170 votes
Accepted

Why does the LIGO observation disprove higher dimensions?

I’m the lead author of the paper. Thanks for being interested in the work! Your question is a good one. Really, our work can’t say anything about extra spatial dimensions if they’re not doing anything ...
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  • 1,116
64 votes
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Why does moving through time not require energy?

Moving through space at a uniform pace does not require energy, or force (Newton's 1. law), but accelerating through space does (Newton's 2. law). Similarly, moving through time at a uniform pace does ...
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  • 10.4k
51 votes

Are the units of energy the same in higher dimensions?

Suppose for a moment that we're specifically interested in the kinetic energy of a single, non-relativistic particle, so that $E=\frac{1}{2}m\vec{v}^2$. I include the vector notation for the velocity ...
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49 votes

If I squeeze something really hard, will it ever become two-dimensional?

From a mathematical point of view you will never make something two dimensional by squeezing it because it will always have a thickness greater than zero. The limit would be something like graphene ...
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45 votes
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Why do physicists say that spacetime is not bending "into" or "out" of a fourth dimension?

You can always embed a (spacetime) manifold in a sufficiently high-dimensional space (if you have a $d$ dimensional manifold it can be embedded in a space of $2d$ dimensions). But that doesn't specify ...
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41 votes

Does it make sense to say that something is almost infinite? If yes, then why?

Almost infinite can make a lot of sense in physics. There isn't a precise definition but I would interpret it as the following: when something is 'almost infinite' the properties we are considering ...
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39 votes
Accepted

Is the "spacetime" the same thing as the mathematical 4th dimension?

Yes, time can be treated as a fourth axis- that idea was developed by a German mathematician called Hermann Minkowski not long after Einstein published his theory of special relativity (Minkowski was ...
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  • 20.1k
38 votes

What exactly is a dimension?

Coming from a math perspective, I would define a dimension as "any property which is orthogonal to all other properties." "Orthogonal" here means you cannot get to one property by applying scalar ...
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36 votes

Why does the LIGO observation disprove higher dimensions?

It doesn't disprove all possibilities for higher dimensions - technically, you can't really disprove something so broad because there's always another way to phrase it that will put it out of reach of ...
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35 votes
Accepted

Why is quantum mechanics called 0+1 dimensional QFT?

In field theory, a field can be thought of as a map from the spacetime $M$, usually a Lorentzian manifold---a particularly popular choice is $\Bbb R^{1,n-1}$ (Minkowski space)---to some other space. ...
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  • 15.8k
35 votes
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Could mass just be light moving in another dimension?

In order to illustrate the difficulties associated with such an approach, I will mention an example. One way to obtain a toy model according to your requirement is Kaluza-Klein theory, which assumes ...
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  • 6,940
33 votes

Does it make sense to say that something is almost infinite? If yes, then why?

"Almost infinite" is a sloppy term that might be used to mean "effectively infinite", in a given context. For example, if a large value of $x$ in $y = 1/x$ produces a value ...
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  • 24.1k
31 votes

If I squeeze something really hard, will it ever become two-dimensional?

By your own definition, "one atom thick" is not two dimensional. In that case, you would have to squish something so hard that the atoms stop existing. In which case it is not two dimensional any ...
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  • 117k
31 votes

How many dimensions does electricity have?

Ask her how many dimensions a garden hose has. A remarkable amount of electricity is well modeled using a garden hose as a metaphor. You have solid analogues for current, voltage, and resistance. ...
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  • 43.1k
30 votes
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Basis for the Generalization of Physics to a Different Number of Dimensions

Great question. First of all, you're absolutely right that until we find a universe with a different number of dimensions in the lab, there's no single "right" way to generalize the laws of physics ...
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  • 41.9k
29 votes

What exactly is a dimension?

In this context, I usually explain it (non-mathematically) by saying that the number of dimensions is the number of values you need to specify where an event occurs. For most people this involves ...
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  • 7,069
29 votes

Triviality of interacting QFT

One can get a physical sense of the theory might be trivial in more than four dimensions by thinking of the trajectories of the $\phi$-field particles. In $d$ dimensions two geometric objects of the ...
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  • 42.6k
26 votes

Without saying "cross product" explain why there is a skew-symmetric angular momentum tensor

Rotation is more intimately related to notions of area and planes than it is related to length or lines. Consider Kepler's second law, which says that the line between a planet in orbit and the focus ...
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  • 2,761
25 votes
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How many dimensions does electricity have?

Here's an idea for what you maybe could say: Well, there are kind of two "types" of things in the world. First, there are physical objects, like you, me, this house, and so on (here she might chime ...
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  • 6,828
24 votes

Why do physicists say that spacetime is not bending "into" or "out" of a fourth dimension?

I would say the answer is just the scientific principle of parsimony: if an empirically inconsequential entity can be dropped from a theory, it is preferable to drop it. As you have pointed out, the ...
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20 votes
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Are atoms unstable in $d\geq 4$ spatial dimensions when quantum mechanics is taken into account?

First of all, note that different authors disagree on what should be the Coulomb potential $V$ in $d$ spatial$^1$ dimensions. We will assume that it satisfies Gauss's law, i.e. $$ V(r)~\propto~\left\{\...
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  • 172k
20 votes
Accepted

How does the LHC explore extra dimensions?

First, no evidence for other dimensions has been found. However, there are ways for particle colliders to detect other dimensions. One of the main ones is to see if any energy "disappears" under ...
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  • 6,828
20 votes
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Why are the generators of rotation in the 4-dimensional Euclidean space correspond to rotations in a plane?

Does it mean that a given rotation in 4-dimensional Euclidean space cannot be associated with a unique axis ($\hat{\textbf{n}}$) of rotation? If yes, why is that the case? Yes, this is absolutely ...
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20 votes
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Proof of Coulomb's law in two and higher dimensions

As with all derivations, it depends on what you want to treat as fundamental. Typically we would derive Coulomb's law from the Maxwell equations, so we're trying to solve $$\nabla\cdot \mathbf{E} = -\...
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  • 53.9k
18 votes
Accepted

Is it possible to generalize the Maxwell equations to higher dimensions?

Maxwell's equation can be given in the form $$\text dF = 0$$ $$\text d\star F + J = 0$$ where $F$ is a 2-form and $J$ an $n-1$-form (a current density) which in principle can be generalised to any ...
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  • 9,309
18 votes

In a universe with four spatial dimensions would there be elementary particles with intrinsic isoclinic spin?

A sketch of how spin arises in particle physics. There is a theorem in quantum mechanics, called the Coleman-Mandula theorem, that tells you that under very reasonable assumptions, the most general ...
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18 votes

Basis for the Generalization of Physics to a Different Number of Dimensions

Here is one line of reasoning: E&M is supposed to be a fundamental theory. Having an action principle may facilitate developing a consistent quantum theory. The structure of the Maxwell Lagrangian ...
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  • 172k
18 votes
Accepted

Counting independent components of the Riemann curvature tensor

The $n^2(n^2-1)/12$ comes from the symmetries of the Riemann tensor and the algebraic Bianchi identity. $R_{abcd}$ is antisymmetric in $ab$ and in $cd$. This means that these pairs of indices can ...
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  • 50k
17 votes

What is known about the hydrogen atom in $d$ spatial dimensions?

A nice overview of the problem is given in arXiv:1205.3740. I'll summarise the most important points here. Let $d$ be the number of space dimensions. Then the Laplace operator is given by $$ \Delta=\...
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17 votes
Accepted

Does the CPT theorem hold for all spacetime dimensions?

With one minor qualification, the answer is yes: the CPT theorem holds for all spacetime dimensions. The qualification is that the P in CPT should be interpreted as a reflection of an odd number of ...
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