Does the meter link a circumference to c?

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2 minutes ago, TakenItSeriously said:

Your quoting my post out of context.

What context? How does it make any difference: using metric (or feet and inches) has nothing to do with whether the circumference of a circle is a rational value or not.

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5 hours ago, TakenItSeriously said:

I’ve often wondered why Cosmology chose the Parsec over the Lightyear. since the light year makes it so much easier to use c = 1 ly/yr.

I guess its because when c =1, then the unit circle makes the wavelength of light an irrational number again?

No. It's because the parsec relates directly to how astronomical distances are actually measured.

Having irrational units isn't a big problem- which is just as well.

If you measure the diagonal of a unit square the units are apparently irrational because he side and the diagonal are incommensurate.

The definition of the ampere means that the permeability of a vacuum is irrational.

Measured things (like the length of my keyboard) are actually irrational anyway.

It's nominally 40 cm, but if I measure it to the nearest millimetre it's 40.1. If I measure to a tenth of a mm it's 40.13.

If I keep measuring to more precision I keep getting more digits. If I could measure to an infinite precision then the length would have an infinite number of digits and so it would be irrational.

Please don't waste time introducing the Planck distance.

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On 11/14/2017 at 4:24 PM, TakenItSeriously said:

BTW, I forgot to mention that their was also what I initially thought must be a strange coincidence in that the paradigm shift seemed to begin having an impact at around 30 MHz or 30 million cycles/sec.

The relativistic effect begins to be significant at about 0.1c or roughly 30 million m/s.

So, like I said, I thought it had to be a coincidence because I thought the definition of a meter was arbitrary relative to light. But thats one hell of a coincidence because 30 million is a very large number.  Then once I discovered a meter wasnt so arbitrary after all, I started to try and understand the concepts involved.

The result implies a link to how a meter is defined and what we know about a cycle which could be thought of as a wavelength (or period). the one thing we know is the fact that a wave stops behaving like a wave at geometries smaller than 1/2 λ. and that harmonically speaking, they must always be in hole units of 1/2λ

Also note that if you plot the inverse of the Lorentz factor vs speed from 0-c it is 1/4 of a circle.

I’m quite sure that I understand what you’re getting at, and I think I understand the way that this should be properly explained (mathematically.)  We consider the basis of the sine to be a ratio (mathematically) when in real fact it is based on an actual quantity (mathematically.)

Work is currently being done on this front.  The distinction is very subtle, hence your inability to pin it down any better.  I just want to validate that what you say is correct, despite the reactions from the skeptics.  The new geometry which includes the turn as a base quantity is called synchronous geometry.

If anyone fails to understand the mathematical proof of the existence of a turn as a quantity, please feel free to ask questions.  If anything that I’ve said here (or elsewhere) can be falsified by any method whatsoever, I’d sure be interested to hear about it.

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8 hours ago, steveupson said:

I’m quite sure that I understand what you’re getting at, and I think I understand the way that this should be properly explained (mathematically.)  We consider the basis of the sine to be a ratio (mathematically) when in real fact it is based on an actual quantity (mathematically.)

Work is currently being done on this front.  The distinction is very subtle, hence your inability to pin it down any better.  I just want to validate that what you say is correct, despite the reactions from the skeptics.  The new geometry which includes the turn as a base quantity is called synchronous geometry.

If anyone fails to understand the mathematical proof of the existence of a turn as a quantity, please feel free to ask questions.  If anything that I’ve said here (or elsewhere) can be falsified by any method whatsoever, I’d sure be interested to hear about it.

Thanks for the feedback.

Since my skills are strongly biassed towards logic but not necessarily math (depending on how you think about the two) providing a proper mathematical explanation could be a huge benefit towards a more widely based understanding, which I would have a very difficult time deriving completely on my own.

Edited by TakenItSeriously

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17 hours ago, steveupson said:

The new geometry which includes the turn as a base quantity is called synchronous geometry.

!

Moderator Note

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Never mind about the definition of the meter. If the diameter  of the circle is one unit then the circumference is pi units. If the circumference is one unit then the diameter is 1/pi units. This means that at least one of the two measurements is an irrational number. How can this be reconciled with the fact that the diameter and the circumference are real physical quantities? And what does it tell us about accuracy of measurements?

Ken.

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18 minutes ago, John Kenneth Swinswood said:

How can this be reconciled with the fact that the diameter and the circumference are real physical quantities?

That is only true for a real physical object, which won't be perfectly circular anyway.

19 minutes ago, John Kenneth Swinswood said:

And what does it tell us about accuracy of measurements?

Not much. You don't need very many decimal places of pi to calculate the circumference of the observable universe to an accuracy of a millimetre (about 30, I think).

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30 minutes ago, John Kenneth Swinswood said:

Never mind about the definition of the meter. If the diameter  of the circle is one unit then the circumference is pi units. If the circumference is one unit then the diameter is 1/pi units. This means that at least one of the two measurements is an irrational number. How can this be reconciled with the fact that the diameter and the circumference are real physical quantities? And what does it tell us about accuracy of measurements?

Ken.

What's to reconcile?

Draw a line four inches long.

Before your pencil reached 4 inches and after it reached 3 inches from the start, you must have drawn a straight line exactly pi inches long.

Edited by studiot

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What is pi exactly?

Ken.

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pi is pi.

As such it is one of the infinity of what we call real numbers that cannot be represented in decimal format.
Since it is so important to us we give it a special name - pi.

This is no different from asking what is one half exactly, when using the counting numbers.

One half is one of the infinity of what we call rational numbers that cannot be represented in integer format.
Since it is so important to us we give it a special name - one half.

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46 minutes ago, John Kenneth Swinswood said:

What is pi exactly?

Ken.

That page has a neat animation showing the definition:

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Not only neat, but beautiful. Thanks.

The point I'm trying to get at is this... Looking at the line in the animation we can see that pi is between 3 and 4. Using a ruler we could find that it is between 3.1 and 3.2; with a vernier scale or micrometer between 3.14 and 3.15, etc. If we could improve the accuracy of measurement by a factor of ten every day for a thousand years we would still not have the exact measurement. In fact it would never be accurate. Is this another "uncertainty principle"?

Ken.

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5 minutes ago, John Kenneth Swinswood said:

Is this another "uncertainty principle"?

It is just a matter of measurement accuracy. Which is always limited. It has nothing to do with the value of pi, though. As someone else said, it is equally true of the value 2.0000....

Edited by Strange

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9 minutes ago, John Kenneth Swinswood said:

Not only neat, but beautiful. Thanks.

The point I'm trying to get at is this... Looking at the line in the animation we can see that pi is between 3 and 4. Using a ruler we could find that it is between 3.1 and 3.2; with a vernier scale or micrometer between 3.14 and 3.15, etc. If we could improve the accuracy of measurement by a factor of ten every day for a thousand years we would still not have the exact measurement. In fact it would never be accurate. Is this another "uncertainty principle"?

Ken.

This is similar to the realization of any defined standard, like the second. The definition is exact, but our attempts to mark an exact interval are limited in precision.