Valeriy V. Pimenov , 2011
"Are we living in the lattice-vacuum?"
http://www.communities-server.net/Docs/Pimenov_book_ENG.doc
From "vacuum” of Dirac to "lattice-gauge-field” of Yang-Mills;
Lattice-gauge field as a "crystal grid” in The Theory of Solids;
Transient-dynamic processes in the lattice-grid;
Electro-magnetic effects in the lattice-vacuum;
What sir Newton had in mind under his "infinitesimals”?;
`Time` as a measure of changes - new physics conception.
Connect to author at site:
http://www.communities-server.net/
Preface
In this book author is trying to preview the consequences of accepting the hypothesis of «lattice-space» («discrete grid of vacuum»). The idea of “not empty” vacuum was first mentioned by Paul Dirac (around 1930). Next the term itself (lattice-space) was proposed by С. Yang and R.Mills (in 1954) when trying to explain the “strong interactions”. Later a lot of various types of such kind of “calibrating” (gauge) fields were proposed – most of them based on the idea of massless fields in which particles do acquiring mass through symmetry-breaking of those massless discrete gauge-fields…
But all those theories have tried to look at the particles and lattice-space as to separate entities. In this book author presents results of some computer simulations in which the nodes of such lattice-fields are the particles itself. Meaning that lattice-nodes becomes “nuclear particles” in some conditions. And “free movements” of “nuclear particles” is nothing more than “jumping” of those special conditions of node – onto the nearest node…
Details see in the book.
One of the main requirements of Yang-Mills theory was “gauge invariance” of nuclear particles description while they are moving through lattice field – which was possible only when nodes of grid is massless. At those times (1954) it had looked “hardly possible” for massless “particles” (nodes of grid) to be both massless and unmoving…
In our times such “exotic” do not scare any physicist, I hope (:0).
The consequences of such approach could be:
-convincing explanation of gravitation effects, including inert-to-gravity mass-equality;
-correct physical interpretation (extrapolation) of Riemannian geometry by discrete “field” with additional “dimension(s)” because of revealed additional physical parameters of this discrete filed.
Simply speaking, the “four-dimensional curvature” of Riemann-space – physically could consist of deformation tensor of our “lattice-grid”…
One chapter of this book is dedicated to attempts of correct physical interpretation of Newtonian idea of “infinitesimal particles”.
Should we think of them as literally “dimensionless entity”? Or according to Max Planck should we stop “downsizing” any field-elements at some discrete limit?
In more wide (philosophical) sense – Newtonian equations are correct only until we reach the “qualitative boundaries” of the system under consideration. And thus all those “continuous” equations and “continuous metrics” (like Minkowski’s) – could NOT be correct ground for convincing physical models…
But mathematicians invented one brilliant “trick” – in all cases where they need to apply to the explored system one or more additional “degree of freedom” – they apply “imaginary numbers”…
Author has tried to understand – do those “imaginary numbers” could have any physical interpretation? And found that those additional degree of freedom (which “imaginary numbers” always added to “continuous fields of dimensionless points”) – in all cases will give much more correct physical results of equations.
Yes, “imaginary numbers” are “trick” – but author right now could not propose “physically correct” alternative… except possibly computer-simulation in cellular automaton logic.
Last chapter is dedicated to attempts of correct physical interpretation of the essence of “time”. Author had found “long-ago-forgotten” idea of Titus Lucretius Carus (55 year b.c., ancient Rome) – that there does not exist any “time by itself”. Time is only the measure of local changes…
It looks like this idea does not contain any contradictions with Minkowski-Einsteinian time… but… ok – read the book (:0).
About the style (and thus audience) of this book.
Author have tried do not overload this text with mathematical analysis. I do not think that “strict” discussion of Yang-Mills equations could be interesting to such a wide range of people (:0).
So, I invite to discussion in this book anyone who feels that he has something to say about it (:0).
Feel free to contact me by e-mails:
Or at sites:
Pictures in text are the “snap-shots” from the “simulations” made by author - in the logic of cellular automaton. But this was done by my own simulation program - not by Wolfram applications (:0).
