[Physics] Physics Digest, Vol 19, Issue 5

Mon Dec 3 22:35:27 CET 2018

 Tufail, 

I have been meaning to write back to you and John .. from my investigations about systems dynamics, and mathematical interpretations.  I shall do that soon, as time permits, but for the moment, I want to comment on your closing question, 

       "What alternative 3-D truth exists which mathematically appears/behave as 4D continuum?"
Superb question.  The possible answer requires a deeper analysis of mathematical relations - and - how they correspond with our intuited~experienced notion of 'dimensions', and, if information retains the same initial interpretations .. when .. we change frames of reference.
We intuit einsteinian~reimann notions related to 'physical~temporal spaces'.   But no one has dissected if similar elastic relations or translations happen when we navigate alternative (adjacent) exponential 'frames of reference' (in mathematical senses).
We assume that the math relations and physical relations map exactly, but from my analysis - that might not be the case.
Examine calculus integration~differentiation for example (where in simple cases the most obvious effect is whole integer increase and decrease of exponents that result after a calculus operation is calculated).
Area under a curve ; slope of a line at a point along a curve ; etc. eg.   That is. the functions produce what look like totally -different- math information.

Now, use polar trig calculus instead.   Such as X=r sin Theta  (a circle with a one perimeter point at (0,0).  

Integrate or differentiate the equation.   What results is x = r cosine theta  (+ or - depending on which operator).  Graph the result.The graph is a RETAINED circle ... that is ... exactly the same geometric "information" ... except:  transposed 90 degrees.
So, what is REALLY happening with calculus - as a general operator?   Is information dimensionally transformed (compressed; expanded), or, is intrinsic information "dimensionally retained" .. just dimensionally transposed?
I know this deduction is going to sound crazy .. but the answer to coordinating QM with relativity (where dimensions and continuums are freshly understood as more fundamental than the QM statistical mathematics which we currently rely on) ... resides in going back down into basic math definitions and correcting omissions and omitted interpretations.
QM math - as well as it seems to work in physics descriptions - is effectively a 'work around', because humanity is struggling with a limited understanding of math~information~dimensions~continuum relations .. and is totally missing the relations about entropy -- which is -not- (in my paradigm) limited to only thermodynamics.  Entropy is applicable to gradients everywhere and that includes -fields- ... that have intrinsic differential strengths and values.  Fixation on thermodynamics is like chaining our minds to a limited fixed definition .. one and only one example form of 'entroepy'.     Even -those- analyses are larger and more complicated~inter-related.
Just some 2018 'holiday' thoughts   :-)
Jamesintegrity at prodigy.net

==================  

    On Monday, December 3, 2018, 12:56:46 PM PST, Tufail Abbas <tufail.abbas at gmail.com> wrote:  

 Tom,
Usually I do not believe in criticizing unless an alternate possible solution is discussed. Relativity is a well formulated and widely accepted theory.
So my question would be that if not Relativity then what?.
Every theory is built upon certain basic assumption and if those assumptions are not actual truth, then it is certain that theory is in error. 
In case of relativity that assumption is  about the physical existence of a "body of reference"/ coordinate system  extending from -infinity to infinity for every moving body. The truth may be completely different from what Einstein has proposed.
Quoting from the paper which you shared, Einstein himself admitted that: 

"In practice, the rigid surfaces which constitute the system of co-ordinates are generally not available ; furthermore, the magnitudes of the co-ordinates are not actually determined by constructions with rigid rods, but by indirect means. If the results of physics and astronomy are to maintain their clearness, the physical meaning of specifications of position must always be sought in accordance with the above considerations"

Despite the above admission, he assumed as follows for formulation of his theory of relativity.  

"Every description of events in space involves the use of a rigid body to which such events have to be referred. The resulting relationship takes for granted that the laws of Euclidean geometry hold for "distances;" the "distance" being represented physically by means of the convention of two marks on a rigid body".

We have to recognize that in  practice/reality , atmost only a 2-D surface is ever available as a rigid body of reference: like the surface of earth. 

Due the practical non-existence of such a "rigid body of reference"/"coordinate system" for 3-D, for all those applications to which relativity is related, the validity of the theory is doubtful if it is based upon such a coordinate system which assumes that.

1. All length intervals or distance between neighbouring points are equidistant.
2. All points of space are available(continue) for positioning a physical object made of matter. 

Indeed, maths should represent what is physical, and we should seek for truth of physically existing coordinate system that represent our reality, not the mathematical coordinate system assumed by Einstein.
POSSIBLE ALTERNATE REALITY
Physical properties of space are based on all kinds Fields that exists in that space. The existence and interaction  of Fields should possibly alter some configuration of space, so that length separation between neighbouring  "available points" are not same everywhere, but time interval is same. 
IMPLICATIONS OF PROPOSED ALTERNATIVE 

1. Space is divided by equidistant time interval , hence time becomes absolute.2. Space is not divided by equidistant length interval, hence it may still become possible to explain constant speed of light for all observers. 
RELATED QUESTIION 

What alternative 3-D truth exists which mathematically appears/behave as 4D continuum?
Regards,

Tufail 
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