Heisenberg's uncertainty says
pd = h/(2.Pi)
where p is uncertainty in momentum, d is uncertainty in distance.
This comes from his imaginary gamma ray microscope, and is usually written as a minimum (instead of with "=" as above), since there will be other sources of uncertainty in the measurement process.For light wave momentum p = mc,
pd = (mc)(ct) = Et where E is uncertainty in energy (E=mc2), and t is uncertainty in time.Hence, Et = h/(2.Pi)
t = h/(2.Pi.E)
d/c = h/(2.Pi.E)
d = hc/(2.Pi.E)
This result is used to show that a 80 GeV energy W or Z gauge boson will have a range of 10^-17 m. So it's OK.
Now, E = Fd implies
d = hc/(2.Pi.E) = hc/(2.Pi.Fd)
Hence
F = hc/(2.Pi.d^2)
This force is 137.036 times higher than Coulomb's law for unit fundamental charges.
Notice that in the last sentence I've suddenly gone from thinking of d as an uncertainty in distance, to thinking of it as actual distance between two charges; but the gauge boson has to go that distance to cause the force anyway.
Clearly what's physically happening is that the true force is 137.036 times Coulomb's law, so the real charge is 137.036. This is reduced by the correction factor 1/137.036 because most of the charge is screened out by polarised charges in the vacuum around the electron core:"... we find that the electromagnetic coupling grows with energy. This can be explained heuristically by remembering that the effect of the polarization of the vacuum ... amounts to the creation of a plethora of electron-positron pairs around the location of the charge. These virtual pairs behave as dipoles that, as in a dielectric medium, tend to screen this charge, decreasing its value at long distances (i.e. lower energies)." - arxiv hep-th/0510040, p 71.
The unified Standard Model force is F = hc/(2.Pi.d^2)
That's the superforce at very high energies, in nuclear physics. At lower energies it is shielded by the factor 137.036 for photon gauge bosons in electromagnetism, or by exp(-d/x) for vacuum attenuation by short-ranged nuclear particles, where x = hc/(2.Pi.E)
This is dealt with at http://einstein157.tripod.com/ and the other sites. All the detailed calculations of the Standard Model are really modelling are the vacuum processes for different types of virtual particles and gauge bosons. The whole mainstream way of thinking about the Standard Model is related to energy. What is really happening is that at higher energies you knock particles together harder, so their protective shield of polarised vacuum particles gets partially breached, and you can experience a stronger force mediated by different particles!
UPDATE as of 25 Feb 06:
http://cosmicvariance.com/2006/02/22/on-the-plus-side/
posted by nige @ 7:30 AM
3 comments
3 Comments:
Copy of fast series of comments from:
http://motls.blogspot.com/2006/02/albion-and-rg-flow.html
Lubos,
Heisenberg's uncertainty says
pd = h/(2.Pi)
where p is uncertainty in momentum,
p is uncertainty in distance.
This comes from his imaginary gamma ray microscope, and is usually written as a minimum (instead of with "=" as above), since there will be other sources of uncertainty in the measurement process.
For light wave momentum p = mc,
pd = (mc)(ct) = Et
where E is uncertainty in energy (E=mc2), and t is uncertainty in time.
Hence, Et = h/(2.Pi)
t = h/(2.Pi.E)
d/c = h/(2.Pi.E)
d = hc/(2.Pi.E)
This result is used to show that a 80 GeV energy W or Z gauge boson will have a range of 10^-17 m. So it's OK.
Now, E = Fd implies
d = hc/(2.Pi.E) = hc/(2.Pi.Fd)
Hence
F = hc/(2.Pi.d^2)
This force is 137.036 times higher than Coulomb's law for unit fundamental charges.
Notice that in the last sentence I've suddenly gone from thinking of d as an uncertainty in distance, to thinking of it as actual distance between two charges. I don't think this affects the result, because the gauge boson has to go that distance to cause the force anyway.
Clearly what's physically happening is that the true force is 137.036 times Coulomb's law, so the real charge is 137.036. This is reduced by the correction factor 1/137.036 because most of the charge is screened out by polarised charges in the vacuum around the electron core:
"... we find that the electromagnetic coupling grows with energy. This can be explained heuristically by remembering that the effect of the polarization of the vacuum ... amounts to the creation of a plethora of electron-positron pairs around the location of the charge. These virtual pairs behave as dipoles that, as in a dielectric medium, tend to screen this charge, decreasing its value at long distances (i.e. lower energies)." - arxiv hep-th/0510040, p 71.
I just think there is a wrong attitude in modern physics that simple ideas are crackpot.
Nigel
Nigel Cook | Homepage | 02.17.06 - 10:32 am | #
Nigel,
Humm...
http://www.crank.net/physics.html
Guess who leads the pack?
Simple ideas are not synonymous with crackpot physics.
Yours are.
Michael Varney | Homepage | 02.17.06 - 11:17 am | #
Varney to the crackpot rescue... I was just talking about you the other day in context with a crank website that is maintained by your old buddy, "nemesis"... hahaha
LTNS, Mikey... I hope that you haven't turned into a string theory crackpot, like Lumo...
island | Homepage | 02.17.06 - 2:07 pm | #
Hi Michael Varney,
Glad you checked the maths. Notice that the guy who runs "Crank Dot Net" a certain Erik Max Francis
"Mr. Francis, 29, is not a scientist, and has taken only a handful of classes at a community college."
-- Bonnie Rothman Morris in The New York Times of Dec. 21, 2000 -
http://en.wikipedia.org/wiki/Tal...i/Talk: Symmetry
Notice that this Erik does not include himself despite having links to his own pages claiming to have proved Kepler's laws from other stuff which is based on Kepler's laws!!! (Hint: crackpot circular argument.)
Notice that this Erik does not include Tony Blair for the dodgy dossier theory that Saddam woulc wipe out Earth in 3 seconds, or Hitler's cranky schemes.
If he likes mass murderers and so does not include them in his list of cracks, then I'm glad to be in the list and not favoured by the man. …
By the way, I do find Archimedes Plutonium's post http://groups.google.com/group/ s...16c0857d09ccb6f very funny. See http://en.wikipedia.org/wiki/ Arc...medes_Plutonium for where egotism can go wrong.
Nigel Cook | Homepage | 02.18.06 - 8:42 am | #
Let's see if Plato has the guts to face real facts: http://eskesthai.blogspot.com/ 20...t.html#comments
Plato,
Thanks for that diagram showing unification of electromagnetism, strong and weak forces as a function of energy. I think it is good the Standard Model does that, even if there is still doubt over exact unification details at grand unification energy (is SUSY real?).
However, what I don't like is that nobody explains the unification physically as I will do here:
Heisenberg's uncertainty says
pd = h/(2.Pi)
where p is uncertainty in momentum, d is uncertainty in distance.
This comes from his imaginary gamma ray microscope, and is usually written as a minimum (instead of with "=" as above), since there will be other sources of uncertainty in the measurement process.
For light wave momentum p = mc,
pd = (mc)(ct) = Et where E is uncertainty in energy (E=mc2), and t is uncertainty in time.
Hence, Et = h/(2.Pi)
t = h/(2.Pi.E)
d/c = h/(2.Pi.E)
d = hc/(2.Pi.E)
This result is used to show that a 80 GeV energy W or Z gauge boson will have a range of 10^-17 m. So it's OK.
Now, E = Fd implies
d = hc/(2.Pi.E) = hc/(2.Pi.Fd)
Hence
F = hc/(2.Pi.d^2)
This force is 137.036 times higher than Coulomb's law for unit fundamental charges.
Notice that in the last sentence I've suddenly gone from thinking of d as an uncertainty in distance, to thinking of it as actual distance between two charges; but the gauge boson has to go that distance to cause the force anyway.
Clearly what's physically happening is that the true force is 137.036 times Coulomb's law, so the real charge is 137.036. This is reduced by the correction factor 1/137.036 because most of the charge is screened out by polarised charges in the vacuum around the electron core:
"... we find that the electromagnetic coupling grows with energy. This can be explained heuristically by remembering that the effect of the polarization of the vacuum ... amounts to the creation of a plethora of electron-positron pairs around the location of the charge. These virtual pairs behave as dipoles that, as in a dielectric medium, tend to screen this charge, decreasing its value at long distances (i.e. lower energies)." - arxiv hep-th/0510040, p 71.
The unified Standard Model force is F = hc/(2.Pi.d^2)
That's the superforce at very high energies, in nuclear physics. At lower energies it is shielded by the factor 137.036 for photon gauge bosons in electromagnetism, or by exp(-d/x) for vacuum attenuation by short-ranged nuclear particles, where x = hc/(2.Pi.E)
This is dealt with at http://einstein157.tripod.com/ and the other sites. All the detailed calculations of the Standard Model are really modelling are the vacuum processes for different types of virtual particles and gauge bosons. The whole mainstream way of thinking about the Standard Model is related to energy. What is really happening is that at higher
Nigel Cook | Homepage | 02.18.06 - 8:45 am | #
- energies you knock particles together harder, so their protective shield of polarised vacuum particles gets partially breached, and you can experience a stronger force mediated by different particles!
Full heuristic interpretation of quantum field theory.
The 2.Pi factor in the Schwinger 1st coupling correction of the magnetic moment of the electron, in 1 + 1/(2.Pi.137) Bohr magnetons is almost certainly due to the spin effect shielding.
Physically, the core of the first electron has a magnetic moment of 1 Bohr magneton because the polarised vacuum around the electron core only reduces the radial electric field and transverse magnetic field, not the polar magnetic field vector which is of course parallel to the radial electric field at the poles.
The electric field of the core is reduced by a factor of 137 by the polarised virtual charge surrounding it in the vacuum. The real core couples up with a particle (virtual positron?) in the vacuum which adds to the magnetic moment by aligning with the magnetic axis of the electron core. This is the reason for the 137 factor in Schwinger correction for the first coupling effect, the 1/(2.Pi.137) = 0.00116 term added to Dirac's 1 Bohr magneton.
The 2.Pi is an additional shielding factor, and is due to geometry. When you have a cylinder and you look at it side-on, you see only 1/(2.Pi) of its surface area. Similarly, when you look at a loop side on, you see a line with only 1/(2.Pi) of its total length.
The 2.Pi factor is heuristically explainable in terms of the geometry which stems from the aligned real electron core and the virtual particle which is aligned with it to add to its magnetic moment. The vacuum is full of virtual particles, but because they are normally orientated randomly, their magnetic fields cancel each other out as seen on a macroscopic scale.
Now, the virtual electron which is outside the polarised shield surrounding the real electron core, and which adds 1/(2.Pi.137) Bohr magnetons to the magnetic moment of the latter, itself has the same effect on another vacuum particle! So there is another correction, which is even smaller, by another 137 factor, and another geometric factor... and so on.
This is how you heuristically explain the extra couplings required for more decimals than 1.00116 Bohr magnetons. Also, you need to take account of different vacuum particles, as occurs with the magnetic moment of the muon, which is slightly different to that from the electron.
This vacuum interpretation of the actual dynamics is completely compatible with the Standard Model and even with string theory, but nobody gives any attention to it.
The nearest I get is your dismissals that it is 'crackpotism following aether rejuvination' which is a plain insult, based on ignorance.
Above I've proved in simple clear physics that the unified force is 137 times Coulomb's law and why. If you want to say it's nonsense you should point out where the error is, or why it
Nigel Cook | Homepage | 02.18.06 - 8:46 am | #
- is nonsense.
Thanks
Nigel Cook | Homepage | 02.18.06 - 8:47 am | #
Example of Michael Varney's intellect:
http://fermiproblemoftheday.blogspot.com/2006/01/hey-masterbator-pic.html
Another tirade from Varney, this time against his own aunt:
http://fermiproblemoftheday.blogspot.com/2006/03/peril-of-fermi-problems-or-fermius.html
"Now, my aunt is the kind of person who will argue the color of the sky and the smell of dog shit. She likes to argue, period. She also is the type who likes to attempt to show off her intelligence whenever she can. She does this not by making meaningful observations, or witty comments, but by... you guessed it... arguing. Her idea of wit is put people down while she argues. This is one smart lady."
Here's the whole thing:
http://fermiproblemoftheday.blogspot.com/
Fermi Problem of the Day
Fermi problems, both politically correct and not. All you need is common sense and some basic physics and math skills. Sometimes even less!
Friday, March 31, 2006
The Peril of Fermi Problems: Or Fermius Interruptus (PIC)
Fermi problems represent a method of thinking... a place where you can be creative and playful. Many a pleasant lunch break have I spent with friends coming up with Fermi problems. The silly ones, the political ones, the environmental.
And don't think that only physics geeks spend time contemplating the Fermi. After a short introduction to the concept many of my non-physics friends become enamored with Fermi problems. One of my ex girlfriends became quite good at positing such problems!
However, one can always find company who will phoo phoo the whole concept, try and argue over the minutia, and in general act like an utter ass about the whole thing.
Take for instance my Aunt.
A few days ago I was invited to dinner by my grandmother, a sort of going away dinner since she was moving to California to live near her daughter (my Aunt).
We went to the old perennial, the Olive Garden, where I decided to order a Martini. The olives on this particular drink were skewered by this huge twizzle stick. Clear emerald green plastic in the shape of the crystal used by Superman in the first movie to create the fortress of solitude. It was monstrous, HUGE!
I comment that due to its size, the restaurant could probably wash it with the dishes and reuse it.
Now, my aunt is the kind of person who will argue the color of the sky and the smell of dog shit. She likes to argue, period. She also is the type who likes to attempt to show off her intelligence whenever she can. She does this not by making meaningful observations, or witty comments, but by... you guessed it... arguing. Her idea of wit is put people down while she argues. This is one smart lady.
After suggesting the recycling of the twizzle stick, she of course says that this is against health code and this it was a stupid idea to suggest.
Now, my Grandmother, who is sitting quietly in the corner of the booth starts looking distressed. I can see why, after all, she is leaving the only home she has had for the last 50 or so years. Leaving all her friends, etc. The last thing she needs is to witness an argument.
So rather than playing to my Aunt's game and partake in an argument, I try to lighten up the mood and say. Hey, lets Fermi the twizzle!
"Who is Fermi?" My Aunt asks.
"He was a very famous physicist in the early half of the 20th century. They named the Fermi labs after him. He worked on the atomic bomb. More importantly, he has had a a type of Gedanken experiment name for him, where you use order of magnitude estimates to solve seemingly difficult problems." I rather long windedly respond.
"Humm, well... I never heard of him," She responds: "so he must not have been all the famous or important."
Now, one thing you must realize here is that my Aunt said all this in a rather pretentious and snooty British accent. The funny part is that she is white bread WASP American. Born and raised in the good old USA in the late 60's, her nickname (self endowed) in high school was DICA, which explains her stunning lack of IQ. The reason she has acquired the affectation of mumbling in a pseudo English accent is because she married a British/Welsh mathematician much older than she, who's only claim to fame was that he was drinking buddies with Stephen Hawking. Not the fact that good old Hawking would not even remember my Uncle does not keep my Uncle from resting on Hawking's laurels. But I digress.
So, one must be able to empathize with my feelings and be astounded at my self control after hearing that because my Aunt has never heard of Fermi, that he must have been an obscure nobody.
I respond: "Humm, well... anyhow... lets consider how many twizzle sticks are used each day in the US. Lets assume that on average each person uses 2 of them a week so..."
"That number seems way to large... that is a silly assumption." My Aunt interrupts belligerently.
"Well" I politely respond, "A Fermi problem is order of magnitude. So I can range from one to ten and still be ok, considering that later when we estimate the size of the average twizzle..."
"What if the average use was 0.45 per person?" She interrupts.
"Well, that still might be ok since we are averaging the size which..." I start.
"We can just as well assume that 22.3 of them are used per person a day... so this is a stupid problem since we cannot exactly determine the number of twizzle sticks!" She pontificates.
I look into her bovine face with disgust and think to myself that if she and her lush of a husband were to go out and drink commensurately with their in house consumption of booze, that the national average usage of twizzle sticks might indeed be 20 per person per day. But I hold my tongue.
My Grandmother at this time decides that the best way to end this is to take the side of her daughter and say: "Well, this is a boring topic... how was your snowboarding trip last week Mike?"
In all fairness to my Grandmother this was the best tack to take. After all, her daughter would not be satisfied until she won the argument, and my Grandmother realized that although in the short term I might feel put down a bit, in the end I would live. Plus, my grandmother had to deal with her daughter for the rest of the week during the move, and live close by in California for the rest of her life.
I conceded the victory to my Aunt via silence, and spent the rest of the evening listening to her whine and moan about how much she hates her job (computer programming, go figure), hates the lack of water in Santa Barbra, hates her weight, hates her life and hates her brother.
However, I had to wonder if perhaps my choice of Fermi problem was indeed silly and boring. To test this I brought up the topic the next day at the coffee shop, and received a vastly different attitude and response.
To see how fun a Fermi problem can be, I will outline how the general flow of how the discussion went.
First we discussed the average size of the Twizzle stick. This lead to a digression of the various types of twizzle sticks each person has seen. One friend of mine mentioned that at her friends bachelorette party the twizzle sticks were in the shape of a penis. Which led to how hard it is to make twizzle sticks in the shape of breasts, and a discussion of the phallic connotations of twizzle sticks in general.
After discussing the various shapes and sizes we agreed to the "average length" and size of twizzle sticks and proceeded to estimate that there were probably 3 to 6 hundred million of them used in the US per week. It was agreed that 3 billion a week was too high and perhaps 30 million of them were too little. There was no recrimination or posturing during this estimation as after all, it was order of magnitude.
From there we estimated the volume of plastic used in the creation of the Twizzle, and one person asked how big of an olive could be skewered by a giant twizzle stick made from all that plastic. A friend from Turkey jokingly asked what would happen to Greece if that olive was dropped from orbit onto the tiny island. This lead to discussion of orbital food fights which led to how astronaut piss could crack the windows of the shuttle which lead to... well... you get the idea.
The solution of a Fermi problem is not its own end, but a way to have fun, to be a little silly, to use ones mind. It can bring friends together (but perhaps not family), and can be a great icebreaker and flirtation device. A good Fermi problem can lighten the mood dragged down by the violence and abject stupidity proliferating in the world.
So perhaps the perils of the Fermi problem are overwhelmed by its benefits.
posted by Mike Varney at 12:20 PM 0 comments links to this post
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