String Theory = Theory of Everything?

Peter Woit on Note Even Wrong recalls a podcast with Eli Frenkel about string theory:

• In particular, one thing that happened to Frenkel since last spring is that he attended Strings 2023 and gave a talk there (slides here, video here). The experience opened his eyes to just how bad some of the long-standing problems with string theory have gotten, and starting around here in the podcast he has a lot to say about them.
• It’s pretty clear that his reaction to what he saw going on at the conference was colored by his experience growing up in late Soviet-era Russia, where the failure of the system had become clear to everyone, but you weren’t supposed to say anything about this. He pins responsibility for this situation on senior leaders of the field, who have been unwilling to admit failure.

String theory was initiated in the 1970s as a grand attempt to unite all forces into a Theory of Everything ToE. My good friend Lars Brink at Chalmers was one of the early pioneers with a thesis in 1973 and subsequent work with all the senior leaders during a 50 year career until Sept 2022 when he had to give up his search for a ToE. A Memorial Meeting took place on the web Febr 18 2023 remembering a great physicist.

According to Eli Frenkel, sad to say, string theory has not delivered a credible ToE and so it is time to move on to something different building on the experience of a failed attempt. But this is not what the  leaders of string theory still alive are saying, which creates a big problem for the young generation asking for guidance and hope/inspiration for a career in physics. String theory? If not string theory, what then? What has fundamental physics de facto delivered the last 50 years? Why are the foundations of modern physics (quantum mechanics and relativity) still incompatible after 100 years? Why is there a crisis in fundamental physics if its leaders are smartest on Earth?

Eli Frenkel gives a perspective that is important to listen to if you are a young scientist in search of a mission. Old professors/theories never die, they just fade way.

What is Wrong with Newtonian Gravity?

This is a continuation the previous post on the Universality of Newtonian Gravity. If Newtonian Gravity is Universal, how come that this is not what modern physics is saying? In what sense was Newton wrong?

Here are the main answers to the question What is Wrong with Newtonian Gravity?:

1. Newtonian Gravity is an “action-at-a-distance” theory. Newton himself was deeply concerned about this.
2. Newtonian Gravity is not compatible with the world of special relativity. 
3. Newtonian Gravity is contradicted by observation of the perihelion advance of Mercury and gravitational waves.
4. Newtonian Gravity does not interact with propagation of light. 

Let us now analyse the validity of these arguments. In our non-standard view with gravitational potential primordial, there is no action at distance and so 1. is not an issue. 

Special relativity is a theory empty of real physics as shown in Many-Minds Relativity and so 2. is neither an issue. 

The claimed disagreement of Newtonian Gravitation with observations of the perihelion advance of Mercury may very well depend on neglect of proper influence from other planets and from the Sun. Until all such aspects have been taken properly into account, it is impossible to say that Newtonian Gravitation is wrong and so 3. is not necessarily an issue.

Newtonian Gravitation concerns dynamics of particles/bodies with mass and so say nothing about interaction with massless light, and so 4. is neither necessarily an issue. 

Summing up, we find that the reasons behind viewing Newtonian Gravity to be wrong are weak. The price to pay by dismissing it is very high, since Newtonian Gravity appears as the only Theory of Everything in  physics.  

Universality of Newton's Law of Gravitation

Newtonian Gravitation and Quantum Mechanics is a Theory of Everything ToE.

This is a continuation of previous post on the connection between gravitational potential $\phi (x)$ and mass density $\rho (x)$ through the relation $\rho =\Delta\phi$ where $\Delta$ is the Laplacian differential operator with respect to $x$ as Euclidean space coordinate. 

We take here a non-standard view and consider the gravitational potential $\phi$ to be primordial, from which mass density $\rho =\Delta\phi$ is given to matter by differentiation as an instant local action. 

This is to be compared with the standard view with $\rho$ primordial and $\phi$ obtained by solving the equation $\Delta\phi =\rho$ as a global integration/summation process requiring instant global action or instant action at distance.

Here instant local action, like establishment of contact forces, does not pose the problem of instant action at distance, which may be unsolvable. 

Let us now see how the connection $\rho =\Delta\phi$ can be established viewing $\phi$ as primordial. 

The first step is to see that $F=\nabla\phi$ represents gravitational force field and as such is a conservative force, which means the the work required to move a body from one point to another is independent of the path. As an example the work required to lift a body in the gravitational force field of the Earth only depends on change of level and not path with motion without change of level not requiring work. The gravitational force field is thus given as the gradient of a potential.

The next step is to show that $\nabla\cdot F=\rho$, where $\nabla\cdot F$ is the divergence of $F$. We recall from Calculus  that 

• $\int_\Omega \nabla\cdot F\, dx =\int_\Gamma F\cdot n\, ds$

for a volume $\Omega$ with boundary $\Gamma$ with outward unit normal $n$ with $dx$ volume element and $ds$ boundary surface element.  Viewing $F$ as a flux, $F\cdot n$ is the flux out of $\Omega$ and $\nabla\cdot F$ is the corresponding source inside $\Omega$. 

We can now (simply) define gravitational mass density $\rho =\nabla\cdot F=\nabla\cdot\nabla\phi =\Delta\phi$ to be the source of the gravitational field given by the potential $\phi$, and we can from this relation derive Newton's Law of gravitation in its familiar form as did Laplace in his Celestial Mechanics. 

We see that Newton's Law of gravitation reflects (i) observation that a gravitational force field is conservative, together with (ii) definition of gravitational mass density as the source of this field. 

Newton's Law of Gravitation thus comes out from assuming that a gravitational force field is conservative, which is supported by observation, together with definition of gravitational mass. 

Connecting to Newton's 2nd Law of motion with inertial mass the same as gravitational mass, brings universality to cosmic interaction.

We conclude that Newton's Law of Gravitation can be seen much like an a priori statement about physics in the sense of Kant. We compare with the a priori statement that the length of the circumference of a circle with radius $1$ is equal to $2\pi$, which has universal validity. 

This gives Newton's Law of Gravitation universal validity leaving Einstein's General Theory of Relativity without mission. In particular, it resolves the main dilemma of modern physics of the perceived incompatibility between Quantum Mechanics and General Relativity, since Newtonian gravitation is fully compatible with Schrödinger's quantum mechanics as a Theory of Everything ToE.  

We recall Niels Bohr:

• How wonderful that we have met with a paradox. Now we have some hope of making progress.          

How wonderful that we have found incompatibility of Quantum Mechanics and General Realativity. Now we can make some progress...

Why Euler CFD is a Zero-Cost Parameter Free ToE

The fact that for slightly viscous incompressible bluff body flow with Reynolds number $Re>500.000$, Euler CFD with slip boundary condition (without boundary layers) serves as a parameter-free essentially zero-cost computational model without dependence on Reynolds number as a Theory of Everything ToE in the spirit of Einstein, depends on two key circumstances:

1. Finite rate of turbulent dissipation effectively independent of $Re$ after transition to turbulence (e.g $Re >200$ in isotropic turbulence) (reference).
2. Slip serving as effective boundary condition for $Re > 500.000$ (NACA0012 previous post).

Here 1. reflects Kolmogorov's conjecture and means that a mesh size of around 1/200 of gross dimension is sufficient to capture turbulence. Further, 2. reflects that Euler CFD with slip can capture drag and lift with little dependence on $Re$ beyond drag crisis around $Re=500.000$.  

Altogether, Euler CFD can capture drag and lift beyond drag crisis with a mesh size of around 1/200 of gross dimension thus at essentially zero computational cost (because no thin boundary layers have to be resolved). 

The fact the drag and lift coefficients do not include dependence on $Re$ (with $Re =\frac{UL}{\nu}$,  $U$ typical flow speed, $L$ typical length scale and $\nu$ typical viscosity) and yet can serve as measures of drag and lift for $Re$ beyond drag crisis, gives observational evidence that indeed drag and lift have a very weak dependence on $Re$ beyond drag crisis, as shown in the previous post (see reference showing drag independence for $Re>10000$ for a collection of blunt bodies).  Also recall that drag and rate of turbulent dissipation balance, and so observed independence of drag beyond drag crisis supports 1.