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1

To explicate what we mean by no significance, I would suggest that you understand the indexing as a convenient type of naming. We need some way to say which dimension we are referring to and using numbers lets us use convenient notation, but we could just as well have named the dimensions. The ones we experinece might be Tim, Alice, Bob, and Carol. Any new ...


3

There is no significance to the numbering of the dimensions. When we refer to a vector it's common to write is as $x^\alpha$, where $\alpha$ runs from zero to the number of spacetime dimensions minus one. $x^0$ is frequently used to refer to the timelike dimension, so $x^1$ to $x^n$ refer to the $n$ spatial dimensions. However there is no signficance as to ...


3

A soliton is a localized, non-dispersive solution of a nonlinear theory in Euclidean space. It certainly is a real object: you have a famous story about a certain John Russell who observed soliton-like waves made by a boat on a river (wikipedia knows everything about it!) The so-called morning glory clouds in Australia ...


3

I would say that the questions that String/M-theory try to answer are the last ones that our current knowledge of reality allows us to ask. One may think they are the last ones because they are already indirect, as no obvious experimental fact contradicts the current theories (General relativity and the Standard model of particle physics). Instead of ...


1

The place to start is, of course, by finding a prediction of string theory that differs from that of made by competing theories. The prediction made by naive string theory are Extra dimensions. Naively this is a problem, but it can be patched up. All we have been able to do on this front so far is to require that the extra ones be compact and put ...


2

Where a string carves out a $2$-dimensional world-sheet and a point particle carves out a $1$-dimensional world-line of spacetime, the instanton carves out a $0$-dimensional world-point. Counting only spatial dimensions, a string is $1$-dimensional and a point particle is $0$-dimensional. By logical extension, an instanton has dimension $-1$, if we only ...


0

(expand my comment as an answer) First, in supergravity theories (e.g the Kaluza-Klein type) the vacua solutions may be infinite or many. This immediately poses a problem for a physical theory which needs some uniqueness properties. Then the property of stable vacua (aka stable solutions) is used as a condition for selecting among the possible soluions ...


6

In my opinion you are exaggerating the power of strings. In my perception it is the all pervading harmonic oscillator potential of quantum mechanical potentials taken to a higher dimensional level. You must know that all symmetric potentials have as a first term the harmonic oscillator in the expansion. When in doubt of the form of the potential, approximate ...


3

Simulation implies an author, so this is another attempt at trying to find a creator for the universe, imo. Thus it is metaphysics and not relevant to the subject of physics. Physics as a discipline starts from observations and fits them with mathematical models that have predictive power, having accepted axioms and postulates. The mathematical forms are ...


2

I am on record of having the opinion that there is no real argument against us being a simulation in a general sense, however we frequently find people jumping to quick into the simulation pool and stating there new what-ever-it-is proves the universe is a simulation. The example given above sounds like one of them. First off, Quantum Error Correcting Code ...


2

As Count Iblis pointed out, The Church–Turing–Deutsch principle makes this impossible to decide using the structure of the laws of physics as it will always be compatible with the universe being simulated by a quantum computer. Nevertheless, in this well-known paper the author argues that if we accept some very reasonable assumptions, then is is almost ...


-2

If you were a simulated person inside an emulation, would you ever be able to tell the universe was emulated? the answer is no, not if it is set up correcty.


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A function can be interpretable as a scattering amplitude if that function satisfies the axioms of relativistic S-matrix theory [1]: Lorentz invariance Unitarity (Not realized by the beta function, but may be dropped if the function is interpreted as a Born approximation to the exact amplitude) T, C, P invariance (only for strong nucl. interactions) ...


1

There exists a precise way of calculating the entanglement entropy in a conformal field theory via the Ryu-Takayanagi (RT) prescription in the context of the AdS/CFT correspondence. The RT prescription says that the entanglement entropy of a sub-system $A$ in the CFT$_{d+1}$ that lives on the boundary of AdS$_{d+2}$ is given by the minimal area surface ...


2

Yes, if all the dimensions are compact, well, we really mean that all spatial dimensions are compactified on a torus $T^9$, then (multiple) T-duality may map any simple D$p$-brane aligned with some dimensions to a D0-brane. Under T-duality, D$p$-brane is mapped either to a D$(p+1)$-brane or a D$(p-1)$-brane, so its dimension either increases or decreases. ...


1

Tong is alluding to the standard trick in the derivation of Noether's theorem by promoting the (infinitesimal) $x$-independent parameter $\epsilon$ to become $x$-dependent, see e.g. this Phys.SE post.


1

The derivation of the Virasoro algebra is obviously a very important calculation in ST/CFT. For starters, OP (v1) does not mention explicitly the normal ordering ": :" in the definition of the Virasoro generators $$ L_n ~=~ \frac{1}{2}\sum_{k\in\mathbb{Z}} :\alpha^I_{n-k}\alpha^I_k: $$ Normal ordering is important for $L_0$. Here the index $I$ runs over ...


1

We do not know if the universe is closed or open, so space could very well be infinite. However, that does not mean that there is an infinite amount of space in anything. Such a conclusion does not quite make much sense in terms of a logical,mathematical (or even philosophical) argument. Take Zeno's paradox for instance: The paradox states(in summary) that ...


2

Ok, I will sketch a some important steps here for relating spinor representation of $D_n$ to vector representation. For $E_8$, the adjoint representation 248 can be written in terms of positive chirality spinor representation 128 of SO(16) and adjoint representation 120 of SO(16) as, $248=120+128$ Now carrying out the trace in 120 representation can be ...


2

Your diagram looks like an illustration of the Ekpyrotic universe. In this model the extra dimensions are not compactified (i.e. curled up) so there is no uncurling of them. The reason we don't see the extra dimensions is because our universe is confined to a 3D brane, not because the extra dimensions are curled up. One well known theory for what determines ...


1

If you're talking about the same thing, the long string picture of a black hole which was originally referred to as a "long brane", it was introduced in the paper by Susskind and Maldacena in 1996 http://arxiv.org/abs/hep-th/9604042 See also its 200+ followups.



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