
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1answer
69 views

Do Black Strings Violate Black Hole Uniqueness in Higher Dimensions?

Most black string solutions are obtained by adding flat directions to lower dimensional black holes, for instance in the Gregory-Laflamme instability argument. I had the following question; Is this ...
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How can extra dimensions be small?

I have a super basic gap in my understanding of the theory of extra spacial dimensions - one piece of the explanation that never felt right. As I've heard it, it's theorized that there may be extra ...
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1answer
58 views

Trajectories of Free Particle in (3+1) Dimension

It is often mentioned that due to long range attractive forces in 4D spacetimes, the particle trajectory at large time t looks like: $$r(t) = v*(t+ c_1 \ln(t)).$$ I'm interested in understanding how ...
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How exactly does spacetime change inside a black hole? [closed]

There are a few coordinate systems to describe the inside of the BH: Schwarzschild, behaves oddly inside the BH Kruskal-Szekeres, space and time do not swap Gullstrand-Painlevé, $t$ is the time ...
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2answers
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Do physical fields always have dimension of the Tangent Space at a point?

Say we only consider classical fields in 3 dimensions. In a 3 dimensional space you have scalar or vector fields, where scalar fields can be understood as vectors of one dimension. The other physical ...

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