Problem with the two slit experiment, Observing later

Hi GE,

Glad to see you are recovered. Your argument floored me, it was not what
I expected from you!

Apparently, we are heretics who dare to question "doctrine".

Just keep saying this to yourself....

The world is flat, the world is flat, the world is flat.....

Remember, "there are lies, damned lies, and statistics".

LL

Hi Janrinze,

Like I said... I will not win this one...

I am not worrying about the "absolute units of time and distance and their values" but I am worrying about defining an "enduring" value for © in terms of integers of the other units with a knock on Philosophical effect. I prefer to see the velocity of light to be "experimentally" derived from the defined units of distance and time (whatever they are) instead of simply stating for all time ... and this is the intention... that C = 299,792,458 metres per second (exactly an integer based on a historic value that has been "rounded off").

I realize that this may seem obsessive (and it is) but there are equally as many people that obsess over this point as "meaning" something fundamental... Believe me I have been very strongly rebuked... irrationally... by people about this point so it has "deep philosophical meaning" to some... similar to the ideas espoused by Charles Piazzi Smyth whose "mindless followers", holding strong religious convictions, have tried in the past to render the Pyramid of Giza to the exact proportions of the "Sacred Cubit" using a chisel. I am sure that Charles Piazzi Smyth did not intend to go that far but in a way it was "inevitable" once you introduced the idea as part of ones "faith". Never underestimate "belief" and its role in "meaning" in Human Affairs and in Science.

While you are right there have been "far worse" means of defining standards, we should be trying to provide philosophically unbiased interpretations of the information we hold in our possession so everyone (even non-Christians like "elves" and others) can understand Science without being confronted by an "irrational belief". These points when they arise will only lead to divisions such as the former desire to define the value of Pi to be exactly 3.2 (Wikipedia: Indiana Pi Billl) rather than to allow it to be "transcendental" and "non-rational".

Forgive the "obsession", I am not the first...

Cheers

Let's see, it's the absolute standard, but there is some uncertainty as to the
accuracy. "Let's make it an absolute integer value"

This post has been edited by Laserlight on Aug 20 2007, 03:05 AM

Hey TRoc, jal, Good Elf, Jan Rinze, Confused 2, Laserlight, and everyone else that is following along...

When we talk about "riding on a beam of light", it is clear that there is a upper limit, a "maximum" value for the spacetime interval, rate, “speed of light”. For a photon, emission and absorption occur simultaneously in time, but not necessarily in the same place in space. IMHO, there should be an equivalent for space. As you shrink the scale, there should come a point when even "co-moving" properties break down to the point where the only way "things" can be co-moving is if they are separated by less than a minimum spacetime interval, which for light would imply a minimum distance. Nothing measurable is ever quantified as infinite.

Exactly. The twelfth root of 2 defines the value of the 12 pieces of pi. As LL pointed out a few replies ago, this relationship also appears as the rms of a sine wave. Jal pointed out something interesting regarding the number of unit spheres that can be packed around a unit sphere way back when with the thread on Kissing Numbers. Good Elf pointed out that a photon always propagates spherically and continually reminds us of that there is no privileged frame.

Anyway, maybe a refresher is in order…

Concerning an Heuristic Point of View Toward the Emission and Transformation of Light

Do you think he heard Pandora opening her box?

Mahalo

This post has been edited by Why Not? on Aug 20 2007, 04:44 AM

Hi all,


jal Posted: Aug 17 2007, 09:03 PM

Yes, but try to resist giving "dimension" or units to these parts. We can not know how to "measure" which "domain" until the other part is measured. IE you are suggesting that the "distances" between these parts are equal because the series that I listed was in frequency. That is correct.

You could also, however, look at that same series, and decide that they represented wavelength, which would mean that we had divided "frequency domain" into equal parts, causing our lengths to expand by the same quanta/rate.

Yes, but again, we need a little more detail in the measurement. The "middle" could be the center of values (mean), the center of a series of rates (harmonic mean), etc.

If we know "what kind of parts", then we can give a more definite answer.



I also just wanted to note agreement & appreciation for the following statements:

Why Not? Posted: Yesterday at 6:54 PM

janrinze Posted: Today at 1:36 AM

Neil Farbstein Posted: Today at 1:54 AM

Some points I disagree on:

Why Not? Posted: Aug 17 2007, 08:41 PM

Rate is more general than that. What you described is a rate, better known as velocity. But we also have rates of cycles over units of time (Hz), and the rate of cycles over distance (wavelength).

I'm going to take a similar route to jan:

janrinze Posted on Today at 12:33 AM

There are no quantum (EM) absorbers anywhere near that range. (?)

You can't measure what you are not resonant with.

So, while I understand the intent of WN?'s statement (that we can measure the "overage" of energy in the velocity of an ejected electron), I will say that "you won't, because there are NO work functions (1/2 ionize level) that will be met by those frequencies".

If you want to "scale" these numbers up to the WF level (of your choice), then my answer is still "you won't", because I have given you a "1-4-8 spread". Strictly speaking, and this was my intent, is that you can NOT measure all 3 of these superimposed waves. If "1" is the WF, then ionization happens at "2"; during that period of time the other frequencies are not measurable by that same detector.


This is what I mean by "superimposed waves having a combined amplitude".


http://www.kettering.edu/~drussell/Demos/s...erposition.html


We can only measure the resonant value. It doesn't matter how that value was met, AT THAT MOMENT in SPACE & TIME. This is totally different that saying that the energy is "cumulative" OVER time, which is all that the photoelectric effect "proves" to not happen.


regards,

T.Roc



This post has been edited by TRoc on Aug 20 2007, 06:46 AM

Hi TRoc, Laserlight, "Why Not?", Siau, Confused2, yquantum, Jal, Neil Farbstein, Terry Giblin, "THEY" and "THEY2", Janrinze, Montec, et al,

I agree that the combined amplitude leads to instantaneous maxima depending on the instantaneous phase between the two superimposed waves. These respective "packets" have different "timestamps" and "source stamps" on them and they can instantaneously "mix" but not actually gain or lose any nett energy but they may "cross imprint" information from their respective sources being carried three dimensionally. In the end the absorption of the photons can still only occur one at a time for "atomic" absorbers. A single absorber site can only absorb one photon at a time. The energy must then be either re-emitted or redistributed as some other form of energy (plus possible lower energy photons).

The most instructive animation is the "Two sine waves traveling in opposite directions create a standing wave"... If the two "directions" are the past (retarded waves) and the future (advanced waves), there are various ways to view this "ensemble".

Clearly these "matter waves" interfere and do not cancel around their origin in the evanescent field. This fine detail is not actually shown in the Wheeler Feynman Absorber theory as indicated above but a source where the particle is located is necessary in order that you have a primary emitter and a primary absorber. These standing waves are the particles themselves. If the picture shown above is the "Cramer Event Driven Universe" then the Feynman Perspective is the right one. What is also part of this view is that for real atoms etc. this picture must include all the primary "shells" in the atom as superpositions of state primed for events to happen.

As also been stated the more sophisticated electromagnetic Feynman-Wheeler wave packet is two counter advancing waves as indicated in the model as shown in this paper (...or a first cut of this is similar to the one shown there). Check the figures in this paper...

Hi all,


I had to go back and read through the last few pages again; a lot of good stuff, and we all seem to not only agree as to what we should talk about, but that there are, indeed, some "questionable Scientific assumptions" being made.


On one hand, we all know that the "simple" version of measuring waves works (f x w = c) , and throughout the early years, that it WAS a "measurement", and not a "plug-in".


Later, it was made a "constant", because no one ever measured anything else.

Until many years later; AFTER generations of entrenchment, etc.


The "standard" comeback now, is that the "information" has a speed limit, and nothing else. The problem there, is the same as in my last few posts: introducing "new" parameters, does not help us to better define existing ones. If we don't have a "Fundamental" understanding, then why throw more stuff on top?


I'll mention, again, that this HAS BEEN addressed already: in an attempt to "break out" of the circular logic trap, some folks invented the WAVENUMBER, who (basically) only differed by being the "inverse cm". I don't think that this helped our understanding much.


For all of the reasons that everyone here has been discussing over the last few pages, we are still locked into this circle, which (not too obviously) DEMANDS that we have several "fundamental" ONES in place at the same time. In other words, we have NO WAY of establishing some ORDER of importance to the various phenomenon that we are talking about.


Again, this has caused all of us (just in this thread alone) to "argue" over things that really were about "redundant definitions", and not "concepts". I think, at this point, that we all agree that the Speed of Light (SOL) has many different situations where it is not constant. Perhaps a smaller group of us will agree that "wavelength" is flexible, and can change to accommodate a variable wave speed.

However, down at the " bottom of the list" (of our agreement rate, IMO), is "frequency". At first, my own "ignorance" (innocence? haha), could NOT understand WHY no one wanted to agree that "frequency can change". Then, including a lot of help from Copenhagen, I realized that, JUST LIKE the SOL having been always measured constant, one will find too, that in all experiments, THAT is what is measured - the same frequency that "left" the sender is what is measured.

It took a lot more "digging" to come to the conclusion, that this "fact" is because we are using "quantum oscillators" that are "in tune" with each other. Tuning in always also means tuning out -- that which is NOT measured (by beats, or resonance) is always = or > than what is measured. This is in "whatever" terms you wish to impose.


This is why I insist on a deeper understanding (and re-defining) of "Resonance".


If we measure with more frequencies, we will get a different picture. "Spherical" in fact, rather than "planar". I will state my premise again, that "QM is a "monochromatic" theory", and that Relativity, and the "one observer" means, at the quantum scale, "one frequency". These 2 statements fit together. QM is all about "resonance", an action that requires the 2 bodies to have the same frequency, in order to "exchange energy". Relativity says that if you measure from one frequency (observer), you will get some aberration, Doppler shift, etc.

Of course, this is "oversimplification", but I am trying to just make the small point first. That, because the spherical nature of a wave requires phase difference, SO TO will an accurate measurement need to have some "spread" in frequency.

This could be accomplished by a group of oscillators of the same frequency but spread out in locations, or by a group of oscillators of small variation (discreet) in frequency, and in the same place.


I am out of time, again.


I will leave with the "answer", even though no one has asked a specific enough question to make it immediately applicable to something.

The minimum (unit), measurable by the limits created by cyclic behavior, is 1.0267092999..


Now the can of worms is gong to hit the fan!




regards,

T.Roc

Hi G.E.,

pi is a ratio.. not some obscure chosen value

speed is strictly defined as distance divided over time. Each component here (distance and time) doesn't have some 'natural' reference. We simply choose one and stick to it so we can all use a single frame of reference for measurements. There are no objects with a constant length neither is there an infinite and universal constant metronome to measure time. So we resort to other definitions that come the closest to the requirements.
As for the choice of an integer. This is no more relevant to the definition of a meter as to the definition of time by a cesium atom.

in mathematics unity and integers have special properties. they are per definition infinitely precise. This in turn shifts the focus from the constants towards measurements. When doing physics we need to propagate errors when calculating with measured values. If we can assume a property to be infinitely precise (an integer) we can do much more calculations without losing accuracy.

I hope I have made my point and that it has come across..

There a three different kinds of constants:

1 : constants chosen to make things simple (like c )
2 : constants derived from mathematical rules (like e and pi )
3 : constants derived from measurements (like the mass of a proton or Planck's constant)

The latter will always be imprecise but as our knowledge and abilities improve we can improve the accuracy of those constants. It is in those constants that we learn about our universe .. not in the ones we have chosen..

If we can see the difference between each of these types of 'constants' we can more easily distinguish between problems in induction or reasoning versus the quality of measurements and the notions of something being 'constant'.

As for the numerologists amongst us.. There is no sacred number sequence only forms of steganographic tricks devised by men..

as an illustration: the number PI has indefinite (assumption here) digits and the chance of finding a work of Shakespeare hidden in these digits seems therefore logically one.

(as long I am on a roll I should just continue with the rest of my thoughts here..)

since 1 second and 1 meter are both arbitrary there is no real logic in assuming that f needs to be an integer in QM.. Frequency cannot be determined at a singular moment in time. The reason for this is that frequency relates to change over a period of time. Any measurement done over a period of time shorter than one period of a wave can hardly identify the presence or frequency of such a wave.
On top of all the commotion about Fourier transforms, we need to consider that resonance is a process not a mathematical ubiquitous fact. It is local and over a defined period of time. So any wave that is coherent within this locality and time span will interact with this resonant system anything the wave would look like outside the locality and time span would be of no consequence to the process itself. So anyone who loves to make waves mathematically 'perfect' far outside the domain of interest is merely trying to fill in non existing 'gaps' in theories.. Therefore the concept of a retarded wave i.m.h.o. is just some mathematical comforter without any physical meaning.

Yes a wave with an envelope will have more frequency characteristics but keep in mind that a single burst in itself is not a repetitious phenomenon so how can we say that there are more frequencies 'hidden'.. outside the 'burst' there are no frequencies at all to interact with and inside the 'burst' only the wave frequency is present. Here we can get back to the 'lock' and 'key' analogy mentioned before. Is there enough energy in one 'cycle' of a wave (like in the photo-electric effect) to make something happen? could it be that the only way that in QM interactions are realized that the number of cycles needed to 'do something' (work function) is some kind of integer?

enough ramblings from my part..

I don't have the answers I guess. But I can ask critical questions

Jan Rinze.

Hi JanRinze et al,
Imagine we throw a cricket ball into soft ground. We remove the cricket ball and analyse the result .. eventually we conclude that the ball followed say parabola_A from the point it was thrown from to the point where it landed. Was the hole made by parabola_A? I say not, imo parabola_A is 'other information' .. the hole is the result of size/direction/momentum and soft ground.

If the path of a ball is determined by (say) the de Broglie wavelength, Schrodingers equation etc. is it inevitably true that the same information is linked (as you seem to claim) to both the path AND the cause/effect?
Best wishes -C2.

Hi C2,

the nice thing is that if we know the size/direction/momentum we can calculate where it came from.. all because we know it was a parabola. you cannot separate the one from the other. They all belong to the variables defining/describing the event. In a sense in physics it does not really matter if a property belongs to a particle or to some describing behavior/trajectory.. they are just variables in a complex equation..

About the following:

Actually I don't believe I have claimed anything but if you like: I do agree that If we can determinate size/direction/momentum and we know the laws of physics we can calculate trajectory and therefore calculate (in the case of the DSE) from which slit it originated.. (call me deterministic..)

Assumptions here are that light (even though it bends around corners) will travel in a straight line.. Or we could say the sum of the momenta of all possible routes should be used. Either way it should at least be one of the above.. I don't believe the answer to that question has yet been answered by any experiment yet.

Jan Rinze.

Hi Jan, GE, et al,

Jan,

First, good argument. It was well stated and succinct.

Exactly why a precise full wave cycle count, of a specific reference
frequency, should be the standard for 1 meter. For all intents and purposes,
a specific frequency is a constant. It will never change value, and it is also
bound by the speed of light in a vacuum, and it establishes time to an absolute
fixed reference.. A multi-redundant and perfect standard, IMO.

So we establish a time reference, a distance reference, a wavecount/frequency
reference, and the speed of light reference, that are all absolutes/constants.

Perhaps it is just my anal nature for perfection when viewed from any point of
reference.

Second,

Does light bend around corners, or do wavefronts
EXPAND or radiate around corners?

Maybe it's just a matter of semantics. Bending is a change of path from a straight
course, and has tangential characteristics. Radiating/expanding is associated
more with the the spherical,radiating model of EM energy that follows the ISL.

GE, for what it's worth, a standing wave doesn't "physically" exist, other
than as a concentration/displacement of energy as it relates to a fixed relative
postion in space-time. Two energy impulses travelling in opposite directions
synchronously superpose in time and space, but no energy transfer takes place
since there is no workfunction performed. I would assume, from a heuristic
point of view, that the refractive index of the local space-time would change, but
by itself, it is relatively a non-event, unless it affects matter in some
fashion.

JMHO,
LL

This post has been edited by Laserlight on Aug 21 2007, 12:44 AM

Hi Janrinze,

Like I said I do not think this argument can be won by me because it is not "compelling". Still I will point out a couple of your points and ask you "is this what you mean?"

I am not trying to be "picky" but if I define a meter as "in the new SI system as equal to 1,650,763.73 wavelengths of the orange-red emission line in the electromagnetic spectrum of the krypton-86 atom in a vacuum" then the distance of a meter is defined by interferometric technique according to "time" (or reciprocal frequency) so the velocity is in effect the ratio of two "times". Is this any different to the ratio of two distances (the value of pi).

An important aspect of pi is that it is transcendent and irrational... what if © was also a similar "number"? Is this any different from the Indiana Pi Bill in trying to "fix" the value of pi to be effectively a rational number? The "speed of light" is not simply some arbitrary number like the speed of sound at sea level it is a "Fundamental Property of the Universe" like pi. For instance the velocity of light is not only defined as a "speed" but as the vacuum properties of free space...

where...

and...

Which number is the more important.... © or pi? Is © transcendent or irrational? I can effectively vary pi by causing a simple plane disk to rotate and I know that the ratio of radius to circumference will change due to Relativity... not so © .... why not?

Cheers

Hi Laserlight, TRoc, "Why Not?", Siau, Confused2, yquantum, Jal, Neil Farbstein, Terry Giblin, "THEY" and "THEY2", Janrinze, Montec, et al,

Please accept temporarily that in order to account for "one photon at a time" properties of the DSE it is essential that everyone understand that EM radiation is propagated as a resonant standing wave. You cannot account "in realistic terms" for the properties of the photon's self interference without it. Also you cannot account for Holography without it either. We can discuss this point later. Once again I am still riding this "old horse"... In the case of standing waves in spacetime created by advanced and retarded waves, we are unable to appreciate the advanced waves... this means that depending on circumstances you cannot observe both phases (advanced and retarded) simultaneously so we can only "see" the one retarded wave forming part of the pair of standing wave patterns.

In the case of light lets say the top waveform is the retarded waves (propagating from the past... what we normally see) and the middle waveform is the advanced waveform (propagating from the future... which we cannot see because of our predilection to "causality").

Lets not become involved in the overall "shape" of the bosons as they spread... using the analogy in the paper quoted previously which are photons confined to a waveguide so "fixed" in geometry...
A photon-like wavepacket with quantised properties based on classical Maxwell’s equations:John. E. Carroll
While not observing the advanced waveform the energy is trapped all the same. Now recall the picture that I have used previously to illustrate the composition of a continuous wave of EM radiation composed of a "train" of sync functions... only in the "more realistic case" they are sync spirals propagating in the + direction.

... Click to enlarge...
Here we see seven of them (simplified versions of the spiral sync function) forming the simplest segment of continuous wave lets say also propagating as the retarded field on seven successive wavefronts from left to right. These would appear as seven "frozen" sync spiral packets hooked/summed up in a "train" and moving to the right and thus this would appear as a short segment of the top illustration/animation of the standing wave pattern. Unseen due to causality we do not "appreciate" the backward moving time symmetric pulse coming from the future to cancel the retarded forward progressing wave. I will explain later why there is a time reversed pulse.

So what we have is time symmetric phenomena... the emission of a photon and the absorption of a time reversed photon. These two together create permanent standing waves. These two can't be appreciated separately except in the evanescent zone of the retarded photon as it progresses through time as it "illuminates" the standing waves in its own personal evanescent zone as the perception of the retarded photon is a progressive phenomena in time. This can best be illustrated by this animated image (albeit for an electron) that Zephir has contributed to the forum.

You can see how the standing waves only exhibit in the evanescent zone of a "propagating particle"... in our case a photon... this is along the wavefront (which can exist in many places though spreading on the surface of the sphere) as time progresses. It is important to understand just how this process can be seen to work and still remain hidden to a world dominated by causality.

It is also important to realize that the actual spiral packet is "stationary" as it propagates though it is distorted in the way it responds to "spreading". The other point to really "get" is that the photon moves via a path of least action to the point at which it is absorbed and this is the path of least time... there is no need for the photon to "bounce around" to exhibit a full interference picture since the space is filled with an instantaneous standing wave pattern that already exists through which the photon moves "expediently" to the screen or to an emulsion where it finds a place in which to be absorbed in a direct relation to the standing waves in that space. Remember it does this in least time and this is the path of least action in flat spacetime. It cannot "bounce" around in space because the photon wave function collapses instantly along its entire wavefront wherever it may be when it is absorbed at the sink. It also means that all spatial interference with itself is permanently etched in the space it is passing through, everywhere end for all time... for just that one photon and for no other..

.. click to enlarge...
But there is the possibility that the wave may re-emerge in other places if the conditions are correct. You may see that example I previously quoted of faster than light tunneling in the light of this process as being advanced and retarded waves through media "transporting" a photon to "somewhere" that a reemergence might occur... with the use of special materials or conditions.
Animation of "Backward" (and forward) moving light...
If these "events" were on the opposite ends of a 100 Km optic fiber cable then you have potentially teleported a photon 100 Kms potentially faster than the speed of light ... at least a couple of these photons eh!! These "sources" and "sinks" have become new sources at the far end and are not necessarily absorbed. Functionally the opposite of the Delayed Choice Quantum Eraser Experiment where the "future" is affecting our "present".

One photon sees the entire interference pattern and it is always waiting for it when it passes through the intervening space, Recall the single photon collapses the wave function at the instant of absorption so there is never any time for the photon to "explore the Universe" after the wave function collapses. This is the same for each and every photon at every frequency that is possible and is a superposition of states, one of which each and every individual photon recognizes as its own "personal" set of standing waves that waits for it in space created by the Wheeler Feynman Absorber Theory plus the Cramer Transactional Model which acts photon by photon.

Recapping... the advanced and retarded waves act photon by photon creating spatial standing waves in time... these are captured by the progressing "retarded" photon as it moves from left to right in that animation above. In actual fact the actual photon packet occupies only "about" one wavelength in the temporal direction not several "wavelets" as the animation shows. Individually they represent a single spindle packet carrying the spin but the internal Schrodinger harmonics are not progressing or changing with time, it is "frozen" against the light cone surface as it spreads through the space as it sees it. Remember at the speed of light no time passes from when it is emitted and it is absorbed, and space is all compressed to a single point ... or very close to it... A single evanescent zone for both source and sink for the photon... and in its frame of reference these two processes happen at the same instant and at the same evanescent point in its time. This maintains the separation of the wave and particle aspects as you can still see. Relativity separates them but cannot change the event in how it actually operates (I have recently discussed this point about relativity with "Why Not?" above). These "events" seem separated in our time but in the rest frame of the photon occur simultaneously and so these two time inverted photons are simply the expression of an impulsive transform with a instantaneous "reaction" from the other end (absorber) to this "emission" by a reverse wave that feeds from "our future" into the past where it meets the source. Remember this is the way we can understand the Delayed Choice Quantum Eraser Experiment.... it is Wheeler Feynman Absorber Theory and the emission and absorption are a single temporal event. It happens all before our very eyes but we are all too "stupid" to see it because of our causal nature.

Cheers

PS: You can now understand why "time stamping" and "coordinate stamping" of photons means that though photons can "add" instantaneously they cannot "cancel" since they will have different time and position stamps such that their advanced and retarded packets will not match any others because they represent "interferences" related to that solitary event and the one retarded photon "designed and created" by that one event through Wheeler Feynman Absorber Theory. Event by event the Universe and time is constructed. Each retarded photon from a source has chosen the one sink in the Universe to proceed to at the instant of its creation.

This post has been edited by Good Elf on Aug 21 2007, 01:13 PM

Hi Laserlight and others,

Umm.... seems there might be a problem directly accessing the "user posted image" above in my last post...
It is the animation that relates to the topic...

Two sine waves travelling in opposite directions create a standing wave

On this page...
Superposition of Waves:Dan Russell PhD
Animation courtesy of Dr. Dan Russell, Kettering University.

Sorry about that... I can't change it now.

Cheers

This post has been edited by Good Elf on Aug 21 2007, 02:56 PM

Hi GE,

I am not trying to be "picky" but if I define a meter as "in the new SI system as equal to 1,650,763.73 wavelengths of the orange-red emission line in the electromagnetic spectrum of the krypton-86 atom in a vacuum" then the distance of a meter is defined by interferometric technique according to "time" (or reciprocal frequency) so the velocity is in effect the ratio of two "times". Is this any different to the ratio of two distances (the value of pi).

Yes there is much difference. The value of pi is mathematically defined.
velocity is not a ratio of two times. Unfortunately it appears hard to grasp that it really does not matter which reference you would take to define a unit of a specific dimension. When we choose a reference it makes sense to do these choices based on knowledge about invariant features. With the assumption of the constant speed of light we can define both time and space at once. To implement such a definition we resort to using practical implementations which can be consistently reproduced.

It will be hard for most people to 'see' the difference between a constant and 'a constant of nature'. Any number I can pick can be defined a 'constant' ..

This is one of my favorites..

Notice that any value of pi will still yield a correct solution in the formula for c!
pi is a mathematical property of euclidean space (mathematical concept) so you might wonder why pi pops-up with the permeability and permittivity of space.
It is very closely related to the formula of the surface of a sphere.

I have no idea how your example of varying pi would work.. the effects of rotation are very hard to calculate in regard to relativity.. Non-euclidean space (like curved space-time) has obviously different results in regard to the circumference of a circle. This has nothing to do with the definition of pi! (pi is defined as 1/2 the circumference of a circle in euclidean space with unity radius..)

Jan Rinze.

P.S. even though this might look like side-tracking, having knowledge of mathematics is a prerequisite for physics..