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The Empirical Models of Theoretical Physics

June 14 2017 at 4:51 AM
Pentcho Valev 

Sabine Hossenfelder: "Many of my colleagues believe this forest of theories will eventually be chopped down by data. But in the foundations of physics it has become extremely rare for any model to be ruled out. The accepted practice is instead to adjust the model so that it continues to agree with the lack of empirical support."

Sabine Hossenfelder (Bee): "The criticism you raise that there are lots of speculative models that have no known relevance for the description of nature has very little to do with string theory but is a general disease of the research area. Lots of theorists produce lots of models that have no chance of ever being tested or ruled out because that's how they earn a living. The smaller the probability of the model being ruled out in their lifetime, the better. It's basic economics. Survival of the 'fittest' resulting in the natural selection of invincible models that can forever be amended." http://www.math.columbia.edu/~woit/wordpress/?p=9375

The models that "can forever be amended" are not deductive constructions (the amendments are not deduced from axioms), but then how can they be defined? They are empirical compilations, according to this text of Einstein:

Albert Einstein: "From a systematic theoretical point of view, we may imagine the process of evolution of an empirical science to be a continuous process of induction. Theories are evolved and are expressed in short compass as statements of a large number of individual observations in the form of empirical laws, from which the general laws can be ascertained by comparison. Regarded in this way, the development of a science bears some resemblance to the compilation of a classified catalogue. It is, as it were, a purely empirical enterprise. But this point of view by no means embraces the whole of the actual process ; for it slurs over the important part played by intuition and deductive thought in the development of an exact science. As soon as a science has emerged from its initial stages, theoretical advances are no longer achieved merely by a process of arrangement. Guided by empirical data, the investigator rather develops a system of thought which, in general, is built up logically from a small number of fundamental assumptions, the so-called axioms."

Non-deductive models in physics are essentially equivalent to the "empirical models" defined here:

"The objective of curve fitting is to theoretically describe experimental data with a model (function or equation) and to find the parameters associated with this model. Models of primary importance to us are mechanistic models. Mechanistic models are specifically formulated to provide insight into a chemical, biological, or physical process that is thought to govern the phenomenon under study. Parameters derived from mechanistic models are quantitative estimates of real system properties (rate constants, dissociation constants, catalytic velocities etc.). It is important to distinguish mechanistic models from empirical models that are mathematical functions formulated to fit a particular curve but whose parameters do not necessarily correspond to a biological, chemical or physical property."

Einstein's general relativity is the paradigm of empirical model in physics. Here Michel Janssen describes the anti-deductive approach of Einstein and his mathematical friends - endlessly adjusting and amending the model until "excellent agreement with observation" is reached:

Michel Janssen: "But - as we know from a letter to his friend Conrad Habicht of December 24, 1907 - one of the goals that Einstein set himself early on, was to use his new theory of gravity, whatever it might turn out to be, to explain the discrepancy between the observed motion of the perihelion of the planet Mercury and the motion predicted on the basis of Newtonian gravitational theory. [...] The Einstein-Grossmann theory - also known as the "Entwurf" ("outline") theory after the title of Einstein and Grossmann's paper - is, in fact, already very close to the version of general relativity published in November 1915 and constitutes an enormous advance over Einstein's first attempt at a generalized theory of relativity and theory of gravitation published in 1912. The crucial breakthrough had been that Einstein had recognized that the gravitational field - or, as we would now say, the inertio-gravitational field - should not be described by a variable speed of light as he had attempted in 1912, but by the so-called metric tensor field. The metric tensor is a mathematical object of 16 components, 10 of which independent, that characterizes the geometry of space and time. In this way, gravity is no longer a force in space and time, but part of the fabric of space and time itself: gravity is part of the inertio-gravitational field. Einstein had turned to Grossmann for help with the difficult and unfamiliar mathematics needed to formulate a theory along these lines. [...] Einstein did not give up the Einstein-Grossmann theory once he had established that it could not fully explain the Mercury anomaly. He continued to work on the theory and never even mentioned the disappointing result of his work with Besso in print. So Einstein did not do what the influential philosopher Sir Karl Popper claimed all good scientists do: once they have found an empirical refutation of their theory, they abandon that theory and go back to the drawing board. [...] On November 4, 1915, he presented a paper to the Berlin Academy officially retracting the Einstein-Grossmann equations and replacing them with new ones. On November 11, a short addendum to this paper followed, once again changing his field equations. A week later, on November 18, Einstein presented the paper containing his celebrated explanation of the perihelion motion of Mercury on the basis of this new theory. Another week later he changed the field equations once more. These are the equations still used today. This last change did not affect the result for the perihelion of Mercury. Besso is not acknowledged in Einstein's paper on the perihelion problem. Apparently, Besso's help with this technical problem had not been as valuable to Einstein as his role as sounding board that had earned Besso the famous acknowledgment in the special relativity paper of 1905. Still, an acknowledgment would have been appropriate. After all, what Einstein had done that week in November, was simply to redo the calculation he had done with Besso in June 1913, using his new field equations instead of the Einstein-Grossmann equations. It is not hard to imagine Einstein's excitement when he inserted the numbers for Mercury into the new expression he found and the result was 43", in excellent agreement with observation."

Pentcho Valev

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Pentcho Valev

Re: The Empirical Models of Theoretical Physics

June 14 2017, 1:04 PM 

If the model is empirical, not deductive, or if the validity of arguments in the deductive model is broken, we have ideology, not science - there is nothing preventing the biased modeler from "deriving" his pet conclusions.

This means that Einstein made physics ideological already in 1905, despite the fact that special relativity was deductive. It all started with the false constancy of the speed of light. Einstein plagiarized ("borrowed") it from the Lorentz equations, called it "postulate", and finally derived, for the gullible world, the Lorentz equations from the "postulate" (reverse engineering):

Albert Einstein: "...I introduced the principle of the constancy of the velocity of light, which I borrowed from H. A. Lorentz's theory of the stationary luminiferous ether..."

John Stachel explains that the constancy of the speed of light seemed nonsense to Einstein but he introduced it nevertheless:

John Stachel: "But this seems to be nonsense. How can it happen that the speed of light relative to an observer cannot be increased or decreased if that observer moves towards or away from a light beam? Einstein states that he wrestled with this problem over a lengthy period of time, to the point of despair."

Indeed, the idea that the speed of light is independent of the speed of the observer is nonsense. Consider the following setup:

A light source emits a series of pulses equally distanced from one another. A stationary observer (receiver) measures the frequency:

[linked image]

The observer starts moving with constant speed towards the light source and measures the frequency again:

[linked image]

Premise 1 (Doppler effect; experimentally confirmed): The moving observer measures the frequency to be higher.

Premise 2 (obviously true): The formula

(measured frequency) = (speed of the pulses relative to the observer)/(distance between the pulses)

is correct.

Conclusion: The speed of the pulses relative to the moving observer is higher than relative to the stationary observer. In other words, the speed of light varies with the speed of the observer, in violation of Einstein's relativity.

The introduction of the false postulate was Einstein's original sin. The malignancy was there but it was sterile - all VALIDLY deducible consequences of the false postulate were obviously absurd and repugnant. This is still not ideology - the conclusions of the theory are unfavorable for the author and he cannot change them because the requirement for VALIDITY of the arguments prevents him from doing so.

However Einstein's second sin - a fraudulent and INVALID deduction - produced a miraculous result that was irresistibly attractive. In 1905 Einstein derived, from his two postulates, the conclusion "the clock moved from A to B lags behind the other which has remained at B":

Albert Einstein, On the Electrodynamics of Moving Bodies, 1905: "From this there ensues the following peculiar consequence. If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which has remained at B by tv^2/2c^2 (up to magnitudes of fourth and higher order), t being the time occupied in the journey from A to B."

The conclusion

"The clock moved from A to B lags behind the other which has remained at B"

does not follow from Einstein's 1905 postulates - the argument is INVALID. The following two conclusions, in contrast, VALIDLY follow from the postulates:

Conclusion 1: The clock moved from A to B lags behind the other which has remained at B, as judged from the stationary system.

Conclusion 2: The clock which has remained at B lags behind the clock moved from A to B, as judged from the moving system.

Conclusions 1 and 2 (symmetrical time dilation) in their combination give no prediction for the readings of the two clocks as they meet at B - in this sense the false postulate is sterile. In contrast, the INVALIDLY deduced conclusion (asymmetrical time dilation) provides a straightforward prediction - the moving clock is slow, the stationary one is FAST. The famous "travel into the future" is a direct implication - the slowness of the moving clock means that its (moving) owner can remain virtually unchanged while sixty million years are passing for the stationary system:

Thibault Damour: "The paradigm of the special relativistic upheaval of the usual concept of time is the twin paradox. Let us emphasize that this striking example of time dilation proves that time travel (towards the future) is possible. As a gedanken experiment (if we neglect practicalities such as the technology needed for reaching velocities comparable to the velocity of light, the cost of the fuel and the capacity of the traveller to sustain high accelerations), it shows that a sentient being can jump, "within a minute" (of his experienced time) arbitrarily far in the future, say sixty million years ahead, and see, and be part of, what (will) happen then on Earth. This is a clear way of realizing that the future "already exists" (as we can experience it "in a minute")."

The year 1905 can be regarded as the year of the death of physics. Science died and idiotic ideology was born.

Peter Woit: "I think the worst thing that has happened to theoretical physics over the past 25 years is this descent into ideology, something that has accelerated with the multiverse mania of the last 10-15 years."

Correct, except for the number 25 - it should be replaced by 112:

"This paper investigates an alternative possibility: that the critics were right and that the success of Einstein's theory in overcoming them was due to its strengths as an ideology rather than as a science. The clock paradox illustrates how relativity theory does indeed contain inconsistencies that make it scientifically problematic. These same inconsistencies, however, make the theory ideologically powerful. [...] The gatekeepers of professional physics in the universities and research institutes are disinclined to support or employ anyone who raises problems over the elementary inconsistencies of relativity. A winnowing out process has made it very difficult for critics of Einstein to achieve or maintain professional status. Relativists are then able to use the argument of authority to discredit these critics. Were relativists to admit that Einstein may have made a series of elementary logical errors, they would be faced with the embarrassing question of why this had not been noticed earlier. Under these circumstances the marginalisation of antirelativists, unjustified on scientific grounds, is eminently justifiable on grounds of realpolitik. Supporters of relativity theory have protected both the theory and their own reputations by shutting their opponents out of professional discourse. [...] The triumph of relativity theory represents the triumph of ideology not only in the profession of physics bur also in the philosophy of science." Peter Hayes, The Ideology of Relativity: The Case of the Clock Paradox http://www.informaworld.com/smpp/content~content=a909857880

Pentcho Valev

Pentcho Valev

Re: The Empirical Models of Theoretical Physics

June 15 2017, 7:03 AM 

Einstein's general relativity is an empirical concoction - a malleable combination of ad hoc equations and fudge factors allowing Einsteinians to predict anything they want. This means that general relativity has no postulates:

What are the postulates of General Relativity? Alexander Poltorak, Adjunct Professor of Physics at the CCNY: "In 2005 I started writing a paper, "The Four Cornerstones of General Relativity on which it doesn't Rest." Unfortunately, I never had a chance to finish it. The idea behind that unfinished article was this: there are four principles that are often described as "postulates" of General Relativity:

1. Principle of general relativity

2. Principle of general covariance

3. Equivalence principle

4. Mach principle

The truth is, however, that General Relativity is not really based on any of these "postulates" although, without a doubt, they played important heuristic roles in the development of the theory." [end of quotation]

Sometimes Einsteinians call Einstein's 1915 final ad hoc equations "postulates" (we all live in Einstein's schizophrenic world, don't we):

"Postulates of General Relativity
Postulate 1: A spacetime (M^4, g) is a Riemannian 4-manifold M^4 with a Lorentzian metric g.
Postulate 2: A test mass beginning at rest moves along a timelike geodesic. (Geodesic equation) ...
Postulate 3: Einstein equation is satisfied. (Einstein equation) ..." [end of quotation]

For a deductive theory, demonstrating an absurdity implies that a postulate is false - the theory can be falsified in this way. For a non-deductive model (empirical concoction), demonstrating an absurdity has no consequences because there are no postulates. The demonstrated absurdity remains a small local nuisance, apparently unrelated to other parts of the model, and can be either ignored by the modelers or neutralized by introducing some additional fudge factor.

So in Einstein's general relativity we find the absurdity ("idiocy" is more precise) that the speed of light DECREASES as the light falls towards the source of gravity - in the gravitational field of the Earth the acceleration of falling photons is NEGATIVE, -2g. This is not deduced from postulates of course - the absurdity is a fudge factor Einstein and his mathematical friends had to introduce to make the gravitational redshift and gravitational time dilation compatible:

Albert Einstein: "Second, this consequence shows that the law of the constancy of the speed of light no longer holds, according to the general theory of relativity, in spaces that have gravitational fields. As a simple geometric consideration shows, the curvature of light rays occurs only in spaces where the speed of light is spatially variable."

"The change in speed of light with change in height is dc/dh=g/c."

"Contrary to intuition, the speed of light (properly defined) decreases as the black hole is approached."

"Einstein wrote this paper in 1911 in German. [...] ...you will find in section 3 of that paper Einstein's derivation of the variable speed of light in a gravitational potential, eqn (3). The result is: c'=c0(1+φ/c^2) where φ is the gravitational potential relative to the point where the speed of light c0 is measured. Simply put: Light appears to travel slower in stronger gravitational fields (near bigger mass). [...] You can find a more sophisticated derivation later by Einstein (1955) from the full theory of general relativity in the weak field approximation. [...] Namely the 1955 approximation shows a variation in km/sec twice as much as first predicted in 1911."

"Specifically, Einstein wrote in 1911 that the speed of light at a place with the gravitational potential φ would be c(1+φ/c^2), where c is the nominal speed of light in the absence of gravity. In geometrical units we define c=1, so Einstein's 1911 formula can be written simply as c'=1+φ. However, this formula for the speed of light (not to mention this whole approach to gravity) turned out to be incorrect, as Einstein realized during the years leading up to 1915 and the completion of the general theory. [...] ...we have c_r =1+2φ, which corresponds to Einstein's 1911 equation, except that we have a factor of 2 instead of 1 on the potential term."

Pentcho Valev

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