Ripping Apart Einstein

Florin,

The problem is that you, like the vast majority of people, have confused "group velocity" for "phase velocity". Einstein simply DEFINED the phase velocity of light, in a vacuum, to be a constant. He said nothing about group velocity being constant.

Group velocity is the velocity at which the envelope of a signal propagates, such as might be measured by timing the arrival of a leading edge of a pulse.

Phase velocity, on the other hand, is the velocity of a signal with a constant envelop - in other words, an infinitely long signal that has no leading or trailing edge. Since the envelop is constant, no measurement of it will provide any indication of a non-zero velocity, whatsoever.

So how do you then DIRECTLY measure the velocity of an infinitely long, ideal sinusoid, that never interacts with anything, (because it is in a vacuum)? The answer is that you can't. You can only measure a changing phase. But that could be caused by EITHER a non-zero velocity, or a change in its frequency, or any combination of the two. So which is it? There is no way to tell. Not even in principle. So just pick one or the other as being CONSTANT, and attribute the phase shift has being entirely caused by the other.

Einstein simply observed that the math transformation would be simpler, if you picked the velocity to be constant, rather than the frequency. Hence, we have Doppler frequency shifts and constant phase velocity, rather than constant frequency and Doppler velocity shifts.

Rob McEachern

Variable Speed of Light Topples Einstein

You walk along the fence. Relative to you, the posts have speed c (not the speed of light of course) and the frequency you measure is f=c/d, where d is the distance between the posts.

Now you start running along the fence and your speed increases by v. Relative to you, the speed of the posts shifts from c to c'=c+v. This shift in the speed of the posts relative to you causes the frequency you measure to shift from f=c/d to f'=c'/d=(c+v)/d.

A light source emits a series of pulses the distance between which is d (e.g. d=300000km) towards you (the observer/receiver). Relative to you, the pulses have speed c and the frequency you measure is f=c/d, where d is the distance between the pulses.

Now you start running towards the light source and your speed increases by v (v is small so that the relativistic corrections can be ignored). Relative to you, the speed of the pulses shifts from c to c'=c+v. This shift in the speed causes the frequency you measure to shift from f=c/d to f'=c'/d=(c+v)/d:

"Doppler effect - when an observer moves towards a stationary source. ...the velocity of the wave relative to the observer is faster than that when it is still."

If you had started running away from the light source, then, relative to you, the speed of the pulses would have shifted from c to c'=c-v and the frequency you measured from f=c/d to f'=c'/d=(c-v)/d:

"Doppler effect - when an observer moves away from a stationary source. ...the velocity of the wave relative to the observer is slower than that when it is still."

Clearly one can only explain the shift from f=c/d to f'=(c±v)/d in terms of the shift from c to c'=c±v. However the equation c'=c±v is fatal for special relativity so Einsteinians usually avoid the topic:

"Crimestop means the faculty of stopping short, as though by instinct, at the threshold of any dangerous thought. It includes the power of not grasping analogies, of failing to perceive logical errors, of misunderstanding the simplest arguments if they are inimical to Ingsoc, and of being bored or repelled by any train of thought which is capable of leading in a heretical direction. Crimestop, in short, means protective stupidity."

Pentcho Valev

Tom, I was not kidding, I do consider the argument brilliant, and I think it deserves a clear counter-argument. Also I did scratched my head to find it. Here it is:

Consider this:

"An observer/receiver moving with speed v (let v be small so that the relativistic corrections can be ignored) towards the light source measures the frequency of the light pulses to be f'=(c+v)/d"

It states: "let v be small so that the relativistic corrections can be ignored". The Lorenz factor gamma = 1/sqrt(1 - v*v/c*c) so 1/gamma = sqrt(1-v*v/c*c) = sqrt((1-v/c)(1+v/c)). In the quoted argument, the factor 1/gamma due to time dilation is ignored probably as being consider second order in v/c. However, even in relativity there is a Doppler shift of the order of v/c so this is not enough to distinguish between Lorentz and Galilean transformations, and one needs to go to second order v/c terms. In Galilean transformations there are none, but not in relativity.

Bottom line, when v 0 is the same as c/v->infinity or c->infinity and "infinity + v = infinity". The point here is that we are not talking about adding small velocities v1+v2, but talking about adding a small velocity with an "infinite" velocity.

Long story short: for small v, the relativistic effects are second order in v/c, and c->infinity. Therefore the c+v=c because c = infinity. Also I did like the argument against special relativity: it is clear, concise, and it deserves a to the point refutation without appealing to higher authority, experiments, or geometric arguments.

" ... it deserves a to the point refutation without appealing to higher authority, experiments, or geometric arguments."

Does it deserve to be subjected to division by zero?

One more thing:

I think the confusion stems from demanding uniform convergence when only point-convergence exists. The limit from Lorenz to Galileo has one kind of convergence when ALL velocities are small (second order in v/c) and another kind of convergence when combining small with large velocities (first order in v/c). Functional analysis has tons of examples when uniform convergence is not true, but the weaker form of convergence holds.

Correction:

a paragraph was completely messed up during upload:

"Bottom line, when v 0 is the same as c/v->infinity or c->infinity and "infinity + v = infinity". The point here is that we are not talking about adding small velocities v1+v2, but talking about adding a small velocity with an "infinite" velocity."

a large section is missing in between: "Bottom line, when" and "0 is the same as..."

I did not save the original text, but hopefully my explanation remained clear. Special relativity refutation is based on assuming uniform convergence of the limit from Lorenz to Galilean transformations.

"I think the confusion stems from demanding uniform convergence when only point-convergence exists."

What confusion? Infinities sum linearly -- that's where you are confused -- however, a point at infinity lives only on a compact manifold.

A simple arithmetic theorem informs us that any point can simultaneously approach any set of points provided that it is far enough away. That's point convergence, finite for any point, to the limit of infinity. And that's what makes the "brilliant argument" nothing more than a steaming pile -- the limit of the speed of light is finite because physically real measurements are only between mass points, not spacetime points.

Albert Einstein Institute: "The frequency of a wave-like signal - such as sound or light - depends on the movement of the sender and of the receiver. This is known as the Doppler effect. (...) Here is an animation of the receiver moving towards the source: (...) By observing the two indicator lights, you can see for yourself that, once more, there is a blue-shift - the pulse frequency measured at the receiver is somewhat higher than the frequency with which the pulses are sent out. This time, the distances between subsequent pulses are not affected, but still there is a frequency shift: As the receiver moves towards each pulse, the time until pulse and receiver meet up is shortened. In this particular animation, which has the receiver moving towards the source at one third the speed of the pulses themselves, four pulses are received in the time it takes the source to emit three pulses."

Let "the distance between subsequent pulses" be 300000 km. Then the frequency measured by the stationary receiver is f = 1 s^(-1) and that measured by the moving receiver is f' = 4/3 s^(-1). Accordingly, the speed of the pulses relative to the moving receiver is:

c' = (4/3)c = 400000 km/s

in violation of special relativity.

The relativistic corrections change essentially nothing. The speed of the receiver is (1/3)c so gamma is 1.05. Accordingly, the corrected f' is (1.05)*(4/3) s^(-1) and the corrected c' is (1.05)*(400000) km/s. Special relativity remains violated.

Pentcho Valev

Poor Einstein, you are not a saint but why do they keep telling lies against you? Some say they love you but refuse to heed your statements. Others hate you and refuse to listen to any of your defense. Did you not say this -

"... according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity and to which we have already frequently referred, CANNOT claim any unlimited validity... ONLY SO LONG as we are able to disregard the influences of gravitational fields (OF THE EARTH) on the phenomena {e.g. of light}", p.89. Yet they lie you said constancy of light velocity MUST have unlimited validity!

And this

"Furthermore, we can regard an atom (e.g. Caesium 133) which is emitting spectral lines as a clock, so that the following statement will hold: An atom absorbs or emits light of a frequency which is dependent on the potential of the gravitational field in which it is situated. The frequency of an atom situated on the surface of a heavenly body (e.g. EARTH) will be somewhat less than the frequency of an atom of the same, element which is situated in free space (or on the surface of a smaller celestial body)",p.157. Yet BIPM insist on using Caesium 133 frequency on earth to determine 'the second' and force light velocity to be constant at EXACTLY 299792458m/s universally, when in free space it will be 2999792458.2087m/s.

And this

"The principle of the constancy of the velocity of light holds good according to this theory in a different form from that which usually underlies the ordinary theory of relativity...the velocity of light in the gravitational field is a function of the location...", p.903. Still they would not listen. What else can you do?

Please don't turn in your grave. I beg you to forgive Pentcho, Tom, Florin and Robert. May your precious soul continue to rest in peace. Amen!

Akinbo

Akinbo,

Consider Rob's point very carefully, you should find it correct. Certainly I agree most are highly culpable and asymmetrically cherry pick Einstein's views to maintain their rigid beliefs.

Rob,

I do like that way of describing it, but some time ago I found a 'limitation' to the domain of a (simplest) model of the phase/group approach, which I recall related to observer frame dependence. It didn't then provide the complete 'solution set' alone. I believe it can be overcome by taking the LOCAL background view, but that then itself needed to be demonstrated anyway. Can your incisively logical mind find a better way?

Happy new year.

Peter

Akino:

You stated that "the velocity of light in the gravitational field is a function of the location". But if there is a gravitational field, then there is no inertial (un-accelerating) frame. Consequently, Special Relativity does not apply, General Relativity is required.

Peter,

Recall that Einstein POSTULATED the speed of light to be constant. He did not OBSERVE it to be constant. He did not PREDICT it to be constant. While there a variety of definitions for POSTUlATE, the basic idea is to take something as an unquestioned given, and then use it as a starting point, for deducing some interesting conclusion.

What was the conclusion that he was aiming at? A simple conversion system.

Special Relativity is nothing more than a "Currency Exchange"; I say this can of soup costs 1.23 dollars and you say it costs 0.68 pounds. So which is it, 1.23 or 0.68? The answer is both. You just need to convert numbers in one measurement system to numbers in different systems.

Special Relativity is nothing more than the "Measurement Exchange" system used to convert measurements in one inertial system into measurements in another.

Maxwell observed that certain constants in his equations for Electrodynamics can be combined to yield the "speed of light". Maxwell's equation are formulated in the rest frame of the observer. Wouldn't it be nice if observers in relative motion could ALL use Maxwell's equations in there own personal rest frame, in which his equations yield a constant speed of light? So, given the ambiguity in phase, noted in my previous post, why not just go ahead and POSTULATE that the speed is constant and the same for everyone, and see if that leads to an interesting conclusion, a simple "Measurement Exchange" system? It did. End of story.

But not quite. Even in real currency exchange systems, there can be subtle but significant effects. The whole field of arbitrage is based upon exploiting such effects.

Rob McEachern

The only reasonable way to derive the Doppler frequency shift (moving observer) is by assuming, explicitly or implicitly, that the speed of light (relative to the observer) varies with the speed of the observer, in violation of special relativity:

Tony Harker, University College London: "The Doppler Effect: Moving sources and receivers. The phenomena which occur when a source of sound is in motion are well known. The example which is usually cited is the change in pitch of the engine of a moving vehicle as it approaches. In our treatment we shall not specify the type of wave motion involved, and our results will be applicable to sound or to light. (...) Now suppose that the observer is moving with a velocity Vo away from the source. (....) If the observer moves with a speed Vo away from the source (...), then in a time t the number of waves which reach the observer are those in a distance (c-Vo)t, so the number of waves observed is (c-Vo)t/lambda, giving an observed frequency f'=f(1-Vo/c) when the observer is moving away from the source at a speed Vo."

Tony Harker: "In a time t the number of waves which reach the observer are those in a distance (c-Vo)t."

Consequence: The speed of the light waves relative to the moving observer is:

c' = distance/time = (c - Vo)t/t = c - Vo,

in violation of special relativity.

It takes constant and painful exercise in crimestop, singing hymns, going into convulsions etc to convince oneself that:

c' = c - Vo = c,

as required by special relativity. This picture is extremely inspirational.

"He set to work to exercise himself in crimestop. He presented himself with propositions - "the Party says the earth is flat", "the party says that ice is heavier than water" - and trained himself in not seeing or not understanding the arguments that contradicted them. It was not easy. It needed great powers of reasoning and improvisation. The arithmetical problems raised, for instance, by such a statement as "two and two make five" were beyond his intellectual grasp. It needed also a sort of athleticism of mind, an ability at one moment to make the most delicate use of logic and at the next to be unconscious of the crudest logical errors. Stupidity was as necessary as intelligence, and as difficult to attain."

Pentcho Valev

No, no, no Rob, while I am ready to consider your thoughts carefully as Peter J says I should, you need to check out those quotes carefully because I provided links to them to show they are not fabricated. So when you make a statement like, "But if there is a gravitational field, then there is no inertial (un-accelerating) frame. Consequently, Special Relativity does not apply, General Relativity is required", I don't understand. Firstly, where then does Special relativity apply? Not on Earth? Was it not Earth-based experiments that gave birth to it? Does the Earth not have a gravitational field? Can the Earth not be regarded as an inertial frame, despite having a gravitational field? We have to be careful in some of our statements so Einstein will not wake up one day to torment the living.

Akinbo

*Peter J, I will study more on this group vs. phase velocity thing. I hope it is not another mathematical magic.

Yes, yes, yes Okinbo.

I do not dispute your quotes. As you correctly observed, it is your misunderstanding of those quotes that is at issue. For Einstein, in Special Relativity, a "vacuum" has no gravitational field. Recall that Einstein was the person that first predicted that light would interact with a gravitational field; he famously predicted that during a total eclipse of the sun, light would be deflected as a result of this interaction. In Special Relativity, "Vacuum" means "nothing for light to interact with". Consequently, it means no Gravitational field.

You asked "Was it not Earth-based experiments that gave birth to it?" No. Never. It was purely conceived as a "thought" experiment. It (the constant speed of light) is POSTULATED, not Experimentally Observed nor Theoretically Predicted. Of course, it was Maxwell's Theory and the Michelson-Morley experiment then lead Einstein to these Postulates. Recall that, at the time of the latter, it was supposed that light propagated by INTERACTING with the Aether. But that experiment demonstrated that there was no Aether. So this lead to the question: How does light behave, in the absence of any interaction with anything? Special Relativity is Einstein's answer to that question.

Special Relativity, like Newton's theory of gravity, can obviously be used on earth. But only as an approximation. In most circumstances, they are very good approximations, but if you what maximum accuracy, as in GPS location systems, then General Relativity is required.

Rob McEachern

Roger Barlow, Professor of Particle Physics: "The Doppler effect - changes in frequencies when sources or observers are in motion - is familiar to anyone who has stood at the roadside and watched (and listened) to the cars go by. It applies to all types of wave, not just sound. (...) Moving Observer. Now suppose the source is fixed but the observer is moving towards the source, with speed v. In time t, ct/lambda waves pass a fixed point. A moving point adds another vt/lambda. So f'=(c+v)/lambda."

Paul Fendley: "Now let's see what this does to the frequency of the light. We know that even without special relativity, observers moving at different velocities measure different frequencies. (This is the reason the pitch of an ambulance changes as it passes you it doesn't change if you're on the ambulance). This is called the Doppler shift, and for small relative velocity v it is easy to show that the frequency shifts from f to f(1+v/c) (it goes up heading toward you, down away from you). There are relativistic corrections, but these are negligible here."

That is, if the frequency measured by the stationary observer is f=c/L (L is the wavelength), the frequency measured by an observer moving towards the light source with speed v is:

f' = f(1+v/c) = (c+v)/L = c'/L

where c'=c+v is the speed of the light waves relative to the moving observer. Special relativity is violated.

Pentcho Valev

Rob, Akinbo,

You're both right but trivially incomplete. Rob you ignore all from Romer to binaries in dismissing an empirical basis for postulating CSL, but no matter. You also distracted from the key point by apparently dismissing not just 'generalising' SR in gravity.

Akinbo you allowed Robs overstatement to distract you, Rob's central analysis is correct and just another way of describing discrete field dynamics. What the DF Model does is complete the ontology with the quantum mechanisms implementing the postulates and the LT, ergo 'curved space time'.

SR, GR and QM are like 3 complex 3D dynamic jigsaw puzzle pieces with dried mud on them. When they fit together, as the DFM and in line with Rob's description, SR 'becomes' GR, and both are implemented by logical quantum mechanisms (QM).

Speed is only a relative concept. c is then relative locally to ALL matter, which moves relative to other matter. The secrets were then only the mechanism for c to change (which also explains GR as plasma 'vortices' have G-potential) and for the non-linear asymptotic Limit represented by the Lorentz Factor. Those were the final pieces that made it all fit and work, exposing the great and simple beauty of nature. (I posted the LT link to Florin).

Rob. Shockingly Maxwell's equations need some massaging to rid them of anomalous virtual electrons, 'partial time derivatives' and Fraunhofer refraction, and to recover Snell's law or refraction. Are you up for discussing it and manipulating a few symbols? Do you recall my references to the (orig 1950's) 'two-fluid' plasma dynamics, surface plasmoids etc?

Best wishes

Peter

Very nice, Rob. If only the relativity deniers would appreciate it.

Rob,

Did Einstein really define "the phase velocity of light, in a vacuum, to be a constant"? In his 1905 SR paper he used Poincaré synchronization and two-way speed of light.

I came across of the phase/group velocity matter when Nimtz claimed having measured transmission of light with a speed in excess of c.

Today I found "The Great Einstein/de Broglie Velocity Equation derivation and notes by Douglass A. White" and an argumentation that questioned the correctness of Michelson's null result as measuring phase.

My own argument is perhaps the only one that is consistent with Michelson 1881/83 and Michelson/Pale 1925.

Eckard

Here the fatal equation c'=c+v is explicitly used in the derivation of the Doppler frequency shift:

Professor Sidney Redner: "The Doppler effect is the shift in frequency of a wave that occurs when the wave source, or the detector of the wave, is moving. Applications of the Doppler effect range from medical tests using ultrasound to radar detectors and astronomy (with electromagnetic waves). (...) We will focus on sound waves in describing the Doppler effect, but it works for other waves too. (...) Let's say you, the observer, now move toward the source with velocity vO. You encounter more waves per unit time than you did before. Relative to you, the waves travel at a higher speed: v'=v+vO. The frequency of the waves you detect is higher, and is given by: f'=v'/(lambda)=(v+vO)/(lambda)."

For light waves v is replaced by c:

f' = c'/(lambda) = (c+vO)/(lambda)

where c'=c+vO is the speed of light relative to the observer. Clearly special relativity is violated.

Pentcho Valev