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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4
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0answers
43 views

Same number of independent parameters for $SO(n)$ and $O(n)$ [migrated]

Why is the number of independent parameters for $SO(n)$ and $O(n)$ same, in spite of an additional constraint of unit determinant for $SO(n)$?
3
votes
3answers
209 views

Is it time or duration? [on hold]

Taking this post: "Is there a proof of existence of time?", as a starting point. Therein was mentioned that there is confusion between: "time" and "flow of time". There was a comment (of mine) that ...
1
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0answers
31 views

Could a fourth dimension be “spatially simulated” one point at a time by using movements?

I wonder if time and movement can be translated into a simulation of an extra spatial dimension. At least in one point at a time. I'll try to explain. Imagine a fixed probe which measures the ...
1
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1answer
59 views

Instantons as a -1 dimensional object

I don't know much about Instantons, and looking through the Wiki page it seems like one must have a lot of knowledge about QFT to understand them. However recently I've encountered a statement (which ...
1
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1answer
29 views

Robertson-Walker metric and stable orbits

The RW metric is defined using 4 spatial dimensions, but stable planetary orbits require 3 spatial dimensions. Does this indicate a problem with the assumption of the RW metric to describe the cosmos? ...
8
votes
4answers
2k views

Could negative dimension ever make sense?

After some quick check I found that negative dimensions are not used. But we have negative probability, negative energy etc. So is it so likely that we won't ever use negative dimension(s) ? Update ...
5
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2answers
736 views

Does the Hilbert space of the universe have to be infinite dimensional to make sense of quantum mechanics?

Does the Hilbert space of the universe have to be infinite dimensional to make sense of quantum mechanics? Otherwise, decoherence can never become exact. Does interpreting quantum mechanics require ...
0
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3answers
1k views

If we had three eyes, would our visual perspective be fourth dimensional?

If one covers up one eye, then he loses depth perception (two dimensional perspective). When we uncover that eye, we can now see depth (three dimensional perspective). My question is if we had four ...
1
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1answer
37 views

Coordinates of the extra dimensions

If we live in more than three spatial dimensions, is it not right to conclude that all matter observable to us shares almost the same coordinates of extra dimensions. Or is it just that ordinary ...
1
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1answer
133 views

A two-dimensional event horizon?

Today, I came across an article which says that the Universe began with the collapse of a 4-dimensional [spatial] Universe. Well, I don't know if there's any way to confirm these like it is with all ...
0
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1answer
84 views

Why doesn't the number of space dimensions equal the number of time dimensions?

It seems as though symmetry is a driving force behind theoretical physics. With symmetry in mind, should we expect that the number of time dimensions should be the same as the number of spatial ...
11
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7answers
2k views

Experimental evidence of a fourth spatial dimension?

As human beings, we observe the world in which we live in three dimensions. However, it is certainly theoretically possible that more dimensions exist. Is there any direct or indirect evidence ...
-3
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0answers
33 views

What is string theory? [duplicate]

What is string theory? By that I mean: Why has the theory, as I have heard, postulated multiple dimensions outside our reach, and How does its mathematical proof account for this?
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2answers
50 views

Is any one compact dimension for one particle the same as for another particle?

In the 3+1 dimensions of everyday life and GR particles can share the same extended dimensions. Probably all particles share the same 3+1 dimensions. In string theory compact dimensions seem to be ...
-3
votes
2answers
170 views

Can quantum entanglement be a proof of a 4th spatial dimension?

What I know about quantum entanglement is almost nothing. What I know can be resumed to: "two particles created together have a correlated behaviour no matter the distance between them". This is ...
2
votes
1answer
195 views

Can the compactified dimensions of M-Theory/String Theory become uncurled?

Is it possible for the curled dimensions described in superstring theories to become uncurled and open up. I have read that the big bang could have been the uncurling over 3 dimensions through ...
2
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3answers
898 views

What could we observe if we see a 4 dimensional object and how could it change our physics view about our universe?

My question is little bit philosophical. I would like to explain my ideas with a 2 dimensional universe model. If we had lived in 2 dimensional universe like a plane, What could we observe when ...
0
votes
2answers
45 views

Straight line on 8-axis [closed]

How would a straight line appear in a 8-axis co-ordinate system. Will it continue to look like a straight line or will it appear like zig-zag line. We can see that straight line appears like a dot in ...
0
votes
0answers
40 views

Compactification and off-diagonal terms of the metric tensor

In standard 3+1 dimensional spacetime, the metric tensor is of order 4 and had ten independent coefficients, hence there are 6 terms off the diagonal in the corresponding $4\times 4$ real symmetric ...
3
votes
2answers
178 views

Why time is considered a dimension?

Why time is considered to be a dimension? And the other 7 (except the 3 dimensions of space, and the dimension of time) dimensions that string theory suggests, why can't they be realized?
4
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2answers
2k views

What does the Reynolds Number of a flow represent physically?

What does the Reynolds Number of a flow represent physically? I am having trouble understanding the meaning and the utility of the Reynolds number for a certain flow, could someone please tell me how ...
3
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0answers
33 views

Structure of Hilbert Space in Bosonic String Theory

My question is about the canonical quantization of free bosonic string theory as described by Green, Schwarz & Witten. There they use spurious states to calculate a value for the ambiguity ...
2
votes
1answer
37 views

Creating a 3-D object from 2-D objects

I'm reading a book, 'Warped Passges' by Lisa Randall. In it she mentions how we can envision higher dimensions by explaning how higher dimension ojects can be created from lower dimension objects. So ...
6
votes
3answers
83 views

Is there any intuitive interpretation of compactification?

Obviously the question's title has an unspecified subtext: intuitive to me. Some background to pitch the discussion appropriately: I have a broad understanding, more qualitative than quantitative, of ...
1
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1answer
42 views

Duality in arbitrary finite dimension using the Levi-Civita tensor

In 4-D flat metric E&M context, given a rank $p$ tensor, one can construct dual of $4-p$ rank tensor by Levi-Civita tensor. Here dual is not in the same sense of mathematical dual. I do not know ...
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1answer
106 views

Are subatomic partices n-dimensional hyperspheres or another n-dimensional shape?

This guy derives the formula for the volume of an n-dimensional hypersphere, which can also be found here on the Wikipedia page, and he shows that it is equal to this equation: $V_n = ...
-2
votes
1answer
84 views

Why and how the Universe has (at least) 3 spatial dimensions [closed]

We are conscious to live in a 3 dimension universe. Maybe it has more than 3 spatial dimensions (like the 10 mentioned in the string/M-theory) but that is not my concern here. My question is the ...
1
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1answer
67 views

Is it reasonable to visualise an additional dimension of time as a part of 4th dimensional spacetime

[EDIT] In the spirit of asking a "good question", this question is considerably more refined that the one I decided to blurt out earlier thanks to a little additional research and nudges from ...
0
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1answer
135 views

Our universe the surface of a 4-dimensional sphere?

The cosmic microwave background that we observe uniformly around us is usually explained by assuming that our universe is the surface of a four dimensional sphere. That way the uniformity makes sense ...
2
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3answers
192 views

Number of Parameters of Lorentz Group

We embed the rotation group, $SO(3)$ into the Lorentz group, $O(1,3)$ : $SO(3) \hookrightarrow O(1,3)$ and then determine the six generators of Lorentz group: $J_x, J_y, J_z, K_x, K_y, K_z$ from the ...
1
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1answer
38 views

If QFT is a sum over 1-D topologies and String Theory over 2-D topologies, what is the corresponding theory for N-D topologies?

My understanding is that perturbative QFT can essentially be described as a weighted sum over 1-D topologies (ie Feynman graphs), and String theory is essentially the generalization to a sum over 2-D ...
0
votes
1answer
63 views

Is there no fourth dimension (time) in the universe? [closed]

In this article (and numerous others) http://phys.org/news/2011-04-scientists-spacetime-dimension.html and http://www.rebelscience.org/Crackpots/notorious.htm they suggest that there is no time ...
8
votes
6answers
515 views

More than one time dimension

We know that space-time dimensions are 3+1 macroscopically, but what if 2+2? Obviously it is tough to imagine two time dimensions, but mathematically we can always imagine as either having two ...
2
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0answers
37 views

Hierachies of AdS/CFT holographies

One of the most disturbing aspects of General Relativity is the 'Marble versus Wood' duality of the theory: Matter creates curvature, and curvature doesn't create curvature (at least not directly) ...
15
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3answers
660 views

Has the concept of non-integer $(n+m)$-dimensional spacetime ever been investigated by theoretical physicists?

The following image serves to aid the reader in understanding the "privileged character" of $3+1$-spacetime. The wikipedia article on spacetime, and the sub-article "The priveleged character of ...
2
votes
1answer
113 views

Quantum Field Theory with (2,2) metric

Does someone know some reference which treats QFT in a space with the following non-Lorentzian signature: $g_{\mu\nu}=\text{diag}(-1,-1,1,1)$. I'm interested in basic stuff like the shape of the ...
-5
votes
2answers
93 views

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?
3
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3answers
5k views

Is imagining 10 dimension video by Rob Bryanton has any invalid/wrong information?

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 ...
12
votes
1answer
301 views

How can two time theories be compactified to 3+1 without any Kaluza-Klein remnants

I have recently been looking into the two-time theories and the implied concepts. For me this seems slightly hard to grasp. How can I see the basic concept in this theory in a fundamental way based ...
5
votes
2answers
375 views

Need explanation for a sketch of various spacetime dimensions

I came across this picture/sketch on the internet, however there is no any explanation about it: What is "UNPREDICTIBLE"? "UNSTABLE"? "TOO SIMPLE"? "elliptic", "ultrahyperbolic"??
5
votes
2answers
72 views

Number of supersymmetric charge and the meaning of $\cal N$

I have been thinking about the definition of the notation $\cal N$ and its relation to the number of supercharges in SUSY, but still feel a little confused. In dimension 2, we usually denote, for ...
0
votes
1answer
48 views

Dimension of gamma matrices in higher dimensional Dirac equations

Reading about Dirac's equation in higher dimensional space-times I have read that the gamma matrices are $2^{[D/2]}\times{}2^{[D/2]}$. So, if we have $D=11$, for example, how is this formula supposed ...
1
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1answer
112 views

Can “state” be considered a 5th dimension?

I searched for an answer to this question on Google but just found articles that mention either string theory or a 5th dimension in passing (such as Maxwell equations as they relate to Riemann ...
33
votes
6answers
2k views

Is 3+1 spacetime as privileged as is claimed?

I've often heard the argument that having 3 spatial dimensions is very special. Such arguments are invariably based on certain assumptions that do not appear to be justifiable at all, at least to me. ...
6
votes
0answers
153 views

Why dimensionality of the Electric Charge varies with the spacetime dimensions?

The point is: We can find via dimensional analysis that the electric charge dimensionality varies with the dimension of space-time. $$[\text{charge}] = eV^{(3-D)/2}$$(You can see below the way I did ...
3
votes
1answer
139 views

How can one learn to visualize 4 dimensional spacetime?

I was watching Professor Leonard Susskind's lecture on Quantum Entanglements and he said that there are physicists and people who study physics, who 'rewire' themselves so they can visualize 4 ...
2
votes
1answer
89 views

Where do our 4 macroscopic spacetime dimensions reside in multidimensional models of the universe?

In models such as M-theory with 7 'higher dimensions' plus the 4 macroscopic spacetime dimensions, where do our 4 macroscopic spacetime dimensions reside ordinally? My reason for asking is TV shows ...
6
votes
4answers
526 views

Measuring extra-dimensions

I have read and heard in a number of places that extra dimension might be as big as $x$ mm. What I'm wondering is the following: How is length assigned to these extra dimensions? I mean you can ...
4
votes
3answers
217 views

What Does it Mean for an Extra Dimension to Have Size?

Recently I watched this presentation by Brian Greene on string theory. In it he describes how the reason we don't observe the extra dimensions required by string theory could be because they are very ...
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3answers
160 views

Quantum entanglement: does it necessarily imply superluminal information transfer? [duplicate]

From what I understand, information is communicated instantly between two quantum-entangled particles regardless of the spatial distance between them. However, does this necessarily imply superluminal ...