# Am I interpreting Einstein correctly?

Minor point regarding the energy/frequency business;

The energy of a classical EM wave does not depend on frequency, only amplitude. This is also true of the Maxwell stress tensor.

When a classical EM wave is Doppler-shifted due to motion of the source or observer, the power changes. This is the rate of Energy flow or flux through a surface in Watts (joules/second).

[..]True, however you are assuming here that the POE occurs at the origin x,y,z=0,0,0
I concluded from the form of the equation that the source is at the origin, as that not only makes most sense; I think I forgot to mention that only that corresponds to a surface that moves at c [EDIT: I lacked imagination, see PS]. Thus all pieces of the puzzle fit. [EDIT: again wrong, I forgot two little pieces that didn't perfectly fit].

[..]
I disagree Harry. While it is true that R2=0 at t=t'=0, this does not matter for Einstein's purpose at hand here. [..[
I was talking about an apparent mistake by Neuenschwander: not only it leads to R=0 at t=0, his interpretation leads to R=0 at all times. Thus R would be meaningless in that equation.

I may add that the misunderstanding, as I perceive it, already started with the word "a pulse". I see no reason for that assumption, instead I take it that Einstein considered the light of a continuous source like a star. He defined [edit: may have defined, see PS] around that light source "a spherical surface moving with the velocity of light". That surface has radius R at t=0. And as Einstein put it, "We may therefore say that this surface permanently encloses the same light complex."

Cheers,
Harald

PS: I now saw the mathpages approach, which assumes a plane wave. That interpretation has the advantage that he does not switch the location of the source compared to section 7 and that "moving" is the most appropriate phrasing.
So, in the end, after perceiving two other mistakes in Neuenschwander's interpretation I also agree that Einstein probably contemplated a plane wave - but this plane wave still is part of light that is emitted isotropically in all directions from a distant star.

PS.PS: A third little piece of the puzzle confirms that: Einstein further on mentions that "the frequency of a light complex" depends on the state of motion of the observer. That only makes sense for a single frequency. I think that that settles the issue.

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It always was my impression that there Einstein was referring to a plane wave.
But I'm not sure how to fit the flat wavefront of a plane wave in the spherical wavefront the isotropic (rotationally invariant) light propagation would seem to demand. (And I guess Einstein argument should be valid not only as approximation at certain distances?)

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It always was my impression that there Einstein was referring to a plane wave.
But I'm not sure how to fit the flat wavefront of a plane wave in the spherical wavefront the isotropic (rotationally invariant) light propagation would seem to demand. (And I guess Einstein argument should be valid not only as approximation at certain distances?)
The light that Einstein started discussing in section 7 is to very good approximation a plane wave coming from a distant star that is far from the origin of K. It is part of a spherical wave front.
As elaborated in my last message, I now think that in section 8 he continues the development based on exactly that case; this has the advantage of analyzing one very small "piece" of radiation of uniform direction, intensity and frequency. The result should also be valid - as Neuenschwander suggests in his fig.3 - for the integral of all light inside a radius from the light source to the observer.

Harald

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Well, it looks like I'm in a position where I've solicited other people's opinions on this, have received a unanimous response, and am convinced that the unanimous response is wrong :-)
After reading Dr. Greg's comments I also think that my opinion was wrong. I didn't study the equation carefully enough so I thought it was the equation of a sphere with constant center whose radius was expanding at c instead of a sphere with constant radius whose center was moving at c.

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Minor point regarding the energy/frequency business;

The energy of a classical EM wave does not depend on frequency, only amplitude. This is also true of the Maxwell stress tensor.

When a classical EM wave is Doppler-shifted due to motion of the source or observer, the power changes. This is the rate of Energy flow or flux through a surface in Watts (joules/second).
The energy of a classical EM wave depends on its amplitude and its volume. When you do a Lorentz boost, both the amplitude and the volume change, and therefore the energy changes.

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It occurs to me now that there is a much more elementary argument that the volume of a light wave scales in the way it does. Suppose that a finite wave train of length x takes time t to pass by a certain observer. Since the speed of light is constant, any scaling factor applied to t must also be applied to x when we change frames.

I would speculate that the reason for the complication in Einstein's argument is that he knows that a wave-train with finite volume has to diffract. He wants to show that his result is exact, not some kind of approximation that only applies in the limit of small diffraction effects.

The result should also be valid - as Neuenschwander suggests in his fig.3 - for the integral of all light inside a radius from the light source to the observer.
Neuenschwander's discussion makes no sense, especially his fig 3. In that figure he shows a spherical surface expanding at the speed of light, and then suggests that this expanding sphere transforms into an expanding shortened ellipsoid in terms of a different reference frame - but of course that's not true. An expanding sphere of light in terms of one system of inertial coordinates is an expanding sphere of light in terms of ANY system of inertial coordinates. So his contracted ellipsoid in the primed coordinates consists of a locus of non-simultaneous events in those coordinates. In other words, his "one wavelength surface" isn't a coherent surface in the primed coordinates, so he can't just integrate the transformed energy density within this "surface" at a single instant of time in the primed coordinates. Also, he obviously can't use a constant energy density, nor even a constant ratio of energy densities between the primed and un-primed systems, because even the ratio varies from point to point.

He obviously doesn't realize any of this, because he depicts the ellipsoid as shortened, whereas the volume formula he gives (which he obviously just lifted from Einstein's paper without comprehension) is the equation for an *elongated* ellipsoid. Worse still, he then multiplies this by Einstein's ratio of energy densities, which obviously is not applicable here, first because the ratio varies with position thoughout the sphere, and more importantly because it doesn't apply to loci of non-simultaneous spatial regions, which is what Neuenschwander's ellipsoid represents in the primed coordinates. So it wouldn't even be correct to integrate Einstein's energy density ratio over the "volume". Basically, Neuenschwander's discussion is gibberish.

Of course, one could make a valid derivation of the energy of an expanding pulse, but it would not bear any resemblence to Neuenschwander's discussion. One simple approach would be to carry out Einstein's derivation for an infinitesimal region, from which the general result follows immediately.

Samshorn,

There's little doubt that Neuenschwander could have done a better job in stating what his figure 3 represents. As worded, and as depected, there are indeed problems with it. I'm not yet convinced his paper is incorrect otherwsie though. I'll need a little more time with it. It's interesting that his paper obtains the same result while starting with the initial assumption I did, ie that the radius R represents and expanding lightsphere from origin. It would seem the result "should" be the same. If so, then the big question is ... which approach did Einstein envision when he wrote his paper.

GrayGhost

There's little doubt that Neuenschwander could have done a better job in stating what his figure 3 represents.
He's quite clear about what he thinks it represents - he's just utterly wrong, as is his entire discussion on the energy transformation.

It's interesting that his paper obtains the same result while starting with the initial assumption I did, ie that the radius R represents and expanding lightsphere from origin.
No, his paper doesn't "obtain" the same result. He gives some completely erroneous verbiage, and then merely appropriates Einstein's equations, which are completely unrelated to his verbiage. (See my previous message.) Furthermore, the energy ratio for the case of an expanding sphere is NOT the same as for the moving light complex - it is simply E'/E = 1/sqrt[1-(v/c)^2], so he didn't even get the right answer for the situation he thought he was solving.

It would seem the result "should" be the same.
It may "seem" that way to you, but you're wrong. The answer for an expanding light pulse is not the same as for a light complex of the kind Einstein discussed.

If so, then the big question is ... which approach did Einstein envision when he wrote his paper.
You're not making any sense. Einstein's paper clearly and explicitly describes the energy content of a spherical region of constant radius moving along with a plane wave. He correctly derives the ratio of the energy content relative to two different frames of reference. Neuenschwander describes a completely different situation, and makes several huge conceptual errors (described in detail in the previous message), and arrives at the wrong answer (not surprisingly).

It's just sad that students are exposed to that kind of nonsense.

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Samshorn,

Well, you do sound pretty sure of yourself. You're right, the ellipsoid cannot encompass the EM complex under Neuenschwander's interpretation of the section 8 scenario, assuming that the ellipsoidal surface per the moving system represents a spherical surface that precisely coincides with the leading edge of expanding spherical wavefront in the stationary system (at any arbitrary time t). Here's the thing though ...

Is Neuenschwander "that bad" that he does not know light is isotropic, or does his figure 3 maybe represent something a little different from what you assume it does? I must say, his figure 3 doesn't make sense to me either, and the related description seems bad at best. Let's face it, the rocketeer does not record anything indicative of what he depicts there. It suggests he does not understand the desynchronisation of moving bodies, however that's also hard to swallow. If he really does have some sort of intent that we don't quite realize, I cannot imagine teaching it as such. Who is this fellow, Neuenschwander, anyways?

EDIT: There is only 1 way to interpret Neuenschwander's figure 3b as drafted. However, it cannot exist as such per any frame's POV, including the rocket's POV, and is thus contrary wrt his assertion that the rocketeer sees it as such.

GrayGhost

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Samshorn,

There's little doubt that Neuenschwander could have done a better job in stating what his figure 3 represents. As worded, and as depected, there are indeed problems with it. I'm not yet convinced his paper is incorrect otherwsie though. I'll need a little more time with it. It's interesting that his paper obtains the same result while starting with the initial assumption I did, ie that the radius R represents and expanding lightsphere from origin. It would seem the result "should" be the same. If so, then the big question is ... which approach did Einstein envision when he wrote his paper.

GrayGhost
Isn't that clear by now? As discussed, everything(?) is consistent with the interpretation that Einstein continued his discussion of a planar wave originating from "an infinitely distant" light source, while more than a few things are inconsistent with Neuenschwander's interpretation.

Harald

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I emailed Neuenschwander a few days ago to let him know about the error. He replied cordially and said he'd take a look at it. I don't think it's unpardonable that he made this mistake, since almost everyone who posted in this thread (including me) initially misread the paper in the same way. I think it's commendable that he wrote this commentary, complete with hand-drawn illustrations, and made it available for free on the web. It would only be really unfortunate if he failed to correct the error.

harrylin,

It's clear to me, now. I had never looked at sections 7 and 8 before, except at glance. I too originally suspected the energy-enclosing-surface corresponded to the leading edge of an expanding EM lightsphere. Now, it seems to me that it cannot be the case. The plane wave appears the logical intention of Einstein, based on the eqn he drafted and the requirement that the spherical surface always enclose the EM complex in both systems.

I tried to follow it thru assuming my original interpretation. Say the enclosing surface is expanding and spherical. For any time t, the spherical surface maps to a moving contracted ellipsoid per the rocket POV. However, considering the spherical surface at time t ... then when the EM intersects it simultaneously per the LAB (let's assume this occurs after precisely 1 wavelength of EM was generated, as Neuenschwander did), we might consider each photon's intersection as "an event". The mapping of "all said events", would be an elongated ellipsoid (not moving) in the rocket POV, however the events would not all occur at once. The events would occur as follows ... imagine a plane-surface parallel to the Y/Z plane, and move this plane in the direction of +x such that it passes thru the elongated ellipsoid while considering only the intersection of the 2 surfaces. That's the order of event occurances. Just guessing here, but maybe Neuenschwander intended to draft something such as that? Yet, said ellipsoidal surface would not exist per the rocket observer in the way Neuenschwander depicted it.

GrayGhost

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I emailed Neuenschwander a few days ago to let him know about the error. He replied cordially and said he'd take a look at it. I don't think it's unpardonable that he made this mistake, since almost everyone who posted in this thread (including me) initially misread the paper in the same way. I think it's commendable that he wrote this commentary, complete with hand-drawn illustrations, and made it available for free on the web. It would only be really unfortunate if he failed to correct the error.
The cartoons are very good. I especially like how the lab rat raises his arms when the rocket flies by, and the CAPT of the starship wears a hat. He doesn't have to worry about windage blowing the hat off :) I also wonder what he meant by his depicted frame-rotation?

GrayGhost