Einstein’s Relativity and Relativism

As a physics professor at the University of Illinois, Chicago, I frequently taught introductory physics to pre-professional students in medicine or dentistry. During lunch at the university cafeteria I would see students from one of my classes, and sometimes we would sit together and talk.

Wanting to understand some of their thinking about life, I liked to ask them whether they believed that absolute truth in general, and particularly some absolute moral code, existed, or whether truth was relative. It was no surprise that most of them said, “relative.” Then I would ask them why they thought that. The most frequent answer was, “Because Einstein proved that everything is relative.” Remember, they were science students and I, a scientist

I found this quite humorous, since I understood precisely what Einstein had been driving at in his special and general theories of relativity. The actual content of relativity theory flatly contradicted the conclusion they and our mainstream culture were drawing from it. I began to include in my teaching of special relativity a focused answer to this error to help set the record straight in people’s minds, which I want to share with you now.

We need to set the stage for Einstein’s main points, so let’s define first an “event.”  An event is something that happens at a certain place at a certain time. It is defined by these 4 “coordinates.” So, it is represented by a point in a four dimensional coordinate system with three space dimensions and one time dimension.

Think of someone on a train moving at constant speed in a straight line along a track. The person is wearing a wrist watch that emits a light signal every time it ticks. You can think of the train as carrying with it a three dimensional coordinate system for space measurements, and the watch for measuring time. The ground has a three dimensional coordinate system and its own watches, but all are moving with respect to the one on the train. The four dimensional reference frame of the train is moving at constant velocity with respect to the four dimensional reference system of Earth.

Earth qualifies as what Einstein called an inertial reference system to a good approximation. This means we can show that Newton’s laws of motion accurately describe motion in the Earth frame. Then Einstein defines a whole class of inertial reference frames: all frames that are moving at constant speed in a straight line with respect to Earth (the first one we found by checking Newton’s laws.)

Many people are aware that an Earth-based measurement of the time interval between two events on the train, like two successive clock ticks one second apart, does not give one second when measured in the Earth frame. It gives a time interval more than one second. The faster the train is traveling, the longer than a second the Earth frame measures. This is called time dilation, and it means that time intervals are no longer absolute, as people believed before Albert showed us otherwise.

Also, the length of a train car is measured to be shorter in the Earth frame than the people on the train measure it to be. This is called length contraction, and it means that space intervals are no longer absolute, as people before also believed. What was considered absolute became relative, as the name of Albert’s theory of special relativity suggests. So the values of time and space intervals are not absolute, but depend on the reference frame in which they are measured.

Before this physicists believed that time and space intervals were absolute, independent of the state of motion of the observer. So, Einstein was definitely challenging that absoluteness, claiming that both were relative to the state of motion. On the surface this seems to support the idea that truth, even moral truth, also depends on who is defining it or looking at it.

The error of this interpretation of what Einstein was saying is clear from the two postulates of the special theory of relativity:

The first postulate says that the laws of physics must be the same in any inertial reference system.

Please notice the words “the same” and “in any.” They are absolute words. This is an absolute law.

The second postulate says that observers in every inertial reference system will measure the same value for the speed of any light signal, and that value is about 2.998x10⁸ meters/second.

Again, please notice the words “every” and “the same value.” They are absolute words. This is an absolute law. The theory also predicts that the speed of light is an absolute speed limit for any motion.

Using only Einstein’s two postulates an undergraduate university student can prove the formulas for the relativity of space and time that describe exactly how our state of motion will affect our measurements of the time and place of events. So Einstein was not abandoning absolute truth by denying absolutes. He was identifying the real absolutes.

What Albert was telling us is, “You think that space and time are absolute. They are not. Let me show you the real absolutes: the laws of physics and the speed of a light signal.” When I would explain it this way, it would definitely make my students, who believed that truth and morals were relative, think more deeply about it.

If the laws of nature in the hard sciences were absolute, could it be that there actually was absolute truth, and even absolute moral values? Would it be foolish to be guided by the properties of natural law when it comes to analyzing the rest of life? Judeo-Christian students got it right away. They saw that the Creator had made a lawful universe with absolute founding principles, so why would the Creator not also have established absolute moral principles? Atheistic, agnostic, or unsure students at least showed signs of thinking more deeply about the question, beyond a flippant reference to Albert Einstein’s relativity theory.

The case gets even stronger with Einstein’s general theory of relativity

Einstein’s general theory of relativity makes the case for absolute truth even stronger. Its two postulates are similar to those of special relativistic mechanics. But now the set of reference frames where the postulates must hold is much larger. It includes accelerating, rotating, and “warped space-time” systems.

The first general relativity postulate is the same as in special relativity: the laws of physics must be the same formulas when expressed in any one of the much larger class of coordinate systems.

The second postulate also addresses the motion of a light signal as observed in any coordinate system from the larger class, which includes all inertial systems: Observers in any coordinate system will observe that a given light signal will always follow a shortest distance path between two events in the system’s four-dimensional space-time.

Both postulates contain absolute words like “the same,” “in any,” and “always.” By making statements for a much larger set of coordinate systems, they make the postulates even more absolute. In fact, we do not know of any coordinate systems with physical meaning that is not included in general relativity.

To work out the mathematics of general relativity you would need to be in an advanced graduate program in physics. But, some of the predictions we can describe so most can understand. What you get out of the bigger group of reference frames and the focus on the minimum distance light travel path are (1) all of the effects of special relativistic mechanics and (2) all of the effects of gravity. This includes weak gravitational effects like the Earth’s elliptical orbit around the Sun, as predicted by Newton’s well-know law of gravity.

But general relativity also takes into account that a coordinate system fixed to Earth is accelerating as it follows its elliptical orbit around the Sun. This acceleration causes small, but measurable, deviations from the expected orbit predicted by Newton’s laws. The axes of the elliptical orbit do not stay fixed in direction. They rotate very slowly as the years pass. The exact amount of year by year rotation has been predicted and measured! This more comprehensive theory predicts other fascinating astrophysical structures like black holes.

A model of 'folded' space-time shows how a wormhole bridge might form with at least two mouths that are connected to a single throat or tube.

To review the main point, in general relativistic mechanics the two postulates or laws are also absolute statements about the real absolutes. This theory, now well established experimentally, strengthens the idea of possible absolute truth in all of reality. Maybe someday we will even learn how to do the “Star Trek” thing and travel through a “wormhole” in a short time to a distant galaxy. But first we need to locate a place where space-time is warped into one, if they actually exist.

My colleagues thinking on relativism of truth and morals

When I would raise the same question with my faculty colleagues in the lunch room or in social settings, they would often make what seemed more challenging objections in arguing against absolute truth. They would refer to the postmodern consensus in Western culture that absolute truth and morals do not exist, because all truth and moral statement are at best only valid relative to a culture and a community, even in science. They would sometimes quote science historian Thomas Kuhn, who first argued that scientific “paradigms” change radically amid cultural struggle (The Structure of Scientific Revolutions, Univ. of Chicago Press, 1962). He and others claim that this fact makes scientific truth culturally relative. A “paradigm” is a set of mental pictures and a logical approach to the science of some particular area. Let’s test Kuhn’s idea using what we know of physical theories of mechanical motion!

Sir Isaac Newton developed mechanics by imagining objects as made up of many small point-like pieces he called particles. These particles had a definite position and speed at any time, which could be measured experimentally. Each particle was subjected to pushes and pulls he called forces. His famous second law describes how each particle moves under the sum of the forces acting on it. This is the paradigm of classical mechanics, represented by the “large/slow” shaded box in the upper left rectangle of Fig. 1. It is very successful for large objects with sizes from a micron to a solar system, and for speeds small compared to the speed of light.  Newtonian classical mechanics provided the means by which NASA planned and executed their trips to the moon.

Fig. 1: Paradigm shifts and correspondence principles.

But scientists wanted to understand mechanics at small sizes like those of atoms, and for high speeds that were a significant fraction of the speed of light. To describe each extreme required a major paradigm shift. We have already described relativistic mechanics, which forces us to give up the paradigm that space and time intervals are absolute, but gives us better absolutes for fast relative motion. For atomic and molecular systems the early 20^th century saw the development of quantum mechanics. This theory describes both large and small systems moving slowly compared to light, the two upper boxes in Fig 1.

Its paradigm says you cannot deal directly with the velocity and position of objects. They have a unique existence, but you can only know the position within a range and the velocity within another range. The product of these uncertainties can never be less than a certain universal constant. The better you know the speed, the less you know the position, and vice-versa. Motion of these objects becomes indeterministic in principle, not just in practice.

So, what can we know about an electron, for example? We can know an abstract entity called its wave function or the probability wave of where we will measure it to be. We can’t pursue this concept and behavior of the probability wave farther in this limited article. But, it is obvious that a huge paradigm shift has been made. The figure to the right illustrates the difference in the two paradigms.

Finally, to include a description of small fast systems you have to use both special relativity and quantum mechanics, a combination called relativistic quantum mechanics! I have managed to teach it and its successes to first year graduate students, so even this paradigm can be mastered within reason.

So far, it seems that Kuhn’s idea is holding up. Scientific truth seems to be relative and changes radically through “revolutions” as history progresses. Culture strongly resists each paradigm shift until the evidence reaches some critical mass, then the “revolution” occurred. But not so fast …

If you apply relativistic mechanics to large slow systems, you get exactly classical mechanics with negligible effects like time dilation or length contraction. This is pictured by the vertical arrow between the left two rectangles in Fig. 1. Physicists require that any theory of fast large objects must reduce to Newton’s theory when applied to slow large objects—this is called a correspondence theorem. Correspondence theorems represent the presupposition by scientists that newer theories will not negate physical truth captured in older theories within the range of physical situations where the old ones were proven by experiment. Therefore they demanded that relativistic mechanics, to be accepted, must give classical mechanics when applied to slow large objects including absolute space and time intervals to an excellent approximation, which it does. The new paradigm must include the old one; it does not replace it.

If you apply the most comprehensive theory in Fig. 1, relativistic quantum mechanics, to large slow systems, you also get classical mechanics. This is another correspondence theorem represented in Fig. 1 by the arrow from the lower right box to the upper left box. In Fig. 1 the total of five correspondence theorems are represented by the five arrows. The two dashed arrows with the small two-way arrowheads at either end represent theorems saying that two boxes of the most comprehensive theory reduce to two boxes of a less comprehensive theory.

Old paradigms for older, less comprehensive theories, are never revoked. They are still valid for objects with sizes and speeds that fit the conditions under which they were proven and tested. But to move to descriptions of a larger amount of reality, more and more distant from everyday life, we had to discover new paradigms. These paradigms were quite different from how we imagined reality for the more restricted part of physical reality we can experience directly.

This is far different from the claim that the truth of each theory is culturally relative to a certain era. Each theory remains true in its proper realm—like absolute truth about that realm. And the more comprehensive theories describe increasing parts of the real material or natural world we live in. We even hear talk from intellectual giants like Stephen Hawking of hopes to define a “theory of everything!” some day.

But, Hawking has since sadly realized that mathematician Kurt Gödel had actually proved a theorem that forces the conclusion the theory of everything cannot exist in a finite number of formulas. With our scientific tools of logic, mathematics, and observation we are apparently forever kept away from knowing everything about physical reality. This would be a proper limitation for beings that were themselves created by the actual Creator of all things, who must have all understanding!

So, I present this interpretation to my faculty colleagues, and most of them fall silent. I assume it makes them think more seriously about the possible existence of absolute truth, even in the moral realm. They really do seem to see how it makes their belief in relativity of truth questionable.

For the very determined ones who still want to argue the relativity of scientific truth, I have a simpler challenge. I say something like, “Why don’t you go up on the roof of this building, step off into space and show us upward motion?” Then they do stop arguing and no one yet has taken the challenge, thankfully!

Could there be a basis for absolute moral truth?

I found myself at my retirement luncheon a few years ago sitting at a table with a couple of other retirees from my College of Liberal Arts and Sciences, a couple of department heads, and the Dean of our college. The Chancellor was the Mistress of Ceremonies. My Dean’s job was to treat me well for this luncheon at my “goodbye” from the institution. He had an international reputation as an ardent apologist for postmodernism. He was also known for never losing arguments as he forcefully silenced opposition ideas. Faculty members were wary of ever publically disagreeing with him. I had followed his thinking with interest for some years to learn more about postmodern thought.

He was sitting next to me, and I suddenly realized that at this luncheon I was “bulletproof.” I had nothing to lose by engaging in polite disagreement with his ideas. I raised the possibility of a universal absolute moral system, and its desirability. He became vigorously engaged in arguing against this, claiming that no one actually followed such a system. He said people always end up acting in their narrow self interest. I had often seen people acting morally against their immediate self interest, and pointed this out. But, he persisted in his absolute claim of no absolute morals.

It especially upset him when I spoke of the value of a person approximating totally moral behavior. I think most of us can only approximate this ideal, because most of our actions have some taint of self interest or other imperfection, however small.

His firmest point was that you cannot build a moral system “from the bottom up,” that is, by reasoning from the existing human community. After we discussed this view for a while, I realized that I basically agreed with it. There is no basis for a universal moral system that is derived from collective human culture and behavior, although social science statistics strongly favor Biblical family moral values as more beneficial for individuals who grow up in their framework.

So, I said, “I agree with you that you cannot build one from the bottom up. But, could it be built from the top down? What if there really is a Personal Creator who followed a specific very excellent design for the world and for human life, and doesn’t want us to mess it up? What if the Creator even wrote a book spelling out how we should live to follow that design?”

To my utter amazement, the Dean completely calmed down and said, “That is a consistent position.” As a fair-minded postmodern philosopher, he sees that the Biblical world view is consistent and reasonable, but he does not believe it describes reality.

Based on the Bible, we Christians believe that our Creator followed a good design for the world, human life, and our relationship to Him. We believe that in the Bible God took the initiative, speaking through human minds, to share with us the fixed moral laws He has built into Creation. “Do not be deceived: God cannot be mocked. A man reaps what he sows. Whoever sows to please their flesh, from the flesh will reap destruction; whoever sows to please the Spirit, from the Spirit will reap eternal life. Let us not become weary in doing good, for at the proper time we will reap a harvest if we do not give up.” (Galatians 6:7-9, NIV)

Though often taught in poetic language in the Old Testament, we have a Biblical basis for believing that there are fixed laws for the natural world, and there is absolute truth about physical reality. For example, “Thus says the LORD: If I have not established my covenant with day and night and the fixed order of heaven and earth, then I will reject the offspring of Jacob and David my servant ... ” (Jeremiah 33:25-26a, ESV) or  “When he gave to the wind its weight and apportioned the waters by measure, when he made a decree for the rain and a way for the lightning of the thunder, then he saw it and declared it; he established it, and searched it out.” (Job 28:25-27, ESV)

Because Genesis says that men and women are made in the image of God, we believe that our minds share a measure of the logic by which He created all things. So, we can trust science, which comes out of the human mind and our observation powers, to learn and comprehend a lot about physical reality (the natural world.) Combining these Biblical teachings, we have a rational basis for believing our search for truth about physical and moral reality can succeed in large measure.

This leaves each person with a couple of decisions. Will we seek absolute truth, even when our approach to it is only partial? Will we seek to live by the Biblical set of revealed moral principles, no matter how hard it seems? Will we take the Creator’s offer to help, and seek that help to do both? Will we realize that this world view is philosophically consistent, and has a claim to describe actual reality—to be TRUE? This is the framework in which I have chosen to live. What about you?

Richard Carhart is Professor of Physics Emeritus at the University of Illinois at Chicago, having taught there and done research for 35 years.

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