no, absolutely not.

@Hinnerk Albert Why not?

In quantum Yang – Mills theory at any time instant, the Minkowski space can be divided into infinitesimal small volume regions, say, β and one can assign quantum Yang - Mills field amplitude to each of these β. Now, the dynamical field variables (generalised coordinate and momenta variables), of the Coulomb gauge action defined in [arXiv:hep-th/9802180], constitute canonically conjugate pair, the simultaneous measurement of which is governed by the uncertainty principle. The ultraviolet (UV) behaviour of quantum Yang – Mills theory possess no instability as the separation between physical gluons becomes exceedingly smaller & smaller in the limit of approaching the origin of field space and also, in the said limit the dynamical conjugate field variables (generalised coordinate and momenta variables) goes on reducing in magnitude. Now, in the limit of approaching the origin of field space, the Minkowski space β becomes ‘empty space’. But what we understand of ‘empty space’ cannot be completely empty because that would mean that all the fields such as Yang – Mills field dynamical variables (generalised coordinate and momenta variables) would have to be exactly zero. As already stated above, the dynamical conjugate field variables (generalised coordinate and momenta variables), of the Coulomb gauge action defined in [arXiv:hep-th/9802180], constitute canonically conjugate pair like the position and momentum of the particle: the uncertainty principle implies that the more accurately one knows one of these quantities, the less accurately one knows the other. So, in the ‘empty’ space β the Yang – Mills dynamical field variables cannot be fixed exactly at zero because then it would have both a precise (generalised coordinate) value (zero) and a precise rate of change (generalised momenta variable) value (also zero). There must be certain minimum amount of uncertainty in the value the Yang – Mills field dynamical variables (generalised coordinate variable). One may think of this certain minimum amount of uncertainty as the least possible value [of the dynamical field variable(generalised coordinate)] dubbed as single physical gluon at trivial UV fixed point of asymptotically free quantum Yang – Mills theory under flat space-time assumption. In other words, at trivial UV fixed point, one may think of the Minkowski space β as spherical region consisting of only single physical gluon and to be of the order of the gluon wave-length. As such, at the trivial UV fixed point the Quantum Yang – Mills theory no longer remains a field theory that describes infinite number of particles; it becomes single particle theory in which the dynamical variables (both generalised coordinate and momenta variables) represent a single physical gluon say ‘G’.

Accordingly, one can show that at Gribov horizon, the application of Gauss Divergence theorem to this single physical gluon ‘G’ leads to singularities of color-Coulomb potential spread all over a spherical surface β. After acquiring additional degree of freedom in the form of free color-Coulomb potential at Gribov horizon, the gluon ‘G’ has the aforesaid spherical system β firmly attached to it. At Gribov horizon, the uncertainty principle forbids this spherical system β, of constant radius equal to some plancks constant multiple, to undergo any Lorentz – Fitzgerald contraction in any inertial frame and rather, demands the motion of gluon ‘G’ to instantaneously drop to zero speed in the any inertial reference frame. This sudden deceleration in the speed of gluon ‘G’ at Gribov horizon assigns an inertial mass to gluon ‘G’ in accordance with General Relativity theory. This inertial mass of gluon ‘G’ produces gravitational effect in its surroundings because of equivalence between inertial mass & gravitational mass in General Relativity theory. The experimentally observed short range of strong force validates the unification of gravity with quantum theory as predicted by the uncertainty principle.

For more discussion, please refer to my preprint http://dx.doi.org/10.13140/RG.2.2.25092.65926

No. Whether the spectrum of Yang-Mills theory, defined on flat spacetime, has a mass gap or not doesn’t and can’t imply anything about the quantum fluctuations of spacetime, which is what quantum gravity means.

Incidentally, that Yang-Mills theory does have a mass gap is known, from numerical simulations of the full theory; what’s not known is how to prove that the systematic effects due to the lattice artifacts and the statistical effects due to finite sampling, are , indeed, negligible, as expected and as checked in the simulations, as the lattice spacing is taken to zero and the lattice size to infinity. The proof of the mathematical statement won’t change what we know now about this particular problem. What is hoped is that the techniques, that are developed to realize the proof, will have applications to other problems.

That Yang-Mills theory has a mass gap does not mean that the gauge fields that define it acquire a mass-which is what a longitudinal polarization means. It means that bound states of the gauge fields (that are only possible for Yang-Mills gauge fields, since photons don't interact, in the absence of matter) have non-zero mass; the smallest such mass is called the mass gap. It doesn't have anything to do with the Planck mass, since gravity doesn't play any role, spacetime is flat.

A mass gap means that there don’t exist any states with energy less than a finite, non-zero, quantity (which thus, defines a``gap'' in the energy spectrum) above the ground state, i.e. the state of least energy (which is unique in flat spacetime).

Cf. for instance here: https://inspirehep.net/literature/169588 for the simplest case.

Incidentally, the ghosts don't ``disappear at the Gribov horizon''-they are used, in perturbation theory, to cancel the contribution of other unphysical degrees of freedom. So they don't appear in any final result, in any event-if they did, this would mean there was a mistake...But it's not possible to compute the mass gap in perturbation theory, so it doesn't make sense bringing them up at all.

In the lattice formulation of gauge theories there's no reason to introduce ghosts in the first place, since it's always possible, for numerical simulations, to use a gauge-in order to produce statistically independent configurations-that doesn't have ghosts, such as axial gauge.

@ Stam Nicolis

When we do normal physics we traditionally visualise particles as little balls zipping around in empty space in the form of probability waves. It’s a useful way of picturing the Universe but it doesn’t explain why different types of particle follow different sets of laws. Quantum field theory solves the conundrum by making a radical change to the picture: scrap the idea of particles altogether because they don’t really exist.

In quantum field theory, empty space is not genuinely empty. It is filled with what physicists call ‘fields’ - fluid-like substances which extend in all directions.

However, the non-linear nature of Yang-Mills fields forces one to reintroduce the particle or probability waves concept as the Yang Mills field amplitudes alone cannot be visualised to directly interact with each other in localized manner. In other words, the non-zero uncertainty in position of the gluon particle due to uncertainty principle does leave scope for the creation of empty space of the order of Planck size for the physical gluon particle to zip around in the form of probability waves. At trivial UV fixed point of YM theory, the continuous definition of field amplitudes breaks down and one is forced to assign non-zero single field amplitude to infinitesimal empty space so created with the existence of physical gluon particle inside it.

At Gribov horizon, this infinitesimal empty space becomes permanently attached to physical gluon at light speed due to Gauss law. From this point onwards, relativity comes into picture to lead one to unification of gravity with quantum theory.

@ Stam Nicolis

In general, the Yang – Mills field is characterized by specifying the values of vector potential at all points of the space at a particular time instant. Now, these values of vector potential are assumed to be ‘generalized co-ordinates variables’ and their derivatives are assumed to be ‘generalized momenta variables’. Now, here I propose altogether new mathematical definition of the term ‘generalized co-ordinates variables’ by postulating that the specified value of the vector potential at any point in space at a particular time instant is in-fact distributed as probability wave distribution over the adjacent points of the space at that instant. Accordingly, closer and closer specification of the vector potential to any point in space at a particular time instant means more and more uncertainty in the measurement of the value of their derivatives as ‘generalized momenta variables’. In other words, the specification of the value of vector potential at any point of the space at a particular time instant corresponds to a probability wave-packet centered at that point. This probability wave-packet can be restricted to infinitesimal region say β of space in accordance with uncertainty principle.

As such, in quantum Yang – Mills theory at any time instant, the Minkowski space can be divided into infinitesimal small volume regions β and one can assign quantum Yang - Mills field amplitude to each of these β. Now, the dynamical field variables (generalised coordinate and momenta variables), of the Coulomb gauge action defined in [arXiv:hep-th/9802180], constitute canonically conjugate pair, the simultaneous measurement of which is governed by the uncertainty principle. The ultraviolet (UV) behaviour of quantum Yang – Mills theory possess no instability as the separation between physical gluons becomes exceedingly smaller & smaller in the limit of approaching the origin of field space and also, in the said limit the dynamical conjugate field variables (generalised coordinate and momenta variables) goes on reducing in magnitude. Now, in the limit of approaching the origin of field space, the Minkowski space β becomes ‘empty space’. But what we understand of ‘empty space’ cannot be completely empty because that would mean that all the fields such as Yang – Mills field dynamical variables (generalised coordinate and momenta variables) would have to be exactly zero. As already stated above, the dynamical conjugate field variables (generalised coordinate and momenta variables), of the Coulomb gauge action defined in [arXiv:hep-th/9802180], constitute canonically conjugate pair like the position and momentum of the particle: the uncertainty principle implies that the more accurately one knows one of these quantities, the less accurately one knows the other. So, in the ‘empty’ space β the Yang – Mills dynamical field variables cannot be fixed exactly at zero because then it would have both a precise (generalised coordinate) value (zero) and a precise rate of change (generalised momenta variable) value (also zero). There must be certain minimum amount of uncertainty in the value the Yang – Mills field dynamical variables (generalised coordinate variable). One may think of this certain minimum amount of uncertainty as the least possible value [of the dynamical field variable(generalised coordinate)] dubbed as single physical gluon at trivial UV fixed point of asymptotically free quantum Yang – Mills theory under flat space-time assumption. In other words, at trivial UV fixed point, one may think of the Minkowski space β as spherical region consisting of only single physical gluon and to be of the order of the gluon wave-length. As such, at the trivial UV fixed point the Quantum Yang – Mills theory no longer remains a field theory that describes infinite number of particles; it becomes single particle theory in which the dynamical variables (both generalised coordinate and momenta variables) represent a single physical gluon say ‘G’.

Accordingly, one can show that at Gribov horizon, the application of Gauss Divergence theorem to this single physical gluon ‘G’ leads to singularities of color-Coulomb potential spread all over a spherical surface β. After acquiring additional degree of freedom in the form of free color-Coulomb potential at Gribov horizon, the gluon ‘G’ has the aforesaid spherical system β firmly attached to it. At Gribov horizon, the uncertainty principle forbids this spherical system β, of constant radius equal to some plancks constant multiple, to undergo any Lorentz – Fitzgerald contraction in any inertial frame and rather, demands the motion of gluon ‘G’ to instantaneously drop to zero speed in the any inertial reference frame. This sudden deceleration in the speed of gluon ‘G’ at Gribov horizon assigns an inertial mass to gluon ‘G’ in accordance with General Relativity theory. This inertial mass of gluon ‘G’ produces gravitational effect in its surroundings because of equivalence between inertial mass & gravitational mass in General Relativity theory. The experimentally observed short range of strong force validates the unification of gravity with quantum theory as predicted by the uncertainty principle.

For more discussion, please refer to my preprint http://dx.doi.org/10.13140/RG.2.2.25092.65926

The Gribov horizon is the frontier in the space of fields, not in spacetime, where the Faddeev-Popov determinant changes sign. Which just means that a new change of variables is needed. This is just a completely routine technical point, that doesn’t affect perturbative calculations and can be avoided on the lattice. Thzt’s why bringing it up doesn’t help.

The mass gap can't be found by solving the classical equations of motion for Yang-Mills fields, so discussing this issue is irrelevant to the mass gap.

The equations themselves are partial differential equations, that describe not only dynamical degrees of freedom, but, also, constraints, just like Maxwell's equations do for the electromagnetic field. How to deal with these constraints is easy for Maxwell's equations, non-trivial for Yang-Mills, but, once more, this only will describe classical solutions, not quantum properties.

Preprint A Heuristic View on the Composition of Space

Preprint A New View on the Composition of Matter