THE PROTECTIVE BELT OF SPECIAL RELATIVITY

[Pentcho Valev]

http://books.google.com/books?id=JokgnS1JtmMC
"Relativity and Its Roots" By Banesh Hoffmann, p.92: "There are various remarks to be made about this second principle. For instance, if it is so obvious, how could it turn out to be part of a revolution - especially when the first principle is also a natural one? Moreover, if light consists of particles, as Einstein had suggested in his paper submitted just thirteen weeks before this one, the second principle seems absurd: A stone thrown from a speeding train can do far more damage than one thrown from a train at rest; the speed of the particle is not independent of the motion of the object emitting it. And if we take light to consist of particles and assume that these particles obey Newton's laws, they will conform to Newtonian relativity and thus automatically account for the null result of the Michelson-Morley experiment without recourse to contracting lengths, local time, or Lorentz transformations. Yet, as we have seen, Einstein resisted the temptation to account for the null result in terms of particles of light and simple, familiar Newtonian ideas, and introduced as his second postulate something that was more or less obvious when thought of in terms of waves in an ether. If it was so obvious, though, why did he need to state it as a principle? Because, having taken from the idea of light waves in the ether the one aspect that he needed, he declared early in his paper, to quote his own words, that "the introduction of a 'luminiferous ether' will prove to be superfluous."

This is a remarkable text written by one of the most famous Einsteinians. It turns out that, "without recourse to contracting lengths, local time, or Lorentz transformations", only Newton's emission theory of light with its tenet that the speed of light does depend on the speed of the emitter can explain the null result of the Michelson-Morley experiment. That is, in 1887 the experiment unequivocally confirms the variable speed of light predicted by the emission theory but then "contracting lengths, local time, or Lorentz transformations" are introduced ad hoc and the experiment becomes compatible with the constant (independent of the speed of the emitter) speed of light predicted by the ether theory and adopted in special relativity.

How then can "contracting lengths, local time, or Lorentz transformations" be characterized? Imre Lakatos calls such ad hoc hypotheses "protective belt":

http://bertie.ccsu.edu/naturesci/PhilSci/Lakatos.html
"Lakatos distinguished between two parts of a scientific theory: its "hard core" which contains its basic assumptions (or axioms, when set out formally and explicitly), and its "protective belt", a surrounding defensive set of "ad hoc" (produced for the occasion) hypotheses. (...) In Lakatos' model, we have to explicitly take into account the "ad hoc hypotheses" which serve as the protective belt. The protective belt serves to deflect "refuting" propositions from the core assumptions..."

That is, one very much wants the speed of light to be constant (independent of the speed of the emitter), assumes so and introduces an efficient protective belt ("contracting lengths, local time, or Lorentz transformations") able to deflect refuting propositions such as the null result of the Michelson-Morley experiment from the cherished assumption.

Yet, if protective belts are a legitimate tool in theorizing, how can one claim that the experiment is the ultimate judge of the theory? Any core assumption, if false, can be equipped with a suitable protective belt deflecting experimental challenges...

Pentcho Valev

[Pentcho Valev]

Is there a protective belt in general relativity? Yes, a very subtle one - it is called "gravitational time dilation". Consider light falling (or climbing up) in a gravitational field:

http://sethi.lamar.edu/bahrim-cristian/Courses/PHYS4480/4480-PROBLEMS/optics-gravit-lens_PPT.pdf
Dr. Cristian Bahrim: "If we accept the principle of equivalence, we must also accept that light falls in a gravitational field with the same acceleration as material bodies."

http://www.wfu.edu/~brehme/space.htm
Robert W. Brehme: "Light falls in a gravitational field just as do material objects."

http://courses.physics.illinois.edu/phys419/lectures/l13.pdf
University of Illinois at Urbana-Champaign: "Consider a falling object. ITS SPEED INCREASES AS IT IS FALLING. Hence, if we were to associate a frequency with that object the frequency should increase accordingly as it falls to earth. Because of the equivalence between gravitational and inertial mass, WE SHOULD OBSERVE THE SAME EFFECT FOR LIGHT. So lets shine a light beam from the top of a very tall building. If we can measure the frequency shift as the light beam descends the building, we should be able to discern how gravity affects a falling light beam. This was done by Pound and Rebka in 1960. They shone a light from the top of the Jefferson tower at Harvard and measured the frequency shift. The frequency shift was tiny but in agreement with the theoretical prediction. Consider a light beam that is travelling away from a gravitational field. Its frequency should shift to lower values. This is known as the gravitational red shift of light."

http://www.youtube.com/watch?v=FJ2SVPahBzg
"The light is perceived to be falling in a gravitational field just like a mechanical object would. (...) The change in speed of light with change in height is dc/dh=g/c."

http://www.einstein-online.info/spotlights/redshift_white_dwarfs
Albert Einstein Institute: "One of the three classical tests for general relativity is the gravitational redshift of light or other forms of electromagnetic radiation. However, in contrast to the other two tests - the gravitational deflection of light and the relativistic perihelion shift -, you do not need general relativity to derive the correct prediction for the gravitational redshift. A combination of Newtonian gravity, a particle theory of light, and the weak equivalence principle (gravitating mass equals inertial mass) suffices. (...) The gravitational redshift was first measured on earth in 1960-65 by Pound, Rebka, and Snider at Harvard University..."

The picture is more than clear - in a gravitational field, the speed of light varies like the speed of any material body, just as predicted by Newton's emission theory of light, and this variation has been confirmed by the Pound-Rebka experiment. Yet some Einsteinians find it safe to ignore all this and teach the blatant lie that the speed of light remains constant in a gravitational field:

http://www.amazon.com/Why-Does-mc2-Should-Care/dp/0306817586
Brian Cox, Jeff Forshaw, p. 236: "If the light falls in strict accord with the principle of equivalence, then, as it falls, its energy should increase by exactly the same fraction that it increases for any other thing we could imagine dropping. We need to know what happens to the light as it gains energy. In other words, what can Pound and Rebka expect to see at the bottom of their laboratory when the dropped light arrives? There is only one way for the light to increase its energy. We know that it cannot speed up, because it is already traveling at the universal speed limit, but it can increase its frequency."

http://www.oapt.ca/newsletter/2004-02%20Newsletter%20Searchable.pdf
Richard Epp: "One may imagine the photon losing energy as it climbs against the Earth's gravitational field much like a rock thrown upward loses kinetic energy as it slows down, the main difference being that the photon does not slow down; it always moves at the speed of light."

http://www.amazon.com/Brief-History-Time-Stephen-Hawking/dp/0553380168
Stephen Hawking, A Brief History of Time, Chapter 6: "A cannonball fired upward from the earth will be slowed down by gravity and will eventually stop and fall back; a photon, however, must continue upward at a constant speed..."

Where does the courage of Brian Cox, Jeff Forshaw, Richard Epp and Stephen Hawking come from? The blatant lie (the speed of light is constant in a gravitational field) can be taught relatively safely if the teacher has assumed that a clock on the ground runs slower than a clock at the top of a tower ("gravitational time dilation"). With this assumption, light emitted by the top will be measured to have a higher frequency on the ground not because its speed has increased, as predicted by the emission theory, but because the unit of time on the ground is dilated and encompasses more wavecrests.

Pentcho Valev

[Pentcho Valev]

Einstein introduced the gravitational time dilation in 1911, in an attempt to explain the fact that the frequency as measured at different gravitational potentials is different when identical clocks are used:

http://www.relativitybook.com/resources/Einstein_gravity.html
Einstein 1911: "Let the two material systems S1 and S2, provided with instruments of measurement, be situated on the z-axis of K at the distance h from each other, so that the gravitation potential in S2 is greater than that in S1... (...) It follows, then, that a ray of light emitted in S2 with a definite gravitational potential, and possessing at its emission the frequency v2 – compared with a clock in S2 – will, at its arrival in S1, possess a different frequency v1 – measured by an identical clock in S1. (...) v1=v2(1+phi/c^2) (...) If there is constant transmission of light from S2 to S1, how can any other number of periods per second arrive in S1 than is emitted in S2 ? But the answer is simple. We cannot regard v2 or respectively v1 simply as frequencies (as the number of periods per second) since we have not yet determined the time in system K. What v2 denotes is the number of periods with reference to the time-unit of the clock U in S2, while v1 denotes the number of periods per second with reference to the identical clock in S1. Nothing compels us to assume that the clocks U in different gravitation potentials must be regarded as going at the same rate."

On close inspection it becomes clear that this protective belt (gravitational time dilation) is quite inefficient. In the absence of additional ad hoc hypotheses, the interpretation based on gravitational time dilation implies shifts in both the MEASURED frequency and the MEASURED speed of light in S1. That is, v1=v2(1+phi/c^2) implies c1=c2(1+phi/c^2). Clever Einsteinians know that and sometimes ignore, even dismiss, gravitational time dilation when discussing the gravitational redshift:

http://www.amazon.com/Relativity-Its-Roots-Banesh-Hoffmann/dp/0486406768
Banesh Hoffmann: "In an accelerated sky laboratory, and therefore also in the corresponding earth laboratory, the frequence of arrival of light pulses is lower than the ticking rate of the upper clocks even though all the clocks go at the same rate. (...) As a result the experimenter at the ceiling of the sky laboratory will see with his own eyes that the floor clock is going at a slower rate than the ceiling clock - even though, as I have stressed, both are going at the same rate. (...) The gravitational red shift does not arise from changes in the intrinsic rates of clocks. It arises from what befalls light signals as they traverse space and time in the presence of gravitation."

There is an alternative to the protective belt based on gravitational time dilation which is sillier but more efficient: The speed of light is constant, Divine Einstein, yes we all believe in relativity, relativity, relativity, so if the frequency changes, the wavelength MUST change accordingly:

http://www.astronomynotes.com/relativity/s4.htm
"Prediction: light escaping from a large mass should lose energy - THE WAVELENGTH MUST INCREASE SINCE THE SPEED OF LIGHT IS CONSTANT."

This protective belt (the wavelength always changes so that the speed of light can remain constant, Divine Einstein, yes we all believe in relativity, relativity, relativity) is quite universal in Divine Albert's world:

http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/big_bang_observed/index.html
John Norton: "Here's a light wave and an observer. If the observer were to hurry towards the source of the light, the observer would now pass wavecrests more frequently than the resting observer. That would mean that moving observer would find the frequency of the light to have increased (AND CORRESPONDINGLY FOR THE WAVELENGTH - THE DISTANCE BETWEEN CRESTS - TO HAVE DECREASED)."

http://www.lp2i-poitiers.fr/doc/aps/albatros/uk/pages/doppleffet.html
"The observer moves closer to the source. The wave received has a shorter wavelength (higher frequency) than that emitted by the source. The observer moves away from the source. The wave received has a longer wavelength (lower frequency) than that emitted by the source."

http://highered.mcgraw-hill.com/olcweb/cgi/pluginpop.cgi?it=swf::800::600::/sites/dl/free/0072482621/78778/Doppler_Nav.swf
"EXERCISES: 2. Now click on the "Observer Approaches" button. The ship will start flying towards the source. What is the wavelength of the waves now, as the ship approaches the source? Does the frequency increase or decrease? SOLUTIONS: 2. The wavelength shrinks so that about three waves now fit within the graph. (...) The frequency increases."

Pentcho Valev

[Pentcho Valev]

The original miracle that converted Albert the Plagiarist into Divine Albert:

http://www.fourmilab.ch/etexts/einstein/specrel/www/
ON THE ELECTRODYNAMICS OF MOVING BODIES, by A. Einstein, June 30, 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. It is at once apparent that this result still holds good if the clock moves from A to B in any polygonal line, and also when the points A and B coincide. If we assume that the result proved for a polygonal line is also valid for a continuously curved line, we arrive at this result: If one of two synchronous clocks at A is moved in a closed curve with constant velocity until it returns to A, the journey lasting t seconds, then by the clock which has remained at rest the travelled clock on its arrival at A will be tv^2/2c^2 second slow."

The above conclusion obviously transcends special relativity - what the theory predicts for uniform movement in a straight line is extended to polygonal and even circular movements involving acceleration. So in the years after 1905 Einstein's concern was to minimise the impact of acceleration. In 1911 he successfully explained away sudden changes of direction:

http://www.informaworld.com/smpp/content~content=a909857880
Peter Hayes quotes Einstein writing in 1911: "The [travelling] clock runs slower if it is in uniform motion, but if it undergoes a change of direction as a result of a jolt, then the theory of relativity does not tell us what happens. The sudden change of direction might produce a sudden change in the position of the hands of the clock. However, the longer the clock is moving rectilinearly and uniformly with a given speed in a forward motion, i.e., the larger the dimensions of the polygon, the smaller must be the effect of such a hypothetical sudden change."

If time dilation as predicted by special relativity is a real effect (it isn't of course), Einstein's 1911 minimisation of the impact of sudden changes is obviously correct - the argument is used even today:

http://www.damtp.cam.ac.uk/research/gr/members/gibbons/gwgPartI_SpecialRelativity2010.pdf
Gary W. Gibbons FRS: "In other words, by simply staying at home Jack has aged relative to Jill. There is no paradox because the lives of the twins are not strictly symmetrical. This might lead one to suspect that the accelerations suffered by Jill might be responsible for the effect. However this is simply not plausible because using identical accelerating phases of her trip, she could have travelled twice as far. This would give twice the amount of time gained."

Yet mounting criticism forced Einstein to devise, in 1918, a dishonest protective belt going against the 1911 explanation: The acceleration involved in sudden changes of direction was not insignificant any more; rather, Einstein declared it crucially responsible for the asymmetrical ageing of the twins:

http://en.wikisource.org/wiki/Dialog_about_objections_against_the_theory_of_relativity
Dialog about Objections against the Theory of Relativity (1918), by Albert Einstein: "However, this is more than compensated by a faster pace of U1 during partial process 3. According to the general theory of relativity, a clock will go faster the higher the gravitational potential of the location where it is located, and during partial process 3 U2 happens to be located at a higher gravitational potential than U1. The calculation shows that this speeding ahead constitutes exactly twice as much as the lagging behind during the partial processes 2 and 4. This consideration completely clears up the paradox that you brought up."

http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/spacetime_tachyon/index.html
John Norton: "Then, at the end of the outward leg, the traveler abruptly changes motion, accelerating sharply to adopt a new inertial motion directed back to earth. What comes now is the key part of the analysis. The effect of the change of motion is to alter completely the traveler's judgment of simultaneity. The traveler's hypersurfaces of simultaneity now flip up dramatically. Moments after the turn-around, when the travelers clock reads just after 2 days, the traveler will judge the stay-at-home twin's clock to read just after 7 days. That is, the traveler will judge the stay-at-home twin's clock to have jumped suddenly from reading 1 day to reading 7 days. This huge jump puts the stay-at-home twin's clock so far ahead of the traveler's that it is now possible for the stay-at-home twin's clock to be ahead of the travelers when they reunite."

So today's Einsteinians believe that the acceleration suffered by the travelling twin is both insignificant and crucially responsible for the asymmetrical ageing of the twins. Apart from Divine Albert's world, such beliefs exist in Big Brother's world:

http://ebooks.adelaide.edu.au/o/orwell/george/o79n/chapter2.9.html
"Doublethink means the power of holding two contradictory beliefs in one's mind simultaneously, and accepting both of them."

http://farm5.staticflickr.com/4010/4611948391_4122552b04_z.jpg

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