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Albert Einstein's Special Theory of Relativity: Emergence, 1905 and Early Interpretation, 1905-1911 by Arthur I. Miller
This book analyzes one of the three great papers Einstein published in 1905, each of which would alter forever the field it dealt with. The second of these papers, "On the Electrodynamics of Moving Bodies," had an impact in a much broader field than it established what Einstein sometimes referred to (after 1906) as the "so-called Theory of Relativity." Miller uses the paper to provide a window into the intense intellectual struggles of physicists in the first decade of the 20th the interplay between physical theory and empirical data, the fiercely held notions that could not be articulated clearly or verified experimentally, the great intellectual investment in existing theories, data, and interpretations -- and associated intellectual inertia -- and the drive to the long-sought- for unification of the sciences. Since its original publication, this book has become a standard reference and sourcebook for the history and philosophy of science; however, it can equally well serve as a text in the history of ideas or of twentieth-century philosophy. From reviews of the previous ÄMillerÜ has written a superb, perhaps definitive, historical study of Einstein's special theory of relativity.... One comes away from the book with a respect for both the creative genius of the man and his he simply brushed aside much of the work that was going on around him. - The New Yorker
- GenresScience
Hardcover
First published January 1, 1980
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May 24, 2020
This is an excellent book. It examines in detail the history and context leading up to Einstein's 1905 papers, steps through the core argument of his relativity paper, and then discusses the reception (and adoption) of special relativity.
I had been digging more and more into the history of special relativity, mostly to understand exactly what Einstein's arguments were. This was motivated by conversations with a few friends where the question was broadly raised, "why does relativity apply to rockets and particles and things like this, when the paradoxes that led to relativity were about light and electricity and magnetism? Why isn't it just a 'light thing' ?" I recalled that once a professor mentioned in passing that relativistic length contraction and time dilation were just features of "how we measure things", perhaps meaning that they were not "real" in some sense. That never sat quite right with me, either.
Specifically, the introduction of special relativity feels different because it seems to start by considering kinematics and electromagnetism, and ends by revolutionizing our understanding of space and time. How do you make the leap from the specific to the more general? How do classical physics and modern physics describe velocity, space, and time? Is it true that special relativity means that all motion truly is relative and absolute spacetime does not exist, and how does this all relate to Galilean invariance?
Newton famously argued for absolute space and time (although a modern understanding of Newtonian mechanics is that it doesn't require them). If you believe in absolute space and time*, then you believe there is a sense in which you really truly are moving, or are really truly at rest. If that is the case, then every object in the universe comes equipped with an absolute velocity, v, that exists just as surely as the object itself exists. Your laws of physics can depend on this v, meaning the fundamental equations can include v as a variable.
Does absolute space mean that we dispense with notions of relative velocity? Definitely not: all velocity has to be defined relative to some frame of reference. Absolute space means that the "true" velocity is the velocity relative to the absolute space frame. In this sense, any frame of reference moving relative to this absolute space is a mathematical convenience, but strictly speaking unnecessary. You may as well only ever work (write equations, etc.) in the reference frame of absolute space. Absolute space picks out one particular inertial reference frame as of special importance, and (essentially) discards the rest (although you are still free to use them).
Let's examine the contrasting position, that absolute space and time is not real. In this case, there is no such thing as an object's "absolute velocity." There is no meaningful sense in which something "really is" at rest, or truly moving. The laws of physics cannot depend on your absolute velocity at all: if they did, then they could predict physically different outcomes depending on your velocity, and then your absolute velocity would have experimentally-testable consequences.
Instead, all inertial reference frames are equal when there is no absolute space and time. None is picked out as "the real reference frame of physics." The equations of physics are necessarily written the same way in every inertial reference frame, meaning the equations themselves have to be invariant under Galilean transformations. Any frame of reference is as good as any other, so long as they're all moving at constant velocities relative to one another. Velocity is only meaningful within a given frame of reference.
Newton's laws of motion do not include "v" anywhere. Therefore, they never lead to a testable prediction that tells you how fast you're "really moving." You can describe how fast you're moving relative to other things in the universe, but Newton can pick none of them out as "actually moving" or "actually at rest".
Maxwell's equations do include "v". The Lorentz force acting on an electron moving through a magnetic field depends on the velocity of the electron. An electron that is not "really moving" does not experience the same force. Maxwell also unambiguously predicts a velocity as well. Included among the solutions to Maxwell's equations are descriptions of a wave traveling through empty space with a velocity fixed by fundamental constants.
Velocity relative to what then, the magnetic field? A field has a universal reference frame now? Okay, that's the aether. In this way, the aether frame is epistemologically equivalent to Newton's imagined absolute space. The laws of physics are written relative to one frame of reference in particular. Not many equivalent inertial frames: just one.
Now, since Galilean invariance is violated, then "v must be real", meaning there ought to be measurable differences between when you are "really moving" and "really at rest" that would let us "see" v. But even though Maxwell's E&M describes a magnet and conductor in relative motion in two completely different ways depending on if the magnet or the conductor is "really moving", it still always works out to predict the exact same net force, i.e. the outcome is always experimentally identical. Therefore, there is no way to use the measurable properties of inductance to tell whether the magnet or the conductor "really is" moving, although Maxwell assures us that one of them is! This is strange and disconcerting. (Einstein said that "this was enough" to lead him to special relativity).
Secondly, if "v is real", then we ought to be able to measure our v, i.e. detect our motion relative to the aether frame. If c is a constant relative to the aether frame, then it should be a simple matter to measure the apparent speeds of light in various directions (i.e. the speed of light relative to us) and use this to determine our velocity relative to the aether. That velocity, being real, has real consequences for the speed with which we see the light travel through the vacuum. But, repeated experiments gave consistently negative results here, as well. Nobody was ever able to measure a velocity relative to the aether.
So we have broken Galilean invariance in order to have Maxwell's equations, but the main profit we expect from this symmetry breaking (the existence of absolute velocity) has failed to materialize, neither in making predictions about inductance, nor in an ability to measure v. It turns out that we must believe "v is really real" while also believing we can never measure it and v behaves for all intents and purposes as though it isn't real.
Lorentz tried to salvage this situation. He had the best formalism of Maxwell's laws at the time. He analyzed the kinematics of electromagnetism by the creation of "purely mathematical" transformations of frame of reference that changed time coordinates, and explained the non-detection of v by hypothesizing a further physical ad-hoc theory: matter is physically compressed when traveling relative to the aether, and it just so happens that this compression exactly cancels the relative travel-time difference so that the relative motion is undetectable. This plasters over the Michelson-Morley non-detection to order v^2/c^2, and it seems he had offered a completely separate explanation for non-detection to order v/c (via other experiments) as well.
Clearly this situation is untenable. But what made Einstein's solution so clearly correct?
1. He started from operative definitions of space and time, and distant synchrony. This removed all ambiguity about the epistemological and physical content of the theory, did away with Lorentz's weird and ambiguous "purely mathematical" reference frames, and gave explicit physical meaning to the coordinates.
2. Even though Maxwell violates Galilean relativity, its strange and suggestive asymmetry in the description of inductance, together with the non-detection of motion relative to aether cried out for Galilean invariance: it seemed that there was no measurable way in which "v" is real, even though the equations depended on v. This suggests that there is a way to rewrite the equations from a new perspective that would remove v while still being consistent in every way with experiment.
3. Einstein showed how all of Lorentz's results followed from, i.e. could be derived from, a much simpler pair of axioms, removing the additional ad-hoc physical hypothesis of contraction. This alone would have been a very interesting result about any other theory whatsoever, and usually by itself is sufficient for theorists to ascribe reality to the new axioms.
4. Einstein understood that there was no point in "mechanizing" electromagnetism (explaining the aether as a universal fluid or series of springs or whatever) nor "electromagnetizing" mechanics (explaining matter as purely aether phenomena of some sort) because his previous 1905 papers starkly showed the limits of the existing theories of matter and electromagnetism (Brownian motion and Planckian blackbody, respectively), opening the door for completely new physics at the microscopic level (quantum mechanics, although it was barely suspected at the time). Einstein had realized that neither branch of physics could truly be fundamental, so could not furnish the basic ingredients of the unified physics, and he was ready to start clean with a new "theory of principles".
From here, the general current of modern physics becomes more and more concerned with this basic interplay of symmetry, invariance, and identity.
*strictly speaking, "absolute space" could mean several things. it could mean there is a sense your x coordinate "really is 0" or "really is 10". the equivalent relativization here is the removal of the origin, and restricting to affine geometry. For the simplicity of this review, we can take it to mean an "absolute frame of reference."
I had been digging more and more into the history of special relativity, mostly to understand exactly what Einstein's arguments were. This was motivated by conversations with a few friends where the question was broadly raised, "why does relativity apply to rockets and particles and things like this, when the paradoxes that led to relativity were about light and electricity and magnetism? Why isn't it just a 'light thing' ?" I recalled that once a professor mentioned in passing that relativistic length contraction and time dilation were just features of "how we measure things", perhaps meaning that they were not "real" in some sense. That never sat quite right with me, either.
Specifically, the introduction of special relativity feels different because it seems to start by considering kinematics and electromagnetism, and ends by revolutionizing our understanding of space and time. How do you make the leap from the specific to the more general? How do classical physics and modern physics describe velocity, space, and time? Is it true that special relativity means that all motion truly is relative and absolute spacetime does not exist, and how does this all relate to Galilean invariance?
Newton famously argued for absolute space and time (although a modern understanding of Newtonian mechanics is that it doesn't require them). If you believe in absolute space and time*, then you believe there is a sense in which you really truly are moving, or are really truly at rest. If that is the case, then every object in the universe comes equipped with an absolute velocity, v, that exists just as surely as the object itself exists. Your laws of physics can depend on this v, meaning the fundamental equations can include v as a variable.
Does absolute space mean that we dispense with notions of relative velocity? Definitely not: all velocity has to be defined relative to some frame of reference. Absolute space means that the "true" velocity is the velocity relative to the absolute space frame. In this sense, any frame of reference moving relative to this absolute space is a mathematical convenience, but strictly speaking unnecessary. You may as well only ever work (write equations, etc.) in the reference frame of absolute space. Absolute space picks out one particular inertial reference frame as of special importance, and (essentially) discards the rest (although you are still free to use them).
Let's examine the contrasting position, that absolute space and time is not real. In this case, there is no such thing as an object's "absolute velocity." There is no meaningful sense in which something "really is" at rest, or truly moving. The laws of physics cannot depend on your absolute velocity at all: if they did, then they could predict physically different outcomes depending on your velocity, and then your absolute velocity would have experimentally-testable consequences.
Instead, all inertial reference frames are equal when there is no absolute space and time. None is picked out as "the real reference frame of physics." The equations of physics are necessarily written the same way in every inertial reference frame, meaning the equations themselves have to be invariant under Galilean transformations. Any frame of reference is as good as any other, so long as they're all moving at constant velocities relative to one another. Velocity is only meaningful within a given frame of reference.
Newton's laws of motion do not include "v" anywhere. Therefore, they never lead to a testable prediction that tells you how fast you're "really moving." You can describe how fast you're moving relative to other things in the universe, but Newton can pick none of them out as "actually moving" or "actually at rest".
Maxwell's equations do include "v". The Lorentz force acting on an electron moving through a magnetic field depends on the velocity of the electron. An electron that is not "really moving" does not experience the same force. Maxwell also unambiguously predicts a velocity as well. Included among the solutions to Maxwell's equations are descriptions of a wave traveling through empty space with a velocity fixed by fundamental constants.
Velocity relative to what then, the magnetic field? A field has a universal reference frame now? Okay, that's the aether. In this way, the aether frame is epistemologically equivalent to Newton's imagined absolute space. The laws of physics are written relative to one frame of reference in particular. Not many equivalent inertial frames: just one.
Now, since Galilean invariance is violated, then "v must be real", meaning there ought to be measurable differences between when you are "really moving" and "really at rest" that would let us "see" v. But even though Maxwell's E&M describes a magnet and conductor in relative motion in two completely different ways depending on if the magnet or the conductor is "really moving", it still always works out to predict the exact same net force, i.e. the outcome is always experimentally identical. Therefore, there is no way to use the measurable properties of inductance to tell whether the magnet or the conductor "really is" moving, although Maxwell assures us that one of them is! This is strange and disconcerting. (Einstein said that "this was enough" to lead him to special relativity).
Secondly, if "v is real", then we ought to be able to measure our v, i.e. detect our motion relative to the aether frame. If c is a constant relative to the aether frame, then it should be a simple matter to measure the apparent speeds of light in various directions (i.e. the speed of light relative to us) and use this to determine our velocity relative to the aether. That velocity, being real, has real consequences for the speed with which we see the light travel through the vacuum. But, repeated experiments gave consistently negative results here, as well. Nobody was ever able to measure a velocity relative to the aether.
So we have broken Galilean invariance in order to have Maxwell's equations, but the main profit we expect from this symmetry breaking (the existence of absolute velocity) has failed to materialize, neither in making predictions about inductance, nor in an ability to measure v. It turns out that we must believe "v is really real" while also believing we can never measure it and v behaves for all intents and purposes as though it isn't real.
Lorentz tried to salvage this situation. He had the best formalism of Maxwell's laws at the time. He analyzed the kinematics of electromagnetism by the creation of "purely mathematical" transformations of frame of reference that changed time coordinates, and explained the non-detection of v by hypothesizing a further physical ad-hoc theory: matter is physically compressed when traveling relative to the aether, and it just so happens that this compression exactly cancels the relative travel-time difference so that the relative motion is undetectable. This plasters over the Michelson-Morley non-detection to order v^2/c^2, and it seems he had offered a completely separate explanation for non-detection to order v/c (via other experiments) as well.
Clearly this situation is untenable. But what made Einstein's solution so clearly correct?
1. He started from operative definitions of space and time, and distant synchrony. This removed all ambiguity about the epistemological and physical content of the theory, did away with Lorentz's weird and ambiguous "purely mathematical" reference frames, and gave explicit physical meaning to the coordinates.
2. Even though Maxwell violates Galilean relativity, its strange and suggestive asymmetry in the description of inductance, together with the non-detection of motion relative to aether cried out for Galilean invariance: it seemed that there was no measurable way in which "v" is real, even though the equations depended on v. This suggests that there is a way to rewrite the equations from a new perspective that would remove v while still being consistent in every way with experiment.
3. Einstein showed how all of Lorentz's results followed from, i.e. could be derived from, a much simpler pair of axioms, removing the additional ad-hoc physical hypothesis of contraction. This alone would have been a very interesting result about any other theory whatsoever, and usually by itself is sufficient for theorists to ascribe reality to the new axioms.
4. Einstein understood that there was no point in "mechanizing" electromagnetism (explaining the aether as a universal fluid or series of springs or whatever) nor "electromagnetizing" mechanics (explaining matter as purely aether phenomena of some sort) because his previous 1905 papers starkly showed the limits of the existing theories of matter and electromagnetism (Brownian motion and Planckian blackbody, respectively), opening the door for completely new physics at the microscopic level (quantum mechanics, although it was barely suspected at the time). Einstein had realized that neither branch of physics could truly be fundamental, so could not furnish the basic ingredients of the unified physics, and he was ready to start clean with a new "theory of principles".
From here, the general current of modern physics becomes more and more concerned with this basic interplay of symmetry, invariance, and identity.
*strictly speaking, "absolute space" could mean several things. it could mean there is a sense your x coordinate "really is 0" or "really is 10". the equivalent relativization here is the removal of the origin, and restricting to affine geometry. For the simplicity of this review, we can take it to mean an "absolute frame of reference."
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