|HPS 0410||Einstein for Everyone|
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John D. Norton
Department of History and Philosophy of Science
University of Pittsburgh
This chapter continues the discussion of the last chapter on morals that we might try to draw from special relativity. This chapter collects morals that pertain to the nature of scientific theories, the concepts they use and how we can have evidence for them.
Einstein eliminated the ether from physics since there were no observable circumstances in which our motion through it could be revealed. This is compatible with a verificationist approach to all propositions. According to it, a proposition is meaningless unless there are circumstances conceivable under which it could be proven true (verified) or at least confirmed.
|Einstein's establishment of special relativity has been judged by many to embody the core insight of a strong movement in philosophy from the earlier part of the 20th century. Hans Reichenbach was a German philosopher who learned relativity theory from Einstein in Berlin in the 1910s and became one of his principal, philosophical interpreters. He wrote in his contribution to the 1949 volume Albert Einstein: Philosopher-Scientist, which celebrated Einstein, in his chapter "The Philosophical Significance of the Theory of Relativity" (pp. 290-91) [with my added paragraph breaks]:|
"To advocate the philosophical significance of Einstein's theory, however, does not mean to make Einstein a philosopher; or, at least, it does not mean that Einstein is a philosopher of primary intent. Einstein's primary objectives were all in the realm of physics.
But he saw that certain physical problems could not be solved unless the solutions were preceded by a logical analysis of the fundamentals of space and time, and he saw that this analysis, in turn, presupposed a philosophic readjustment of certain familiar conceptions of knowledge.
The physicist who wanted to understand the Michelson experiment had to commit himself to a philosophy for which the meaning of a statement is reducible to its verifiability, that is, he had to adopt the verifiability theory of meaning if he wanted to escape a maze of ambiguous questions and gratuitous complications.
It is this positivist, or let me rather say, empiricist commitment which determines the philosophical position of Einstein. It was not necessary for him to elaborate on it to any great extent; he merely had to join a trend of development characterized, within the generation of physicists before him, by such names as Kirchhoff, Hertz, Mach, and to carry through to its ultimate consequences a philosophical evolution documented at earlier stages in such principles as Occam's razor and Leibniz' identity of indiscernibles."
Reichenbach's analysis depends upon comparing Einstein's view with that of his contemporaries:
|Two theories in 1905||Einstein's special theory of relativity||H. A. Lorentz's electron theory|
|Agreed on what could be observed||moving rods contract, moving clocks slow, ..., no observably distinguishable state of rest.||moving rods contract, temporal processes of moving bodies slow, ..., no observably distinguishable state of rest.|
|Disagreed on the unobserved things posited by theory||no such thing as an ether with a preferred ether state of rest||Motion through
the ether with respect to its preferred state of rest causes rods to
contract and clocks to slow, etc.
They do so in just the right amount to prevent us distinguishing which inertial state of motion coincides with rest in the ether.
One sees in this comparison the essential intuition that guides Reichenbach's analysis: something seems to be wrong with Lorentz's theory. It has an extra element, the ether with its state of rest, that is not present in Einstein's theory, even though both theories make the same prediction.
|The elusive nature of this ether state of rest and Einstein's reaction to it was later captured in the slogan "the difference that makes no difference is no difference." That slogan seems to capture an obvious and simple view.||To illustrate the idea, imagine that I insist that there are pixies in the mountains, but that you will never see them, no matter how hard you search, since they hide perfectly behind the trees whenever you come near. You would surely doubt my assurance and properly suspect that there really are no pixies in the mountains. If their presence leaves no observable trace, my insistence that they really are there looks like a delusion.|
What about the pixies in the mountains? We would no longer have to worry about whether they are really there. For the positivist, a proper theory of living beings in the mountains would only include a register of what we have seen. There would be no pixies since there are no experiences associated with them.
|Reichenbach located Einstein's thought in a
tradition that was built around the intuition captured in this slogan.
The doctrine of positivism was August Comte (1789-1857) and Ernst Mach
(1838-1916). One of its central ideas was that a theory in science is
nothing more than a compact summary of
For example, Galileo noted that, on many occasions, the distance a body fell in times 1, 2, 3, ... was proportional to the square of these times 1, 4, 9, ... He then announced his law of fall, that the the distance of fall is proportional to the square of the time. All he was announcing was a compact summary of these experimental results.
In so far as our assertions in science go beyond these compact summaries they are disparaged as idle metaphysics.
|The central themes of positivism were picked up and developed in the 1920s by a tradition that came to be known as logical positivism. It added to positivism a serious engagement with the use of the machinery of formal logic. The hope was that formalizing language by its machinery would reduce all disagreement to issues that could be settled by its precise techniques. Its leading figures took Mach as their patron spirit and met in Vienna as the celebrated "Vienna Circle," with leading members including M. Schlick, R. Carnap, O. Neurath and F. Waismann. A comparable movement developed in Berlin under Hans Reichenbach and used the label "logical empiricism."||For example, imagine that I insist that the latest
sage of my favorite cult is immortal. You disagree and think he is
mortal. We resolve our dispute by finding premises on which we agree.
You might check whether I agree that 1. All men are mortal; and 2. The
sage is a man. If so, then logic forces the conclusion that 3. The sage
is mortal. And if we don't agree on these premises, we just move things
back a step and see what grounds them.
The logical structure of arguments can be represented symbolically:
1. If A then B. 2. A. 3. Therefore B.
So the hope was that this entire procedure of resolution could be conducted symbolically.
Its core slogan was initially formulated by Friedrich Waismann in 1930 and then developed by Carnap, Schlick and Neurath. It is the "verifiability principle" according to which
"The meaning of a proposition is the means of verification."
where verification is just the demonstration of the proposition's truth.
|At first, the principle seems to make no sense. How can the meaning of something be a "means," that is, a way of doing something. The meaning of the proposition "There are three marbles in the box," one would think, is just what the proposition says: somewhere there is a box and it has three marbles in it. The means of verification of the proposition is something different. It is whatever technique we may use to locate the box, open it and count up the marbles inside.||
One of the famous hoax photos of the Cottingley fairies, taken in 1917. They fooled Sir Arthur Conan Doyle, author of the Sherlock Holmes stories.
|Odd as this definition is, the motivation for it becomes immediately clear if we apply it to the problem cases we've been looking at. Take the proposition "there are exactly three pixies in the mountains." We have seen that there is no means of verifying this. So the verifiability principle immediately gives us a comfortable result. The proposition has no meaning.|
So a more straightforward version of the principle makes this interest in the meaningfulness of propositions directly apparent. It asserts:
A proposition is meaningful if and only if it is possible
--to verify or falsify it (strong version)
--confirm or disconfirm it (weak version).
To verify or falsify is to demonstrate truth or falsity. Finding that an electron has negative charge falsifies the proposition that all electrons are uncharged. But it does not verify it since it is still possible that other electrons have no charge. To confirm or disconfirm is to display evidence that increases or decreases the probability of the proposition. So the finding of an electron with negative charge confirms to some small degree that all electrons have negative charge.
Public domain image from http://www.wpclipart.com/tools/hammer/mallet/mallet.png.html
The verifiability principle demonstrated great power to cut off long standing philosophical disputes. Proposition after proposition fail the principle's test. So they are judged meaningless--well disguised forms of babble--and thus no longer worthy of philosophical scrutiny and debate. Here are examples of propositions all beaten to meaninglessness by the cudgel of the verifiability principle.
Reality is spiritual.
The moral rightness of an action is a non-empirical property.
Beauty is significant form.
God created the world for the fulfillment of his purpose.
(These from the Encyclopedia of Philosophy.)
What distinguishes live from dead matter is more than
chemistry; it is the presence of a life force.
Against this background, one can see immediately why Reichenbach could mount such enthusiasm for Einstein's work in special relativity. Typical applications of the verifiability principle are located in long standing philosophical debates. But here is Einstein using reasoning in a signal scientific breakthrough that looks just the same.
Take the proposition: there is an ether with a unique state of rest. What Einstein found in developing his special theory of relativity was that no observation could distinguish it. So Einstein banished it from physics--and, Reichenbach in effect notes--with essentially the same reasoning as led the logical positivists to discard the spirituality of reality and life forces.
Some of you may notice notice a similarity with these ideas and Karl Popper's celebrated analysis of what it is to be scientific. While Popper energetically defended his priority and creativity, it is not hard to see that his formulation is a minor variation of the logical positivists' views. Where they say to be meaningful is to be verifiable or falsifiable, Popper says that to be scientific is to be falsifiable. In retrospect, these are small differences that only a true zealot could muster the energy to debate fiercely.
There is a lot that is right in
this approach. Einstein found a circumstance in which something was claimed to
exist (an ether state of rest) while at the same time our best theories
predicted that we could never detect it. Such a circumstance ought to be
troubling and signal to us that something has gone seriously awry in our
theorizing. We have created a physical notion that is by construction shielded
from all possibility of physical test.
However I also believe that the verificationists went too far. They urged not just that the proposal for things like the ether state of rest was defective. They urged that it was meaningless. That goes too far. The proposition "There is an ether state of rest." is judged by them to be meaningless blather, cognitively equivalent to a grunt or a drool. Surely the proposition is perfectly meaningful--we understand just what it says and presumably so did Einstein. The problem, as I suggested above, is that we have no good reason to believe it. Our best judgment would be to say it is probably false.
By recognizing that the meanings of all concepts are fixed solely by the operations needed to verify them, we avoid smuggling arbitrary preconceptions into our conceptual systems that may prevent us learning new things from experience.
|Percy William Bridgman (1882-1961) was a Nobel prize winning, experimental physicist who also wrote about scientific methodology, especially in his 1927 Logic of Modern Science. He believed that one could learn an important moral about the nature of concepts in scientific theories by attending to what Einstein did. Here is his review of what Einstein did and the morals we should draw from them.|
|What Einstein did||Bridgman's moral|
|Einstein learned the principle of relativity and the light postulate.||New experience is always possible|
|Einstein could not initially accept them. They appeared irreconcilable because of Einstein's tacit, but erroneous, presumption of absolute simultaneity.||We may not be able to accommodate new experience in our conceptual system because of false presumptions hidden in it.|
|Einstein defined the concept of simultaneity through operations with light signals and revealed the falsity of the presumption of absolute simultaneity.||If we define all our concepts operationally, we purge our conceptual system of harmful, false assumptions.|
|Einstein's revised concepts of space and time are now able to accept new experiences, including relativistic length contraction and time dilation.||Our conceptual
system is now prepared for new experiences.
In sum, Bridgman's goal was to revise our system of concepts so that we might never again face a revolution triggered by concepts that had false presumptions buried in them. Had we realized that different operations are used to measure the length of moving bodies and the length of resting bodies, we might have been prepared for the possibility that the two might not be the same. He proclaimed:
"We must remain aware of these joints in our conceptual system if we hope to render unnecessary the services of the unborn Einsteins."
Bridgman used the length of a rod as a way of illustrating his basic idea. Before operationalism, we just talked of the length of a rod, assuming that there is just one length for it. So we were ill-prepared to learn that moving rods have a length different from rods at rest.
Bridgman presumed that a concept was meaningful just up to the operations used to determine it. That meant that if different operations were used, one had different concepts. So we might measure lengths by repeatedly laying out of rulers; that would give one notion of length--call it the "ruler length." Or we might measure length by an operation that times light signals; that would give another notion--call it "light length."
Had we attended to the operations used to measure the length of a rod, we would have realized that different operations are used to measure the length of a rod at rest and the length of a moving rod. That means they are different concepts and, in principle, may have different values. We are prepared for the possibility of different values, which turns out to be the result relativity delivers.
Bridgman formulated his operationism is a way similar to the
His central claim was:
"In general, we mean by any concept nothing more than a set of operations; the concept is synonymous with the corresponding set of operations."
It does seem peculiar to say that a concept is a set of operations and the idea does not seem very attractive now. What made it attractive to Bridgman is that it immediately gave him the results he wanted. If two quantities are measured by different operations, then their concepts are automatically different. And if we have a quantity, such as our velocity through the ether, that no operation can measure, then there is no physical basis for concept. It is an illicit concept as far as proper physical theorizing is concerned.
Once again there is something
right and important in Bridgman's ideas. If we have a concept,
especially a quantitative one, but no clear idea of the operations needed to
fix it or its magnitude, we may have something defective in our concept. This
is a warning that must be heeded.
What is wrong about Bridgman's system is that it is too strict. We may well avoid being surprised again by a
false assumption buried in some concept if we become operationists. But, as
Hempel pointed out, the cost will be that science becomes unworkable. Every
distinct operation will yield a new concept. Even rest length would cease to be
single concept; there would be as many variants as ways we can devise to
measure it: ruler length, light length, ruler length measured on Wednesdays;
ruler length with steel rulers; ruler length with brass rulers; etc. Our
theories would need to leave open the question as to whether each of these are
For better or worse, a workable science must presume, even if provisionally, that the different operations are measuring the same concept.
Image sources: http://en.wikipedia.org/wiki/File:Galileo_Thermometer_24_degrees.jpg http://en.wikipedia.org/wiki/File:Clinical_thermometer_38.7.JPG http://en.wikipedia.org/wiki/File:Backofenthermometer.jpg http://en.wikipedia.org/wiki/File:Irthermo.png
Einstein's rejection of Lorentz's ether based electrodynamics in favor of a novel theory of space and time is a paradigm example of the appropriate use of evidence.
The simplest form of this idea has already been developed in the context of the verificationist moral. Objects moving and at rest in the ether differed in their relation to the ether state of rest. But it was a difference that made no difference. So we had good reason to believe that there really was no difference.
That is, the invisibility of the ether state of rest is simply good evidence that there is no ether state of rest.
Recent work has brought to light a stronger way of understanding how Einstein used what he found as evidence. Recall the difference between Einstein and Lorentz' theories:
|There is an ether state of rest, but all matter shrinks, all processes slow, etc., so as to make it invisible. Every theory of matter must predict these processes to assure this invisibility.||Space and time are such that lengths shrink and clocks slow with motion. Every theory of matter must predict this since every theory of matter is about substances that reside in the one space and time.|
Lorentz' theory depends on what, in retrospect, seems to be an extraordinary coincidence. Maxwell's electrodynamics predicts the length contraction and time dilation effects and so must every theory of every other form of matter.
Einstein's theory requires no such coincidence. Space and time are the way they are--as described in relativity theory. That explains why every theory of matter must predict these effects.
So Einstein's theory explains better because it posits fewer arbitrary coincidences and therefore is better supported by the evidence of these effects. To use a notion pioneered by Wes Salmon, we might may that the spacetime is the single, common cause of these effects in all matter theories. Or, to use the expression preferred by Michel Janssen, who has developed these ideas, Einstein displayed a common origin for all these effects. So he calls the related inferences "COIs"--common origin inferences.
That we find common origins to explain better and so to be better supported by evidence is really a commonplace. Imagine that there is suddenly a series of burglaries in an otherwise quiet street. We are much more likely to infer to a common cause--one burglar robbing repeatedly--than to many independent causes--many burglars who by chance all happen to be robbing at the same time.
|Another illustration is closer to the case of special relativity. Imagine a darkened hallway. We notice that everyone walking down the hallway, from either direction, stumbles at the same place in the dark. We could give a "Lorentzian" explanation that every person is somehow constituted so that they all happen to stumble at exactly this same spot. This makes the stumbling into an unexplained coincidence.
Or we could give a "Einsteinian" explanation that there is a fold in the carpet and that everyone trips over just this one fold in the dark. Then the people become probes of the surface of the hall, just as matter probes the background structure of spacetime. The probes all report that there is something to trip over at the same place in the hall, just as all matter reports a Minkowskian structure for spacetime.
|These inferences also appear throughout science. A famous example is Copernicus' inference that the earth moves. He noted that the motion of the outer planets, Mars, Jupiter and Saturn, when viewed from the earth, each had a wobble superimposed upon them. What was curious about the wobbles was that they were perfectly synchronized with each other and also the motion we see for the sun around the earth. He inferred that the apparently coincidental synchronization of the wobble has a common origin. The earth was really moving around the sun and the wobble was merely the superimposition of our motion on the planets.||The situation is not so different from what someone on a pogo stick might see. Everything around them is jumping up and down in synchronized bounces. Of course all they are really seeing is the superimposition of their own bouncing on the things around them.|
Copyright John D. Norton. February 2001; October 2002; July 2006; February 2, 13, September, 23, 2008; February 1, 2010; January 11 February 2,, 2013.