Cumrun Vafa: 2017 Breakthrough Prize Symposium

The 2017 Breakthrough Prize Symposium was held December 5, 2016 at UC San Francisco and co-hosted by Stanford University and UC Berkeley. The daylong event included talks and panels featuring Breakthrough Prize laureates in Fundamental Physics, Life Sciences and Mathematics, as well as other distinguished guests.

[kaushaltimilsina]

I have not studied string theory yet, but am really excited to make a guess and ask this question.

Special relativity says that if you stretch in one dimension (any of 3+1), you shrink in the other dimension, as regulated by the constancy of the speed of light. General relativity describe how you stretch and shrink given a certain mass. So you can shrink to 0 in some way (volume) (compacting mass to singularity as observed by a distant observer), you can stretch to infinity in other direction (time) (an object freezing in the horizon as observed by a distant observer). So even though speed of light seemed like some sort of constraint, we could still end up with “infinity-zero” solutions, singularities.

Einstein’s general relativity describes how a (point) mass adds it’s metric to any preexisting metric. So, you add the metric contribution due to the earth’s gravitational field to the metric contribution of the sun, and the galaxy and so on, to describe the motion of the moon. In some sense you add the metric contributions layer by layer(some sense of linearity although the general relativity equations are really non-linear). In particular, there is a distinction between intrinsic metric (due to point mass) and extrinsic metric (background curvature). So one could ask, what happens if you add arbitrary amount of dark energy to the universe? If we could increase the mass of the earth and the sun and everything else in the required proportion, would we be able to tell the difference. The answers seems like no, from our ordinary intuition about geodesics, but that might really be misleading us. The answer could be no, because of topological or geometric constraints coupled with the amount of dark energy. If our universe has a slightly negative curvature, and we increase the curvature by a bit we could have a positive curvature and things could be really different.

With string theory, we could unify the ideas of extrinsic and intrinsic contribution the metric, with the added degree of freedom that point particles can be replaced by vibrating extended objects. The unification comes with the assumption that the vibration can not be arbitrary but rather quantized in some sense. If the vibration was not quantized, the Fourier transform of a general vibration could be described with non-zero contributions from all possible modes (based on the vector space analogy of the algebra describing the decomposition). This could be described as: non-locality could be observed in all dimensions. So, one could possibly stretch in all dimensions giving non-renormalizable solutions. The way to regulate that would be to impose at least one (or some) directions to be renormalizable, or to have locality in at least one directions. This would be the extension of special relativity that you can stretch to infinity in one direction but then you’d have to shrink to zero in some other. In the string sense, if all the fundamental units of spacetime (no reference to their size) were made up of strings, only strings that vibrate in the same frequency (or some analogue) would be able to interact, and not that everybody would be able to talk to everybody else. So, if two neighboring strings were vibrating at the same frequency and then while the first one ran out of phase (went to different mode), another one came into phase with the second one; this could describe a free stable particle moving through spacetime. The necessity of extra dimensions that we might not be able to observe (described often as small and coiled up), could describe that we need non-local solutions. As before, we could stretch to infinity in some directions, shrink to zero in some directions but we stay finite in some other dimensions (the ones we observe). This regulation could perhaps be done by supersymmetry -by allowing non locality in only certain directions.
With this description, string theory would bring together extrinsic and intrinsic contribution to the metric as seen in Einstein’s relativity, by requiring certain relationship between what can be local and what can not be. So, if the dark energy contribution was different, different particles would be realized in universe with different dark energy. That immediately comes with a caveat that when the dark energy contribution was different in the past and would be different in the future according to our current understanding, different kinds of particles would be realizable.

One example that might initially seem inconsistent would be as follows. In the middle school definition, I learned that charge is a property by which a particle feels force in an electric field. So, if there as just one charged particle in the universe, it wouldn’t feel any force and so its charge would be meaningless. With Dirac equation, a photon could decay into a particle – anti particle pair, so there would be no single charge, and any particle would have at least one other charge that it could feel and so its charge would not be meaningless. So, that’s a good upgrade to the definition. But say now that a photon decayed into a particle anti particle pair, and imposing translation symmetry momentum conservation caused two particles to fly off in opposite directions. Imposing non-locality would imply that each of the two particles can pick up an antiparticle from the background field (without any other particle) and annihilate. This might also be understood as the two particles annihilating each other at infinity (even), without the universe being closed (coiled up micro dimensions expressed as loops extending to infinity). In that sense we’ve stretched the distance between them to infinity, but allowed a non-local interaction in some other direction. So, vibrating particles could here be understood as particles that can seemingly feel their own field. Or perhaps the fact that particle anti-particle pair running away from each other could each pick up a partner to annihilate with the field, is perhaps described as the photon of electric field between the two particles running away corresponding to its supersymmetric state fermion that would allow for annihilation. In this sense, supersymmetry would regulate what can and what can not be non-local. This could be a gauge field interaction in the non-perturbative regime, or perhaps a non-definite signature of the metric (could fluctuate between + and -).

Does this make any sense? I was just really excited to make this speculation that in many ways might seem inconsistent or perhaps even totally wrong?

Thanks very much!

[davidwilkie]

The QM-TIME unit vector duality is the principle of connection connection seen as probable existence-resonance in perspective, and so the String Theory analysis is a combination of dot-matrix points and tangential shell-surfaces of the "simpler" dimensions in a possible range of irrational continuity of diminishing-inflated vanishing points.
The structures shown are the an impressive achievement, except for the proposed ending. The landscapes, p-brane resonant cosmological objects and vanishing point objectives that may appear to terminate at a Black Hole, are equivalent to relative-related pulses within the same eternal principle, so everything in this observable universe is cyclical and changes shape without any total finality.(?)

[MrRaki]

It's called String Hypothesis, not Theory!