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

• Vikram Khanna
In summary, the conversation discusses the potential consequences of using an incorrect definition of 1 meter in developing scales of measurement. It raises questions about the accuracy of calculations involving pi and other scales such as mass, force, and gravity. The conversation also questions the universality of mathematics and the purpose of developing a system of units. The thread is closed without reaching a conclusion.
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 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.

Vikram Khanna said:
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.

1. What is the definition of 1m?

The definition of 1m is one meter, which is a unit of length in the International System of Units (SI). It is equal to 100 centimeters or approximately 39.37 inches.

2. How is the definition of 1m determined?

The definition of 1m is based on the speed of light in a vacuum. It is defined as the distance traveled by light in a vacuum in 1/299,792,458 of a second.

3. Why is 1m considered a standard unit of measurement?

1m is considered a standard unit of measurement because it is defined in the SI system and is used as a base unit for length. It is also easily understood and can be converted into other units of length.

4. Is the definition of 1m constant?

Yes, the definition of 1m is a constant value. It is not subject to change and is used as a reference for other units of length.

5. Are there any other definitions of 1m?

No, the definition of 1m is universal and accepted internationally. There are no alternative definitions for 1m in the scientific community.

• General Math
Replies
5
Views
2K
• Classical Physics
Replies
138
Views
4K
• General Math
Replies
1
Views
1K
• Special and General Relativity
Replies
55
Views
2K
• Other Physics Topics
Replies
8
Views
4K
• New Member Introductions
Replies
34
Views
278
• General Math
Replies
3
Views
801
• Special and General Relativity
Replies
12
Views
1K
• Other Physics Topics
Replies
2
Views
3K
• Special and General Relativity
Replies
101
Views
10K