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Analysing the Laws of Physics

Page history last edited by Ian Kimber 13 years, 5 months ago

 

The laws of physics are the basic laws and rules by which our universe operates.

 

Firstly I must state that I do not wish to deny any of the painstaking work carried out by many people on gauge theories, symmetries,  Hamiltonians, Lagrangians  or vector and tensor calculus.  This is the detail that has allowed us to analyse and understand to a great deal of precision the world around us but sometimes the detail involved in all this work can hide important underlying relationships and questions.

 

This work has produced some very important general relationships that go way beyond any of the physical laws that exist in our universe to cover laws that would apply in ANY universe that had a reasonable degree of continuity and stability.

The references quoted are not definitive source references but sources of useful extra information and explanation for those who wish to confirm the background details.

 

The most fundamental physical law that would apply in ANY universe  

 

                    The second law of Thermodynamics 

 

This is the critical law that states how things will change in a complex system containing many bodies interacting according to some local physical laws once some initial condition has been established.  The second law of Thermodynamics states categorically that the direction of time is always towards the increase of "entropy".  Students are usually told that this is towards an increase of disorder like gas expanding to fill a container and distribute itself evenly.  This is true for dynamic particles that only interact via elastic collisions.  What really happens in every case depends strongly on the physical laws that apply between the particles and fields in that place and time.  For example a universe consisting of electromagnetic particles with gravitating mass that an interact and radiate energy to lose excess angular momentum the preferred structure is condensed masses (planets, stars and black holes) and not evenly distributed gas.  we are all familiar with gasses condensing liquids freezing and crystals forming when particles interact in various ways A better way of describing what is happening is that universes evolve in the direction that produces the most probable outcome that is if a universe can be described as being in a particular state at a particular moment the next state it will be is at (or very close to) the most probable state of all the states that it might occupy.

 

Let us now assume we start with a universe that has energy and the potential to become anything with no restrictions or limits to dimensions of space-time in any way and allow it to evolve in some way.  Physical laws will arise out of choosing the most probable states that can arise.

 

 Conservation laws come from Local invariance

 

For a universe to be understandable it is a fundamental requirement that is laws are reasonably consistent.  Note carefully I have not stated this to be absolute because there can be circumstances where within strict limits laws may be "bent".  It is also possible that some aspects may change as a universe evolves.

 

The first and most fundamental relationships are those generated by Noether's theorem

a ref for this is  http://www.applet-magic.com/noetherth.htm

 

This proves that in order to create some local stability or invariance in a physical system there mist be an associated conservation law.       These are:

 

The conservation of energy                          required to ensure physical laws are largely invariant with time    

The conservation of linear momentum        required to ensure physical laws are largely invariant with location

The conservation of Angular momentum     required to ensure physical laws are largely invariant with direction

 

Dimensionality from stability requirements

 

The next important feature is the dimensionality of a reasonably stable and complex universe.

ref  http://en.wikipedia.org/wiki/Time-space#Privileged_character_of_3.2B1_spacetime 

 

One or two dimensions of space just do not allow a reasonable level of complexity.  Our familiar three dimensions does allow enough complexity in fact it has been shown that three and four dimensions allow the maximum complexity and higher numbers of dimensions are more restricted.  A three dimensional universe also has one other extremely important feature.  The dimensionality of the universe determines the way that any long range conservation laws behave.  Any force fields change as they are spread out so, in a one dimensional universe any force fields are independent of distance (for example optical fibres). In a two dimensional universe they drop as the inverse first power of distance,  In a three dimensional universe the drop as the area of the distance.  That is an inverse square law.  This is the only relationship that allows stable orbits for planets and orbitals for electrons.  A four dimensional universe would have an inverse cube law which does not allow stable orbits.  All higher dimensionalities are also unstable.  There must also only be one dimension of time.   It is interesting to note that others have shown that the complementary relationship is also allowed that is, three dimensions of time and one dimension of space.

 

Long Range Physical laws from conservation and dimensionality plus?

 

The main ones that we are familiar with are the laws of electromagnetism and Gravitation.  These consist of inverse square laws with constants associated with them.  The general approach is that these constants are either "given"  or determined by some sort of random symmetry breaking process.  The short range interaction processes of the weak and strong interactions are less easy to express simply and cannot be separated from quantum processes They are also strongly related to the electromagnetic process so will not be dealt with in detail in this initial preamble. I hope to be able to tackle these later.

 

Now until I reached these constants. There is a strong thread that given an initial condition of energy and an unlimited number of dimensions for a physical universe.  Any universe that exists for a significant amount of time should have these properties as an emergent characteristic.

 

One of my main theses in this is that these and other critical constants are not given or random but settle on their particular values in a process of evolution to enable complexity as a universe develops. 

 

This covers the basic physical laws of how things interact individually.  The next stage is to consider the collective properties of any universe

 

The collective properties of a dynamic universe

 

As we stated as the most fundamental property time evolution determined by the second law of Thermodynamics

 

 

 

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