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DXWarlock
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 Posted: Fri, 19th Oct 2012 23:10 Post subject: Another useless, pointless Math/Physics question |
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Maybe some of the math/quantum physic nuts can help me out here..Im stuck in a loop of logic.
Its a given Pi is infinite, with no repeating patterns. its been calculated to 10 trillion places (I think) as the world record.
But if the shortest distance is a 'Planck Length' wouldnt either pi be finite, or the Planck length wrong?
For example if the shortest possible distance is the Planck, that means when zoomed into that distance, the circle no longer 'curves', because to do so mean there is a distance shorter, for example the distance from the apex of the curve to the interection of the slice you are looking at. drawing a line from the 2 'ends' of the curve you can see creates an 'defined' area' a dome shape of sorts.
Like here the 'segment' area...no matter how far you zoom into that arc..you can still make a segment 'cresent' shape.
So how can Pi be infinite, based on the fact a circle no matter how far 'zoomed into' always exhibits a curve...if a planck distance defines whats the shortest possible distance something can have 'measurement of area', as that crescent will ALWAYS have an area measurement (for Pi to be infinite).
Am I making sense?
-We don't control what happens to us in life, but we control how we respond to what happens in life.
-Hard times create strong men, strong men create good times, good times create weak men, and weak men create hard times. -G. Michael Hopf
Disclaimer: Post made by me are of my own creation. A delusional mind relayed in text form.
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| Posted: Fri, 19th Oct 2012 23:17 Post subject: |
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Pi is a mathematical construct regarding a ratio of a geometrical figure, and in math you always work with infinte, unconstrained sets.
The planck lenght is a feature of the universe, and none can conclusively state that there are no sub planck structures. According to current models, there is no need to presume their existence, but our current models are only that, models.
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DXWarlock
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| Posted: Fri, 19th Oct 2012 23:18 Post subject: |
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yes, but wouldnt PI show planck length to be wrong? as how would you define a circle with a diameter of planck? that implies there is a radius of 1/2 a planck. (which according to itself) cant exist.
-We don't control what happens to us in life, but we control how we respond to what happens in life.
-Hard times create strong men, strong men create good times, good times create weak men, and weak men create hard times. -G. Michael Hopf
Disclaimer: Post made by me are of my own creation. A delusional mind relayed in text form.
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| Posted: Fri, 19th Oct 2012 23:23 Post subject: |
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| DXWarlock wrote: | | yes, but wouldnt PI show planck length to be wrong? as how would you define a circle with a diameter of planck? that implies there is a radius of 1/2 a planck. (which according to itself) cant exist. |
Why would it?
When you work with Pi, you're working with an abstraction, unless you're working with a mathematical function that limits the shortest lenght to a planck unit, there is no reason for Pi to have a limit, there is no reason for any mathematical value to have a limit, until you set limits on your functions.
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aevis
Posts: 522
Location: Absurdia
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| Posted: Fri, 19th Oct 2012 23:29 Post subject: |
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I think an easier analogy would be taking a distance between two points and constantly halving it in order to get an even smaller distance. Theoretically nothing would stop you \o/
The difference is that in this concept as well as the one you described distances(radius/ length) are purely theoretical notions, whereas the planck length is a physical limitation.
Thus there is no problem with actually defining a circle with a diameter of planck as a theoretical model , it's just physically impossible to create (as far as we know ).
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| Posted: Fri, 19th Oct 2012 23:35 Post subject: |
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| aevis wrote: | I think an easier analogy would be taking a distance between two points and constantly halving it in order to get an even smaller distance. Theoretically nothing would stop you \o/
The difference is that in this concept as well as the one you described distances(radius/ length) are purely theoretical notions, whereas the planck length is a physical limitation.
Thus there is no problem with actually defining a circle with a diameter of planck as a theoretical model , it's just physically impossible to create (as far as we know ). |
This!
And I underline the "as far as we know"..
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DXWarlock
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| Posted: Fri, 19th Oct 2012 23:42 Post subject: |
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Ah maybe thats its, Im thinking in absolutes of the knowledge we have.
Either a circle can have an infinitely small curve, or it stops at the planck length in the 'real world'.
So in 'real world theory' as far as we know a circle can only be a polygon with LARGE numbers of planck length sides...(as far as we know fitting what we know).
But mathematically infinity is a possibility(even if an undesirable one)...but its 'mathematically possible'.
So either there is more beyond planck length we dont understand, or pi is an example of 'infinity that is correct in math, but only exists in formulas"
-We don't control what happens to us in life, but we control how we respond to what happens in life.
-Hard times create strong men, strong men create good times, good times create weak men, and weak men create hard times. -G. Michael Hopf
Disclaimer: Post made by me are of my own creation. A delusional mind relayed in text form.
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| Posted: Fri, 19th Oct 2012 23:52 Post subject: |
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| DXWarlock wrote: | Ah maybe thats its, Im thinking in absolutes of the knowledge we have.
Either a circle can have an infinitely small curve, or it stops at the planck length in the 'real world'.
So in 'real world theory' as far as we know a circle can only be a polygon with LARGE numbers of planck length sides...(as far as we know fitting what we know).
But mathematically infinity is a possibility(even if an undesirable one)...but its 'mathematically possible'.
So either there is more beyond planck length we dont understand, or pi is an example of 'infinity that is correct in math, but only exists in formulas" |
And that is the reason why mathematicians love infinities and physicists are dreaded by them.
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DXWarlock
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| Posted: Sat, 20th Oct 2012 00:00 Post subject: |
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Then I wonder where pi would end in real world understanding (as we know it).
Not that its useful for anything. but if you made a circle with planck length sides..and calculated it, what would it be?
Wouldn't that be a version of a 'physicist' definition of pi based of laws of physics?
You know, what would Pi's value be using the laws we have in place now.
-We don't control what happens to us in life, but we control how we respond to what happens in life.
-Hard times create strong men, strong men create good times, good times create weak men, and weak men create hard times. -G. Michael Hopf
Disclaimer: Post made by me are of my own creation. A delusional mind relayed in text form.
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| Posted: Sat, 20th Oct 2012 00:26 Post subject: |
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| DXWarlock wrote: | Then I wonder where pi would end in real world understanding (as we know it).
Not that its useful for anything. but if you made a circle with planck length sides..and calculated it, what would it be?
Wouldn't that be a version of a 'physicist' definition of pi based of laws of physics?
You know, what would Pi's value be using the laws we have in place now. |
I think that most real calculations with pi rarely go past the 40 digits mark, 40 digits is all it is needed to make computations regarding the entire volume of the known universe with a precision inferior to the size of an electron.
Perhaps some calculations with higher dimensional structures would require a few more digits, but I would presume that nothing over 100 digits has any physical relevance.
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| Posted: Sat, 20th Oct 2012 09:37 Post subject: |
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| DXWarlock wrote: | Then I wonder where pi would end in real world understanding (as we know it).
Not that its useful for anything. but if you made a circle with planck length sides..and calculated it, what would it be?
Wouldn't that be a version of a 'physicist' definition of pi based of laws of physics?
You know, what would Pi's value be using the laws we have in place now. |
Pi would always be pi, like e is always e (2.718...). They are a mathematical constants (constants is a loose term here, because you don't really know it's full value because it's irrational number).
What do you mean by 'circle with planck length sides? First of all, a circle doesn't have a side xD
Second of all, even if you took the circumference or the radius of a circle a planck length, when taking ratio of the circumference to diameter, you'll always get pi! No matter what number you take, you'll get pi.
In that sense it's a constant.
And often in physics we approximate things, my professor at uni once approximated pi to 5 
Oh, and I'm still not yet sure how pi comes into play when looking at higher dimensions or different curvature of space... Plus then you don't play with 2-spheres embedded in 4d Minkowski space, but with n-spheres embedded in whatever space xD O.o
Don't think too much about it, you may go insane... trust me 
"Quantum mechanics is actually, contrary to it's reputation, unbeliveably simple, once you take the physics out."
Scott Aaronson | chiv wrote: | | thats true you know. newton didnt discover gravity. the apple told him about it, and then he killed it. the core was never found. |
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DXWarlock
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| Posted: Sat, 20th Oct 2012 10:16 Post subject: |
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Im talking mathematics constants vs "real world".
Not talking about how pi is formed, the logical loop of like above "even if you took the circumference or the radius of a circle a planck length, when taking ratio of the circumference to diameter, you'll always get pi! No matter what number you take, you'll get pi" well if a circles radius is one planck..how can you have a pi of 3.14 plancks? isnt the .14 not possible by the laws?
Sort of a "chalkboard numbers" vs "numbers that don't break current laws"
I know its a theoretical numbers using a flatland plane vs tangible objects.
But still isnt there some form of mathematical twitch going on there if the 2 type are compared?
-We don't control what happens to us in life, but we control how we respond to what happens in life.
-Hard times create strong men, strong men create good times, good times create weak men, and weak men create hard times. -G. Michael Hopf
Disclaimer: Post made by me are of my own creation. A delusional mind relayed in text form.
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| Posted: Sat, 20th Oct 2012 11:53 Post subject: |
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| DXWarlock wrote: | Im talking mathematics constants vs "real world".
Not talking about how pi is formed, the logical loop of like above "even if you took the circumference or the radius of a circle a planck length, when taking ratio of the circumference to diameter, you'll always get pi! No matter what number you take, you'll get pi" well if a circles radius is one planck..how can you have a pi of 3.14 plancks? isnt the .14 not possible by the laws? |
If you have a radius of 1 Planck length = 1.6*10^-35 mm the circumference will still be 2*r*pi.
I don't get what's the problem here?
| DXWarlock wrote: | Sort of a "chalkboard numbers" vs "numbers that don't break current laws"
I know its a theoretical numbers using a flatland plane vs tangible objects.
But still isnt there some form of mathematical twitch going on there if the 2 type are compared? |
I still am not quite sure what your problem is?
"Quantum mechanics is actually, contrary to it's reputation, unbeliveably simple, once you take the physics out."
Scott Aaronson | chiv wrote: | | thats true you know. newton didnt discover gravity. the apple told him about it, and then he killed it. the core was never found. |
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DXWarlock
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| Posted: Sat, 20th Oct 2012 21:08 Post subject: |
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Im not arguing your wrong, far from it, you know this far better than me. Just trying to get what you know, and compare it with the problem to see which of them is the way it works. Since it seems confusing to think of both possible to me.
How can you end up with a decimal length of plancks?
Like something cant be 2.5 plancks long. 1/2 a planck isnt a real thing.
so .14 of a planck wouldnt be a real thing.
here I found this
Maybe this will help..it puts it much better than I can, and is saying what I am trying to say:
It seems to me that geometry at the Planck length cannot be Euclidean. Since a fractional value of a Planck length is nonsense, then there would be no way of measuring the hypotenuse of a right triangle with arms 1 Planck length long. How would one measure the circumference of a circle with a radius of 1 Planck length (note the impossibility of a diameter equal to one Planck length--"diameter" implies two radii--each 1/2 Planck-length long)? What kind of geometry WOULD apply at the Planck length level?
perhaps that triangle is a better example, less variables...triangle with arms 1 Planck length long
how long WOULD the hypotenuse be? you could say its "well its 1:1:[squareroot of 2] ratio,its always that" (cant do a square root symbol in a post.)
And that would be the formula to get that measurement..but what would the measurement be that makes sense it would be 1:1:(what)?
And seeing how 1 is the smallest thing possible (if its a planck) the last variable would have to be a multi of it..with no decimal. which doesn't fit with pythagorean theorem answer.
so is it after a certain size down, the theorem no longer applies? or is it that planck lengths are volatile and break down when euclidean math is applies?
-We don't control what happens to us in life, but we control how we respond to what happens in life.
-Hard times create strong men, strong men create good times, good times create weak men, and weak men create hard times. -G. Michael Hopf
Disclaimer: Post made by me are of my own creation. A delusional mind relayed in text form.
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| Posted: Sat, 20th Oct 2012 22:26 Post subject: |
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Oh, so you say, if 1 l_pl (Planck length) is the smallest length in which our physics works, then 0.5 l_pl wouldn't make any sense since it would be smaller than that.
Right?
And in that respect you'd be correct (altho I still don't see a problem with the triangle since square root of 2 is ~1.41 >1). But if you treat it as any number, you can do any math in any space you like (Riemann or Lobachevsky, whatever you choose  ).
If you look at smaller scales, then physically things stop to make sense. You could make something up, but current models (string theory or quantum gravity) are based on the fact that you can't go smaller than that...
"Quantum mechanics is actually, contrary to it's reputation, unbeliveably simple, once you take the physics out."
Scott Aaronson | chiv wrote: | | thats true you know. newton didnt discover gravity. the apple told him about it, and then he killed it. the core was never found. |
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| Posted: Sat, 20th Oct 2012 22:48 Post subject: |
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DXWarlock, think about it this way, a Googleplex (10^100^100) is exceedingly larger than every individual planck unit within the entire observable uiverse, yet, mathematically, we can do calculations with numbers considerably larger than a Googleplex. Consider Graham's number for example, a number so tremendously large that we do not know it's full lenght, the mere amount of digits that it contains could never be written down, even if you used the entire universe to do it.
A mathematical model is not modeled to physical laws, unless it is defined as such, mathematics may be used to represent nature, because of it's logical foundation, but do not mistake mathematical concepts as tangible or even as possible.
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DXWarlock
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| Posted: Sat, 20th Oct 2012 22:55 Post subject: |
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Oh Im not Ron, It was more a question what math is used to explain the tangible objects of that size.
Like if the number is a number than can be calculated, but cant equal anything in the real universe that size, what would that 'thing' be measured with? since the only number we have to represent it, doesnt have anything that can be made of it.
Think its more of a catch22 of sorts, since we cant prove (as it is now) that anything can be that small, that the math used to explain it works, but without proof of it that it works beyond paper, we cant prove that it cant be that small to vaildate the math in the phsyical world:P
-We don't control what happens to us in life, but we control how we respond to what happens in life.
-Hard times create strong men, strong men create good times, good times create weak men, and weak men create hard times. -G. Michael Hopf
Disclaimer: Post made by me are of my own creation. A delusional mind relayed in text form.
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DXWarlock
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| Posted: Sat, 20th Oct 2012 23:04 Post subject: |
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| dingo_d wrote: | Oh, so you say, if 1 l_pl (Planck length) is the smallest length in which our physics works, then 0.5 l_pl wouldn't make any sense since it would be smaller than that.
Right?
And in that respect you'd be correct (altho I still don't see a problem with the triangle since square root of 2 is ~1.41 >1). But if you treat it as any number, you can do any math in any space you like (Riemann or Lobachevsky, whatever you choose ).
If you look at smaller scales, then physically things stop to make sense. You could make something up, but current models (string theory or quantum gravity) are based on the fact that you can't go smaller than that... |
Something like that..and true square root of 2 is ~1.41 >1,but its not divisible by 1. so to measure it it would be 1 and (something smaller than that) in planck distance.
IS it that i confuse planck distance as being the absolute smallest distance in nature (like a pixel on a screen, a sort of 3d universe pixel of space time) vs the smallest being able to measure, as to measure it would be using something larger than it to try to gauge it by.
Is it impossible to be smaller than that, or just its impossible to measure smaller than that, because the smallest particle is that size. To measure something smaller, would mean you'd need something its size to bounce off it to see the edges.
Like trying to measure how big a golf ball is using beach balls. The golf ball IS smaller, but the smallest thing in existence to measure it with is beachball sized.
But if its the last one, wouldn't the golfball be the new standard of 'small' until someone discovered a pea?
Edit:I think its just the confusion of my trying to apply logic to quantum distances, and theorems. And been 20 years since I Took it in school.
But I do remember my professor saying "if you are trying to think logical absolutes in quantum mechanics, you are approaching it wrong." Since my approach is trying to picture in my head what something that size would look like, and if there is a 'distance' that cant be shorter...everything would be made of "toothpicks' of that length, nothing can be smaller, or divisions of it..so trying to make a triangle with a set multiplier size doesn't work visually.
-We don't control what happens to us in life, but we control how we respond to what happens in life.
-Hard times create strong men, strong men create good times, good times create weak men, and weak men create hard times. -G. Michael Hopf
Disclaimer: Post made by me are of my own creation. A delusional mind relayed in text form.
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| Posted: Sun, 21st Oct 2012 09:06 Post subject: |
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| DXWarlock wrote: | | dingo_d wrote: | Oh, so you say, if 1 l_pl (Planck length) is the smallest length in which our physics works, then 0.5 l_pl wouldn't make any sense since it would be smaller than that.
Right?
And in that respect you'd be correct (altho I still don't see a problem with the triangle since square root of 2 is ~1.41 >1). But if you treat it as any number, you can do any math in any space you like (Riemann or Lobachevsky, whatever you choose ).
If you look at smaller scales, then physically things stop to make sense. You could make something up, but current models (string theory or quantum gravity) are based on the fact that you can't go smaller than that... |
Something like that..and true square root of 2 is ~1.41 >1,but its not divisible by 1. so to measure it it would be 1 and (something smaller than that) in planck distance.
IS it that i confuse planck distance as being the absolute smallest distance in nature (like a pixel on a screen, a sort of 3d universe pixel of space time) vs the smallest being able to measure, as to measure it would be using something larger than it to try to gauge it by.
Is it impossible to be smaller than that, or just its impossible to measure smaller than that, because the smallest particle is that size. To measure something smaller, would mean you'd need something its size to bounce off it to see the edges.
Like trying to measure how big a golf ball is using beach balls. The golf ball IS smaller, but the smallest thing in existence to measure it with is beachball sized.
But if its the last one, wouldn't the golfball be the new standard of 'small' until someone discovered a pea?
Edit:I think its just the confusion of my trying to apply logic to quantum distances, and theorems. And been 20 years since I Took it in school.
But I do remember my professor saying "if you are trying to think logical absolutes in quantum mechanics, you are approaching it wrong." Since my approach is trying to picture in my head what something that size would look like, and if there is a 'distance' that cant be shorter...everything would be made of "toothpicks' of that length, nothing can be smaller, or divisions of it..so trying to make a triangle with a set multiplier size doesn't work visually. |
I see what you mean, but as ron said, the mathematics works with any set you choose (with its own axioms, theorems and such), but the physics says: you don't have anything meaningful in spaces smaller then l_pl.
You can look at QM in pure logical sense, but then it's no longer physics. It's just mathematics of Hilbert spaces, but that doesn't mean that you'll have a physical meaning to describe the results you got by simply 'playing around with mathematics'.
"Quantum mechanics is actually, contrary to it's reputation, unbeliveably simple, once you take the physics out."
Scott Aaronson | chiv wrote: | | thats true you know. newton didnt discover gravity. the apple told him about it, and then he killed it. the core was never found. |
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