Science and the Human Prospect

Ronald C. Pine 

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Chapter 7
image of world Our Time: 1. Understanding the Theory of Relativity
  The dogma (absolute space and time) was so ingrained that the thought of questioning it never arose. It was Einstein's great genius to question the self-evident. The theory of relativity is not basically difficult. It may seem hard to come to grips with it and understand it, but the reason is neither mathematical nor conceptual. It is simply that the theory of relativity apparently violates common sense; that is, it overthrows the dogma. In actual fact, it does not violate common sense in everyday life at everyday speeds. . . But it poses that threat, and since everyone tends to be basically conservative (that is, fears the unknown), it is much easier to say 'this is too hard for me' than to come to grips with it. Claude Kacser, Introduction to the Special Theory of Relativity

In principle one could reach the year 2000 in a few hours. (Written in 1983)  Paul Davies

 Modern scientific epistemology. . . justifies discoveries of such farreaching consequences as would, in former times, have been merely empty speculation, phantasies without empirical foundation.  Hans Reichenbach
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copyright Ronald C. Pine

Slow Time and Fast Time

If you do not ask me what is time, I know it; when you ask me, I cannot tell it.  St. Augustine

When your sitting in a room listening to a very boring speech or lecture, it seems to take forever, and time "drags"; when the lecture is so interesting that it all seems to take place in a matter of moments, time "flies." But we all know that this is only a subjective experience, that the real time measured by an objective instrument such as a clock clicks along at the same rate whether we are interested or not in what is happening.

But do we really know this? Our knowledge of the objective world must be pieced together on the basis of our subjective experiences. For all we know at the moment we become engrossed in some interesting activity, at that precise moment everything in the universe speeds up, including the clock! Or, perhaps at the precise instant that we become bored the universe decides to slow everything down, including the clock! So when we look at the clock and see that an hour has passed, we conclude that an objective hour has passed, but how do we really know if it was a fast hour or a slow hour? If everything in the universe could speed up or slow down, then the clock would either speed up or slow down as well, and there would be no way to tell.

Preposterous says our common sense. All that is needed is for two people to be in the room, one bored and the other not, and then have both see that based upon the objective clock time, one hour has passed. Case closed. As Socrates and Plato noted long ago, it is impossible for a single individual to be objective. The experiences of others and communication with others about what they experience are necessary conditions for understanding the world. Part of what we mean by objective knowledge is a public knowledge, a knowledge established by a community of observers. Also implied is a definite state of existence independent of our observations. In the case of time, it is what it is independent of our emotional states.

It never occurs to me that if I leave my home at 8:00 and arrive at my office at 8:30 that I am assuming that it is not then 9:00 at home.

But wait. Suppose someday we finally discover another intelligent form of life separated from us by a great distance. How would we know that time for them is the same as it is for us? We could synchronize two clocks on Earth and then transport one to their location. How would we know that the two clocks stay synchronized? How do we know that time will not speed up or slow down for them in their part of the universe? Our common sense tells us that if nothing is physically wrong with the clocks, they should stay synchronized. However, thinking this way is an assumption on our part. Science must base its conclusions on experience, so unless we have a way of directly comparing the time these clocks are measuring, we would not know whether they are still synchronized.

That time could speed up or slow down in a part of the universe may seem far-fetched, but its possibility demonstrates that unless a universal, objective standard of time measurement exists we cannot say we know that time flows uniformly on as our common sense dictates. Unless we can compare separated clocks, we cannot say that time is the same throughout the universe as it is here on Earth. Instead we must admit that we are assuming that time behaves throughout the universe the way we experience it here on Earth. We are assuming that on some other planet "now" is the same as "now" here on Earth; that at any given moment there is a slice of simultaneity throughout the universe.

It seldom occurs to us that when we leave our homes at 8:00am and arrive at our offices at 8:30am that we are assuming that it is not 9:00am at home. It also would seem silly of us to be so paranoid that we must call home when we arrive at 9:00am and check with a loved one what time it is at home. The assumption of a slice of simultaneity is safe and reasonable for most practical purposes on Earth. But is it true throughout the universe? The history of science has shown us repeatedly that we should be very careful in projecting those views of reality that are practical, that work, as real. Most of what human beings do on this Earth can be accomplished by assuming the same set of beliefs accepted in the Middle Ages. We see the Sun moving every day and we do not feel the Earth moving. We have learned, however, that our experience on this planet encompasses but a small portion of all that exits and that the universe is not required to conform to our view of things.

Strange indeed. The fact that we have no way of knowing if the universe is slowing down or speeding up at any given moment, that we must assume that it is not, is a paradox. It is the kind of thinking that the average person would not take seriously. It is similar to a perennial philosophical problem: that logically no one has ever been able to prove the existence of the external world! With problems like this, small wonder that few people major in philosophy at universities. History shows us, however, that great thinkers have always taken such paradoxes seriously, seeing them as nature's way of waking us up to some possible secret and revealing the fallibility of our "normal" thinking. In this chapter we will see that Albert Einstein's realization that Newtonian scientists only assumed, like the rest of us, that time stays normal stimulated a very great discovery.

  David Hume: The Problem of Causality

As the Sophists had challenged the ancient Greeks centuries before, Hume was challenging all Newtonians to demonstrate how this new science provided a durable knowledge, to show how the "truths" of this new science would not be overthrown by future experience.

In the eighteenth century the Scottish philosopher David Hume (1711-1776) discovered another paradox, a paradox which clashed with the astounding success of the new science of his time and its rudimentary technological applications. We saw in Chapter 6 that by the end of the seventeenth century Newton had discovered the mechanical laws that unified terrestrial and celestial motion. Scientists were using these same laws and the machine paradigm to further our understanding of the physical world and begin the industrial revolution. The mechanical world view of Newtonianism would soon produce machines of mass production, power looms, factories, and the steam engine for ships and trains. In the light of such practical success, few would question this world view.

Hume discovered, however, that the concepts that served as the foundation for the success of Newtonian science were a philosophical puzzle. Take the fundamental notion of causality. We assume that the job of science is to successfully understand the real world, in part, by revealing the causes of things. Newtonian physics apparently did this job brilliantly. Gravity was the cause of both terrestrial and celestial motion. Into this arena of scientific certainty Hume stepped and stunningly questioned this supposed knowledge with impeccable logic. According to Hume, we cannot know the cause of anything. For instance, if I throw a rock at a window and watch the window break, there is no "logical" way to prove that the impact of the rock caused the window to break. It might be a coincidence. Night always follows day, but surely we do not want to infer that day causes night. We cannot see causation nor can we logically deduce causation, no matter how many rocks we throw at windows. All we can honestly say is that there is a "constant conjunction" of events -- throwing the rock, breaking the window.

Another paradox. The science of the time worked and implied that we knew not only the causes of the motions of the planets but also many important events relevant to daily life, and it held out the promise of a unified knowledge of almost everything important to us. As with causation, gravity could not be seen, and its action at a distance was not understood. Nevertheless, scientists were confident that a final understanding of the universe was at hand. The influential French mathematician Jean Le Rond d'Alembert claimed, "The true system of the world has been recognized, developed and perfected." The prominent physicist, physician, and mathematician Hermann von Helmholtz, declared at an important scientific meeting that the job of science was almost over, that "its vocation will be ended as soon as the reduction of natural phenomena to simple forces is complete and the proof given that this is the only reduction of which phenomena are capable." For Helmholtz, the future of science amounted to no more than a "mopping-up" operation; Newton had already made all the important discoveries. A little logic and experimental tinkering were all that remained.

Physics is finished, young man. It's a dead-end street.  Advice from Max Planck's teacher

With Hume, philosophy was embarrassing the whole show. Philosophical analysis showed that there was no proof that the fundamental concepts of this understanding represented reality. From a logical point of view, all the useful discoveries could be nothing more than a large number of coincidences.(1)

It had happened before. For thousands of years human beings had watched the Sun move from east to west everyday. Belief in a stationary Earth worked when applied to navigation and astronomy, and still works, but was not, and is not, true. It is just a coincidence that geocentric models work. Such logical ruminations convinced Hume, perhaps not unlike Protagoras, that he should retire from philosophy (philosophy was just a game for idle youth) and spend his time on more important things like politics and a successful career. But for a philosophically minded German physicist, Hume's work was the challenge of a lifetime.

Immanuel Kant

Concepts without percepts are empty. Percepts without concepts are blind.   Immanuel Kant, The Critique of Pure Reason

Immanuel Kant (1724-1804) will never be noted for having been an exciting person. He never travelled more than a few miles from his home during his entire life, and he followed such a rigid routine that his neighbors could set their watches based upon his daily habits. He choose instead the life of the mind. He traveled far in the depths of inner space and his major book, The Critique of Pure Reason, will probably always be seen as an important work by those who take philosophy, science, and the life of the mind seriously.

Kant was shaken by Hume's critique of Newtonian concepts. Hume awoke Kant from a "dogmatic slumber," to use Kant's words. Kant taught physics and philosophy at the University of Konigsberg and had contributed to the theoretical applications of Newton's work by proposing a hypothesis of the origin of the solar system, known as the "nebular hypothesis." He also noted that the tides would, over a long period of time, slow the Earth's rotation, and proposed that earthquakes were caused by shifting and faulting of large sections of rock. But he quickly saw that Hume's work questioned the very foundation of not only Newtonian physics but all of science as well and any attempt to know the causes of things.

Kant wrote his book primarily for scientists and scientifically minded philosophers to allay their fears that any attempt at a unified body of knowledge was a hopeless dream. There was a solution to the problem, according to Kant, but the solution would have to be a radical one. Just as the Sun-centered system of Copernicus was a radical revision of our normal thinking about our place in the universe, a switch from being central to being simply on another planet, so the epistemological solution to Hume's problem would also be an "inversion" of our thinking about reason and knowledge.

We ourselves introduce that order and regularity in the appearance which we entitle "nature." We could never find them in appearances had we not ourselves, by the nature of our own mind, originally set them there.  Immanuel Kant, The Critique of Pure Reason

According to Kant, Hume was right to an extent: There would be no way to logically deduce an objective reality of causal connections independent of our thinking about reality. We can, however, deduce from human experience a kind of "meta-knowledge." We can deduce that causality and other fundamental scientific concepts, such as three-dimensional space, a universal time, and the basic principles of mathematics, will always be the framework for which all human observations of the world will take place. These concepts will always be with us and will never be overthrown by any future experience of reality because these notions are an inherent part of the human mind. They are the "filters" through which we will always view the world. No matter where we travel in this great universe, space, time, causality, and mathematics will be the same, not necessarily because the universe itself is always this way but because wherever we go, every interpretation, every observation made by human beings will always conform to our filters, the "categories of understanding" as Kant put it. The objective universe might conform exactly to the way we filter it, but there would be no way to know this. When we observe reality, we must do so through our filters, and there is no way of stepping outside of our minds and filters and seeing how reality is when we are not looking at it.

At first this was very difficult for the people of Kant's time to understand. Kant wrote two more books attempting to communicate the same basic theme to scientists. To the modern person his epistemology should be a little easier to understand. What he is saying is similar, but not identical, to the following well-known scientific examples of human perception.

When I view my room right now and listen to the sounds around me of birds singing and children playing, I assume this is a completely objective reality: that the colors I see of the objects around me and the sounds coming through my window are "there" just the way I perceive them. The blue color of my coffee cup appears to be really there, on my coffee cup. Scientists, however, tell us that the blue color is not really "out there." What is really there is a physical substance that absorbs certain wavelengths of light and reflects others. My coffee cup reflects a particular wavelength of light, which strikes the rods and cones, the light sensitive receptors in my eye, sending an electrical impulse to my brain, where the "blue" of my coffee cup is created. The blueness is not really out there. It is an interpretation due to the neurophysiology of a human being. A creature with a different neurophysiology would not view reality the same way. Similarly, the sounds I hear are due to there being a physical medium (the air) that vibrates as children play and birds sing. These vibrations are carried by the medium to my ear where three little bones are subtly rattled by the vibrations and eventually another electrical impulse is carried to my brain where I finally "hear." Without the physical medium of the air, I would not hear anything. In a vacuum or outer space beyond our atmosphere there would be no sound. Without light, and the different possible wavelengths of light, there would be no color. Without the right receptive physiology there would also be no color and no sound. The colors of the objects in my room and the sounds coming in from my window are interpretations, appearances that serve us well for practical purposes, but interpretations nonetheless due to our neurophysiological filters.


Things which we see are not by themselves what we see .... It remains completely unknown to us what the objects may be by themselves and apart from the receptivity of our senses. We know nothing but our manner of perceiving them.  Immanuel Kant, The Critique of Pure Reason

What Kant is saying about causality, space, time, and the practical application of mathematics is similar but more fundamental. Hume had shocked Newtonians by suggesting that the basic principles of science were secondary rather than primary -- that causality was not a designation of a primary quality of objects, but rather the subjective result of human perception with the same epistemological status as color. Kant responded by reasserting the primary status of the scientific concepts of causality, space and time, but he inverted the notion of primary. The primary concepts are not claimed to designate the way objects are "in-themselves" -- we cannot know this -- nor are they the subjective results of human perception. Rather, they are primary in the sense that they make perception possible; they are concepts we "impose" on the world; they are the categories by which we organize the world. The perceptual features of all human based reality will always be the same. Our essential filters will always be, according to Kant, a necessary part of a "phenomenal realm" of appearances. These filters are the hard-wired elements by which the human mind understands the world. They cannot be overthrown someday by future experience, because they make all human experience possible.

We cannot know if reality itself matches these fundamental concepts, it might, it might not. Rather, we can only be sure that reality will always appear this way for us. It is our view of things, a universal, but human perspective. It is as if all humans regardless of culture were born with rose-colored contact lenses as a natural part of our visual physiology. Suppose that without the lenses we would not be able to perceive anything meaningful; we would be effectively blind. With the lenses we see an organized, but always rose-colored, world. For all we know the real world is rose-colored also, but there will never be any way to tell. In this way Kant turned subjectivity into objectivity and overcame he thought the problem of induction. We do not need to worry about proving on the basis of our experience that causality is a valid concept or that it will not be overthrown someday; we know that it will always be a valid concept and never be overthrown, because it is one of the fundamental concepts that makes any experience of the world possible. The validity of causality does not depend upon experience; it is not "a posteriori," to use Kant's terminology. It is "a priori," it is independent of experience. In other words, we do not derive the concept from our experience of the world, we bring it to the world, just as we would not derive our experience of rose-coloredness from the world, but impose it upon the world.

Kant then tried to show that the basic laws of Newtonian physics can be deduced from the basic "categories of the understanding." Thus, Kant could now say in answer to Hume, we may not know whether the Newtonian world is indeed the real world, but we can say that it is, and always will be, the real world for us -- the way it appears to us. Every observation, every new discovery scientists make in the future, will simply fill in details around a general framework, a mopping-up operation as Helmholtz later suggested, just more facts consistent with the Newtonian world view. No observation or a discovery will be inconsistent with the Newtonian filters, because they are a priori. According to Kant, the answer to Hume's skepticism is that we are all born Newtonians, just as if we were all born with rose-colored contact lenses. We will discover new facts to fill in our concepts, but our basic concepts will never change. Without our concepts we could not discover new facts. Concepts without the perception of new facts are empty, said Kant, but without concepts we are blind.

   Concepts and Other Worlds

The great thing [about Kant's philosophy] was to form the idea that this one thing -- mind or world -- may well be capable of other forms of appearance that we cannot grasp and that do not imply the notions of space and time. This means an imposing liberation from our inveterate prejudice.  Erwin Schrodinger, Mind and Matter

Some modern philosophers and scientists focus on Kant's work as another example of armchair philosophy slowing down scientific progress. After all, if Kant were correct, this would imply an end to science. If no future experience could refute the basic principles of Newtonianism, if the principles were irrefutable and a priori, then there would be no future fundamental discoveries. Kant surrendered to the temptation discussed in Chapter 2: He was so worried about proving his beliefs true that he made them irrefutable so no future experience could overthrow them. His philosophy reflected the confidence scientists of his time had in Newtonian science. He was not alone in believing that the laws of nature as outlined by Newton would never be overthrown. Kant was wrong, but he was wrong in a very important way. Both Kant and Newton prepared the way for Einstein.

To concentrate only on the provincialism of Kant's reaction to Hume's skepticism misses the revolutionary implications of Kant's epistemological inversion and how it prepared the way for much of modern thinking. In drawing attention to the importance of concepts as the organizing force behind perception, Kant awoke other philosophers from their own dogmatic slumbers. The human mind is not a blank tablet upon which truth imprints itself. It is an active instrument in sorting out the infinite amount of data that floods our perception and threatens to overwhelm our attempts of organizing the world into a meaningful perspective. Without thoughts, without perspective, a mass of empirical data is nothing at all. (Remember Sartre's self-taught man in Chapter 2.)

Kant's philosophy also prepared the way to think about the possibility that there are many real events, other worlds, happening all the time right in front of us, so to speak, even though we are incapable of directly experiencing them. It would soon be common place for scientists to believe that there are many realities beyond the perceptual window allowed by Newtonian conceptual filters. Kant was right about our normal perceptual window. It is Newtonian. Every observation scientists make, whether it be in an Earth laboratory or of deep space, will be framed within a normal three-dimensional window. Although Kant himself believed this would never be possible, it would soon be common place to believe that there could be indirect methods of deducing other realities, that observations made in our normal mode could indicate or point to a world totally different from what we normally observe. Scientists would soon be routinely setting up laboratory conditions to reveal the heretofore unimaginable and invisible realities of electromagnetic radiation, of electricity, of X-rays, of AM and FM transmissions, and eventually announce theories such as the Big Bang, the description of which cannot be imagined through our Newtonian common sense.

  Ironically, in his attempt to establish Newtonianism as a priori, Kant prepared the way for us to think the unthinkable: that we could conceptualize, understand, and even have knowledge of new unimaginable realities, that our common notion of three-dimensional space, our normal experience of the unidirectional flow of time, our thoughts about causality, could be but a human point of view.

Einstein and a Philosophical Discovery

Einstein has not ... given the lie to Kant's deep thoughts on the idealization of space and time; he has, on the contrary, made a large step towards its accomplishment.  Erwin Schrodinger, Mind and Matter

Let us return now to our discussion above about time and clocks. Recall that we must assume that a clock measures time the same regardless of our perspective of it. Suppose we synchronize two clocks and separate them. Suppose one clock stays on Earth and another is taken to Mercury. How do we know they stay synchronized? Again following Newton, we assume that time flows objectively on, everywhere being the same, and that assuming that the clocks are both working correctly, they will objectively measure this flow the same way. If the clock on Earth shows two o'clock, we assume that the clock on Mercury would be showing two o'clock if we were there to see it. If two full hours have passed on Earth since we last looked at the clock, we think we know that exactly two full hours have passed on Mercury as well.

One of the great tasks of philosophy is to reveal the assumptions we make when we assert something to be true. Often this is very difficult precisely because it is so easy. Our assumptions are usually so obvious, so fundamentally embedded in our outlook, that we cannot recognize that we are making them. Philosophical analysis is a vital aid to scientific method. As we saw in Chapter 2, many ideas are involved in deducing the possible predictions tested by experiment. Behind every experiment is a "hypothesis set," consisting of the main hypothesis, many minor hypotheses, and background assumptions. This collection of hypotheses and assumptions, along with the conditions of the experiment, serve as premises for inferring what should happen when nature is subjected to our probing. Logically, if the result of an experiment is negative, if what we expect to happen does not happen, then we prove only that at least one of the ideas of the hypothesis set is false. Thus, it is very important to identify as many as possible of the ideas which make up the premises for the predicted result.

When an opinion leads to absurdities, it is certainly false; but it is not certain that an opinion is false, because it is of dangerous consequences.  David Hume

Einstein recognized that we were not being good empiricists when we assume that two separated clocks would stay the same. We were being rationalists indulging in a philosophical bias. Why should the clocks stay the same? If we are to be empirically honest and subject all our assumptions to tests, what we need is some way to measure what time the clocks record. Because there is no big cosmic clock standing in the center of the universe for all to see simultaneously, the only way we can measure the time of our clocks and see if they stay synchronized is by directly comparing them, and at great distances this necessarily involves the speed of light. To know that a clock on Mercury is still keeping the same time as one on Earth, we must communicate with an observer on Mercury by sending an electromagnetic signal traveling at the speed of light. Also, since both planets are moving in relation to each other and because the speed of light is finite, we must take into account the speed of light and what effect, if any, the relative motion of the planets might have on this speed.

At the turn of the century when Einstein as a young man was thinking about such things, the speed of light had also become a paradox. It was known that the speed of light had a finite, but very great, velocity (186,000 miles per second), and it was assumed that the measurement of this velocity, like any other velocity, should change depending upon how fast the source of the light is moving and in what direction. For instance, if we are on an object moving at a speed of 66,600 miles per hour, the speed of our Earth around the Sun, and we send a signal to Mercury in the direction of the motion of the Earth around the Sun, then should not the speed of the electromagnetic signal be the regular speed of light plus the speed of our motion? If a train is moving at 60 miles per hour and a person on the train is walking at 3 miles per hour in the same direction as the train is moving, then that person's accumulated speed, as measured by a stationary observer, is 63 miles per hour. The two velocities are added together. Should not light be the same?

Experiments showed that light did not behave the way our common sense says it should. No matter what the speed or direction an object moved, a beam of light from that object was always the same -- 186,000 miles per second. Whether a beam of light was travelling in the direction of the Earth's motion, at right angles to its motion, or in the opposite direction of its motion, the speed of the light beam was the same.


It requires a very unusual mind to undertake the analysis of the obvious. Alfred North Whitehead

The implications of this result were not easy to digest. If we could travel on a special vehicle, say at only 100 miles per second less than the speed of light, and we turned on a flashlight and pointed it in the direction of our motion, the flashlight beam would move away from us at the regular speed of light. If we increased our speed to 50 miles per second less than the speed of light, we would not gain on the beam of light. Finally, if our vehicle could reach the speed of light, the speed of our flashlight beam would still be the normal speed of light. In the case of light the normal addition of velocities does not work, one plus one is one.

Einstein boldly accepted these paradoxes as axioms: time must be "tested," and the speed of light is the same regardless of the speed of its source. Einstein then recognized that for science to establish universal laws of nature, laws that remain the same regardless of one's point of view, then a price had to be paid. We must accept the fact that when we test time, it will speed up or slow down relative to moving frames of reference. We must accept as commonplace that since Mercury and the Earth are moving in relation to each other, and any electromagnetic communication device will transmit a signal at the speed of light unaffected by the relative motion of the planets, the clocks on these planets will not be synchronized when they are compared. Time must be different, if light is the same.

Cosmic Trains

I can now rejoice even in the falsification of a cherished theory, because even this is a scientific success.  John Eccles

As Kacser points out in the opening quote to this chapter, it is easy to believe such thinking is too hard. Let's use the same example Einstein used, which is easier to visualize than the Earth-Mercury example. In Figure 7-1 imagine a special train moving toward point A and away from point B. On the train is a person we will designate as X. As the train passes by, imagine a person Y midway between points A and B. Suppose as Y watches the train pass, at exactly the moment X is opposite Y, two bolts of lightning strike the ground from Y's point of view simultaneously at points A and B. How would X view the two bolts of lightning? Let's imagine that the train is moving very fast, at about 3/5ths the speed of light. Because X is moving toward point A at such a great speed, the light from A will be received significantly before the light from point B, which will have to "catch up" to the swiftly moving train. Thus, whereas from Y's point of view the two events were simultaneous (happening at the same time), from X's point of view they were not simultaneous, the bolt of lightning struck A before B. Who is right?

It is tempting to respond immediately that Y is right because X is moving. It is comfortable to think that Y's reference frame is the right place from which to view the "actual truth of the matter." Because X is moving so fast, it is easy to believe that his experience is an illusion due to his motion. If X got in the "right place," if he slowed down, then both observers would see the same thing, the bolts of lightning striking the ground at the same time. But wait. Y is moving also. Y is, in fact, moving many different ways, depending upon which reference frame is adopted. If Y is close to the equator of the Earth, he is moving at about 1000 miles per hour. From the point of view of the Sun, Y is moving at approximately 66,600 miles per hour. And from the point of view of the center of our galaxy, he is moving at a speed of over 500,000 miles per hour. Where is the right place? Why can't X assume that Y is the one who is moving?

Imagine someone living on Mercury. The time from noon to midnight for this person is one Mercury year. One complete Mercury day, from noon to noon, takes two Mercury years .... Suppose we choose to land at a location on Mercury where the sun is about to rise. We will be treated to one of the most interesting sights in the solar system .... The sun rises for a while and then stops and sets again! ... After perihelion passage, the sun rises again and this time slowly travels toward the meridian.  Charles E. Long, Discovering the Universe

A Newtonian might object that X could use the Galilean transformation to detect his motion, and on the basis of this he could calculate the simultaneity of the lightning flashes. If the addition of velocities assumed in the Galilean transformation is universally valid, then X should be able to measure the velocity of light coming from A as being the normal speed of light plus another three-fifths the speed of normal light and the speed from B as only two-fifths the speed of normal light. By using these values and measuring the time he receives each flash, he could calculate the "real" time of the original flashes, which would then agree with Y. However, in the case of light nature does not cooperate with the Galilean transformation and our common sense notion of the addition of velocities. If X had the proper equipment to measure the speed of the incoming light signals from A and B, he would find that the speeds of each beam are the same, the normal speed of light. Similarly, if Y had the proper equipment, he would also find the beams coming from A and B to have the same speed. Thus, both observers are entitled to adopt the perspective that they are at rest and the other is moving.

Einstein's solution states that we must obey the empirical facts. The speed of light, as a universal law of nature, is the same everywhere for every observer, and this is true no matter how each observer is moving relative to another. We cannot just make a unwarranted metaphysical assumption. Time must be tested and the belief that there is a "right" place where time is absolute is just an assumption for which there is no evidence.

Time is very much related to our relative place in space. Our time measurements (clocks, calendars) are actually local spatial measurements. On Earth when we measure one hour, we are really measuring a portion of our space, a portion of the rotation of our Earth (approximately 15 degrees). On Mercury this convention would be very inconvenient, because the planet rotates once every 59 Earth days and revolves around the Sun in 88 Earth days. The combination of these rotation and revolution periods makes one Mercury day equal to two of its years!(2)

Einstein's theory of relativity teaches us that when we are relatively close together, and moving together -- when, as on Earth, the speed of our relative motions are very small in comparison to the speed of light -- then time will behave itself. In our train example, if the train is moving at a normal train speed then X also measures the bolts of lightning as simultaneous.(3) But when astronomical objects are widely separated and move at great speeds relative to each other, time does not obey our Earthly standards. Our assumption of an absolute time, the intuitive feeling that time clicks along at a steady rate throughout the universe, that "now" on Earth is the same "now" for all locations, is due to the fact that normally we do not move at such great speeds relative to the speed of light. These relative measurements of time show up only when relative speeds are attained appreciably close to the speed of light. This is the essence of Einstein's great discovery: partly a philosophical discovery (time must be tested) and partly an empirical discovery (the speed of light was the same in all reference frames). For the most part, the rest was logic and mathematical deduction.

It is important to understand that the relativity of time measurements is necessary to preserve the laws of nature. Although two observers will measure the temporal occurrence of events differently, from their respective reference frames they will notice nothing unusual. The theory of relativity does not prove that everything is relative. Both observers in our train example will find that the laws of nature apply normally, regardless of what they might think or wish to be true. If observer X conducted experiments in a laboratory on the train, he would obtain the same results as Y would in a laboratory located in his reference frame.


According to Einstein, as he relates in his Autobiographical Notes,

    After ten years of reflection such a principle resulted from a paradox upon which I had already hit at the age of sixteen: If I pursue a beam of light with a velocity c (velocity of light in a vacuum), I should observe such a beam of light as a spatially oscillatory electromagnetic field at rest. However, there seems to be no such thing. . . on the basis of experience. . . . From the very beginning it appeared to me intuitively clear that, judged from the standpoint of such an observer, everything would have to happen according to the same laws as for an observer who, relative to the earth, was at rest. For how, otherwise, should the first observer know, that is, be able to determine, that he is in a state of fast uniform motion?(4)

Einstein concludes this passage by acknowledging his debt to the skepticism of Hume, referring to Hume's insight that the major assumptions of Newtonian physics had no empirical foundation.

Time Dilation

The idea that time can vary from place to place is a difficult one, but it is the idea Einstein used, and it is correct -- believe it or not.  Richard Feynman

Einstein realized that if the laws of nature are the same from every standpoint, then for physicists to be able to continue to do physics in a universe of relative moving objects, they will need to mathematically transform how time will be viewed from different reference frames. Einstein used a mathematical equation called the Lorentz-Fitzgerald transformation. It worked perfectly. The equation is a relatively simple algebraic relationship:

T' = T 1-(v/c)2

In this equation, T' is the time of an event in a reference frame moving at a velocity v in relation to an observer whose time is T. The small c is a constant, the speed of light. Let's see how it works.

Suppose in our train example that X and Y both possessed clocks that some time ago were synchronized when the train was stationary. Y then moved at a normal speed, very slowly compared to the speed of light, to the point between A and B. Suppose at a prearranged time X departs and that for the last 15 minutes by Y's reckoning the train has left the initial starting point and been moving to the point where Y is at an average speed of three-fifths the speed of light.(5)

What time will the clock of X read according to the Lorentz transformation? If we plug in the data,
T = 15 and v/c =3/5, so T' = 15 1-(3/5)2

When X passes Y, X's clock will show that the train has been moving for only 12 minutes! From Y's point of view, X's time has slowed down relative to Y. It would not just seem to slow down; real physical measurable effects would be seen when X and Y compare their clocks. If X and Y both lit cigars at the prearranged time, X would find that his cigar has burned less than Y's as they pass each other.(6)

X will experience nothing unusual. The laws of nature are the same, including that for burning cigars. For X everything will appear normal including the movement of his clock. At no point will X's clock suddenly slow down dramatically. It will appear normal. Likewise, Y will not suddenly see the last few minutes of his experienced 15 minutes fly by at a different rate. His clock will also appear normal. Nor will either notice anything strange about the rate their cigars burn. Time slows down in reference frame X only in relation to reference frame Y. Within their respective reference frames everything is normal.


If my home and office were separated by many light years, my home (depending on the distance and the speed of my travel) could be many thousands of years in the future when I arrive at work.

The testimony of our common sense is suspect at high velocities.  Carl Sagan

This slowing down of time of a reference frame relative to another reference frame is called time dilation. As unbelievable as it may seem, it is one of the most accepted scientific facts of our time.(7)

It has been tested in numerous ways. Very precise atomic clocks have been synchronized and then compared again after one was flown around the world on a jet airplane. The clock on the fast plane slowed down in relation to the clock that stayed on the ground. A similar test was conducted using one of the U.S. space shuttles with the same result. Scientists now apply time dilation routinely in sophisticated laboratory situations. In the billion-dollar particle accelerator laboratories all over the world, physicists can keep special particles of matter "alive" far longer than would normally be expected because of the time dilation effects that result by accelerating particles close to the speed of light. In this way special forms of energy can actually be "stored" for use in crucial experiments.

As far as most physicists are concerned, time dilation is a fact of nature. Rather than the large fishbowl of time implied by common sense and Newtonian science, Einstein has revealed to us a "chunky" universe of relative reference frames and times. There is no universal "now"; there are only simultaneous events in relation to local reference frames.

Trains, of course, do not move at 111,600 miles per second (three-fifths the speed of light), and hence, it is easy to see why time dilation effects are not noticed by common sense. Theoretically spaceships could. What kind of astronautical scenarios are then possible? Suppose we know twins 20 years of age, one an astronaut who will take a space voyage that will take 20 years by Earth time. Suppose that the astronaut twin averages in his rocketship a speed of three-fifths the speed of light. How old will each twin be when they meet again 20 Earth years from now? Using the time dilation equation we have

T = 20 1- (3/5)2+ 20,

which would equal 36. The twin who stays on Earth will be 40 years of age. The twins will no longer be the same age!

What applies to time will also apply to space. Just as the twins would discover that there is not one time that marches along in a strict Newtonian fashion, so they would also discover that there is not one large fishbowl of space where the distance between two points is the same for every observer. Just as time slows down, so space contracts. Because of the speed he is travelling, between the points of his departure and arrival the astronaut twin will measure his voyage as 14 trillion miles shorter than his twin would with instruments on Earth.

Traveling at great speed slows our histories down from one point of view, and allows us to speed to the future from another.

This example is not science fiction. Time dilation has been shown repeatedly to be a fact of nature; this effect on an astronaut would indeed happen. If it is so hard to believe, it is because we have difficulty realizing that the things we take for granted on Earth do not necessarily apply throughout the cosmos. With Einstein, the cosmos is now our laboratory, and we must adjust to the conditions of this new laboratory.

Stranger still, consider this scenario. The star Vega, a star like our Sun and a possible candidate for a planetary system, is approximately 32 light-years away. Suppose in the near future a 30-year old woman astronaut, who has a five year old son, went on a space voyage to explore this star, averaging the colossal speed of 99.5 percent the speed of light. At such a speed it would take her about 64 1/3 years Earth time to make the trip. When she returned, her son, remaining on Earth, would be into his 69th year. Both would be in for a great shock. The 69-year old son would embrace his long-awaited 36 1/2 year old mother! Their personal histories would have seemed to be normal in all other respects, but it would now be clear that traveling at great speed slows our histories down from one point of view, and allows us to speed to the future from another. If such a voyage were undertaken in the year 2000, the mother astronaut could get to the year 2064 in a little under 6 1/2 years.

An event that required only 6 1/2 years for the mother, required a little over 64 years for the son. In our train example, an event that happened before another event for one observer (lightning striking point A before point B for X ), happened at the same time for another observer (Y). It would also be possible then for another observer moving in the opposite direction of reference frame X at a great speed to record the lightning striking at point B first. Thus, one person's past could be another's future. Would it then be possible for the mother to return at an age before her son was born?

Not according to Einstein's theory, not if the speed of light is a law of nature. Because the speed of light is an absolute that cannot be exceeded, causal connections, such as mothers causing the birth of babies, are preserved in their normal sequences. According to Einstein's theory, the measurement of "before" and "after" may involve a wide latitude, but the order of events will not be changed. The time between the mother's "before" and "after" of her space voyage is much shorter than that experienced by her son, but both would experience her leaving before she came back. If and only if the speed of light is exceeded will the sequencing of causal events be changed, and it is a basic consequence of Einstein's theory that the speed of light cannot be exceeded. According to the theory, it would take an infinite amount of energy to accelerate any object (even an electron) up to the speed of light and thus require more than an infinite amount of energy to exceed the speed of light.(8)

Epistemological Implications

The pane of glass that separated the observer from reality in Newtonian physics has been shattered. To some extent what is real does depend on us.

The epistemological implications of relativity theory are quite significant. Observational perspective creates reality to some extent. The role of the observer is much different from that of Newtonian science. In Newtonian science the variety of perspectives of human observation could be ignored, excused as irrelevant to our descriptions of the real world. The different results of observation due to different reference frames were considered to be simply practical inconveniences that could be reconciled by Galilean transformations. But with relativity theory, the observer is intimately involved in scientific measurement, and what is measured can be different depending on one's reference frame. Our knowledge of the world must unfold from empirical measurement of it. In the destruction of the notions of absolute space and time Einstein showed that an honest empiricism must involve the observer; that to some extent what is real does depend on us. According to the physicist Paul Davies,

The essential element injected into physics by the theory of relativity is subjectivity. Fundamental things like duration, length, past, present and future can no longer be regarded as a dependable framework within which to live our lives. Instead they are flexible, elastic qualities, and their values depend on precisely who is measuring them. In this sense the observer is beginning to play a rather central role in the nature of the world. It has become meaningless to ask whose clock is 'really' right, or what is the 'real' distance between two places, or what is happening on Mars 'now'. There is no 'real' duration, extension or common present.(9)

The universe plays fair. Its tricks may operate by principles of incredible subtlety, and we may never discover all of them, but it keeps performing its illusions over and over again, always by the same method.  Martin Gardner

However, Einstein did not think he had proved that each observer is completely involved in creating reality. Einstein was clearly neither a relativist nor a postmodernist. He did not doubt the existence of an independent physical reality, or whether there must be some universal objective truths. In fact, the very intent of his theory was to preserve universals, the laws of nature. Recall that in Einstein's theory the speed of light is the same for all observers. Einstein thought that the secret structure of nature resembled the internal mechanism of a special, mysterious, cosmic clock. We have no direct access to the internal workings of this cosmic clock. We are forever limited to the empirical surface, of seeing the outside motions of the hands, and can only submit hypotheses about how the internal mechanism is arranged to produce the movements of the hands. But limited as we are, we can judge which hypotheses are better, more reliable, on the basis of which ones predict best the motions that we observe.

Einstein believed as passionately as Socrates and Plato that some ideas are better than others. For Einstein, knowledge of how the clock works is possible, even though we will never know with logical certainty that our best hypothesis is correct. Einstein was an epistemological realist: If our experiences of the world overwhelmingly support a particular hypothesis, no matter how bold and radical the ideas contained in this theory, we are entitled to believe that these ideas refer to real things. Like the man who found his way out of Plato's cave, the going may not always be easy. New ideas often encounter great resistance, engender fear, and lead to ridicule, but according to Einstein, there is a world out there that "beckons like a liberation," and we must "believe in the possibility of knowing the things-in-themselves," no matter how strange the result. As Socrates stated many centuries earlier, we will be "better, braver, and less idle," if we do.

Einstein's basic insights concerning space and time served as only the first premises in the development of the many marvels of twentieth-century physics. From these insights, known as the Special Theory, Einstein later showed in his General Theory that if his ideas on space and time were true, many other hard-to-believe things must be true of our cosmic laboratory.

We cannot predict what comes out of a singularity .... it is a disaster for science.  Stephen Hawking

For instance, after Einstein, physicists understand what Newton could not understand: how gravity can act on bodies great distances apart. To do so, however, we must make use of a new idea -- "warped space." Large massive bodies like the Earth and Sun create multidimensional indentations in the fabric of space, much like a bowling ball in the middle of a trampoline. Because of the curvature of this space, gravity is now like the force on an object that is constrained in its motion to roll towards the center of the indention. With warped space a new geometry applies, where the shortest distance between two points is a curved line rather than the intuitive straight line. Implied also are strange places like that of a "singularity," a place with no spatial dimension, yet a place from which space and time can both emerge (as in the case of the Big Bang) and disappear (as in the case of black holes). Here is Paul Davies description of a black hole. 

    A black hole. . . represents a rapid route to eternity. In this extreme case, not only would a rocket-bound twin reach the future quicker, he could reach the end of time in the twinkling of an eye! At the instant he enters the hole, all of eternity will have passed outside according to his relative determination of 'now'. Once inside the hole. . . he will be imprisoned in a timewarp, unable to return to the outside universe again, because the outside universe will have happened. He will be, literally, beyond the end of time as far as the rest of the universe is concerned. To emerge from the hole, he would have to come out before he went in. This is absurd and shows there is no escape. The inexorable grip of the hole's gravity drags the hapless astronaut towards the singularity where, a microsecond later, he reaches the edge of time, and obliteration; the singularity marks the end of a one-way journey to 'nowhere' and 'nowhen.' It is a nonplace where the physical universe ceases.(10)

Science is our century's art. Horace Freeland Judson

The human mind balks at such thoughts. How can space be warped? Isn't empty space just space? How can an empty something be warped? How can the shortest distance between two points be a curved line? How can a point exist that is not in space, and how can space be inside the point? Our minds rebel against such ideas as illogical, as impossible.

A neo-Kantian perspective explains why. Our normal perspective on the world is Newtonian: there appears immediately to us only one time and a three-dimensional space. For the most part experience takes place within this normal perspective. But Einstein discovered that Kant was wrong. Indirectly we can break out of our filters by radicalizing some of the conditions of our normal perspective. We can move at very great speeds, for instance, and experience results that show how limited our normal perspective is. We can show empirically that what appears as a rational-must-be is only the result of a limited perspective. We discover that what we think must be true is like the beliefs of a small town; when we move away from the small town, we discover ways of thinking that were unimaginable.

Einstein has shown that reality need not obey our sense of certainty or the workings of the human mind.

Davies's description of a black hole is not just something physicists have made up to stay competitive with modern television shows. Black holes are mathematical predictions from Einstein's theory of gravity. Time slows down under the influence of a great gravitational force, and gravity bends space more as it increases. With enough gravity space and time will disappear into a singularity. Astrophysicists believe that many black holes are the result of the deaths of very massive stars. We know such stars exist and we can empirically confirm the existence of black holes from the gravitational effects on other stars and the radiation they "leak." They also can be indirectly observed at the center of many galaxies.   Cataloging the locations of black holes has become almost routine.

Although Einstein did not believe his theory proved that human observers create reality, he did show that the observer begins to play a crucial role in what is real and that Copernicanism had gone too far, or in a sense not far enough. The completion of the Copernican revolution in Newtonianism fulfilled the dream of a unified science; the laws that governed terrestrial motion were the same that governed celestial motion. This enabled other ideas to get in through the backdoor: Our common sense notions of space and time, which worked so well on Earth, could be assumed to be true for the entire universe. It was assumed that what was true about our Earth-based measurements, at Earth-based speeds, must also be true about any possible measurement any where else in the universe. This assumption was so pervasive, so transparently fundamental, that it was not even recognized as an assumption, especially with the success of Newtonian physics. In revealing this assumption as a metaphysical postulate and not an empirical fact, Einstein showed that what was masquerading as a removal of humankind and subjectivism from science was actually a projection of a subjective human point of view; a view that is close enough to the truth at a certain level to enable us to fail to recognize it as a human point of view.

The only way to escape the personal corruption of praise is to go on working. One is tempted to stop and listen to it. The only thing is to turn away and go on working. Work. There is nothing else.  Albert Einstein

Think about this last statement carefully. It is crucial for understanding the paradox of twentieth-century science. Our intuitive feeling that there must be an objective time and space is actually just a projection of a human point of view. As Kant had recognized, objectivity was a projection of subjectivity. We view the world every day as Kant and Newton held. We can accurately calculate the motions of the planets within our solar system using a perspective of three-dimensional space and uniform time. We can send our robot spacecraft to the outer planets and beyond. Our equations work. But that they work in this domain does not prove that the concepts we assume in applying the equations are valid for other domains.

As we will see in our discussion next of quantum physics, this realization is only the beginning. After Newton we thought we knew what the universe was like. Little did we suspect the unnerving surprises it had in store for us in the twentieth-century.

Concept Summary

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copyright 2001, 2004, 2012 Ronald C. Pine


 Notes (Click Back to return to text.)

1. Hume's work showed that the problem of induction could be applied to every Newtonian concept. (Click Back to return to text.)

2. After one rotation, Mercury will be two-thirds of the way around its orbit, but will no longer have the same side of the planet facing the Sun. It requires 176 Earth days to go from one noon to the next noon (one Mercury day).

3. Also, because the relative speeds of Earth and Mercury are very small compared to the speed of light, we would require very precise atomic clocks to show that our clocks are not synchronized.

4. Albert Einstein, Autobiographical Notes, trans. and ed. Paul Arthur Schilpp (La Salle, Ill.: Open Court, 1979), pp. 49-51.

5. Y would need to be 100,440,000 miles away, and it would have taken him a little over 191 years to travel to this point at a speed of 60 miles per hour!

6. The asymmetry between X and Y, that X registers less time passing than Y rather than Y registering less time than X, would be caused by the acceleration of X as he achieved three-fifths the speed of light.

7. A more pronounced effect would be recorded if the train was far enough away and had been moving for five hours by Y's reckoning. X's clock would then register only four hours since he left at the prearranged time.

8. Note, however, that the speed of light would only need to be exceeded by .004358 of a percent for the mother, if she left on the day of her thirtieth birthday, to return on the beginning of the second day after her twenty-fourth birthday, at least one year before her son was born and a few months before his conception! What would happen if she were then involved in a car accident?

9. Paul Davies, Other Worlds: A Portrait of Nature in Rebellion; Space, Superspace and the Quantum Universe (New York: Simon and Schuster, 1980), p. 42.

10. Paul Davies, God and the New Physics (New York: Simon and Schuster, 1983), p. 123.

Suggested Readings

Relativity for the Million
, by Martin Gardner (New York: Macmillan, 1962).

Introduction to the Special Theory of Relativity, by Claude Kacser (Engelwood Cliffs, N.J.: Prentice-Hall, 1967).

Other Worlds: A Portrait of Nature in Rebellion; Space, Superspace and the Quantum Universe, by Paul Davies (New York: Simon and Schuster, 1980).

Einstein's Universe, by Nigel Calder (New York: Viking Press, 1979).

Time's Arrows: Scientific Attitudes toward Time, by Richard Morris (New York: Simon and Schuster, 1984).

Autobiographical Notes, by Albert Einstein, trans. and ed. by Paul Arthur Schilpp (La Salle, Ill.: Open Court, 1979).

The Philosophical Impact of Contemporary Physics, by Milic Capek (Princeton, N.J.: Van Nostrand, 1961).