Chasing The Light PDF Free Download


John D. Norton
Department of History and Philosophy of Science
University of Pittsburgh, Pittsburgh PA 15260
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  1. Catching The Light Book
  2. Oliver Stone Book Character
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Einstein recalled how, at the age of 16, he imagined chasingafter a beam of light and that the thought experiment had played a memorablerole in his development of special relativity. Famous as it is, it has provendifficult to understand just how the thought experiment delivers its results.It fails to generate serious problems for an ether based electrodynamics. I propose a new way to read it that fits it nicely intothe stages of Einstein's discovery of special relativity. It shows theuntenability of an 'emission' theory of light, an approach to electrodynamictheory that Einstein considered seriously and rejected prior to hisbreakthrough of 1905.

For more details, see:
'Chasing the Light: Einstein's Most Famous Thought Experiment,' prepared forThought Experiments in Philosophy, Science and the Arts, eds., JamesRobert Brown, Mélanie Frappier and Letitia Meynell, Routledge. Download.
Sections 5-6 of 'Einstein's Investigations of Galilean CovariantElectrodynamics prior to 1905,' Archive for History of Exact Sciences,59 (2004), pp. 45­105. Download.

Print and download Chasing the Light (Advanced) sheet music by flowkey arranged for Piano. Instrumental Solo in G# Minor.

1. The Puzzle

How could we be anything but charmed by the delightful storyEinstein tells in his Autobiographical Notes of a striking thought hehad at the age of 16? While recounting the efforts that led to the specialtheory of relativity, he recalled

'..a paradox upon which I had already hit at the age ofsixteen: If I pursue a beam of light with thevelocity c (velocity of light in a vacuum), I should observe such a beam oflight as an electromagnetic field at rest though spatially oscillating. Thereseems to be no such thing, however, neither on the basis of experience noraccording to Maxwell's equations. From the very beginning it appeared to meintuitively clear that, judged from the standpoint of such an observer,everything would have to happen according to the same laws as for an observerwho, relative to the earth, was at rest. For how should the first observer knowor be able to determine, that he is in a state of fast uniform motion? One seesin this paradox the germ of the special relativity theory is alreadycontained.'

The thought is simplicity itself.Here is light, a waveform propagating at c:

If the young Einstein were to chase after it at c, he wouldcatch up with the wave and be moving with it, like asurfer riding the wave. He would see a frozen lightwave.

The untenability of that thought led to the downfall of thegreat achievement of nineteenth century physics, the ether, which then providedthe basis for all electromagnetic theory.

The trouble is that it is quiteunclear just how this thought creates difficulties for the ether.Einstein gave three reasons and each of them could be answered readily by anable ether theorist.

Einstein wrote..The ether theorist replies..
'..I should observe such a beam of light as an electromagnetic field at rest though spatially oscillating. There seems to be no such thing, however,..'
1'..neither on the basis of experience..'..but we don't experience frozen light for the simple reason that we are not moving at c through the ether. If we were moving that fast, we would experience frozen light.
2'..nor according to Maxwell's equations..'Not so. A very short calculation shows that Maxwell's equations predict that light becomes frozen for observers moving at c through the ether.
3'..From the very beginning it appeared to me intuitively clear that, judged from the standpoint of such an observer, everything would have to happen according to the same laws as for an observer who, relative to the earth, was at rest.
For how should the first observer know or be able to determine, that he is in a state of fast uniform motion?..'
An observer knows he is moving rapidly with respect to the ether simply because light has become frozen. Analogously a surfer knows he is moving since he stays on the wave.

Catching The Light Book

So what are we to make of the thought experiment? Perhaps itis no more than the recording of the visceralhunches of a precocious 16 year old who did not even study Maxwell'stheory until two years later. This is a possibility we cannot rule out. If itis correct, then we need not puzzle any further over how the thought experimentworks, for there is little more to be found that illuminates Einstein's pathwayto special relativity.

But then we must ask why the thought experiment merits prideof place in Einstein's defining autobiography? Does it have a cogency that extends beyond Einstein's final high schoolyear? That Einstein mentions Maxwell's equations in the thought experimentsuggests their relevance to the operation of the thought experiment and thusthat this operation was pertinent to Einstein's later thought, after he hadlearned Maxwell's equations.

While we cannot know on the evidence available if the thoughtexperiment truly had cogency beyond the mullings of Einstein's 16th year, wecan ask if there are plausible accounts of Einstein's pathway to specialrelativity in which the thought experiment figures more significantly.

2. A Proposed Solution

There is a way of understanding how the thought experimentcould have a significance that extended well beyond the confines of Einstein'sfinal year at high school. The key is not to relate the thought experiment toether theories of electromagnetism. Rather, we know that Einstein devoted someeffort during the years leading up to his discovery of 1905, to so-called 'emission' theories of light and electromagnetism.Einstein eventually found such theories objectionable and untenable.

I propose that Einstein's thought experiment provided anespecially cogent way of formulating thoseobjections and thereby supported Einstein in his final decision: it giveup an emission theory in favor of retaining the celebrated Maxwell-Lorentztheory, but with a radically altered theory of space and time.

3. An Emission Theory of Light and Electromagnetism

On many later occasions, Einstein recalled that, prior to hisdiscovery of special relativity, he had investigated emission theories,indicating a similarity in his approach to that used by Walter Ritz. In thethen standard electrodynamics of Maxwell and Lorentz, electromagnetic actionalways propagated at c with respect to theether. The simplest example was the propagation of a lightwave. Butit held equally for the action of one charge upon another. It was this factthat made it seem impossible to conform the principle of relativity toelectromagnetism. The ether supplied a preferred state of rest essential to thetheory, but incompatible with the idea that all inertial states of motion areequivalent.

So Ritz in 1908, and Einstein sometime before 1905, tried tomodify electromagnetic theory in such a way that electromagnetic effects arealways propagated at c with respect to the source ofthe effect. If such a theory could be found, it would no longerrequire an ether state of rest and it would reasonable to expect that it couldconform to the principle of relativity.

The animation below displays thedifference. On the left, in the Maxwell-Lorentz theory, electromagneticaction propagates from a fixed point in the ether. So when two charges movingtogether act on each other, the source of the effect felt by one is a fixedpoint in the ether left behind by the moving source. Since the effectpropagates from a point left behind by the moving charges, an observer movingwith the charges can use this fact to determine that the charges are moving.

On the right, we see the corresponding process in a modified'emission' theory, such as devised by Ritz and Einstein. The motion of thesource is added to the propagating effect. So now the effect propagatesisotropically from a point that moves with the source. To see this, notice howthe expanding spherical shells remain centered on the moving positive chargethat is their source, just as would happen if the two charges were at rest. Thepropagation of electromagnetic effects can no longer be used by observersmoving with the two charges to detect their absolute motion; the principle ofrelativity is no longer threatened.

The simplest electromagnetic action is the propagation oflight. So in this theory, the velocity of the emitter--the source--is added tothe velocity of the light emitted. For this reason it is known as an 'emission'theory.

Promising as this must initially have seemed to an Einsteinintent on restoring the principle of relativity, the emission theory was ultimately rejected by Einstein. His later correspondenceand papers are littered with remarks on the problems the theory faced. Two willreturn as our story unfolds.

- In a letter to Paul Ehrenfestof June 1912 (and elsewhere), Einstein remarked that an emission theory ranafoul of an elementary result of optics: the physical state of a ray of lightis determined completed by its intensity and color (and polarization).
- In an interview with R. S. Shankland in the1950s, Einstein remarked that the theory could not be formulated as a localfield theory that is, in terms of differential equations.

I forgot to remember pdf free download software. In a local field theory, we reconstructhow a field evolves over time by taking its state at one instant andconsulting the theory's differential field equations. These equations take thepresent state of the fields and tell us how rapidly they are changing. Fromthese rates of change we can then infer the states of the field at futuretimes. (A similar analysis tells us how the field will alter at different partsof space.)

4. Einstein's Thought Experiment in the Context of anEmission theory of Light

Let us now return to Einstein's thought experiment andimagine that its target has become an emission theory of light. We immediatelysee that the three objections Einstein's reports present serious obstacles to an emission theory. Let us take thethree objections in order.

1. The first objectionwas that we don't actually experience frozen light.That is a puzzle in an emission theory of light. We must presume that there arelight sources with all sorts of velocities around us. A light source movingrapidly away from us will emit a lightwave that propagates slowly with respectto us. The most extreme case is of light source moving away from us at c. Thatsource will leave a frozen light wave behind in space, as the animationshows:

So, if an emission theory is the correct theory of light, weshould expect eventually to run into frozen lightwaves, emitted by rapidlyreceding sources. But we experience no such thing.

2. The second objectionwas that frozen light was incompatible withMaxwell's equations. Why should this be a problem for an emission theorywhen such a theory does not employ Maxwell's equations? It will be a problem,but it takes a few steps to arrive at the conclusion.
First note that an emission theory allows frozen light in ordinarycircumstances; we don't need to be moving at c to find it. That means that afrozen light wave must be a part of electrostatics and magnetostatics, thetheories of static electric and magnetic fields. Now Maxwell's electrodynamicsevolved over the course of half a century and built on a long series ofexperiments in electricity and magnetism. An emission theory must adjust thetheory, but it cannot alter it too radically onpain of incompatibility with those experiments. The one part of Maxwell'stheory that seems most secure is its simplest part, its treatment of staticelectric and magnetic fields. So we would expect a successful emission theoryto agree with Maxwell's theory in this simplest and most secure part.

Now we have a problem: An emission theory allows theexistence of frozen light waves. But the emission theory must agree closelywith the treatment of static fields in Maxwell's theory and Maxwell's theorydoes not admit the static fields that corresponds to frozen light waves.

3. In his thirdobjection, Einstein lamented for the observer catching the light beam, '..Forhow should the first observer know or be able todetermine, that he is in a state of fast uniform motion?' Of course, inthe context of an emission theory, the 'state of fast uniform motion' must beread as 'fast uniform motion with respect to the source of the light.'

At first it is not clear why it should matter at all whetherthe observer catching the light beam can make this judgment. It turns out to beimportant if the overall emission theory of light is to bedeterministic; that is, if the present state of fields and the like inspace are to be able to determine how they will develop in the future.Einstein's worry is that determinism will fail. To see why, imagine that youare an observer given a waveform, but all you know of it is its state at thepresent instant.

Light wave at an instant

Would you be able to tell whether the waveform is one that isfrozen in space;

One possible future: a frozen lightwave

or whether it is one that is propagating past you?

Another possible future: a propagating lightwave

Both are possible in an emissiontheory. Which is the case depends upon your velocity with respect to thelight's source. If you are moving at c with respect to the source, the wave isfrozen. If you are at rest with respect to the source, the wave is propagatingat c.

Can you tell which case you have by merely looking at thewaveform at an instant? You cannot. Einstein's earlier remark about light isnow decisive. A light wave is fully characterized by its color, intensity andpolarization and both cases agree on these properties. The waveform has no property at an instant that would enable you to tellwhat its future time development would be. This is indeterminism. The presentstate of the wave does not determine its future time development.

While this circumstance might just be just an oddincompleteness of our knowledge, it becomes a crisis if we imagine that we arenot human observers but the differential equationsof a local field theory. For, as we saw above, a basic function of those fieldequations is to take the present state of the fields and from them infer therates of change of the field. Those rates of change then determine the timedevelopment of the waveform--whether it propagates or not and how fast itpropagates. This essential function will not be possible in an emission theory,for the instantaneous state of the lightwave does not determine the rates ofchange of the field.

Hence, thanks to Einstein'sthought experiment, we infer that an emission theory cannot be formulated as alocal field theory.

We can summarize the problems brought by Einstein's thoughtexperiment to an emission theory:

Einstein wrote..The emission theorist worries..
'..I should observe such a beam of light as an electromagnetic field at rest though spatially oscillating. There seems to be no such thing, however,..'
1'..neither on the basis of experience..'An emission theory allows frozen waveforms for observers in all inertial states of motion, so we should expect to experience them.
2'..nor according to Maxwell's equations..'An emission theory should agree closely on static fields with Maxwell's theory, but Maxwell's theory prohibits the static fields of frozen light (except in the special case of observers moving at c with respect to the ether).
3'..From the very beginning it appeared to me intuitively clear that, judged from the standpoint of such an observer, everything would have to happen according to the same laws as for an observer who, relative to the earth, was at rest.
For how should the first observer know or be able to determine, that he is in a state of fast uniform motion?..'
We cannot tell from the instantaneous state of a light wave whether it is a frozen wave or a propagating wave. So differential field equations cannot tell either and and an emission theory of light cannot be formulated as a local field theory governed by differential field equations.

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5. Conclusion

When Einstein abandoned an emission theory of light, he hadalso to abandon the hope that electrodynamics could be made to conform to theprinciple of relativity by the normal sorts of modifications to electrodynamictheory that occupied the theorists of the second half of the 19th century.Instead Einstein knew he must resort toextraordinary measures. He was willing to seek realization of his goalin a re-examination of our basic notions of space and time. Einstein concludedhis report on his youthful thought experiment:

'One sees that in this paradox the germ of the specialrelativity theory is already contained. Today everyone knows, of course, thatall attempts to clarify this paradox satisfactorily were condemned to failureas long as the axiom of the absolute character of time, or of simultaneity, wasrooted unrecognized in the unconscious. To recognize clearly this axiom and itsarbitrary character already implies the essentials of the solution of theproblem.'

Copyright John D. Norton,December 2004. Rev. February 15, 2005. Reformatted April 14, 2005

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