Guest “forty-two” “one-thirty-seven” by David Middleton
For those unfamiliar with Douglas Adams, this won’t help…
Why the number 137 is one of the greatest mysteries in physics
Famous physicists like Richard Feynman think 137 holds the answers to the Universe.
PAUL RATNER
31 October, 2018
- The fine structure constant has mystified scientists since the 1800s.
- The number 1/137 might hold the clues to the Grand Unified Theory.
- Relativity, electromagnetism and quantum mechanics are unified by the number.
Does the Universe around us have a fundamental structure that can be glimpsed through special numbers?
The brilliant physicist Richard Feynman (1918-1988) famously thought so, saying there is a number that all theoretical physicists of worth should “worry about”. He called it “one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by man”.
That magic number, called the fine structure constant, is a fundamental constant, with a value which nearly equals 1/137. Or 1/137.03599913, to be precise. It is denoted by the Greek letter alpha – α.
What’s special about alpha is that it’s regarded as the best example of a pure number, one that doesn’t need units. It actually combines three of nature’s fundamental constants – the speed of light, the electric charge carried by one electron, and the Planck’s constant, as explains physicist and astrobiologist Paul Davies to Cosmos magazine. Appearing at the intersection of such key areas of physics as relativity, electromagnetism and quantum mechanics is what gives 1/137 its allure.
Physicist Laurence Eaves, a professor at the University of Nottingham, thinks the number 137 would be the one you’d signal to the aliens to indicate that we have some measure of mastery over our planet and understand quantum mechanics. The aliens would know the number as well, especially if they developed advanced sciences.
[…]
42 was wrong anyway.
In the follow up book.
I thought 42 was correct… But this was wrong:
It is correct in base 13
42 in binary: 101010
137 is elegant. it is the first, third and fifth prime number put into a strung. This obviously means that 2 and 5 are totally useless and should be discarded.
shrnfr: By definition, 1 is not a prime number, although one would think it should be since there are no positive integers less than one into which it could be factored.
137 is prime.
Not that it matters since alpha is not an integer.
Just sayin’
42
137 ——– I’ll run it thru my turbo-encabulator when I get time!
Are you suggesting the big giant computer got it wrong?
A big giant computer programmed by human. What could possibly go wrong, you say?
I thought it was programmed by “particularly clever, hyper intelligent, pan dimensional beings” [who appear to humans as white lab rats].
White mice I think
The hyperintelligent shade of blue?
These days there is no right/wrong. It merely is different.
42 in ascii = *
I think the mystery number was something like 42-39-56…yeah, you could say she had it all…
This, then, is the magic number?
So, you’re saying that the answer is…a whole lot of Rosie!
If it isn’t, it oughta be.
+++ Rosie
It’s too much work to actually do it right now but … if you operate on some random physical constants you should be able to come up with a dimensionless number. Why this particular one?
You can make equations dimensionless by choosing a standard for each variable.
All equations lack dimensions. They all simplify to linear coordinates and time based positional data.
Differential equations is what I should have specified.
What if the aliens don’t use base 10 for their number system?
We’d probably transmit it in binary anyway, as all the new radios are digital. Besides, to send it in anything else we’d first have to transmit the full Unicode definition so it would make any sense. Then they’d have to decipher our language to figure out what the definition actually said… Man, first contact is getting more and more complicated…
Considering there’s no reason to believe math is a universal language, yeah, they’d have to decipher the code. I don’t think we’re ready for first contact…..
But simple code is universal for “breaking the ice” so to speak. Dr Sagan took a good stab at it with his book “Contact”.
The radio transmission is still analog though. One might be surprised how much analog still exists in our new digital world: (free book)
http://designinganalogchips.com/
We’ll have to send the message by quantum communications… first we’ll have to slow boat the entangled particles, of course.
And the first transmissions, as well as all other transmissions, are still out there. What the heck is this? Howdy Duty? Maybe, they too, will misunderstand and think the Martians invaded Earth. I saw a plaque commemorating the event in Grover’s Mill, NJ. It’s right there by the pond,not far from the ‘House’ hospital on Rt 1. … and as legends go, all those water towers were really Martian war machines. There are lots of them in NJ.
Some with holes…
137 in binary is 10001001 A rather interesting looking number.
As I mentioned higher up, 42 is also interesting in binary: 101010
And 10001001 + 101010 = 10110011. Coincidence? I think … maybe.
So is the Decimal 0.007299270072992700
What if the aliens think beyond three dimensions?
What if WE are the most advanced civilization in the Universe?
Then the universe is in big trouble.
For now, we’re confined to a single solar system. While there has been a lot of talk about how we could get to another solar system, there remain hurdles that have not been solved. (That could be a posting unto itself.) But, the point is, we can’t get up to significant mischief under the present circumstances, and probably never until we solve or find a work-around for that E=mc^2 thing. (Yes, I like to read science fiction too, and most of it requires some form of physical impossibility, but I still enjoy the stories just fine.) And since I believe this universe is Created, that instantly turns this insurmountable problem into a feature, not a bug!
Then it is an awfully big waste of space!
Probe their asses, see how they like it.
And 137/42 is almost pi 😉
There’s pie?
Yes, but it’s been squared
No, cake are square, pi r round.
The sum of the first 12^2 = 144 digits of pi is 666.
I want some.
You know what happens if you get too close to actually computing pi. There’s a movie about that.
That reminds me of a science fiction story by Fred Hoyle (I forget which one). The underlying thesis was that our universe was created by a race of super-beings, who left clues about themselves in the physical laws of the universe. One clue was that if you calculated pi to about ten million decimal places in base eleven (I think it was eleven) you came to a series of several thousand digits which were all ones or zeros, and which if arranged in a square matrix formed a perfect circle. This was clue number one, while clue number two occurred after about 100 million decimal places and was a much longer string of ones and zeros which formed a specification for a super-computer which would enable us to get in touch with the super-beings.
Was there ever a film made of this?
That sounds like a BBC TV serial from the 60s – A for Andromeda – with Julie Christie. Though the plot description on IMDB sounds a bit different. Certainly it was just after the time that Hoyle was writing Sci-Fi.
I’m not entirely serious about this. It’s just a day dream. But supposing God wanted to give us proof that the Bible was true. All he would have to do is embed in the text an equation or calculation of some sort that would provide the speed of light to some amazing accuracy, or give a listing of the first 500 prime numbers, or provide the E=mc2 equation – provide something that was clearly far beyond the technology of the time. It could be suitably worded that this is a mystery that would one day be revealed and that would prove that these revelations are true. Like I said, this is just a day dream, and I understand that in the final analysis every world view requires faith (even if unrecognized as faith) in something, but still it sure would have been cool if God had done that.
Well, He did maybe. It is 666..for those who have understanding. It is Carbon. It consists of… 6 Neutrons. 6 Protons. 6 Electrons. Thats why we all here fighting this Beast that wants to limit what life is made out of. And food, shelter, heat, A/C, transport, flight and about a million other things that make being human more divine with more carbon. I don’t get it, this obsession with only CO2 and everything solely revolves around this one issue. That’s why I protest this wacky science of CAGW.
Well, actually…. This is a little silly,but … In the bible 1 Kings chapter 7 there is the description of what is called the “molten sea” (King James English), a round tub (laver) that is 10 cubits across, measuring a line 30 cubits around. Not quite “round”, right? However the word used for line is not quite correct. Even the Jewish Masoretes compiling the bible noticed, put piously left the mistake(?) there and put the correct word in the margin. Now the Jews (and many other cultures) use a form of gematria (letters are numbers, too). Well, the gematria of the questionable original divided by the correct word is 3.1415. Not a bad shot at an irrational number.
Was also in Carl Sagan’s book Contact too. Near the end of the book a perfect circle in a bitmap of pi is mentioned.
Ha! That reminds me of the olden days of the pocket calculator, when those devices provided only essential arithmetic operations. If you needed pi in your calculations but your calculator lacked a pi button, use 113355 as a memory trick. 355 / 113 is almost pi. 🙂
Wow, that’s the combination for my luggage!
well that’s better than 1-2-3-4-5.
“That’s the stupidest combination I’ve ever heard of in my life! That’s the kinda thing an idiot would have on his luggage!”
“1, 2, 3, 4, 5? That’s amazing! I’ve got the same combination on my luggage!”
Wow, that’s my robots destruct code sequence!
Meanwhile, was the test program for Colossus the computer in the movie Colossus: The Forbin Project a calculation of pi?
To state Pi accurately, use 22/7. You can’t get more accurate, lol.
You can state PI exactly and to infinite precision as the ratio between the circumference of a circle and its diameter. This is for why ratios so magical. They can be exact representations for an otherwise irrational relationship.
‘This is why ratios are so magical’ is what I thought I typed.
Where’s that comment editor …
44 years ago could calculate Pi using straight series arithmetic (multiply and divide)
sine series, cosine series, or tan series, thats when I realised maths was weird and gave up, along with playing at Pythagoras on a spherical surface (90 +90+90 = 360 deg) and washed down with taxicab geometry where Pi is def not 3.14159. . . .
my brain hurts even now.
When expressed in base PI, PI is exactly 10 based on circular reasoning.
And of course there’s e^(i*PI) = -1. This has i (sqrt(-1), PI and e all in one concise relation.
Halloween = Christmas
Proof: Oct 31 = Dec 25
Didn’t some state legislature pass a law stating that Pi was 3.0?
And was it Miles Mathis who said that in outer space, pi is 4.
Didn’t some state legislature pass a law stating that Pi was 3.0?
you might be thinking of the “Indiana pi bill” (it never became a law). In 1897 the Indiana Legislature put forth bill #246 aka the Indiana Pi Bill. according to Wikipedia: “The bill, written by amateur mathematician Edward J. Goodwin, does imply various incorrect values of π, such as 3.2”. However “The bill never became law, due to the intervention of Professor C. A. Waldo of Purdue University, who happened to be present in the legislature on the day it went up for a vote. ”
https://en.wikipedia.org/wiki/Indiana_Pi_Bill
Actually, 355 / 113 is surprisingly close to pi… much closer than 22/7
http://davidbau.com/archives/2010/03/14/the_mystery_of_355113.html
“The fraction 355/113 is incredibly close to pi, within a third of a millionth of the exact value. This level of accuracy is far beyond its rights as a fraction with such a small denominator […]”
Here is what happens to pi when politicians get involved:
https://en.wikipedia.org/wiki/Indiana_Pi_Bill
Thank goodness Professor C. A. Waldo happened to be on the scene :).
I used 55555566/17683886 for fun. Or just bashed in 3.14215926(53) – the extra digits on those programmable HPs, which had a π key anyway, and checked against 1 arctan 4 * (the joys of RPN). If you ever had an early Sinclair you could set it whirring for 30 seconds calculating tan( 89.999 degrees) as it tried working through the Taylor expansion.
137 staffers at nasa giss and they claim to have 137 years of climate records
spooky or what ?
Almost as good as an infinite number of monkeys typing gibberish.
Over what time period?
If it’s an infinite number of monkeys, they will type War and Peace an infinite number of times, provided they are given enough time to type it at least once.
My mind always ran into a brick wall with that one… If the infinite (or even a million, I have heard it both ways) monkeys hammered away on infinite typewriters for infinite years they most certainly would write War and Peace, as well as all the rest of the world’s great literature, but who (or what computer) would cull through it and separate War and Peace from the parts that are not War and Peace? Imagine an exhaustive concordance, that zips through to the next occurrence of the next letter of whatever novel, and snips out everything in between that is not the novel! Now this means that no new literature would ever emerge from this noisy room, because in order to find any particular novel in all those letters, the selector must first have a template (in this case the novel) to compare against. Sometimes thinking too much gets in the way of a very good analogy.
Not to mention the staggering amount of output that would vary by a single letter or word.
“Does the Universe around us have a fundamental structure that can be glimpsed through special numbers?”
What are ‘special’ numbers?
Special people can make a living from woo.
One is the loneliest number.
Maybe you could get SpongeBob to get a pet snail companion for you Gary.
Two can be as bad as one…..
… but not nearly the trouble that a threesome brings
Two can be as bad as one…..
…It’s the loneliest number since the number one
Yes but the answer to the question of the universe is not 137 instead it’s 1/137 or .0072992700729927
The 00729927 is repeating ad infinitum.
007 repeating, perhaps Ian Fleming was on to something after all
It’s also only that at slow speeds (AKA classical physics) it moves up at higher energies as it is part of the renormalization calculation between the fields. As a guide it’s 1/125 at Z boson energies.
Probably should add the current value as measured by the LHC is 1/α=137.035999046 and is causing a bit of tension with the standard model as its a 2.5 standard deviations off.
Background from Prof Adam Falkowski
http://resonaances.blogspot.com/
After the first 0, symmetrical patterns:
07299270…
Naah, it’s 0.08542454314. Or something. Read your Feynman!
Was it so that QED was a good theory just because this constant is small << 1, enough to make the fourth power etc very small, but QCD required some 50 years of new development since in it, the constant is near 1 and makes the calculation slowly convergent.
The stuff becomes increasingly hard for general populace.
Variations in fine-structure constant suggest laws of physics not the same everywhere
https://phys.org/news/2010-09-variations-fine-structure-constant-laws-physics.html
L.Eaves :
A model to inter-relate the values of the quantum electrodynamic, gravitational and cosmological constants
https://arxiv.org/abs/1801.10012
Feynman’s apparent frustration cited above and “magic” invoked because of the train-wreck called quantum mechanics makes climate science look settled by comparison.
Trace it all to the 1927 Solvay conference – irrationality as a physical law.
Just look at quotes (by J.S. Bell) from Niels Bohr :
The opposite of a great truth is a great truth,
Truth and clarity are complimentary.
And his coat of arms with a yin-yang :
https://en.wikipedia.org/wiki/Niels_Bohr#/media/File:Coat_of_Arms_of_Niels_Bohr.svg
Is it any wonder there is a train wreck? Even if measurements are incredibly precise….
You are making silly comments about things you don’t understand.
It is akin to complaining the value of Pi is something like 3.1415926535897932384626433832795
OMG such as strange number the entire field of mathematics must be wrong.
You just showed alpha varies relativistically – some constant!
One link is to quasar observations showing asymmetric cosmological alpha variations.
At least Feynman was honest. I also tend not to believe in magic, numerological or otherwise, the Pi straw dog notwithstanding.
It isn’t really a constant, it is a function .. but them most people don’t know that and still want to comment on it 🙂
I should add Pi is really just a function .. and is actually identical in behaviour.
So lets do the ABC steps to show you how it works. Take a cup place opening down on a ball and draw the circle around it. Now measure the diameter of the circle over the curved surface. You have the same circumference you drew around it but the cup diameter to the measured diameter on the ball surface differ. Pi = Circumference/ Diameter so you value of Pi differs for the two cases.
The normal value we use for Pi is based on you having a flat euclidean surface, so the value of Pi is a function of the curvature of the surface you describe the circle on.
Yet the ubiquity of pi = 3.14159… in so many seemingly unrelated areas of mathematics shows a predilection for that normal value.
Pi, a trancendental like e and an uncountable infinity of others in the labyrinth of the continuum, belongs in a euclidean world even if curved.
Alpha however belongs in the spacetime domain – it appears to vary asymmetrically over cosmological intervals, and at relativistic speeds. It is measured spectrographically, with line shifts and splitting. Alpha is saying something about spacetime, some property, maybe curvature , topology, or torsion or some yet to be discovered action principle.
Spacetime is fundamentally different to euclidean space, even if curved, as it is from the energy density of the actual world, so physical spacetime. Alpha is in this way very different to Pi.
Just a thought – I presume all values of Pi in various topologies are all transcendental? I wonder if anyone has proved that.
Pi is mathematically derived (you can do it to thousands of decimal places) but on a curved spacetime your ratio of circumference and diameter of a circle isn’t Pi, that is what I did above. So on such a strange universe you would have Pi and then WeirdPi constant thing to do your circle calculations. Lucky we live in a near as dammit flat universe hey 🙂
LdB
“Now measure the diameter of the circle over the curved surface.”
Fine, but you are now measuring the radius distance across the surface of the sphere in curved metres and not in flat Euclidean metres. The problem of Pi occurs because we are measuring the dimensionality of shapes with incompatible units. For example square metre areas cannot be tessellated onto the area of a flat circle. To measure the properties of curvature we need to redefine geometry in the following way:-
First we must define the one dimensional metric of a circle as being associated with its perimeter length (the curved circumference) and not its straight radius. This is because we need to measure in spherical geometry with curved lines and not the straight lines of Euclidean geometry. Let us define a new unit of curved length the Hemi (H). The Hemi of a circle is the perimeter length that subtends an angle of 180 degrees to the centre of that circle and is expressed in curved metres. (Yes I know that this angle is Pi radians, but bear with me for a little while and let’s follow the logic because by definition one curved metre equals Pi flat Euclidean metres). Now the circumference of a circle of unit size 1 Hemi will of course be 2 curved metres (2*H^1) and the area of a circle of unit size will of course be H^2 circular metres (c.f. square metres of Euclidean area and once again by definition one circular metre of area equals Pi square metres). In addition of course a circle of Hemi size 6 curved metres will have an area of 36 circular metres and the perimeter (circumference) length will be the differential of the circular area equation, namely 2*H or 12 curved metres (and so on).
Are you with me so far? Ok so let’s play the same game with spheres.
Take a sphere of unit size in which the Hemi of that sphere is one curved metre. Now the volume of this sphere will be H^3 spherical metres (as opposed to cubic metres and again by definition one spherical metre equals Pi cubic metres) and of course the surface area of the sphere will be the differential of the volume equation namely 3*H^2 circular metres. Notice that the ratio of volume to surface area for the unit sphere is 3 and that the ratio of area to perimeter for the unit circle is 2, in both cases these parameters are the dimensionality of the shape in question. Using this observation let us move on to the case of a 4 dimensional hypersphere. By construction we can compute that the Hype of a 4D hypersphere of unit size of 1 Hemi will be H^4 and that the boundary surface volume of the hypersphere will be given by the differential equation namely 4*H^3.
Returning now to Euclidean geometry, we know that the equation for the volume of a cube of unit length L is L^3 and that the surface area of that cube is two times that volume differential (i.e. 6*L^2). We also know that if we take a cube of a give size that completely encloses a sphere, then that sphere will have a volume (and also a surface area) that is less than that of the enclosing cube (which has a size of L = 2R to fully enclose a sphere of radius R). By construction we know that the Hype of a 4 dimensional hypercube will be L^4 and that its boundary surface volume will be the differential times 2 i.e. 8*L^3. (There are 8 bounding surface volumes to a hypercube, but in 3D space we can only observe one of these volumes). Consequently we know that the Euclidean equation for the surface volume of a hypersphere that is completely enclosed within a hypercube of unit length L must be less than 8L^3 (or 64R^3 where L = 2R).
We also know from Euclidean geometry that the equation for the circumference of a circle of radius R is 2*Pi*R and that the equation for the surface area of a sphere of radius R is 4*Pi*R^2. The key to establishing the fine structure in the constant of proportionality for the geometric formula for curved space lies in the equation for the volume of a 3-dimensional sphere. That constant is 4/3. We can construct this constant using the following fractional algorithm to derive a Quotient of proportionality in which the Dividend is powers of 2 and the Divisor is the dimensional number i.e. (2^(n-1))/n , where n is the number of dimensions.
So for a 1-dimensional angle the Pi Quotient is 1, for a 2-dimensional circle the Pi Quotient is also 1 but for a 3-dimensional sphere the Pi Quotient is 4/3. We can now compute the Pi Quotient for a 4-dimensional hypersphere and this will be (2^3)/4 = 2 and so the Euclidean equation for the Hype of a hypersphere is 2*Pi*R^4. The differential of this equation will provide us with the formula for computing the bounding surface volume of a hypersphere which is 8*Pi*R^3
Now this is fun isn’t it? The Euclidean geometry equation of 8*Pi*R^3 suggests that the total boundary surface volume for a 4 dimensional hyper-spherical universe is therefore 6 times the 4/3*Pi*R^3 volume of the 3 dimensional sphere that we observe out to the Hubble limit. This equation for the surface volume of a hypersphere implies therefore that 5/6th of the Universe is hidden from us.
Some fun with multiply connected space :
Review : The Status of Cosmic Topology after Planck Data
https://arxiv.org/ftp/arxiv/papers/1601/1601.03884.pdf
The universe could appear 120 times larger due to topology.
What I think what it shows old physicists are prone to stupid errors, Michael Atiyah latest paper which this is all about is about as stupid as Hawkings last paper.
The paper is here
https://drive.google.com/file/d/1WPsVhtBQmdgQl25_evlGQ1mmTQE0Ww4a/view
https://www.google.at/search?q=haral+lesch+erkl%C3%A4rt+die+Zahl+f%C3%BCr+alles&oq=haral+lesch+erkl%C3%A4rt+die+Zahl+f%C3%BCr+alles&aqs=chrome.
I had hoped that there would have been a better explanation here of what this is all about. I’m guessing that because the three ‘fields’ are in the same units and plugging a constant from one into another gives this ratio. If so, since doing this was bound to give a number (that happened to be 137) I don’t get its “magic”. Had it given Avogadros number or some other well established number, yeah, that would gave been highly significant.
Pretty much spot on it is the coupling ratio between all the fields in QED and it must have some value in the same way Pi must actually have some value. The value as measured by the LHC at normal classical speeds is known to an accuracy of 10 decimal places and is 1/α=137.035999046.
So even saying it is 1/137 is a like saying Pi is 22/7 and trying to work it out why it is those two numbers.
Thank you LdB. Now I feel I get it. If, out of the blue, we were given a number like pi but didnt know where it came from, how would we go about it? Presumably the answer to that question would go some way in helping us do that.
Yeah it pretty straight forward like Pi
Pi is derived by taking the measured circumference of circle versus it’s diameter Pi = circumference of circle / diameter. It’s 3.1415926 blah blah because that is what the answer in the real world always comes out to.
The fine constant is just the coupling constant determining the strength of the interaction between electrons and photons in our universe. It’s 1/α=137.035999046 because that is what the answer in the real world comes out to.
Both numbers both have an identical physical background, they are what they are because that is what you measure in our universe.
42 ? … 137 ? … really ? … this is a climate blog, and anybody with half a brain who is involved with a climate blog should know that the magic number is 97. We’ve been over and over this ! [fake /sarc censure]
The number is settled; climate alarmists number is up :-))
Eddington and Dirac started this numerology in physics. Pi is also a pure number and might be more fundamental because it is a property of Euclidean space. If another universes exist and they have different laws of physics, the fine structure constant would have a different value but pi is still the same if their space is flat (Euclidean)
If the fine structure constant was not the value it is, fusion would not be possible, stars would not shine and the Universe would not exist. I suspect that if another Universe existed with different physical constants, the one constant that would most likely be the same is the fine structure constant.
The universe could exist without fusion and stars. The first stars were formed about 100 million years after big bang. The fine structure constant is not required for the existence of the universe. It is required for stars and life. But the universe does not need stars and life, humans do.
In there was a Universe with a different fine structure constant, there would be no one around to care, so whether it can or can not exist seems a moot point. But there may be a deeper connection and that the Big Bang may not have happened either if the fine structure constant isn’t what it is.
I’ve also been looking at whether or not the fine structure constant and the golden ratio may have a common mathematical basis as opposing concepts (curvature and anti-curvature) chaotically interacting with a large number of other instances driven by the same balance and seeking an equilibrium with each other. If such a relationship could be found, then the invariance of the fine structure constant would be confirmed.
A deeper connection between fine structure constant and big bang is unknown. What we know is the large scale structure of the universe is governed by gravity, not by the strength of elementary charge in FSC. It is relevant in small-scale processes like atoms and fusion. In the first 300,000 years, there were no atoms and fusion and FSC was not relevant.
Neither FSC nor golden ratio appear in non-Euclidean geometry and chaos theory. FSC is an empirical physical constant. It’s not clear how it will fit in math subjects or if it can be derived mathematically from first principles. The golden ratio fits in number theory and plane geometry.
Phi (the golden ratio) is more fundamental than fine structure constant and pi.
phi = (1 + 5^(1/2)) /2 = 1.618…
Phi is a property of natural numbers in Fibonacci series. The ratio of two consecutive Fibonacci numbers approaches phi as n approaches infinity (where n is the nth term in Fibonacci series)
Elementary particles, mass and energy are discrete, which means you can count them using natural numbers. Hence, phi is constant in all universes with particles, mass and energy regardless of their laws of physics and space (whether Euclidean or non-Euclidean or any number of dimensions)
Mathematicians say God made the natural numbers, everything else is man-made. That would be true even if the multiverse is a computer simulation. The Programmer still needs to write computer programs using a natural number (base N number system where N is a natural number)
The answer to life, the universe and everything is… 1.618…?
Sorry wrong video. This is it (I hope it’s right)
Dr. Strangelove.
Yes, the golden ratio is important and seems to be fundamental to the steady state of the climate system when the system is not otherwise constrained (i.e. the Moon or Venus). The current measured sensitivity is so close to 1.618035 W/m^2 of surface emissions (Ps) per W/m^2 of forcing (Pi) and is so constant from pole to pole and from season to season, it’s hard to accept that it’s just a coincidence, furthermore; numeric simulations starting from arbitrary initial conditions where simulated annealing is applied to determine the equilibrium cloud cover tend to converge to this ratio. Additionally, other aspects of the numeric solution tend to snap into place when Ps/Pi is golden. The definitive proof is still elusive but I’m getting closer and closer every day.
My current hypothesis for why this is so starts with the basic equation for equilibrium as Pi = Po + dE/dt, where Pi and Po are the energy fluxes arriving to and leaving from TOA and E is the energy stored by the planet. Pi varies by albedo while Po as a function of the absorption of surface emissions (Ps), both of which are modulated by clouds, both of which are dependent on E (the energy stored by the system) and both of which send the surface temperature (Ps and hence Po) in opposite directions as a function of clouds. That is, as clouds increase, albedo increases, Pi decreases causing cooling, while at the same time, absorption by clouds increases resulting in warming.
When all the relevant equations are expressed, there are an infinite number of solutions for Ps/Pi in the steady state when dE/dt is zero (dE/dt is what the IPCC calls forcing). This arises because cloud cover is a free variable, moreover; the precise relationship between the relative heating and cooling from clouds seems to chaotically fluctuate around an equal and opposite effect. The counter acting forces of heating and cooling plus the chaos that modulates the effects of clouds combines to converge to a solution where Po/Pi is equal to the golden ratio. This is similar reasoning for why other natural processes also converge to golden ratios.
The necessary condition that constrains the solution to one where Ps/Pi is golden is that the function describing Pi – Po as a function of E must be of the same form as its derivative, that is, if Pi is sinusoidal (for example seasonal variability), both Po and dE/dt must also be sinusoidal. Climate science fails to accommodate this requirement on the solution which is why they have gotten it so incredibly wrong given the otherwise infinite solution space that can theoretically support any possible ECS.
The only functions whose derivative is the same form as itself are functions of e^x. Solutions to the differential equation are decaying exponentials in response to step functions of Pi and sinusoidal solutions when Pi is sinusoidal since sinusoids are of the form e^iwt, per Euler’s equation. Note that this seems to connect i, e and pi to the golden ratio which I don’t think has ever been done before.
The basic analysis is nothing new as this is fundamentally the same differential equation that describes the charging and discharging of a capacitor whose solutions are similarly constrained for the same reasons. The differences from an RC circuit are that the forcing is not also a function of the state, there’s no chaos involved and the relationship between the state (E) and the output (Po) is strictly linear.
Since Pi < Ps, the surface should be cooling. But temperature is constant (more or less) at 288 K so you add greenhouse effect to make Pi = Ps. And the golden ratio disappears when you apply correct physics. BTW there's also convection and evaporation so the physics is more complicated.
The fine structure constant is the dimensionless ratio between the impedance of a free space and the impedance of a photon.
The impedance of a photon arises by considering what L and C are required to be consistent with Quantum mechanics and Maxwell’s equations as they both constrain energy as E = hv and E = q^2/2C. The resonant impedance is then calculated as sqrt(L/C) and becomes E=2h/q^2.
The only way to change the impedance of free space, i.e. changing the L and C given by L=u0*d and C = e0*d. given that there’s no dielectric material. is to modify the geometry of space-time, thus modifying d, making the fine structure a scalar metric of space-time curvature that links General Relativity, Quantum Mechanics and Maxwell’s equations through the required space-time geometry of a photon.
There is no geometry of space time, that’s a unicorn, if there was, all light would travel all geometric alterations to “muh space time”. it doesn’t and has never been observed to do so, all we have observed is refraction and we can’t get light to bend unless we use EM force to control light, or refraction.
You must not accept General Relativity which quantifies the geometry of space-time in the presence of matter and energy. The reason photons bend in space-time curvature fields, and this has been experimentally confirmed many times as a prediction of GR, is because the storage of energy as a photon curves space-time just like matter does, albeit in a different configuration. When you look carefully, the REQUIRED geometry corresponding to the C of a photon must be stretched (the REQUIRED C is 1/137 of the C of free space) while the geometry corresponding to the L is squeezed (the REQUIRED L is 137 times larger than the L of free space), thus the NET space-time curvature is zero, hence the massless quality of photons.
As I see it, conservation of space-time curvature is the missing link in any unification between GR and Quantum Mechanics and is the primordial conservation law from which all others are arise. Keep in mind that E=mc^2 relates energy to space-time curvature and energy is certainly conserved.
Particles of matter squeeze space time on the outside, while they stretch space-time on the inside of the particles event horizon. The squeezed space-time on the outside of a particle overlaps with the squeezed space-time on the outside of every other particle, while the stretched space-time on the inside is isolated from all other stretched space-time.
In other worse. when matter is annihilated with anti-matter, space-time curvature is conserved by the resulting photons, it’s just reorganized differently.
“making the fine structure a scalar metric of space-time curvature that links General Relativity, Quantum Mechanics and Maxwell’s equations through the required space-time geometry of a photon.”
What’s the required spacetime geometry of photon? It can move in 4-dimensional Euclidean and non-Euclidean spacetime geometries. It has been known since 1920s that you can unify general relativity and Maxwell’s equations in 5-dimensional metric tensor. This is the Kaluza-Klein theory but it does not include quantum mechanics.
“conservation of space-time curvature is the missing link in any unification between GR and Quantum Mechanics”
How do you conserve spacetime curvature? I never heard of it. Loop quantum gravity attempts to unify GR and QM
Dr. Strangelove,
The required geometry of a photon is that which is required so that the L and C of the space it occupies is consistent with its energy and frequency and this is definitely not the geometry of relatively flat free-space, although the geometry of free-space is consistent with the propagation of planar EM radiation.
In Kaluza-Klein theory, my suspicion is that the reason it seems to work is that the 5-th dimension is representing the causal relationship between the curvature field and anti-curvature fields that I claim is required to represent matter and energy. While this seems to lead to the higher dimensions of String Theory, considering the relationship in terms of a causally variable space-time geometry doesn’t require all the extra dimensions you need to wrap your brain around in order to map either Kaluza-Klein or String Theory to reality. Both of these theories are manipulating abstract math, rather than understanding any connection to a physical reality.
Conservation of space-time curvature means that the net curvature of existence is zero which is the same as the net curvature before the Universe arose. For example, photons curve half of the space they occupy in one direction and the other half in the other, such that the net curvature is zero and only time separates the curved part of its existence from the uncurved part. Similarly, particles curve space-time on the outside and equally and oppositely uncurve it on the inside, so that the net curvature imposed by all particles on the Universe is zero. Note that in general, curvature is manipulating the local relationship between space and time and is not properly represented as a change to the geometry of space alone which is what tends to confuse people. I like to think of curved and anti-curved space-time as representing time leading space (a positive charge) or time lagging space (a negative charge) relative to the speed of light, where the arrow of time resolves the conflict.
We are blinded to the anti-curvature on the inside of particles and only observe the effects of the space-time curvature on the outside as gravity because the uncurved space-time on the inside of particles doesn’t overlap with the uncurved space-time of other particles, while all the curved space-time on the outside of all particles overlap and sum with each other. Note how stretching a point in space-time into a point in time and a region of space pushes space time out of the way on the outside of the particle and this is what we observe as the spatial curvature responsible for gravity.
The space-time outside the particle records its past, while that on the inside represents all possible futures and the boundary between these two manifests existence and is the source of the arrow of time. Time then arose to resolve the conflict as the Universe fractured from flat space-time into curved space-time. For anti-matter the roles of curved space and uncurved, or anti-curved space, are reversed and except for the direction of the arrow of time are indistinguishable. Based on my hypothesis, whether the Universe ended up a matter or anti-matter Universe depended on the direction of the initial chaotic spark of curvature that curved nothing by so much, time separated from space and the the Universe kicked off. If you consider that the Universe started absolutely flat with time fluctuating around zero as the result of random curvature perturbations, a condition where it curved enough so that time separated from space becomes inevitable.
The Universe evolved by curving space-time in equal and opposite directions such that the result was no different than what it started from. Equating conservation of energy with conservation of curvature is a consequence of relativity theory where E = mc^2. Since mass is proportional to the curvature presented by that matter to the Universe and since energy is conserved, curvature must also be conserved and that what exists now must somehow be conserved with what preceded the formation of the Universe.
BTW, this all arose about 2 decades ago from my hypothesis that space-time curvature is the fundamental unit of existence and that GR is the Unified Field Theory, but just hasn’t been acknowledged as such. Note that GR already implies that everything in the Universe can be described as functions of space-time curvature.
Impedance is for EM field. Spacetime curvature is for gravity. Unless you have a unified theory of electromagnetism and gravity, the two are not equivalent and interchangeable. Kaluza-Klein theory unified it but physicists are skeptical of 5 dimensions (string theory is worse with 11 dimensions) GR is not a unified theory. Einstein himself was searching for a unified theory until his death.
Dr Strangelove,
The impedance of free space is the property of a flat space-time geometry and to the extent that space-time exhibits a different impedance, the ratio of its impedance to that of free space can only be a property of the relative curvature of space-time when there is no other substance that can alter the electrical properties of the space-time exhibiting an impedance other than the impedance of free space. You can add a dielectric to increase the effective e0, but can never decrease it, yet the resonant impedance of an LC circuit whose energy is constrained by E=hv, requires e0 to be e0/137 and u0 to be 137*u0 in order for the correct L and C to emerge and be resonant at the frequency of the photon. Maxwell’s equations must be satisfied by EM energy and photons are the very definition of EM energy. One way to accomplish this is by warping the space-time geometry of the photon, relative to the free space it’s passing through.
This could be considered a unification of EM and gravity by quantifying charge as a manifestation of the relative curvature between space and time which can be thought of in an abstract manner as the phase difference between space and time. Time leading space by PI/2 manifests a unit positive charge and time lagging space by PI/2 manifests a unit negative charge. The hypothesis is just an application of GR constraining the solutions for fundamental particles to be curvature conserving when integrated across the past and the future. The surface of current existence is at the boundary where all possible futures (offsetting anti-curvature) and the past (observable curved space-time) intersect which by definition, is flat, i.e. zero curvature, space-time. The foundation theory is still GR.
Curvature conserving solutions for elementary particles work because when aggregated, they have the same far field behavior as singular point sources of aggregated mass, except that there’s no singularity to distort the near field behavior. One reason to add dimensions is to make singularities go away. This is just another way to accomplish the same thing.
BTW, if you understand the concept of Q, relative to a resonant circuit, 137 is the Q of a photon, relative to free-space.
Q
Wasn’t he that sort of bad-good-bad guy that kept popping up in Star Trek The Next Generation?
In the series finale he sort of ending up saving Life on Earth from being prevented after messing around with Picard one last time.
Between all the Star Treks, he was in 12 episodes.
Therefore “12” is the number. …Maybe…
137/42/12= 0.271825397
Maybe 0.271825397 is the number?
My wife made a pie for a friend the other day. But she already delivered it. If I only had that pie to divide, I could give you all the answer. It was the perfect pie. (Shucks.)
Now we’ll never know.
OOPS!
Sorry.
I forgot the “SARQ” tag
That’s exactly what I was thinking… NOT!!!
The dimensionless constant that applies to the climate system seems to be the golden ratio of 1.618035. When we consider Pi to be the NET input power and Ps to be the NET surface emissions, we can characterize the steady state behavior of the layer between the surface and its environment (space) as,
Ps/Pi = (Ps + Pi)/Ps
Pi/Ps = (Ps – Pi)/Pi
Which constrains Ps/Pi = 1 + Pi/Ps, setting Ps/Pi equal to the golden ratio of (1 + sqrt(5))/2. The data, Pi = 239 W/m^2 @ 255K and Ps = 390 W/m^2 @ 288K confirms these relationships within a percent or so. Of course, the idea that the ECS wants to be a constant 1.618035 W/m^2 per W/m^2 of forcing and is independent of forcing, feedback or anything else disputes everything the IPCC wants us to believe.
This plot of water vapor vs. Ps/Pi from the ISCCP data set shows how this ratio converges to golden from both above and below. Plots of Ps/Pi vs. other variables show the same convergent behavior.
http://www.palisad.com/co2/sens/wc_gs.png
Presumably this also applies to co2 in some way ?
” … applied to co2 …”
Only to the extent that the climate system needs to reorganize in order to achieve the required ratio between net surface emissions and net solar forcing. The main point this illustrates is that the incremental effect from the next W/m^2 can be no different then the average effect applied to all other W/m^2 and that this effect is a relatively constant amount of surface emissions per incremental W/m^2 of input.
Confusion arises from a problem with how the IPCC quantities forcing as the instantaneous difference in input and output flux at TOA, rather than as the total input flux arriving from the Sun. In practice, you can consider a change to the system as being equivalent to a change in the total forcing while keeping the system constant. CO2 concentrations are an attribute of the system and are not technically a forcing influence, even as an instantaneous change in CO2 concentrations will have an instantaneous effect on the flux difference at TOA. This unnecessary level of obfuscation seems to confuse many modelers who tend to apply the equivalent forcing to a changed system.
The Mayans stopped their calendar efforts when they realized this was something to ponder.
Relativity, electromagnetism and quantum mechanics are unified by the number.
Really? 1/137 can combine junk science with actual science? well I never
There is no such thing as space time, ugh. Space is a set of coordinates containing other coordinates, time is procession. Both are human constructs that allow us to define and use space and time in a technical fashion, they are not “real” physical things that can be manipulated.
So bending space and time is the most laughable thing ever. Quantum clockery doesn’t change reality. There is a technical reason why clocks run at different speeds in space, it’s a different environment physically.
How long did the wave particle duality nonsense persist, until we found out that the actual observation of the experiment physically interacted with the experiment, decades?…
Observation of the patterned result of the dual beam experiment does not interfere with the experiment.
Quantum mechanics is the only explanation for (for example) the photoelectric effect and for why electronic orbitals do not decay into the nucleus.
And the Planck solution to the thermal spectrum “ultraviolet catastrophe, quanta h (hilfe), started it all, even when Bertrand Russell had declared physics is settled – only decimals from now on.
At Solvay 1927 Bohr declared physics was again settled.
Now the “standard model” is settled?
Amazing this settled carry-on – what are they afraid of ? That the infinite, or self bounded cosmos is unendingly comprehensible to us?
Throwing out spacetime with the bathwater, just to save Newton?
Sure, spacetime is not a “stuff”, it’s what is happening “in it” – Einstein’s stress-energy tensor. Spacetime waves, gravitation, refraction, tell us dense stuff is acting in some way.
Stuff is invariably discreet, actual, yet spacetime is continuous – ideal.
No wonder Schroedinger had trouble with the apparent conflict between continuous waves and discreet events. And since all measurements come down to a position, spacetime is definitely not a mere chimera – without the use of continuity, all of physics would evaporate.
The always-present continuous-discreet double aspect of nature is not simply “wave-particle”.
The way I would explain this is as follows:
Space-time exists as points in the fabric of space-time.
A particle stretches a point in space-time into the region of space defining the particle. Particles exist at a point in time and across a region of space.
Photons spread a point in space-time into a region of time and a region of space consistent with its wavelength. A photon exists concurrently across both time and space.
The fine structure constant quantifies the spread for photons whose required effort, that is the resistance of the Universe to be curved, is proportional to h. For both the particle and the photon it’s the relationship between the time and space they occupy that’s being curved by their existence.
The variable relationship between time and space is the origin of the Heisenberg Uncertainty Principle since pinning the existence of a particle or photon to either a point in time or point in space doesn’t constrain the other and in this case, h quantifies the spread as uncertainty.
The Aliens are not going to communicate. They are just going to start eating.
As optimistic a person as I am …:-) so true. Just look at us here on earth. And we are all “people.”
Well, “To Serve Man” is a cookbook, 🙂 🙂
I say we eat them! I saw on tv that aliens look just like donuts (Simpsons explains it all, not numbers).
“brilliant physicist” does not mean much. the dumbest kid in math class was a nuclear physicist and math teachers kept telling jokes and real examples about physicists.
the only reason we are stuck on this planet is that rocket science is done by physicists.
The reason we’re stuck on this planet is that the physics to enable leaving is most likely highly classified owing to it’s potential impact if a hostile power were to develop technology based on it. As much as I’m opposed to classifying basic physics, I understand why this is so, as a propulsion technology based on this is well within our means and while the energy technology to enable travel to the stars is elusive, the energy requirements to travel half way around the world are not. Much like stealth, this genie will not be let out of the bottle until we are either forced to deploy it ourselves and/or have established the ability to defend ourselves against the same kind of technology.
Understanding the relationship between space-time curvature and EM energy is the key. Once this is understood, it should be possible to use organizations of EM energy to hide a craft in a space-time curvature field that looks like a photon to the space-time it’s traveling through, thus eliminating the inconvenience of inertia by making the craft appear weightless and in a continuously accelerating free fall relative to the space-time it’s traveling through.
Mathematicians make jokes about engineers, too! Usually something like ” Yes, your bastardized equation works. It’s good enough for engineers but you will get a ” D” from me if you put that kind of thing down 9n your exam paper.
If you want to know how something works, ask an engineer. If you only want to think that that something can work, ask a mathematician to interpret.
For example, Schlesinger was a mathematician who bastardized an engineering equation related to linear feedback amplifiers in order to be able to think that something worked in a way that the laws of physics could not otherwise support.
Engineers (rocket science is a misnomer). God save us from mathematicians taking over the design!!!
We’ve been told recently that the answer is 1/1024th.
Your Metric May Vary.
Funny…
The native base or foundation of all advancement.
From wikipedia:
Feynmanium and elements above the atomic number 137
It is a “folk legend” among physicists that Richard Feynman suggested that neutral atoms could not exist for atomic numbers greater than Z = 137, on the grounds that the relativistic Dirac equation predicts that the ground-state energy of the innermost electron in such an atom would be an imaginary number. Here, the number 137 arises as the inverse of the fine-structure constant. By this argument, neutral atoms cannot exist beyond untriseptium (alternatively called “feynmanium”), and therefore a periodic table of elements based on electron orbitals breaks down at this point. However, this argument presumes that the atomic nucleus is pointlike. A more accurate calculation must take into account the small, but nonzero, size of the nucleus, which is predicted to push the limit further to Z ≈ 173.
https://en.wikipedia.org/wiki/Extended_periodic_table#Feynmanium_and_elements_above_the_atomic_number_137
Awesome!
I wonder though how you can have some half life of 60 ms and yet someone tells it’s solid in STP. It’s not a freaking solid, it’s so hot gas it fries your lungs!
Dr Sheldon Cooper recons 73 the best number.
I thought you all knew by now the MoL is 72
It was a typo. Should have been 72. The author, Douglas Adams, was secretly an economist and statistician who pretended to be a sci-fi writer of comic brilliance to hide his shame. Possibly.
[source BBC (must be correct) : https://www.bbc.co.uk/news/magazine-14217443%5D
Oops matrix glitch: https://www.bbc.co.uk/news/magazine-14217443 ]
If it isn’t, it oughta be.
This is why I visit WUWT, gotta check to see if any of the dust has settled.
BTW, “Sir Anthony” just won its race at Hawthorne.
The punters jumped on it late, so it only paid $5.00 to win.