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Pure Derivation of the Exact Fine – Structure Constant and As a Ratio of Two Inexact Metric Constant
Theorists at the Strings conference in July 2000 were asked about the mysteries yet to be revealed in the 21st century. Participants were asked to help formulate the ten most important unsolved problems in fundamental physics, which were ultimately selected and ranked by a distinguished panel of David Gross, Edward Witten and Michael Duff. No question was more valid than the first two problems posed respectively by Gross and Witten: #1: Are all dimensionless (measurable) parameters that characterize the physical universe in principle calculable or are some simply determined by historical or quantum mechanical accident and incalculable? #2: How can quantum gravity help explain the origin of the universe?
A newspaper article on these millennial mysteries expressed some interesting comments on question #1. Perhaps Einstein indeed “said it more clearly: Did God have a choice in creating the universe?– which also sums up dilemma #2. While the Eternal “may” have had a “choice” in Creation, the following arguments will conclude that the answer to Einstein’s question is an emphatic “No”. comprehensive set of precise and unprecedented fundamental physical parameters are demonstrably computable in a dimensionless universal system which naturally includes a literal “Monolith.”
Similarly, the article asked if the speed of light, Planck’s constant and electric charge are determined indiscriminately – “or do the values have to be what they are because of some deep, hidden logic. These kinds of questions come to a point with a riddle involving a mysterious number called alpha If you square the charge of the electron and then divide it by the speed of light times Planck’s constant (“reduced”) (multiplied by 4p times the vacuum permittivity), all (metric) dimensions (of mass, time and distance) cancel each other out, giving a so-called “pure number” – alpha, which is just above- above 1/137. But why isn’t it precisely 1/137 or some other value entirely? Physicists and even mystics have tried in vain to explain why.”
That is, if constants such as a fundamental particle mass can be expressed as a dimensionless relation to the Planck scale or a relation to a known or available unit of mass somewhat more precisely , the inverse of the electromagnetic coupling constant alpha is uniquely dimensionless like a pure ‘fine structure number’ a ~137.036. On the other hand, assuming a unique, invariably discrete or exact the fine-structured numeric exists as a “literal constant”, the value has yet to be confirmed empirically as a ratio of two on exactly determinable “metric constants”, h-bar and electric charge e (the speed of light c being exactly defined when the SI convention was adopted in 1983 as a whole number of meters per second.)
So, although this riddle has been deeply baffling almost since its inception, my impression on reading this article in a morning newspaper has been one of utter amazement, a numerological problem of invariance deserving of such distinction by eminent modern authorities . For I had been obliquely obsessed with the fs-number in the context of my colleague AJ Meyer’s model for a number of years, but had come to accept its experimental determination in practice, periodically pondering the question without dimension. Gross’s question therefore served as a catalyst for my complacency; acknowledging a unique position as the only fellow capable of providing a categorically comprehensive and consistent answer within the context of Meyer’s main fundamental parameter. However, my pretentious instincts led me to two months of insane intellectual postures until healthily repeating a simple procedure explored a few years earlier. I’m happy to look at to the result using the CODATA 98-00 value of aand the next solution immediately hit with full heuristic force.
Because the fine structure ratio effectively quantifies (via h-bar) the electromagnetic coupling between a discrete unit of electric charge (e) and a photon of light; in the same direction a integer is discreetly ‘quantified’ with respect to the “fractional continuum” between it and 240 or 242. One can easily see what this means by considering another integer, 203, from which one subtracts the base 2 exponential of the square of 2pi. Now add the reciprocal of 241 to the resulting number, multiplying the product by the natural logarithm of 2. It follows that this pure calculation of the fine structure number is exactly equal to 137.0359996502301… – which here (/100) is given at 15, but can be calculated at any number of decimal places.
By comparison, given the experimental uncertainty in h-bar and e, the NIST rating varies up or down around mid-6 of ‘965’ in the invariant sequence defined above. The following table gives the values of h-bar, e, their calculated ratio and the actual NIST choice for a in each year of their records, as well as the 1973 CODATA, where the standard two-digit +/- experimental uncertainty is in bold in parentheses.
year…h- =Nh*10^-34 Js…… e = Ne*10^-19 C….. h/e^2 = a =….. NIST value & ±(South Dakota):
2006: 1,054,571,628(053) 1.602.176 487(040) 137.035.999.661 137.035.999 679(094)
2002: 1,054,571,680(18x) 1,602,176 53o(14o) 137.035.999.062 137.035.999 11o(46a)
1998: 1,054,571,596(082) 1.602.176 462(063) 137.035.999.779 137.035.999 76o(50a)
1986: 1,054,572 66x(63x) 1,602,177 33x(49x) 137.035.989.558 137.035.989 5xx(61xx)
1973: 1,054,588 7xx(57xx) 1.602.189 2xx(46xx) 137.036.043.335 137.036. 04x(11x)
It therefore seems that the choice of NIST is approximately determined by the values measured for h and e alone. However, as explained at http://physics.nist.gov/cuu/Constants/alpha.html, in the 1980s interest shifted to a new approach that provides a direct determination of a by exploiting the quantum Hall effect, independently corroborated by both theory and experiment of the electronic magnetic moment anomaly, thus reducing its already finer uncertainty. Yet it took 20 years before a better measurement of the magnetic moment g/2-factor was published in mid-2006, where the first estimate from this group (led by Gabrielse for Hussle at Harvard.edu) for a was (A:) 137.035999. 710(096) – explaining the greatly reduced uncertainty in the new NIST listing, compared to that of h-bar and e. However, more recently a numerical error in the original QED calculation (A:) was discovered (we will call it 2nd article B:) which shifted the value of a to (B:) 137.035999. 070 (098).
Although reflecting nearly identical uncertainty, this estimate is clearly outside the NIST value consistent with the h-bar and elemental charge estimates, which are independently determined by various experiments. NIST has three years to fix this, but in the meantime faces an embarrassing irony in that at least the 06 choices for h-bar and e appear to be slightly biased against the expected fit for a! For example, adjusting the last three digits of the 06 data for h and e to agree with our pure fs number gives an imperceptible adjustment to e alone in the ratio h628/e487.065. If the QCD error had been corrected before the actual NIST publication in 2007, it could have been fairly easily adjusted uniformly to h626/e489; while questioning its consistency in the last 3 digits of a compared to the comparative 02 and 98 data. In any case, much larger improvements across multiple experimental designs will be required for a comparable reduction in error for h and e to definitively fix this problem.
But again, even then, no matter how accurately the metric measurement is maintained, it is still infinitely short of “literal accuracy”, while our pure fs-number matches the current values of h628/e487. In the first case, I recently discovered that a mathematician named James Gilson (see http://www.maths.qmul.ac.uk/%7Ejgg/page5.html) also devised a pure number = 137.0359997867. closer to the revised 98-01 standard. Gilson further argues that he calculated many of the Standard Model parameters, such as the dimensionless ratio between the masses of a low-gauge Z and W boson. But I know he could never construct a single Proof employing equivalences capable of by deriving the masses Z and/or W per se from there precisely confirmed heavy masses quarks and Higgs fields (see the essay referenced in the resource box), which themselves result from a single dimensionless tautology. Because the numerical discretion of the fraction 1/241 makes it possible to construction physically meaningful dimensionless equations. If we take instead the numerology of Gilson, or the refined empirical value of Gabreilse et. al., for the fs number, it would destroy that discretion, precise self-consistency, and ability to even write an equation without significant dimension! On the other hand, it is perhaps not too surprising that after literally “finding” the integer 241 and deriving the exact fine structure count from the resulting “monolith count”, it only took about 2 weeks to calculate the six quark masses using real dimensionless masses. analysis and various finely structured relationships.
But since we’re not really talking about the fine structure number per se anymore than the integer 137, the result answer definitively Gross’ question. For these “dimensionless parameters that characterize the physical universe” (including alpha) are ratios between selected metric parameters that lack a single unified dimensionless mapping system from which metric parameters like particle masses are calculated from defined equations. The “standard model” gives a single system of parameters, but no means calculate or to predict any and/or all in one system – thus the experimental parameters are set arbitrarily by hand.
Final irony: I am doomed to be belittled as a “numerologist” by “experimenters” who continually fail to recognize solid empirical evidence for the masses of quarks, Higgs, or hadrons that can be used to calculate exactly the current standard for the most precisely known masses. and the heaviest mass in high-energy physics (the Z). On the contrary, the silly ghouls: empirical confirmation is only the final cherry that the chef puts on top before presenting a “Pudding Proof” that no sentient being could resist simply because he did not assemble it himself, so instead he makes a imitated mess, the real deal doesn’t look like it. Because the base of this pudding is made up of melons that I call Mumbers, which are really just numbers, pure and simple!
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