Scale Independent Math Expressions for Physical Processes

Math Expressions
Spiral Galaxy NGC 1232 – ESO

Scientists seek the ability to explain all physical processes by means of single math expressions independent of scale—from the subatomic to the astronomic. Is that possible?

There are also physics anomalies. Or, perhaps, they are best described as dichotomies. For example, light is known to act sometimes as a particle, sometimes as a wave. Can these two behaviors be reconciled into one, describable using one mathematical expression?

I believe the answer in both instances is, Yes. Perhaps I feel so because historically scientists have believed there should be simplicity in the laws of nature.

Disclaimer: The author, though not an unintelligent man, does have moments when his mental prowess can be more closely described as bone-headed. This may be one of those instances. If I have spoken mere foolishness here, please chalk it up to a day of foggy mental processes.

Math Expressions: An Illustrative Function

Imagine a function y in terms of x, such that,

y = (xⁿ) + (nx) + (1/xⁿ)

The value of n is quite large. We label the first term A for astronomical scale, the second term C for common scale, the third term I for infinitesimal scale.

We define x,

x ≧ 0

Evaluating Our Crude Illustrative Function

Our function possesses no meaning in reality, or we would already have solved the issues we delineated in our introduction. But we wish to get a feel for a possible process (at least in this author’s mind).

If x is large A is immense. C though large, is miniscule compared to A. I is so small it isn’t worth mentioning.

If x is much smaller, say 1, A is much smaller—in this instance 1. C is larger than A. C is larger than I.

If x is considerably smaller still, A approaches insignificance. C decreases as well. I grows to immense proportion.

A Starting Point Conclusion

Although the function I chose is perhaps not the best, hopefully the reader will still get the point. A single equation can have component parts that increase or decrease in value as one single variable waxes or wanes. This exercise suggests it should be possible to write natural laws covering all scales microscopic to the astronomic.

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One thought on “Scale Independent Math Expressions for Physical Processes

  • Interesting. I think I see your point but my math is not at a sufficient level to be able to say either “brilliant” or “rubbish”. You have however, explained your idea very clearly, even for a non-mathematician.

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