# Consider the definition of 1m

1. Nov 21, 2016

### Vikram Khanna

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 lets 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.

2. Nov 21, 2016

### Bandersnatch

The ratio of circumference to diameter of a circle is unitless.

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.

Actually, that would be 0.5 meters ;) (edit: oh, sorry, you meant the other way around :) )

3. Nov 21, 2016

### Staff: Mentor

That assumption is wrong.

No, they're not wrong. To say so goes against mainstream science, so such discussion cannot take place at PhysicsForums.