|HPS 0410||Einstein for Everyone|
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John D. Norton
Department of History and Philosophy of Science
University of Pittsburgh
Special relativity has changed our understanding of the nature of space, time, energy and other physical quantities. There is a very widespread feeling that the advent of special relativity has somehow changed the way we look at things in a sense that goes beyond these narrow physical results. What might that sense be?
The problem in answering is that there is scarcely a viewpoint or movement in modern philosophical thought that does not claim support in one way or another from Einstein's achievement. Clearly they cannot all be right. Quite often radically opposed viewpoints claim support from Einstein's achievement. In the end it is up to you to decide, since the issue remains controversial. You should use your knowledge of Einstein's theory and the circumstances surrounding its emergence to assist you.
Deciding what this significance might be is a philosophical
problem of no small interest. It must be resolved by the standard methods of philosophical analysis. These methods
are simple to describe and not so difficult to learn. To begin, we need to keep
two notions in mind:
|Critical analysis of the positions laid out then merely consists in checking that each of these elements is implemented properly. We would check that the thesis is clearly formulated. We could check that the premises of the arguments used are true. We would check that the steps of the arguments are valid; that is, that they conform to the canons of good reasoning.
These requirement concerning thesis and argument are easy to state and look rather simple to satisfy. That is true as long as the problems dealt with are themselves easy. However once we start to entertain the traditionally intractable problems of philosophy, holding to them can be come quite demanding. Success at it may be a significant achievement and the best work in philosophy is distinguished by its success in holding to them in adverse circumstances.
|What is meant by "logic forces"? I just mean that the
inference from X, Y and Z to C is a valid argument, where "argument"
means what it means in any introductory logic class. If you haven't had
such a class, you should. It will help you clarify your thinking a
great deal. There you will learn than an argument is not a shouting match. It is a sequence of
propositions. A valid argument is one in which each proposition
of the sequence is either introduced as a premise or inferred from
propositions earlier in the sequence.
A valid deductive argument is one in which the truth of the premises necessitates the truth of conclusions inferred.
1. All men are mortal. (Premise)
2. Socrates is a man. (Premise)
3. Socrates is mortal. (Inferred from 1.,2.)
is a valid argument since, if premises 1. and 2. are true, then the conclusion 3. must also be true.
A valid inductive argument is one in which the truth of the premises make the conclusion very likely to be true (or, sometimes, merely lend support to the truth of the conclusion). For example:
1. Most elephants are gray. (Premise)
2. Jumbo is an elephant. (Premise)
3. Jumbo is gray. (Inferred inductively from 1., 2.)
is a valid inductive argument.
Our goal is to take something that is puzzling, vague and elusive and make it precise and definite. If we do it right, the resolution of the puzzle should seem so straightforward that we wonder why it ever seemed otherwise.
The obvious candidate is just the basic content of the theory itself. It tells us some pretty surprising things about space and time and the matter they contain: that c is a fundamental barrier to all motions; that moving clocks slow; that simultaneity is relative; that energy and mass are equivalent; and so on. In so far as a perennial problem of philosophy has been to discern the nature of space and time, this is a reasonable answer. However it is usually thought that the advent of relativity somehow changed something fundamental, perhaps in how we see ourselves in the universe, or, more narrowly, in how we conduct our scientific investigations of that universe. Our quest is for morals of that type.
This and the next two chapters will describe some candidate morals of this broader type. I will give you my reaction to them to give you an example of how these claims may be analyzed and also to let you know what I think. Do you agree? Make up your own mind and you proceed. Your decision will be reported in the assignment.
This chapter will develop skeptical morals.
Relativity shows us that we cannot expect our common sense ideas about the physical world to be reliable.
Here is a reconstruction in terms of thesis and argument.
Thesis: Common sense is an unreliable guide to truth.
1. If common sense is a reliable guide to truth, then it will not assure us of falsehoods. (Premise)
2. Common sense assures us that well-made rods and clocks are unaffected by their motion. (Premise)
3. Relativity tells us that well-made rods and clocks shrink and slow when they are moving. (Premise)
4. Common sense assures us of falsehoods. (From 2., 3.)
5. Common sense is not a reliable guide to the truth. (From 1., 4.)
On its face, this is acceptable. This claim is clear enough. The argument employs true premises and valid inferences. Informally, we had commonsense ideas about rods, clocks, simultaneity and more. We believed them because they seemed, well, commonsensical. Relativity showed that they were incorrect. Therefore commonsense ideas are untrustworthy, or at least on some occasions.
While the thesis and argument are acceptable, the view is oversimplified and the oversimplification is misleading.
It suggests that we needed relativity theory to tell us that common sense is unreliable. Anyone who has ever attended to developments in science will find numerous examples of science revealing the fragility of commonsense ideas. Copernicus did just that to our commonsense idea that we are at rest; he showed that we hurl through space at great speed in space, spinning all the while.
More seriously, the implicit assumption is that science and common sense are opposed. That is, they are two distinct ways that we know about the world. They are not distinct. There is an important connection between scientific breakthroughs and common sense.
Here's a list of things that we know through commonsense:
cannot fall down.
Cows cannot jump over the moon.
The earth is spherical.
People venturing to the other side will not fall off.
The earth spins on its axis and orbits the sun.
Matter is made of atoms too small to see.
Nothing goes faster than light.
The items of the list become successively more sophisticated. Indeed inspecting them reveals that each item of today's commonsense is a major result of yesterday's science.
What this suggests is that there is no independent notion of a common sense idea that somehow sits outside what we know through systematic investigations. Rather commonsense is a by-product of those investigation. The broad acceptance of common sense ideas about our physical world is merely the final stage of absorption of the results of scientific investigation. That is why today's common sense is yesterday's scientific breakthrough.
From this we can infer a more subtle moral: there is a kind of reliability in common sense ideas since they are ultimately, though indirectly, grounded in something more solid. Rather than needing a blanket skepticism about common sense ideas, the real thing to guard against is common sense that does not keep pace with newer investigations.
For example, it still seems to be
a part of common sense that "airs" can be good for you. Don't we know of the
benefits of clear mountain air? Similarly the wrong "airs" were thought to be
unhealthy. The disease of malaria--literally "bad air" mal aria--was thought to
be caused by them. Of course we now know that malaria is really caused by
infection from mosquito borne parasites with the mosquitoes coming from swamps
that might also emit bad smells. So the idea of avoiding bad smelling places to
avoid the disease was right, but only indirectly.
Relativity shows us that even the best of our
theories--classical mechanics--are unreliable. Why should we believe any of the
theories of modern science? Should we not expect the Einsteins of tomorrow to
overturn them all?
Alchemist searching for the philosopher's stone that will convert base metals into gold.
Here is a reconstruction of the thesis and argument:
Thesis: All present scientific theories are false.
1. Relativity theory showed that classical Newtonian physics, an apparently secure theory, was false. (Premise)
2. This refutation is common: many apparently secure theories have subsequently been overturned by later theories. (Premise)
3. We should expect this pattern to continue. (Premise)
4. Our best scientific theories will eventually be overturned by new theories, if we persist in seeking new theories. (From 1., 2., 3.)
5. All present scientific theories are false. (From 4.)
The thesis is clear. The argument is also clear. Relativity
is just the latest of many instances of new science
overturning old theories we thought secure. So we should expect our latest
theories will eventually also be overturned, so don't believe them.
In my view this is a lamentable argument, defective because
it rests on false premises. Both 1. and 2. are false. Relativity theory did not wipe away all the physics that went before. The bulk of that physics stays intact. Classical physics only needs
relativistic corrections when we deal with velocities close to the speed of
light. In virtually all applications, from designing bridges to launching
Apollo astronauts, classical physics suffices. Premise 2. fails in the same way for other sciences.
The real pattern is that, once a science reaches some level of maturity, it becomes a fixture in the domains in which it was developed. The much publicized revolutions that eventually do arise supply adjustments outside of those domains. Here are some examples:
|Science||Maturity achieved||Where it eventually fails|
|Geometry||Ancient Greece, Euclid 3rd century BC||On cosmic scales|
|Solar system astronomy||Heliocentrism, Copernicus, Kepler, 16th and 17th century||Very precise measurements correct their predictions but leave the heliocentric layout intact.|
|Dynamics||Newtonian mechanics, 17th century||Domains of
very fast (special relativity)
very heavy (general relativity)
very large (relativistic cosmology)
very small (quantum theory)
There is a much more benign moral in all this: do not trust theories in domains remote from those in which they were devised. The persistence of the skeptical argument is a puzzle to me. It simply rests on defective history of science, yet it remains popular among many historians of science who should know better.
Einstein has shown us that the fundamental quantities of
physics are relative. Is this not a quite general moral? Is not what is true or
false or what is right or wrong relative to the individual? Should we not say
"Everything is relative"?
Here's the thesis and argument reconstructed:
Thesis: Everything is relative.
1. All quantities in relativity theory have a meaning only relative to an inertial frame or to an inertially moving observer. (Premise)
2. Relativity theory revealed that we were mistaken in our earlier belief in absolute quantities in physics. (Premise)
3. Other notions (truth, moral rightness) are like the quantities of physics.
4. The moral of relativity theory can be applied elsewhere. (1., 2., 3., by analogy)
3. Everything is relative. (From 1., 2., 3.)
Reconstructing the argument explicitly is already pretty damning. One sees that the moral is poorly drawn. Although it is obvious, let us spell out why.
First, the argument is invalid. It seeks to use an argument by analogy. (This is like that in some aspects; therefore this is like that in other aspects.) The analogy fails. That certain quantities in relativity
theory are relative to the observer or, better said, state of motion of the
observer, has no real bearing on whether there is
one true standard for the good or the morally right. The same
word--relativism--is used in all cases, but the similarity of meaning is so
superficial as not to allow success in one domain to carry to another.
Second, the first premise is false. It is not true in relativity theory that "everything is relativity". Only certain quantities are, albeit more that in classical physics. Some quantities are not relative. The simplest examples are the so-called "rest" quantities: rest mass, rest length etc. These are by definition the masses and lengths measured by a co-moving observer. They are characteristic properties of bodies and are of fundamental physical importance; (obviously) all observers must agree on their values. They are an absolute.
It is something of an accident of history to do with Einstein's way of thinking about relativity theory that we stress the "relative" aspect of the theory. In the more mathematical approach to the theory, what draws most attention is what is not relative, the so-called "invariants." So early in the history Einstein agreed with the great mathematician Felix Klein that a better name for the theory would have been "theory of invariants."
Working in that mathematical tradition, Hermann Minkowski,
who introduced the notion of spacetime, wrote in his 1908 lecture "Space and
"...the word[s] relativity-postulate for the requirement of an invariance with the group Gc seem to me feeble. Since the postulate comes to mean that only the four-dimensional world in space and time is given by phenomena, but that the projection in space and in time may still be undertaken with a certain degree of freedom, I prefer to call it the postulate of the absolute world (or briefly the world-postulate)."
Had history paid more attention to Minkowski's advocacy of the absolute world, might I now be lamenting the fallacy of inferring that "everything is absolute" from Einstein's theory?!
In the two chapters following, we will see more candidate morals described and analysed. The morals will not be displayed formally in terms of thesis and argument, as was done above. You should, however, remember that they are all to be held to the same standards of clarity of expression and cogency of argument. If thinking about them becomes troublesome, you should revert to the standard philosopher's questions:
What is the thesis? What is the argument?
Copyright John D. Norton. February 2001; October 2002; July 2006; February 2, 13, September, 23, 2008; February 1, 2010; February 10, 2013.