Friday, January 17, 2014

Existence and Uniqueness in Physics

You will see what the title means in a bit.  In my last post I commented on reality from a physics point of view and in modelling this reality.  The modelling is based on what we know in physics say Newton's laws of motion and gravity, electromagnetism, quantum mechanics, general relativity and the standard model of particle physics.  All of these subjects are part of an undergraduate and graduate students studies.  The reason being that they work for the areas that they are intended to study.  Working meaning that their predictions agree so far with experiment in the realms that they are intended to describe.  "So far" being important and that is what part of science does is to test these theories. All of these theories depend upon the use of mathematics. Newton developed calculus so that he could further his studies.  The other theories that I mention are also based on the use of mathematics.  Mathematics is one of the tools that scientists have to study the physical universe.  I remember learning and hearing that the world is all described by differential equations.  More technically I used to hear that if one could understand and solve nonlinear partial differential equations a lot of physics would be at your feet. But alas we were told that this math was too hard to solve at the present time (1970-80's).  The main point being that physicists use math to describe reality. This line of reasoning has worked exceptionally well.

This is on what a large part of our technological existence is based.  If one looks at areas of present research  in physics there are a variety of problems that face physics today which have so far have resisted solutions.  Some of these being:

1).  Quantizing gravity

2).  Complexity

Quantizing gravity comes about in the search understanding matter and forces in the universe.  The problem is the incompatibility of general relativity, a classical theory and quantum mechanics.  General relativity relies on mathematics that is continuous whereas quantum mechanics says that the universe is quantized and not continuous and that space-time comes in little chunks as does energy (whatever energy is).  The best theory so far to describe their unification is string/M-theory.  This is a controversial theory but is taken as the best way so far to work on unifying forces and matter.  The problem is that string theory is 30-40 years old and still has major problems, one being that the math is too hard.  Sound familiar? But some string theory has been useful .

Some parts of theoretical physics are up against walls in that they predict results or are based on theories that are so far not tested.  These being the ideas of the Multiverse and string/M-theory. Multiverses lie outside our observable universe and testing their existence is unclear at best.  Strings are so small that their existence will not be observed in any known accelerator using any known technology.  Some scientists feel that these are not scientific theories but philosophy.  This is a current discussion in physics.

What maybe needed instead is for physicists to stand back and look at the foundations of what physics and the mathematics it uses and what these are based upon.  This is the premise promoted by Eric R. Weinstein in his post to the question of "What Science Idea is Ready for Retirement?"

This collection of essays are from some of the leading research folks in their areas and make fascinating reading.  These essays are collected and then published in book form for all to read, see for more information.  What Weinstein is saying is that the mathematical foundations of physics need to be examined and also subtly implying that string/m-theory needs to lose its cult status which has possibly been a detriment to advances in theoretical physics.

I've commented on the basic problem that quantum mechanics has in that no one really understand it.

Now getting back to the title, are the laws that physics is based upon unique?  Are there other possible ways to describe physical reality that work better than what we have now?  In the twentieth century Newton's laws and other classical theories where shown not to work in the realm of the very small, the very fast, or the very massive.  Quantum mechanics works well for the very small, special relativity works well for the very fast and general relativity works well for the very massive.  Those three theories when extended back to Newtons,(the classical), realm give us the classical results which you would expect for successful theories.  One problem that I'm not really sure about is when exactly do you need to make the transition from Newton (classical) to quantum?  At what size level does that occur?

This is also the problem with complexity problems and their solutions.  This is an area I'm not as familiar with.  What has happened to research in the area of complexity such as chaos, self organizing systems?  These are what I understand are called emergent phenomenon.  What is happening in those areas?  I need to read more about those.

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