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Favorite Einstein Paper

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Which of the five papers Einstein wrote in 1905 do you consider the most revolutionary, significant, impressive, etc? And why? (I've included a list of the papers for your convenience)

March- "On a Heuristic Point of View about the Creation and Conversion of Light"

April- "A New Determination of Molecular Dimensions"

May- "On the Movement of Small Particles Suspended in Stationary Liquids Required by the Molecular-Kinetic Theory of Heat"

June- "On the Electrodynamics of Moving Bodies"

September- "Does the Inertia of a Body Depend on Its Energy Content?"

This should be fun!

Zak

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Which of the five papers Einstein wrote in 1905 do you consider the most revolutionary, significant, impressive, etc? And why? (I've included a list of the papers for your convenience)

March- "On a Heuristic Point of View about the Creation and Conversion of Light"

April- "A New Determination of Molecular Dimensions"

May- "On the Movement of Small Particles Suspended in Stationary Liquids Required by the Molecular-Kinetic Theory of Heat"

June- "On the Electrodynamics of Moving Bodies"

September- "Does the Inertia of a Body Depend on Its Energy Content?"

This should be fun!

Zak

The last two written in June and September because they introduced the Special Theory of Relativity. IMO, they were also his one of the most impressive achievements because of the amount of integration required to compress his entire theory within two postulates.

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Sorry that should be one postulate in the post above, the postulate being "The Laws of Physics are the same in all inertial frames of reference". The constancy of the speed of light in all frames of reference can be derived using Maxwell's electromagnetic theory and assuming the above postulate.

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The constancy of the speed of light in all frames of reference can be derived using Maxwell's electromagnetic theory and assuming the above postulate.

I don't get that point. Isn't the constancy of the speed of light an experimental fact?

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I don't get that point. Isn't the constancy of the speed of light an experimental fact?

Yes it is, but according to my knowledge, Maxwell, assuming that light was actually an electromagnetic wave with sinusoidically fluctuating electric and magnetic fields proved that light speed was inversely proportional to the magnetic permeability and electric permittivity constants.

So in effect, if you take Maxwell's theory to be true and then take the postulate in Einstein's paper to be true, the constancy of the speed of light relative to the observer is automatically true.

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Which of the five papers Einstein wrote in 1905 do you consider the most revolutionary, significant, impressive, etc? And why?

Any single one of those papers would have established any physicist at that time, and Einstein did it five times over! What a year! (In the literature, 1905 for Einstein is often referred to as the modern counterpart to Newton's 1666 annus mirabilis, the miraculous year. Newton himself recounted the amazing work he did during the "plague years" spanning 1665-1666.)

Interestingly, of the first four papers (the fifth derived a result found in the fourth paper) Einstein originally considered only the first (March) quantum paper to be revolutionary. In May of 1905 he wrote to Conrad Habicht (friend and member of their famous study group, the 'Akademie Olympia'):

I promise you four papers in return, the first of which I might send you soon, since I will soon get the complimentary reprints. The paper deals with radiation and the energy properties of light and is very revolutionary... (18th or 25th of May letter to Conrad Habicht, The Collected Papers of Albert Einstein, Vol. 5, p. 20, Princeton University Press, 1995)

Einstein describes the second and third papers, and then of the fourth (special relativity), he says:

The fourth paper is only a rough draft at this point, and is an electrodynamics of moving bodies which employs a modification of the theory of space and time, the purely kinematic part of this paper will surely interest you. (ibid.)

"urely interest you?" What an understatement that was. And, here it is mid-may, and his amazing June paper is only at the stage of a "rough draft!"

My own choice of papers is, unquestionably, the fourth paper, the one introducing to the world what we now call special relativity. Einstein received his Nobel Prize for the first paper on quantum effects, and deservedly so for its achievement and importance. But, were it not for in-fighting and political squabbles of the time (a story for another time), the Nobel would have and should have been given for relativity. Nothing else that Einstein ever did, except for the later general relativity, so profoundly affected our view of the world and so much influenced the course of physics. On the Electrodynamics of Moving Bodies is without a doubt my first choice.

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Sorry that should be one postulate in the post above, the postulate being "The Laws of Physics are the same in all inertial frames of reference". The constancy of the speed of light can be derived using Maxwell's electromagnetic theory and assuming the above postulate.

You have to be careful here. While your loose wording of the first postulate does capture the essence of Einstein's meaning in the paper, your wording of the second postulate adds more than what Einstein claimed. The second postulate, as stated in Einstein's paper, is:

Each ray of light moves in the coordinate system 'at rest' with the definite velocity V independent of whether this ray of light is emitted by a body at rest or a body in motion. ("On the Electrodynamics of Moving Bodies," reprinted in The Collected Papers of Albert Einstein, Vol. 2, p. 143, Princeton University Press, 1989)

Note the absence of your "in all frames of reference," which is actually a further inference from the postulate.

Also, your statement about deriving the postulate from Maxwell's electrodynamics is only the case now, after the fact of special relativity. Prior to Einstein's work, the statement could only be made in reference to the ether frame.

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Isn't the constancy of the speed of light an experimental fact?

It is not possible to experimentally measure the one-way speed of light. Even if the two-way speed was found experimentally to be constant, it might be anisotropic, slightly different in each direction. Since that time experiments have been performed that looked for variations, and none have been found, so now we can talk about experimental fact in regard to the speed of light.

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It is not possible to experimentally measure the one-way speed of light. Even if the two-way speed was found experimentally to be constant, it might be anisotropic, slightly different in each direction. Since that time experiments have been performed that looked for variations, and none have been found, so now we can talk about experimental fact in regard to the speed of light.

I'm not sure I understand why not. If there were two synchronized clocks, one on earth and one on the moon (or some other planet), just send a signal from one location to another and record when the signal was sent and when it was received.

Do you mean by direction, the opposite but parallel direction? That's an interesting supposition. What if three or more mirrors are used. Would each direction that the light traveled potentially have a different speed? Does the reflector affect the measured speed? Does the same beam of light get 100% reflected or does the impinging beam get absorbed on the surface and get retransmitted?

Is there any reason to assume that there might be a difference in the speed depending upon the direction? Or is it simply a matter of actually doing the measurement and seeing what the results yield? Does light travel faster when heading away or toward from a gravitional source (like the sun or the center of the Milky Way)?

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It is not possible to experimentally measure the one-way speed of light.

I'm not sure I understand why not. If there were two synchronized clocks, one on earth and one on the moon (or some other planet) ...

And therein lies the problem. Two clocks can, in principle, be made to be perfectly synchronized when they are side by side, but as soon as they are spatially separated they lose their synchronicity. This is a basic result of relativity, identified and discussed in Einstein's original 1905 paper. Then, any procedure used to synchronize two spatially separated clocks, of necessity makes use of or imposes the two-way speed of light.

Is there any reason to assume that there might be a difference in the speed depending upon the direction?

There are a number of technically complex (but bizarre) relativistic theories that assume an anisotropic speed of light, utilizing a generalized Lorentz transform with rather strange properties. This includes a few ether-based theories. There are also some cosmological theories that assume a variable speed of light, but these are more complicated still (and more bizarre).

Does light travel faster when heading away or toward from a gravitional source (like the sun or the center of the Milky Way)?

It is always on a local level that we speak of the speed of light as being measured as c. Gravitational effects on light are complex and varied, and non-local measurements can certainly depart from c. For instance, before I've mentioned the Shapiro time delay. If a signal from Earth is reflected off a planet, the speed of the signal is measured as less than c when the planet is on the far side of the Sun. This has been done using radar and planets like Mercury and Venus, as well as with satellites like the old Mariner 9 Mars orbiter.

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It is always on a local level that we speak of the speed of light as being measured as c. Gravitational effects on light are complex and varied, and non-local measurements can certainly depart from c. For instance, before I've mentioned the Shapiro time delay. If a signal from Earth is reflected off a planet, the speed of the signal is measured as less than c when the planet is on the far side of the Sun. This has been done using radar and planets like Mercury and Venus, as well as with satellites like the old Mariner 9 Mars orbiter.

That is fascinating. So what you're saying then is that the speed of light is the ulitmate speed, but that speed doesn't necessarily have to be equal to c? Does this have any implications for the equation E=mc^2? Or is c alway c and not the speed of light? You state, "if a signal from Earth is reflected off a planet, the speed of the signal is measured as less than c when the planet is on the far side of the Sun," if a signal was sent in the opposite direction (from the planet on the far side to earth on the near side) would it travel faster than c?

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And therein lies the problem. Two clocks can, in principle, be made to be perfectly synchronized when they are side by side, but as soon as they are spatially separated they lose their synchronicity. This is a basic result of relativity, identified and discussed in Einstein's original 1905 paper. Then, any procedure used to synchronize two spatially separated clocks, of necessity makes use of or imposes the two-way speed of light.

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OK. Suppose you were to start with two clocks that are exactly 1/2 way between the moon and earth, sychronize them and then start moving them away from each other at the exact same rate until you have one on the earth and one on the moon. Would they then still be synchonized since both motions relative to the starting point would be the same?

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It is always on a local level that we speak of the speed of light as being measured as c. Gravitational effects on light are complex and varied, and non-local measurements can certainly depart from c. For instance, before I've mentioned the Shapiro time delay. If a signal from Earth is reflected off a planet, the speed of the signal is measured as less than c when the planet is on the far side of the Sun. This has been done using radar and planets like Mercury and Venus, as well as with satellites like the old Mariner 9 Mars orbiter.

That is fascinating. So what you're saying then is that the speed of light is the ulitmate speed, but that speed doesn't necessarily have to be equal to c?

:)

Not quite. These non-local measurements are coordinate speeds, not physical speeds. They are a consequence of the gravitational effects that alter the otherwise straight-line path of light over global distances. Non-local speeds measured different from c simply indicate a curved path due to gravitational interaction. If we measure the speed along any local part of the path, it will always be c.

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And therein lies the problem. Two clocks can, in principle, be made to be perfectly synchronized when they are side by side, but as soon as they are spatially separated they lose their synchronicity. This is a basic result of relativity, identified and discussed in Einstein's original 1905 paper. Then, any procedure used to synchronize two spatially separated clocks, of necessity makes use of or imposes the two-way speed of light.

OK. Suppose you were to start with two clocks that are exactly 1/2 way between the moon and earth, sychronize them and then start moving them away from each other at the exact same rate until you have one on the earth and one on the moon. Would they then still be synchonized since both motions relative to the starting point would be the same?

Paul, let me assure you that a lot of very smart people have studied this problem for almost one-hundred years, and no matter what scenario you come up with there are endless subtleties from which you cannot extricate yourself. It is much like trying to square the circle, and debunking each "proof" of doing so is really a futile effort. In this case, for instance, how do you measure the spatial distance of each separation without implicitly assuming the two-way speed of light?

You need to understand that any measurement of the one-way speed of light is dependent on the particular synchronization method used, and no meaningfull physical quantity can be so dependent. Each synchronization method makes certain assumptions, and based on those assumptions different values are measured. It is the measurement of the two-way speed of light that has physical significance, and there are many synchronization methods that measure the same two-way speed while even assuming anisotropy in the one-way speed. Here is a little something I wrote a while ago. Perhaps it might be helpful in getting you to see the technical issues involved, or perhaps it might confuse you further. I hope the former is the case, but if you are still unclear please keep in mind that squaring the circle is simply not possible.


I do not think your question was misunderstood, but rather the
discussion which ensued was more general in regard to Lorentz
invariance. Such a "modified" Lorentz transformation is very
much dependent on the physical assumptions you make regarding any
variability of light speed.

To give you a specific example -- a simple one -- let's take what
may be the most simple change to the physical assumptions and see
the effect they have upon the Lorentz transformation. A
generalization of the Lorentz transformation which maintains the
two-way speed of light -- and is therefore consistent with
experiment -- but allows the one-way velocity of light to vary in
terms of a directional parameter, was given by W.F. Edwards in
1963. In another post in an earlier thread I derived some of the
two-way and one-way relationships based on notions of
simultaneity and clock synchronization, and here I will just
state the results which apply to this Edwards generalization.

In the general direction r, the two-way speed of light along a
back and forth path is given by

2(c_r+)(c_r-)
c_r = ---------------
(c_r+) + (c_r-)

c_r+ is the one-way velocity of light along the forward path, and
c_r- is the one-way velocity of light along the return path, and
they are given by

c_r c_r
c_r+ = ------- , c_r- = -------
1 - q_r 1 - q_r

where q_r is the directional parameter in the direction r, given
by

-1 <= q_r <= 1.

So, for instance, in x-y-z coordinates, we would have

c_i c_i
c_i+ = -------, c_i- = -------
1 - q_i 1 + q_i

-1 <= q_i <= 1, i = x,y,z.

In these x-y-z coordinates, for simplicity sake, we will assume
the directional parameter is of the form (q, 0, 0), so that in
frame F we have

c c
c_x+ = ------, c_x- = ------, c_y+ = c_y- = c_z+ = c_z- = c,
1 - q 1 + q

where c is now a constant two-way speed of light. Likewise, for
another frame F', we have

c c
c'_x+ = ------, c'_x- = ------, c'_y+ = c'_y- = c'_z+ = c'_z- = c,
1 - q' 1 + q'

With this as a basis one can then derive, after a lot of algebra,
the Edwards' form of the generalized Lorentz transformation,
which result is

x' = G(x - vt),

y' = y,

z' = z,

t' = G{[1 + (q + q')v/c]t - [(1 - q^2)v/c + (q' -q)]x/c},

1
where G = -----------------------------
sqrt[(1 + qv/c)^2 - (v/c)^2

and v, as usual, is the relative velocity between frames F and
F'.

Note that if the directional parameter is identically zero,
meaning that there is no directional variability to the speed of
light, then this generalized Lorentz transform reduces to the
standard form.

Also, note that another level of complexity is introduced by
assuming that the two-way velocity of light is equal to the
one-way velocity, but allow that velocity to be generally
anistropic, though it remains independent of the motion of the
source. This is known as a Robertson inertial frame, for H.P.
Robertson who first formulated this 1949. And, just as using the
Edwards notion of simultaneity led to a generalization of the
Lorentz transformation with a one-way directional variability of
the speed of light, so the Robertson notion of simultaneity leads
to a further generalization of the Lorentz transformation. The
next level of complexity was introduced by R. Mansouri and R.U.
Sexl in 1977 where the introduced a directional parameter to the
Robertson formulation which leads to a further generalization of
the Lorentz transformation equations. The form of this
generalization is similar to the one I outlined above, but
obviously with somewhat more complicated expressions.

So one can arrive at various forms of an anisotropic
4-dimensional spacetime by relaxing the physical assumptions
imposed in the standard formulation. Below are references of
Edwards', Roberson's, and Mansouri & Sexl's initial work, as well
as a reference to an excellent book which contains these
formulations I have presented, and does so in the context of
experimental relativity.

W.F. Edwards, A. J. Phys. 31 (1963) pp. 482-489.

H.P. Robertson, Rev. Mod. Phys. 21 (1949) p. 378.

R. Mansouri and R.U. Sexl, Gen. Relativ. Grav. 8 (1977) p. 407.

Y. Z. Zhang, "Special Relativity and its Experimental
Foundations," _World Scientific, 1997.

[font="Courier,"]

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OK. Suppose you were to start with two clocks that are exactly 1/2 way between the moon and earth, sychronize them and then start moving them away from each other at the exact same rate until you have one on the earth and one on the moon. Would they then still be synchonized since both motions relative to the starting point would be the same?

The issue of measuring the speed of light is quite a subtle one - one reason is that a background theory is required to _interpret_ any experimental results obtained as being such a measurement. (This issue is quite familiar - usually when one measures physical constants one is assuming other physical facts, e.g. pertaining to how the apparatus works, in order to interpret the result as indeed measuring the relevant constant.)

With no fixed theory in the background it is quite impossible to measure the one way speed of light, because there are ether theories that give precisely the same experimental results as SR while assuming different one way speeds of light to SR.

What is true however is that if you _assume_ SR (i.e. you take SR as your background theory, which is reasonable given its exceptional agreement with experiment) then it is possible to measure the one way speed of light in any particular frame, and you find it does indeed equal c in any frame.

This sounds vacuous at first - by assuming SR isn't one already assuming the one-way speed of light is c? Not quite. In modern formulations SR is usually taken only to postulate that there exists a frame independent finite speed c and is agnostic about whether light (or anything else) actually travels at that speed. To be precise, SR predicts that massless particles move at the invariant speed c and massive particles move at speeds lower than c, but that leaves open the question of whether photons are massive or massless. It is then an experimental question whether light itself travels at c, and it is in this sense that my previous paragraph was intended - yes the experiments show that the one-way speed of light is indeed c, given SR as a background theory. This agrees with Maxwell's theory of electromagnetism, which predicts that electromagnetic radiation moves at the invariant speed c.

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I've been reading every post, but due to time constraints, I've been unable to post.

Stephen, the reason I asked the question was partially due to the quote you mention from Einstein. Do you have any idea why he considered only the March paper "revolutionary"? As to my favorite paper, I would also agree that the June paper is my favorite, but the March paper takes a close second.

I'm thinking hard about the problem proposed by Paul's Here, but I have one more question while we're at it. According to relativity, length is relative. When viewing an object, the dimension that is parallel to the direction of motion contracts. Now, one reason that things can't move faster than the speed of light is because at that speed, the contraction is 100%; the length of the moving object contracts to zero. At any speed faster than the speed of light, the lenght would become negative, so the speed of light is the limit. Right? (Note: I don't have a copy of the paper on hand, so I'm just stating the theory as I remember). Now the part I don't understand is apparently the contraction (and the speed of light) is the same whether or not the observer is stationary or moving alongside the object. Can someone please try to explain this to me, or it just something I have to wrap my head around?

Zak

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Good points overall, but one clarification.

This sounds vacuous at first - by assuming SR isn't one already assuming the one-way speed of light is c? Not quite. In modern formulations SR is usually taken only to postulate that there exists a frame independent finite speed c and is agnostic about whether light (or anything else) actually travels at that speed. To be precise, SR predicts that massless particles move at the invariant speed c and massive particles move at speeds lower than c, but that leaves open the question of whether photons are massive or massless.

While I agree with the essential point, for the advanced reader it is worthwhile to note that there are axiomatic systems of Minkowski spacetime that make no assumptions about the existence of light signals. Here is a little blurb I wrote awhile ago.

At the most fundamental level, the spacetime of special

relativity is based on a system of primitive notions and axioms

which are highly dependent on the choices of the logician. As

John Schutz points out, Euclidean geometry is generally believed

to require five postulates and two primitive relations, but there

exist many assumed properties in Euclid's formulation. Hilbert

was able to express Euclidean geometry by reference to the same

two Euclidean primitive relations, but he used two undefined sets

of points and lines and five independent groupings of axioms,

containing a total of twenty non-independent axioms. Later,

people such as Veblen and the Moore presented a single undefined

set of points along with fifteen independent axioms

Likewise the axiomatic structure of Minkowskian spacetime has

undergone much development. A fairly recent presentation by

Schutz is expressed in two undefined sets of events and paths, a

single three-point betweenness relation, and fifteen independent

axioms. For a brief history of the axiomatic structure, and the

full presentation of the undefined primitives and axioms at the

base of special relativity, see John W. Schutz, "Independent

axioms for Minkowski space-time," _Addison Wesley Longman

Limited_, 1997.

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Stephen, the reason I asked the question was partially due to the quote you mention from Einstein. Do you have any idea why he considered only the March paper "revolutionary"?

Based on everything I have read by Einstein, correspondence and papers alike, I can name with some confidence two specific reasons. The first reason is that at the time I do not think Einstein fully appreciated the revolutionary nature of his work on relativity. It was a great challenge to him, aspects of which he had thought about off and on for a decade, but mentally he was so wrapped up in the challenge and the solution that it was difficult for him to step back and put that work into the historical context it deserved. The second, lesser reason, is that after publication of the paper Einstein questioned certain implications of his theory, at least until he worked out solutions to those implications. I strongly suspect, though cannot prove, that such concerns already existed in his mind during the finalization of the paper, and those concerns needed to be dealt with before he could feel unbridled enthusiasm.

Zak, as to the rest of your concerns, I must note that the words and formulations you use are similar to those used in poor popularizations of the theory, and in my view they lead to nothing but confusion. You can do a search on the many comments I have made in regard to time dilation and length contraction, and that will give you a different perspective on the theory. But, properly, I strongly suggest you read a really good book on relativity, and as an introduction there is probably none better than Spacetime Physics by Edwin F. Taylor and John Archibald Wheeler, W.H. Freeman, 1992. This book will equip you with much better concepts and terminology, altogether leading to a much better understanding. This is a non-technical book, accessible to any high school level reader, but sophisticated enough in precision to make it useful even to the more advanced reader.

Also, as much as I adore Einstein and his work, I do not think that reading his historical papers and books is the best way to learn relativity. Better to first learn the more modern approach, and then later you can better learn and appreciate Einstein's perspective.

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While I agree with the essential point, for the advanced reader it is worthwhile to note that there are axiomatic systems of Minkowski spacetime ...

It was pointed out that this might be misunderstood. My intended meaning was to include member Michael J. as "advanced reader," not to exclude him. I hope this clarifies any possible ambiguity.

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It was pointed out that this might be misunderstood. My intended meaning was to include member Michael J. as "advanced reader," not to exclude him. I hope this clarifies any possible ambiguity.

No slight was perceived, and thanks for the additional information about Minkowskian geometry.

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