How Would Changing the Definition of a Meter Impact Our Scientific Calculations?

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SUMMARY

The discussion centers on the implications of redefining the meter, specifically the distance light travels in 1/299,792,458 seconds. A hypothetical scenario is presented where the meter is defined as the distance light travels in X/2 seconds, leading to significant confusion in mathematical calculations, particularly involving pi and geometric properties. The consensus among participants is that while redefining the meter could theoretically alter calculations, it does not invalidate existing scientific measurements or principles. The conversation concludes with a firm stance that current definitions are accepted in mainstream science.

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Vikram Khanna
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Consider the definition of 1m. It is the distance traveled by light in 1 / 299,792,458 seconds (lets call this X). Fair enough a definition.

Now let's assume, for an instant, that somewhere in our past, while scales were being developed, man erroneously decided that instead of the distance traveled by light in X seconds, 1 meter will be the distance traveled by light in X/2 seconds. Thus, 1 meter would actually be 2 meters, for all practical purposes to be used today.

Ideally this isn’t a problem. Some intelligent mathematician would discover our folly and just divide all distances by 2. Not a major problem. Every scale of distance would half and the result would be EXACTLY half of the older one. No milestones replaced. Only New ones added.

Except in one case.

What about pi ? There is no end to pi. So how would we half it? That means every calculation used by our erstwhile method of calculating distance that involved pi would give a different result when halved. Then what about the area of a circle that we had calculated using the old definition of 1 meter. What about all the polynomial equations?

Now what if the error in calculating 1 meter was the distance traveled by light in X/1.3 seconds. Or X divided by a square root. or any other number on the number scale.

Have all our calculations based on our definition of 1 meter been wrong? Has it been a confirmation bias, since we decided that 1 meter = 1 meter? What about the sizes of planets calculated based on their distance from the Earth. Or their wavelength? or the Red Shift? Does this apply to all our other scales as well? Mass? Force? Gravity? Magnetism?
Isn't Mathematics supposed to be universal? Then how can one definition of a meter on Earth lead to different results when compared to any other definition.
 
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Vikram Khanna said:
What about pi ?
The ratio of circumference to diameter of a circle is unitless.

Vikram Khanna said:
man erroneously decided that
Why would it be erroneous? The point of developing a system of units is not to find some 'true' meaning of a meter or whatnot, but to give everybody the same set of units to use. As long as you and I use the same definition of a meter, we're good.

Vikram Khanna said:
instead of the distance traveled by light in X seconds, 1 meter will be the distance traveled by light in X/2 seconds. Thus, 1 meter would actually be 2 meters
Actually, that would be 0.5 meters ;) (edit: oh, sorry, you meant the other way around :) )
 
Vikram Khanna said:
Now let's assume, for an instant, that somewhere in our past, while scales were being developed, man erroneously decided that instead of the distance traveled by light in X seconds, 1 meter will be the distance traveled by light in X/2 seconds. Thus, 1 meter would actually be 2 meters, for all practical purposes to be used today.
That assumption is wrong.

Vikram Khanna said:
Have all our calculations based on our definition of 1 meter been wrong?
No, they're not wrong. To say so goes against mainstream science, so such discussion cannot take place at PhysicsForums.

Thread closed.
 

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