Monday, 19 August 2013

Newton: and Why I Weigh Exactly the Same as the Earth.

As promised in my profile, the odd article will have nothing to do with fishing or wildlife: this is one such.  Feel free to stop reading now if you so wish.  I won't send out the gendarmes to arrest you and escort you to the guillotine.  Reading any of my drivel is as much optional as it is a waste of your time.

We all know that  Isaac Newton was a genius of his day, the best scientist of his times by some margin.  But I suspect that his true genius can only be seen by those who actually go and look at what he achieved.  To this end I decided to try and read his Principia Mathematica or Philosophiæ Naturalis Principia Mathematica to give it the full name from the title page. Of course this treatise was written entirely in Latin, and my schoolboy Latin, somewhat loosely remembered from a long time ago, is now totally unable to extract any useful grains of intelligence from the text.  Even in its heyday, I suspect my Latin would have been totally inadequate to perform even a fraction of the task.  And the GCE examiner certainly agreed with me all those years ago.  But I found a translated text of the book, one which has striven to maintain the convoluted and complex use of words that characterized the original text.  In short, it is still damned difficult to understand.  Every sentence seems twisted, and you need to be a crossword fanatic to understand much of it.  A good challenge for an idiot like me therefore.

On opening the first few pages, it quickly became apparent to me that old Isaac, way back in 1687 had indeed produced a work of absolute genius and insight. From the very start of the book, his precision in describing the fundamental quantities, mass, weight speed, velocity etc., impressed me greatly. So precise, so detailed.  The reading is hard work, and progresses slowly, but it was not long before one keen piece of insight knocked me sideways.  In effect, and to transcribe it into modern English: one of the corollaries of his law "action and reaction are equal and opposite" can be applied to weight.  What he is saying is that my weight, as seen by the earth, is exactly the same as the earth's weight, as seen by me.  In effect the earth weighs the same as I do.   I have here added my own thought experiment to this, as a way of explaining more simply what Newton said.

If I place the bathroom scales outside, on the patio, and the scales record my weight, then you as an observer, in a generous mood, might say I weigh 200 pounds.  I now turn the scales upside down, and once again stand on them.  You, as an observer, must now stand on your head in order to read the scales.  They still read 200 pounds. What you are now seeing is that the scales have been placed on my feet, with the earth placed on top of the scales.  So you would now see that the scales are indeed weighing, not me, but the entire Earth. You might even photograph the event.  The two scale readings are the same.   So one could say that the earth, in this experiment, weighs exactly the same as I do.  The scales prove it.  Logically, to the man in the street, this seems utter rubbish, but it is not. It  serves admirably to demonstrate the difference between mass and weight.    Mass, as Newton himself defines in Principia, is a quantity of matter.   Weight is a force, a force due to the existence of gravity.   My weight is the force, exerted on my mass, by the mass of the earth.    The Earth's weight is the force exerted on the mass of the Earth, by MY mass. And Newton's laws give credence to this,  in that a force, in action on one body from another, causes an equal, and opposite force on the other body.    And that law applies to gravity, which is the phenomenon that produces the force that we know as weight.  Weight is relative;  its value for a particular mass varies according to  the mass and position of another object, that object from which you are making the measurement.   If my wife does the scales experiment she will record the Earth as weighing less that the value I saw.   If I stand on top of Everest, then the earth ( and myself) will weigh a little less.

In all my school and university days, I have never seen the difference between mass and weight expressed so clearly to me, as it has just been by Mr. Newton.   My thanks to him.   And I must now read on to see what other eye-opening statements I can find. For anyone to have written this, more than 300 years ago is astonishing...and I have barely opened the book.

Reference: http://archive.org/stream/100878576#page/01/mode/2up  : Newton's Principia  Translated

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