# Tag Info

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 ...
• 1,116
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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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### 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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### 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 ...
• 334k
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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 ...

### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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 ...

### 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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### 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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### 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=\...