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1

Indeed, the two effects are very much related! I don't know how your background is, so let me start by defining the four-vector $x^\mu=(t,x,y,z)=(t,\vec{x})$ such that $x^0=t$ and $x_i=x,y,z$ for $i=1,2,3$. (Note that it is convention that greek indices run from $0$ to $3$ (space-time) while latin indices run from $1$ to $3$ (space only). Summation over ...


2

String theory reduces to ordinary field theory in the infinite string tension limit. In this limit, the massive modes are decoupled and we are left with solely, the massless modes. In fact, Bern and Kosower (Please, see a modern review by Christian Schubert. ) proved that the computation of the field theory amplitudes from the string amplitudes at the ...


1

First of all, we still do not know if the 4 fundamentals forces can be unified. The best we have came up to are GUT theories, which join three of the fundamental forces except gravity. The fact that gravitational waves have been detected, may point towards GUT since they address energies of the GUT scale. Nonetheless, assuming that String theory, which is ...


1

Nope, gravitational waves were predicted by Einstein's General Relativity theory which is a very successful theory of gravity. We still though do not have a working theory of Quantum Gravity and cannot therefore unify these forces as of yet.


1

First of all there is no proof of this statement. It is just a general expectation that the more symmetries you have the more reason to expect better quantum properties. This works with SUSY, the more SUSY you have the better the theory is at the quantum level, say $N=4$ SYM, or $N=8$ SUGRA that some people still have hope to be well-defined. If you involve ...


1

Concerning OP's last sentence (v1), the Fourier modes $\alpha^{\mu}_{m}$ are (some of) the fundamental variables of the string. Phrased equivalently, the Poisson bracket reads $$ \{F(\alpha),G(\alpha)\}~=~ \sum_{m\in\mathbb{Z}} \frac{\partial F(\alpha)}{\partial \alpha^{\mu}_{m}} (-im \eta^{\mu\nu}) \frac{\partial G(\alpha)}{\partial \alpha^{\nu}_{-m}}.$$ ...


1

Zeta function regularization is used in other fields, and even in pure mathematics to obtain finite answers from otherwise divergent integrals. In bosonic string theory, the mass of states in lightcone gauge is, $$M^2 = \frac{4}{\alpha'} \left[ \sum_{n>0} \alpha^{i}_{-n}\alpha^{i}_n + \frac{D-2}{2}\left( \sum_{n>0} n\right) \right]$$ where $\alpha'$ ...


0

There is an explicitly three-dimensional version of a Hawking-Page transition in AdS space. It is given by a transition between an asymptotically $AdS_3$ spacetime and the BTZ (BaƱados-Teitelboim-Zanelli) black hole. The line element of thermal (euclidean) $AdS_3$ space is given by ...


2

Think of a very thin wire. It is a 3-dimensional object, but for many purposes you can describe it just as a 1-dimensional line or curve. The two remaining dimensions are curled up in a tiny cross section. In a similar way, the speculations (not the slightest experimental hint exists that it should be so) about our world possibly being higher dimensional ...


-1

Measurement of length or dimension relates to human experience for quantifying and comparing . If human awareness is absent a point can be defined as infinite size or dimensionless or single or multidimensional.


-1

small and big is comparison and comparison is the common denominator. If we view the distant telephone wire with one normal eye and and the other with microscopic vision, this observational dimension conflict as well as an apparent new extra dimension will arise. Physics will have to accept observers consciousness as the canvas for extra spatial dimensions. ...



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