170
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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
52
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 ...
- 35.8k
48
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 ...
- 33.4k
41
votes
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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 ...
- 28.4k
41
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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 ...
36
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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36
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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 ...
- 20.8k
36
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 ...
- 7,554
34
votes
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Why is Spacetime described as flat even though we live in 3 dimensions of space?
"Flat space" means that on large scales, Euclidean geometry holds. All the angles in any triangle drawn in space add up to 180°; the total distance between points separated by $\Delta x$, $\...
- 11.2k
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 ...
- 25k
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. ...
- 51.7k
31
votes
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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 ...
- 52.2k
30
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 ...
- 56.5k
29
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 ...
- 49.4k
27
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 ...
- 5,027
26
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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 ...
- 20.8k
26
votes
Is a 1D universe with a 90° turn 1D or 2D?
It is a 1D manifold. It only takes one coordinate to smoothly label every point.
Furthermore, all 1D manifolds are intrinsically flat. They can have extrinsic curvature, as you described here, but ...
- 109k
25
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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 ...
- 7,087
25
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Is there a true one-dimensional object?
As far as we know, there are no one-dimensional objects in the real world. A one dimensional object (an object that has length but no width or height) is a mathematical abstraction.
Having said that, ...
- 60.4k
23
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 ...
23
votes
Zero dimensional field theory
Zero-dimensional quantum field theory is exactly like a standard quantum field theory, except that the background spacetime is exactly one point.
Consider, for a moment, a $d$-dimensional QFT defined ...
- 8,582
22
votes
Accepted
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} = -\...
- 71.4k
21
votes
Accepted
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 ...
- 89.3k
18
votes
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Features of General Relativity applicable only to 3+1 dimensions?
I'll first discuss some quite physical differences, which might already be enough for your interests. Afterwards, I'll also mention how mathematically things can be sort of unique in four dimensions.
...
- 23k
17
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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 ...
- 213k
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 ...
- 55k
17
votes
Accepted
How exactly does spacetime change inside a black hole?
You fall right across the event horizon without even knowing it is there unless you are paying attention.
In classical General Relativity, spacetime at the event horizon is locally Minskowskian, just ...
- 52.2k
16
votes
Why do physicists say that spacetime is not bending "into" or "out" of a fourth dimension?
Even if spacetime is embedded in something bigger, we don't have access to it or any way of making observations of it. This tells you that our theories should only be formulated using quantities that ...
- 824
15
votes
Can electrons be non-fundamental in higher dimensions?
When I started in particle physics back in 1962 or so, neutrons and protons had not lost their elementary particle status. Quarks were just being dreamed about. At the time we were very happy with the ...
- 235k
15
votes
Accepted
What is the spin-statistics theorem in higher dimensions?
When formulating a physical theory, one usually begins with a set of axioms. The theory itself will be just as useful as its axioms are accurate. In particular, when dealing with a supposedly ...
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