# Tagged Questions

Use this tag for dimensions of a manifold, typically the space-time. DO NOT USE THIS TAG for dimension of a physical quantity.

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### Dimensionality of Hilbert space

Simple question, but I can't seem to find the answer searching very easily. Does the dimensionality of a Hilbert space correspond to the number of possible states a system can take on? ("The system" ...
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### What are the fundamental problems of being in a 2 dimensional world?

I was reading through Stephen Hawking's explanation of two - dimensional space. In that he mentioned that it will be very difficult to design a living being that could exist only in 2 dimension. What ...
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### Extra dimensions and the big bang [duplicate]

If there were extra compact dimensions,and at the big bang all dimensions were compact,my question is why the big bang failed to expand those presumed extra dimensions like it did with the 3 spatial ...
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### Mass of particle w.r.t. dimension

I heard in a lecture recently - just as a comment - that a particle which is massive in say $D=4$ can be seen as a massless particle in higher dimensions and vice versa. Our prof didn't give any ...
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### Doubts regarding dimension of a system:Definitions and algorithms

I need to do phase reconstruction from time series data. In doing so, I encountered Takens' embedding theorem and Cao's minimum embedding dimension $d$ by nearest neighbor method. In paper "Optimal ...
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### How does the warping of time behave as a fourth dimension?

My problem is that I have a hard time grasping something if I can't conceptualize it, though maybe this can not be conceptualized, just accepted, in which case I thank you for your patience. The ...
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### Key difference between 3D and 4D solutions

In many papers in theoretical physics especially in the more advanced theories, I notice that physicists solve problems in 3 dimensions (2 spatial+ 1 temporal). In some specific papers (I can't seem ...
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### Why is space-time four dimensional?

Wikipedia says, "In special relativity, four-momentum is the generalization of the classical three-dimensional momentum to four-dimensional space-time. Momentum is a vector in three dimensions; ...
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### Is it possible to project a problem of mechanics in a lower dimensionality?

I had the intuition that, in classical mechanics, when the trajectory of a body is known, then analysis of its motion can be done in the linear space of that trajectory, if all forces are projected on ...
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### Could we see a lower dimension within our universe? [closed]

My question refers to the fact, that, say if our universe were to be sitting on a 4 (spatial) dimensional plane, that we cannot see, then within our universe could there be a point mass in which 1 or ...
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### 3 Questions about modern Physics [closed]

First i'd like to apologize for both my writting skills (i'm not english) and for my physics knowledge (being them very basic and/or naive). With general relativity from Einstein, gravity is no ...
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### Why does one of the extra dimensions of F-Theory have to be a temporal dimension?

F-Theory, as I understand it, is a realisation of Type IIB String Theory as a 12-dimensional theory in such a way that the $SL(2,\mathbb Z)$ symmetry becomes natural because Type IIB String Theory is ...
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### How can time be a dimension?

In physical terms, dimension refers to the constituent structure of all space and its position in time. Time is same throughout the universe. So, how can time be a dimension?
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### Behavior of black holes in higher- and lower-dimensional space-times

The behavior of black holes in 3+1 dimensional space-time as our own is rather well known: formation, event-horizon size, mass, spin, radiation etc. However, my question is what would black holes ...
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### As 3-dimensional beings, do we really have 3-dimensional vision?

I was watching this video on YouTube of a high school student explaining perception in different dimensions, basically stuff he learned from reading the book Flatand. At one point in the video, he ...
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### Dimension & non - locality problem in string theory

I have some questions with string theory: Why is it that there is exactly 4 large spacetime dimensions while the rest remain small? It is a nonlocal QFT. How could that fit in GR?
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### Does string/M-theory address higher-dimensional membrane vibration modes?

A loop is a 1-sphere that can vibrate in increasingly complex ways as it is embedded in higher dimensional spaces. Does string theory assume that 1-spheres are the only possible vibrating structures,...
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### Bose-Einstein condensation in 3D

I have read in many books that BEC takes place in momentum space and in only 3-dimensions. What is meant by this statement?
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### Should we necessarily express the dimensions of a physical quantity within square brackets? [duplicate]

For example, should we write the dimension of mass, e.g. $\mathrm{kg}$ as $[M]$ or is it enough to write it as $M$?
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### How to prove that we are living in a 3D world?

Is there any scientific experiment that can lead us to conclude we live in 3 dimensions without the premise of the conception of limited dimensions? Thank you all who helped in the improvement of ...
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### What is an $n$ dimensional space? [closed]

How an $n$ dimensional space looks like? Is it possible that we are really in a space of dimension greater than 3?
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### How exactly are Calabi-Yau compactifications done?

To compactify 2 open dimensions to a torus, the method of identification written down for this example as $$(x,y) \sim (x+2\pi R,y)$$ $$(x,y) \sim (x, y+2\pi R)$$ can be applied. What are the ...
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### How is graphene a 2D substance?

How is graphene a 2D substance? It has length, width and some thickness to it, else it would be invisible. Why is it considered a 2D substance?
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### Vectors with more than 3 components

I have some confusion over Vectors, Its components and dimensions. Does the number of vector components mean that a vector is in that many dimensions? For e.g. $A$ vector with 4 components has 4 ...
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### What is *uplift* in respect to extra dimensions and their stability?

What is uplift in respect to extra dimensions and their stability? It's notoriously hard to find something on this, as all possible keyword combinations pull up plethora of unrelated Google hits.
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### To what extent are quantities fundamental?

Arguably the most well-known and used system of units is the SI-system. It assigns seven units to seven ‘fundamental’ quantities (or dimensions). However, there are other possible options, such as ...
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### How many dimensions are there in total? [duplicate]

I happened to get my hands on a string theory book where its been said that the universe's fundamental particle i.e. the string, takes about ten dimensions for specifying itself under symmetry. What ...
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### is gravitational force dependent on objects radius?

I was told that objects with the same mass but different sizes (or densities) will have a different gravitational pull. Is this true? If so, why?
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### Tree level and loop level

I'm trying to read through a paper which explains the following about Universal Extra Dimensions (UED) vs ADD models: The new feature of the UED scenario compared to the brane world is that ...
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### How can Young's modulus be dimensionless, but still have units? [closed]

According to this wikipedia entry: Young's modulus is the ratio of stress, which has units of pressure, to strain, which is dimensionless; therefore, Young's modulus has units of pressure. From ...
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### String theory: why not use $n$-dimensional blocks/objects/branes?

I have a basic question: if we use 1d string to replace 0d particle to gain insight of nature in string theory, and advanced to use 2d membranes, can we imagine that using $3$- or $n$-dimensional ...
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### Is this explanation of “Why nine space dimensions?” correct?

In Gordon Kane's Supersymmetry and Beyond (p. 118), he states: String theory has to be formulated in nine space dimensions or it is not a consistent mathematical theory. There doesn't seem to be a ...
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### Critical Dimension of Bosonic Strings and Regularization of $\sum_{n=1}^\infty n$

If $D$ is critical dimension of Bosonic strings, a particular derivation goes like the following, where we arrive finally at $$\frac{D-2}{2}\sum_{n=1}^\infty n + 1 = 0.$$ Now mathematically this is ...
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### Einstein Field Equations in other space-time dimensions than 3+1?

This question is apparently quite simple but I can't seem to find an answer to it, so I was hopping anyone could clarify me. Are the Einstein field equations (EFE) only valid for a 3+1 dimensional ...
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### the meaning of epsilon in this operator $\epsilon$

Consider the dimensional regularized integral $$\int d^{d}k (k^{2}-m^{2}+i\epsilon)^{-\lambda}$$ For positive $\lambda$ this integral has a pole at $k=m$. Is this the reason we we insert the \$ ...
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### Critical dimension in quantization of p-branes

So I have what might be a fairly basic question, but my understanding that in the quantization of the the string, or the 1-brane, there are conditions on the number of spacetime dimensions to ensure ...
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### Are there real life applications for Hausdorff dimensions, specifically crack formations?

I was curios about Hausdorff dimensions. They seem to neatly describe rough surfaces. So I was wondering if there are common applications of Hausdorff dimensions in things like complicated friction ...
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### A Game Of The Number Of Space-Time Dimensions

Holger Bech Nielsen, one of the founders of string theory, has apparently just played some sort of game between different potential dimensions for space-time and reached the conclusion that D4 wins in ...
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### Units and Dimensions - Use of proportionality constant

In units and dimensions we learn about Establishing a Formula : (example) : to establish a relationship between T (Time Period) , m (Mass) , l (length of the string) and g(acc. due to gravity) - ...
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### Is imagining 10 dimension video by Rob Bryanton has any invalid/wrong information? [closed]

I just watched this youtube video by Rob Bryanton and am wondering that is there anything invalid/wrong in term of real physics. I search for Rob Bryanton and it look like he has not-so-good ...
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### Imaginary time and string theory

Is imaginary time an extra dimension? In other words, are time and imaginary time considered two separate dimensions? If so, does imaginary time appear (as a separate dimension) in string theory (thus ...
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### Why one-dimensional strings, but not higher-dimensional shells/membranes?

One way that I've seen to sort-of motivate string theory is to 'generalize' the relativistic point particle action, resulting in the Nambu-Goto action. However, once you see how to make this '...
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### parallel=time, perpendicular=space? on multiple time dimensions

There are some discussions on more than one time dimensions, e.g., Intuition for multiple temporal dimensions and More than one time dimension. If we define that the parallel direction is time, of ...
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### Can we project a 4D world using 3D video technology?

Traditional movies, TV, etc, faithfully show our 3-dimensional world using 2 dimensions. So can we have a movie that shows a 4-dimensional world using 3D technology?
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### Do we live in an integer dimension?

I have read that there exist non-integer fractal dimensions and the images generated from these dimensions look organic and they seem to provide a new way of describing the world around us, which ...