Thread: Does Quantum theory limit pi to a definite size?

If Quantum theory suggests that time and distance cannot be broken down smaller than planck limits then surely the value of pi is dependent upon the size of the circle and not a fixed constant. Conside a circle of 1 planck length, for this circle the diameter and circumference (and therefore pi) will be just 1.
Of course this could all be bollocks but what do the rest of you think?

I don't think mathematics is limited by physical laws. However, if you are talking about the ratio of the diameter of a real, (approximately) circular, physical object to its circumference, you may have a point.

Constants are called constants for a reason. is the ratio of the circumference of a circle to its diameter. That's always true. The circumference will always be equal to . There's really no reason to think that that would change, even at the smallest scale possible.

Originally Posted by wert

or this circle the diameter and circumference (and therefore pi) will be just 1.

What are you talking about? If the diameter has length 1, then the circumference has length . If the circumference has length 1, then the diameter has length . You can’t have a circle whose circumference and diameter are both 1! :x

Originally Posted by wert

If Quantum theory suggests that time and distance cannot be broken down smaller than planck limits then surely the value of pi is dependent upon the size of the circle and not a fixed constant. Conside a circle of 1 planck length, for this circle the diameter and circumference (and therefore pi) will be just 1.
Of course this could all be bollocks but what do the rest of you think?

1. JaneBennet is absoslsutely correct. Your statement about a circle makes no sense.

2. Quantum theory places no limits on mathematics. Mathematics does place limits on quantum theory.

3. Physical speculations with respect to anyting that happens with respect to space or space-time at the Planck length are just that -- speculations. There is nothing yet that has been proved or that is part of established physical models.

4. Even is someday some effect on space-time is found at the Planck length (e.g. some version of Wheeler's quantum foam) that will still place no constraints on mathematics and the nature of pi will be unchanged. Mathematical theorems don't change. Physical models do evolve.

Sheesh Jane, why so agro? You guys may not know wert, but I can assure you that he is no idiot. Can pi be affected by the warping of multi-dimensional space? At small enough scales those might just have an influence.

Perfect circles exist only in mathematics, in reality the ratio of circumference to diameter of any 'circle' is anything but a constant.

Now think of this, what is the minimum number of atoms you need to place end to end (or side by side) to produce a perfect circle? suppose you start with three, well thats a triangle, 4? a square, 8 and octagon how many for a circle?

If you used all the atoms in the universe you would still not achieve a mathematically perfect circle.

Just as it will shock you all to know that upon the moon, dropping a hammer and feather at the same time the hammer will hit the moon first, (see my Feb 2007 article in the Mensa magazine) so a real circle with a diameter of 1 * 10-10m will have a circumference of either 3 or 4 * 10-10m !! but most definitely NOT 3.141... *10-10m

Originally Posted by wert

If Quantum theory suggests that time and distance cannot be broken down smaller than planck limits then surely the value of pi is dependent upon the size of the circle and not a fixed constant. Conside a circle of 1 planck length, for this circle the diameter and circumference (and therefore pi) will be just 1.
Of course this could all be bollocks but what do the rest of you think?

Having seen the other esponses to this, I propose that the one issue with this argument of yours is this: if something is of the size of a Planck length, I do not believe you can consider it to have a shape, circular or otherwise. It would be akin to asking the colour of a Hydrogen molecule (not its spectrum).

Ergo, I'd suggest the question is moot.

Originally Posted by sunshinewarrior

Originally Posted by wert

If Quantum theory suggests that time and distance cannot be broken down smaller than planck limits then surely the value of pi is dependent upon the size of the circle and not a fixed constant. Conside a circle of 1 planck length, for this circle the diameter and circumference (and therefore pi) will be just 1.
Of course this could all be bollocks but what do the rest of you think?

Having seen the other esponses to this, I propose that the one issue with this argument of yours is this: if something is of the size of a Planck length, I do not believe you can consider it to have a shape, circular or otherwise. It would be akin to asking the colour of a Hydrogen molecule (not its spectrum).

Ergo, I'd suggest the question is moot.

The question is not moot, and here is the reason. Your example of the color of the hydrogen suggests a questoin or assertion that is a non-sequitur. However, the original question posed can be addressed, and addressed clearly and unambiguously.

The question itself reflects a serious misunderstanding of the relationship between mathematics and physics. This is a mathematics forum.

In mathematics a circle is a circle is a circle and the dimensions are totally irrelevant. Planck length has nothing whatever to do with the nature of a circle or of . The ratio of the circumference of a circle to its diameter is . Period. And has the same meaning that it always has, which is 1/2 the period of the function, if you don't like the definition in terms of the circumference and diameter of a circle.

In physics also a circle is a circle is a circle. And is . But there are limitations placed on the accuracy with which position can be determined, and, if some speculation with regard to space-time is correct, at some scale space may not be adequately modeled as locally Eudlidean. A that point the very notion of a circle becomes irrelevant, not different, irrelevant. But this is not fact, it is just speculation at this time.

The question is not moot, It is misguided. It deserves to be put back on course.

Careful there, some on this forum might say that however small something is, it must have a shape, whereas some of us are thinking more of little amorphous quantities of energy. Ah color, no such thing of course, but that's another thread...

Originally Posted by wert

Careful there, some on this forum might say that however small something is, it must have a shape, whereas some of us are thinking more of little amorphous quantities of energy. Ah color, no such thing of course, but that's another thread...

Not on this forum though, eh? Perhaps in physics, or philosophy. But if talking about real world objects, as Dr Rocket pointed out, there's no point having argumentation in the mathematics sub-forum.

I did ponder whether I should have started this in another part of the forum but decided here, I'd have no objection to it being moved.

Originally Posted by wert

Careful there, some on this forum might say that however small something is, it must have a shape, whereas some of us are thinking more of little amorphous quantities of energy. Ah color, no such thing of course, but that's another thread...

Yep. And some people also share your the confusion between mathematics and physics.

Originally Posted by wert

If Quantum theory suggests that time and distance cannot be broken down smaller than planck limits then surely the value of pi is dependent upon the size of the circle and not a fixed constant. Conside a circle of 1 planck length, for this circle the diameter and circumference (and therefore pi) will be just 1.
Of course this could all be bollocks but what do the rest of you think?

Just some actuality if you are interested. I actually machined a wheel. Because it was taught and believed in my circle that circumference in reality was not actually diameter times pi as we know it 3.14159. This was checked by highly accurate machining. Far better then mine.

Mine confirmed though what they were saying. Along with a very strange phenomena.

That to me was revolutionary, even though Archimedes had found it already. He found that if you had very small bumps on a stone wheel. It rolls in one revolution a shorter distance then a perfectly cleaned wheel. I was taught he spent a good portion of his life creating the perfect stone.

If you are at all interested, imagine what I am saying. I was amazed while actually doing the test.

I lazily was arguing with someone about circumference and pi. And we were posting and flaming. So I decided to machine a wheel, measure it, roll it on a very flat surface. And get the results.

I learned so much that I am probably still absorbing the reality of it. Even though I was taught this and learned this all my life. The actuality of it, and just hearing about it were two different things.

Here is how it went. I machined a wheel. I surfaced a plate. I measure the wheel, and roll the wheel, and it rolls a ratio of 3.159, I am depressed. I just took the wheel off the lathe and gave it a wipe with a shop rag. Certainly unscientific, but in my mind, I am thinking (incorrectly) that any little bumps on the wheel will add to the length of the roll. Increase the diameter.

I am a good sport, I say, "I guess my guys were wrong, my teachings are incorrect. I am going to clean this wheel with xylene. To a clean that has never been seen before at least in our shop. And maybe even get a lower pi value as many had suggested real pi is".

I am doing this for the gang that frequented my forum. I am using 70-75 Aluminum tooling plate, hardened to T-8. It creates a very smooth surface when you machine it.

Archimedes always wanted to try it with a less granular substance then his stone wheel and stone base. According to my teachings.

Well anyway I setup, I am still a little down and out about being wrong and saying wrong things, but hey, I am a man. So I roll the wheel, and it rolls much further in one roll.

I am thinking to myself nice try McCormick. So I roll it again and again. And sure enough it keeps rolling long.

The bottom line is that little bumps on a wheel act like a bumpy terrain.

So it always pays to do your leg work.

You can delete this if it is off topic.




Sincerely,


William McCormick