HPS 0410 Einstein for Everyone

Back to main course page

Philosophical Significance of the Special Theory of Relativity
What does it all mean?

John D. Norton
Department of History and Philosophy of Science
University of Pittsburgh

The Project

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.

The Method

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:

The thesis or claim.
Just what is it that is being claimed? This must be stated in as simple and clear a manner as possible. No real progress can be made until we know what this is in precise and unambiguous terms. Often merely finding the clear statement is an advance in itself.
The arguments that support the claim.
A thesis or claim by itself is only of so much value. What now matters is what reasons can be given to believe the claim. These reasons should be laid out in as cogent a form as possible. Typically these reasons will take the form of an explicit argument. To support a claim we might try to show that if you believe the widely accepted X, Y and Z, then logic forces you to accept the new claim C. Or the argument might be that if you fail to believe the thesis you will be caught up in some undesirable consequence, even an outright contradiction.
These two ideas 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.

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.

For a discussion of philosophical morals that can be drawn from relativity theory concerning space and time, see my paper PITT-PHIL-SCI00000138 on philsci-archive. Beware. The discussion is at a more advanced level than presumed in this class, so it is only for the adventurous.

Candidate Morals

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.

Here are 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.

1a. Skepticism about common sense ideas

Relativity shows us that we cannot expect our common sense ideas about the physical world to be reliable.

On its face this is acceptable. This claim is clear enough. The argument for it also takes no imagination to see. 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.


This argument is acceptable. The main part that I don't like is the suggestion that we needed relativity theory to tell us this. 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.

There is a more important connection between scientific breakthroughs and common sense,

Here's a list of things that we know through commonsense:

The sky 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 mosquitos 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.

1b. Skepticism about science

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.

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 a false premise: the idea that relativity theory simply wiped away all the physics that went before. It did not. 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.

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.

2. A General Relativism

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"?

all relativeall relative all realtive

all relative

This argument is defective. First, 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, 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 Time":
...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?!

3. Time is the fourth dimension

With the transition to relativity theory, we no longer conduct our physics in a three-dimensional space; we now employ the four-dimensional spacetime introduced by Minkowski.

This slogan "time is the fourth dimension" is a mischievous slogan, used, as far as I can tell, to intimidate novices. They are supposed to be awed by the apparent profundity of the claim while at the same time never being able quite to grasp its content at the insightful depth apparently accessible to the mischief making sloganeer. If you meet such a sloganeer, you should ask "what precisely do you mean?" Keep in mind the confusion favored by sloganeers sketched below and insist on a precise answer!

There is no interesting content to the claim. The problem lies in the vagueness of the statement of the thesis. There are two readings possible for it and neither yields results of importance.

In a trivial and true reading, we allow that space and time taken together form a manifold of four dimensions. What that just means is that four numbers are needed to locate an event in spacetime. Three of them are the usual spatial coordinates and the last is a time coordinate. That is true and was always true in classical physics as well. There is nothing of novel interest in this reading beyond the usual banalities about how things change with time. The idea that this sort of spatial representation of time is possible is as old as a pocket book calendar in which the passage of time is represented by a sequence of boxes or list of dates.

almanac almanac

There is a profound but false version of the slogan. What if time were a fourth dimension just like the three dimensions of space? That would be extraordinary. It mean that we could move about in the time dimension just as we move about in the space dimension. But time is not just like space in relativity theory. The theory keeps the timelike direction in spacetime quite distinct from the spacelike; the light cone structure does this quite effectively. So relativity theory contradicts this profound reading.

Underlying the profound reading is a simple fallacy. We note that in a spacetime formulation of relativity theory, time is usefully represented spatially in a diagram. So we can infer time must be like space in some aspects or this device would fail. It does not follow that time is like space in all aspects. Analogously, we can represent the spectrum of colors spatially with color wheels and rainbows. That does not mean that colors are spatial. Red is not the fifth dimension of space.

There is an interesting entanglement of space and time in relativity theory captured in the relativity of simultaneity. But the slogan of time as the fourth dimension is a defective and misleading way of expressing it.

4. Verificationism

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]: Reichenbach

"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.

Historical background to Verificationism

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 experience.

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."

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.

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.

Cottingley fairies
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.

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.

What is my view of all this?

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 judgement would be to say it is probably false.

5. Operationism (P.W.Bridgman)

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. Bridgman
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 verificationists.
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.

What is my view of this?

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 the same.

For better or worse, a workable science must presume, even if provisionally, that the different operations are measuring the same concept.

thermometer thermometer thermometer infrared thermometer
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

6. The use of evidence: common causes and common origins

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:

Lorentz Einstein
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.

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.

astronomical systems

7. Change is illusion

The relativity of simultaneity establishes that the future is as determinate as the past and present.


This moral is intended to negate a common sense idea we have about the future. It is the idea that the future is unresolved, whereas the present and past are or have happened and so are fixed. The notion is captured well enough by comparing the outcome of the last presidential election with the next. The outcome of the last election is known and fixed; it is a part of the determinate past. The outcome of the next election is open; it is a part of the indeterminate future.

We popularly imagine that the moment of the now advances through history converting the indeterminate possibilities of the future into the fixed actualities of the present and the determinate facts of the past.

pen writing

It is sometimes thought that merely employing a four dimensional spacetime in physics is already enough to overturn the idea that the future is indeterminate. For in a spacetime diagram, we see both past and present laid out as equally real. This argument is flawed. It depends essentially on confusing the reality of a picture of a thing with the reality of the thing. My diary has equally real squares in it for yesterday and tomorrow. We would not infer from that, that yesterday and tomorrow are equally real (or squares).

The argument from spacetime is also less relevant in the present context since spacetime could also be used with classical physics. So whatever moral we might get from it is equally available from classical physics. Putnam, Rietjdk and others have tried to use what is distinctive about the Minkowski spacetime of relativity theory, the relativity of simultaneity, to get a stronger result about the determinateness of the future. They combine the way the relativity of simultaneity tangles up future and past with two observers in relative motion to get the result.

In brief, their argument goes as follows. Consider some possible event in our future: will there be a blizzard next February 1? We can always find a position and motion for a possible observer who would in our present, judge next February 1 to be in his present. For that observer, whether or not there is a blizzard here on February 1 is a present fact--it is determinate. Since that is true now of that observer, should we not also assume that the blizzard (or otherwise) of next February 1 is determinate?

The figure shows the spacetime diagram that goes with the argument.


The argument is:

Earth observer:
Event "Spaceship now" is simultaneous with respect to event "Earth now."
Therefore Event "Spaceship now" is determinate with respect to event "Earth now."

Spaceship observer:
Event "Earth later" is simultaneous with respect to event "Spaceship now."
Therefore Event "Earth future" is determinate with respect to event "Spaceship now."

Event "Earth later" is determinate with respect to event "Earth now."

There are two weaknesses in the argument.

First, we must accept that simultaneity and determinateness go hand in hand. That is, we must accept that
  "Spaceship now" is simultaneous with respect to event "Earth now."
entails that
  "Spaceship now" is determinate with respect to event "Earth now."
I see no good reason to accept this. In part the problem is that I don't really know what "determinateness" is.

Second, it is not clear that determinateness is transitive. Transitivity is the property that allows us to chain together judgements of determinateness as is done in the little argument above. Again, whether it is admissible depends on what "determinate" means and I am unsure. Certainly simultaneity judgments from different observers cannot be chained together. We cannot infer that the events "Earth later" and "Earth now" are simultaneous. Why should it be different with determinateness

8. Causal Theory of Time (H. Reichenbach):

Einstein defined simultaneity in terms of a light signaling operation. We can generalize his procedure to define the nature of time in terms of signaling with any causal process. To say that "an event P is earlier than an event Q" simply means that it would be possible for some causal process to pass from P to Q.

Reichenbach here attempted to solve an old problem in philosophy, rather nicely expressed in a lament by Augustine:

"What, then, is time?
If no one asks me, I know:
if I wish to explain it to one that asketh,
I know not."

This traditional problem is already captured in the dictionary game. You want to know what time is? Look up the definition of time in the dictionary. And then look up the definition of the definition and soon enough you are back at time, in a closed circuit. There seems no, simple, non-circular way to finish the defining sentence "Time is..."

Definition of time
Definition of duration

Reichenbach Reichenbach's causal theory of time aims to solve this problem. It will complete the "Time is..." sentence with talk of causes. To be more precise, it looks at the time order of events, the notions of earlier and later. Just what does it mean to say that two events are separated in time? Reichenbach's answer is in terms of causal connectibility.

Event P is earlier than event Q just means that event P could causally affect event Q

by, for example, the transmission of a light or signal from P to Q.

The inspiration for this approach is Einstein's 1905 treatment of simultaneity. In Einstein's special theory of relativity, it is true that two events A and B are simultaneous if they are hit by light signals emitted at the same moment from their midpoint. Einstein turned this truth into a definition. Two events are defined as simultaneous if they could be hit by such light signals. That definition was the centerpiece of the first section of Einstein's paper.


Reichenbach extended this thinking to all the time relations between events, being before and being after. It is a truth that P is earlier than Q just if a causal signal could pass from P to Q. Reichenbach now proposed that this truth be a definition.

There is something important and right about the approach. We cannot allow notions like time to become too distant from the physical processes of the world. Special relativity has reminded us that our notions of time must respond to those processes and the physical theories that govern them. Time is deeply entangled with causation. We will see just how much more profound that entanglement is when we deal with the spacetimes of general relativity.

However, in my view, Reichenbach's approach goes too far. We do not just see the entanglement of space and time in his theory. We see the reduction of time order to causal order. Causation becomes the fundamental idea and time order is derived from it. The difficulty is that we end up with a primitive notion, causation, that we seem to understand less well than the thing we started with, time order. So now we must ask "what is causation?" We will have a harder time answering. Theories of the nature of causation remain diverse and controversial. (For my diatribe on causation see "Causation as Folk Science.") Time remains far less problematic; our theories of time are some of the best developed of all physics. A theory that reduces the less problematic to the more problematic seems to me to be most problematic.

My Picks

Everyone will find their own favorites, although it can be quite hard to make the selection. For what it is worth, here are my picks. They have actually mostly been embedded in the earlier critical discussion.

Common sense tracks the latest science. That is, common sense lags behind our latest science, which is very slowly incorporated into that nebulous "what everyone knows." Doesn't everyone now know that matter is made of atoms; or that the air is part oxygen and that oxygen is the bit that matters for our survival? Yet all this was once the most advanced science. The process seems to be continuing with special relativity. Many people somehow know that "nothing goes faster than light" but they are not sure where is comes from. The moral is not solely derived from special relativity, but special relativity does supply a nice instance of it.

Mature theories are very stable in the domains for which they were devised. They are fragile elsewhere. This is what I think should be learned from the long history of fragility of scientific theories, with the advent of special relativity an excellent example. While theories do not retain unqualified validity when we move to new domains, the mature theories remain essentially unaltered in their original domains. We need relativity theory for motions close to the speed light, yet we still use ordinary Newtonian theory for motions at ordinary speed. That does not seem likely to change.

Beware of theories or parts of theories that are designed to escape experimental or observational test. This is the part the verificationists got right. There is something very fishy about theoretical entities with properties so perfectly contrived that we cannot ever put them to observational or theoretical test. We should treat them with the highest suspicion. Asking for the means of verification or falsification is a good test if one is suspicious. Finding clear conditions for verification or falsification is an assurance that a healthy connection between the theory and experience is possible.

Be ready to abandon concepts that hide empirical content. This is the part that the operationists got right. One cannot develop conceptual schemes without making presumptions about the world, yet those very presumptions can be contradicted by emerging science, making acceptance or even formulation of appropriate new theories difficult. A related concern is that some concepts may have no real basis in experience at all (e.g. ether state of rest!). Asking for an operational definition of the concept is a healthy but not final test. If it admits an operational definition, then at least we know it has a connection to possible experience.

Infer to common causes. When you have the choice, the better explanation is the one that posits fewer coincidences and that is the one you should infer to.

Space isolates us causally. The novel results about space and time itself provide some of the most interesting results of special relativity. If we try to look beyond the theory and still have outcomes that pertain to space and time, I think the most important is simply the idea of upper limit of speed of light to causal interactions. That tells us that we are quite powerfully causally isolated from other parts of the universe. Nearby galaxies are already millions of light years away. That means that just sending a signal from our galaxy to another will require eons of time. Conversely, something happening there now will not affect us for the corresponding eons.
If one wishes to press further, special relativity has revealed a relatedness of space and time that we did not formerly suspect. It is hard to know how best to express this entanglement. I think the best way is still our familiar relativity of simultaneity.

What you should know

Copyright John D. Norton. February 2001; October 2002; July 2006; February 2, 13, September, 23, 2008; February 1, 2010.