Planck scale question

[dragonstar57]

recently I heard saw the Planck scale referred to as
the resolution of reality (obviously a matrix reference rofl)

but it got me to thinking would pi stop at a decimal accurate enough to calculate
distances on the planck scale?

(sorry if this is a really stupid question I'm not well versed in physics and a
google search yielded little)

also wouldn't there be a point (if not at the planck scale) that an ending decimal would be so close to pi's true value
that the difference would be completely indiscernible?(like if we could calclulate a circle the size of the observeable universe down to the radius of a electron or something)

Edited June 21, 2013 by dragonstar57

[Delta1212]

The Planck length is, theoretically, the smallest distinguishable distance between two points. We aren't even close to being able to detect things that small (for reference, the radius of an electron is about 10,000,000,000 times the Planck length) so what physical significance the Planck length actually has is, at this point, purely theoretical.

 

That said, it's been mathematically proven that pi doesn't have an end decimal place.

[swansont]

(for reference, the radius of an electron is about 10,000,000,000 times the Planck length)

 

That would be the experimental upper bound on the electron radius, which theory has predicted as a point particle.

[Kramer]

If theory is going against logic , the theory is wrong.

[ACG52]

If theory is going against logic, and theory yields correct predictions, logic does not apply. This is almost always the case in quantum mechanics.

[Delta1212]

 

If theory is going against logic, and theory yields correct predictions, logic does not apply. This is almost always the case in quantum mechanics.

QM isn't really illogical, just counter-intuitive.

[md65536]

also wouldn't there be a point (if not at the planck scale) that an ending decimal would be so close to pi's true value

that the difference would be completely indiscernible?(like if we could calclulate a circle the size of the observeable universe down to the radius of a electron or something)

I think the circumference of a circle that size could be calculated to the nearest Planck length using somewhere around 62 digits of pi.

 

"Taking pi to 39 digits allows you to measure the circumference of the observable universe to within the width of a single hydrogen atom."

-- http://gizmodo.com/5985858/how-many-digits-of-pi-do-you-really-need

 

"So NASA scientists keep the space station operational with only 15 or 16 significant digits of pi, and the fundamental constants of the universe only require 32."

-- http://blogs.scientificamerican.com/observations/2012/07/21/how-much-pi-do-you-need/

 

"Scientific applications generally require no more than 40 digits of π"

-- http://en.wikipedia.org/wiki/Pi

If theory is going against logic, and theory yields correct predictions, logic does not apply. This is almost always the case in quantum mechanics.

It seems whenever this argument comes up, some people are speaking of systematic reasoning, and others are speaking of intuitive reasoning, or maybe something else too and everyone's using the same word "logical".

 

I think if one says "logic doesn't apply", or "If theory is going against logic , the theory is wrong" for that matter, one ought to explain which meaning they're using for the word "logic".

 

Valid logical reasoning still must apply in QM, but some intuitively common-sense assumptions (which some might call logic) don't apply.

 

Edit: That said, I'm making the same mistake of not defining what I mean... From http://en.wikipedia.org/wiki/Logic: "in particular that what physicists have learned about quantum mechanics provides a compelling case for abandoning certain familiar principles of classical logic: if we want to be realists about the physical phenomena described by quantum theory, then we should abandon the principle of distributivity, substituting for classical logic the quantum logic proposed by Garrett Birkhoff and John von Neumann." So if by "logic" one means the classical rules of logical reasoning or whatever, then with QM it's true that logic doesn't apply.

 

http://en.wikipedia.org/wiki/Quantum_logic applies.

Edited June 22, 2013 by md65536

[Kramer]

When Swansont say that “ dimensions of electron particle are zero “ I see here something illogical. But as quantum mechanic theory has eroded too many concepts of reality, and with sophisticated method of high math has sold them as a new reality I think that here needed many than an explanation.
If electron is particle it must have dimensions, it can’t be a point, which mean zero dimensions.
If electron is a point zero dimensional, it can’t be a particle. Call it, if you want, a center of a wave, but not a particle.
A question without answer: How much is the density of mass of electron?.