Stability and Determinism
The Cosmological Constant
Einstein noticed that he could add a term to his general relativity equations. The added term did not violate the self-consistency of the equations. The simplest form of the term was just a constant, but it could have any value, positive, negative, or zero. If one took the value of the constant as zero, the term dropped out, and the equations were as Einstein had first derived them.
Even a nonzero constant term has hardly any measurable effect in an Earth-based laboratory. At interplanetary distances the effect grows, and at interstellar distances it becomes noticeable. At intergalactic distances the term causes a decided effect.
The effect works either with or against the force of gravity, depending on whether the constant is positive or negative. Working with gravity the term accelerates the collapse of the universe. Working against gravity a small value for the term only partially offsets the effect of gravity. It slows the collapse. A larger value overcomes gravity completely and causes the universe to expand. Einstein chose an intermediate value for the constant, to make it counterbalance exactly the force of gravity at large distances. This made his model of the universe stable. The universe could exist forever without either collapsing or expanding. Einstein called the term the “cosmological constant.”
Adding a term to a set of equations is nothing new in physics. Half a century before, James Clerk Maxwell (British physicist, 1831–1879) was working with four equations that governed electric and magnetic phenomena, as they were then known. The equations were mathematically inconsistent with one another, but Maxwell saw that adding a term to one of them would make them consistent. Putting them together with the new term, Maxwell showed that light might be an electromagnetic wave moving at a high but limited speed. The equations predicted the speed of light. Subsequent experiments confirmed, measured, and refined the value of the speed of light. Today we know that light is an electromagnetic wave.
Other scientists had discovered each of the four equations, but Maxwell got his name associated with the full set of four equations because he saw a mathematical inconsistency in them and added a term to fix them up. The added term allowed him to discover that light is an electromagnetic phenomenon and to calculate its speed.
Maxwell’s equations are a beautiful idea. They are a kind of poetry to the initiated. But there is no reason why beautiful ideas should have anything to do with reality. For instance, the beautiful thought may strike me that I possess a trillion dollars. Also, I might conceive of myself as extraordinarily generous and willing to give out checks for a million dollars to anyone who writes in and asks. Now that is beautiful for everyone, isn’t it? We can all be happy with these beautiful thoughts until the recipients of the checks discover that my bank funds never come close to covering even one million-dollar check.
There is no reason to suppose before examining reality that it is beautiful. However, when we discover that it is, the discovery cries out for an explanation.
Maxwell connected the phenomena of electricity and magnetism into one theory of electromagnetism and showed that light was an electromagnetic phenomenon. Einstein went farther with each of his two theories. His special theory of relativity connected the speed of light with mechanics. The fastest one can go in any vehicle and the fastest speed any natural particle can acquire is the speed of light. Einstein’s general theory of relativity connected light and gravity. Einstein showed that a beam of light can be bent by gravity.
Even though Einstein was cautious, he chose a value for the cosmological constant that made the universe stable. Why did he do that? The answer has to do with a philosophical conflict between those who held to physical determinism and those who thought people have free will. Let’s look at the idea of determinism and then see what motivated Einstein’s preference for a stable universe.
Even a nonzero constant term has hardly any measurable effect in an Earth-based laboratory. At interplanetary distances the effect grows, and at interstellar distances it becomes noticeable. At intergalactic distances the term causes a decided effect.
The effect works either with or against the force of gravity, depending on whether the constant is positive or negative. Working with gravity the term accelerates the collapse of the universe. Working against gravity a small value for the term only partially offsets the effect of gravity. It slows the collapse. A larger value overcomes gravity completely and causes the universe to expand. Einstein chose an intermediate value for the constant, to make it counterbalance exactly the force of gravity at large distances. This made his model of the universe stable. The universe could exist forever without either collapsing or expanding. Einstein called the term the “cosmological constant.”
Adding a term to a set of equations is nothing new in physics. Half a century before, James Clerk Maxwell (British physicist, 1831–1879) was working with four equations that governed electric and magnetic phenomena, as they were then known. The equations were mathematically inconsistent with one another, but Maxwell saw that adding a term to one of them would make them consistent. Putting them together with the new term, Maxwell showed that light might be an electromagnetic wave moving at a high but limited speed. The equations predicted the speed of light. Subsequent experiments confirmed, measured, and refined the value of the speed of light. Today we know that light is an electromagnetic wave.
Other scientists had discovered each of the four equations, but Maxwell got his name associated with the full set of four equations because he saw a mathematical inconsistency in them and added a term to fix them up. The added term allowed him to discover that light is an electromagnetic phenomenon and to calculate its speed.
Maxwell’s equations are a beautiful idea. They are a kind of poetry to the initiated. But there is no reason why beautiful ideas should have anything to do with reality. For instance, the beautiful thought may strike me that I possess a trillion dollars. Also, I might conceive of myself as extraordinarily generous and willing to give out checks for a million dollars to anyone who writes in and asks. Now that is beautiful for everyone, isn’t it? We can all be happy with these beautiful thoughts until the recipients of the checks discover that my bank funds never come close to covering even one million-dollar check.
There is no reason to suppose before examining reality that it is beautiful. However, when we discover that it is, the discovery cries out for an explanation.
Maxwell connected the phenomena of electricity and magnetism into one theory of electromagnetism and showed that light was an electromagnetic phenomenon. Einstein went farther with each of his two theories. His special theory of relativity connected the speed of light with mechanics. The fastest one can go in any vehicle and the fastest speed any natural particle can acquire is the speed of light. Einstein’s general theory of relativity connected light and gravity. Einstein showed that a beam of light can be bent by gravity.
Even though Einstein was cautious, he chose a value for the cosmological constant that made the universe stable. Why did he do that? The answer has to do with a philosophical conflict between those who held to physical determinism and those who thought people have free will. Let’s look at the idea of determinism and then see what motivated Einstein’s preference for a stable universe.
Physical Determinism
Prior to the 20th century the laws of physics were completely deterministic. People thought the universe was a great clockwork machine.
On a clock 60 revolutions of the second hand occur during one revolution of the minute hand, and 12 revolutions of the minute hand occur during one revolution of the hour hand. A clockmaker usually aligns the hour, minute, and second hands at twelve and winds the spring. He then sets the clock to the current time and starts it. The mechanism maintains the hands in fixed relationship. The minute hand advances through the 60th part of a circle while the second hand completes a full circle. Likewise the hour hand advances through the 12th part of a circle while the minute hand completes a full circle. This insures that every twelve hours the three hands will momentarily line up at twelve again. Even if the clock does not keep perfect time, the hands must come together at 12 unless they have slipped on their shafts, because the gears hold them in a fixed relationship. Setting the initial conditions achieves the result. The three hands move at different speeds, but they eventually come back to their initial alignment, and then repeat the same movement cyclically.
The relative motions of different clock parts are completely deterministic. This means that the clockmaker has predetermined how the different parts will move in relation to one another. Human clockmakers are not able to predetermine everything about the motion. Especially they would like to determine the rate of movement, so that a revolution of the hour hand would require exactly 12 hours. If they could do that, the clock would keep time perfectly. Clockmakers would achieve the purpose of their design.
Many intelligent people of antiquity tried to find simple relationships in the speeds of the Sun, planets, and stars to make the movement of the celestial bodies cyclical also. The Sun returns to nearly the same position high overhead in 24 hours, but the stars appear to move faster. They rise, pass overhead, set, and rise again in about 23 hours 56 minutes and 3.45 seconds. The Moon appears to move still faster. It rises, passes overhead, sets, and rises again in about 23 hours and 13.5 minutes. We now understand that the difference in speeds arises from three distinct motions. The rotation of the Earth on its axis makes the stars appear to rise periodically. The revolution of the Earth around the Sun makes the Sun’s period of rising different from that of any other star. The Moon circles around the Earth while the Earth moves around the Sun. The three periods, 24 hours exactly, 23 hours 56 minutes and 3.45 seconds, and 23 hours and 13.5 minutes, are incommensurate. There is no simple relation between them.
The motions of the Earth, Moon, and planets are like the motions of the hour, minute, and second hands on a clock. However, there are no gears to hold the Sun, Earth, Moon, and planets in a fixed relationship. We do not know if there was an initial alignment, or if they will all come together again to the same alignment after a long time. We do know that the Earth is not a perfect sphere. The Moon’s gravity acts on the Earth’s equatorial bulge and makes the Earth wobble as it rotates. The crashing of the ocean tides against the Earth’s continents dissipates the Moon’s orbital energy. Over the course of many centuries the Moon moves farther from the Earth, and the lunar month becomes longer. Therefore the analogy to a clockwork machine is doubtful. We can describe the wobbles and slowing, but we cannot solve all the equations exactly. No one has ever even proved that the solar system is stable over the long term. The long-term stability of the universe is even less certain.
If the universe is unstable then it cannot have existed forever in its present condition. Einstein had explored various models of the universe.
In some, the universe remains compact for an infinite time, from the infinitely remote past to the recent past, and then, at a crucial moment, it begins to expand. There was no physical way to define either the crucial moment or the cause that triggered the expansion.
If the universe was not static, forever approximately the same, then there had to be a nonphysical cause that initiated change. Someone or something had to cause the beginning, if there was one.
On a clock 60 revolutions of the second hand occur during one revolution of the minute hand, and 12 revolutions of the minute hand occur during one revolution of the hour hand. A clockmaker usually aligns the hour, minute, and second hands at twelve and winds the spring. He then sets the clock to the current time and starts it. The mechanism maintains the hands in fixed relationship. The minute hand advances through the 60th part of a circle while the second hand completes a full circle. Likewise the hour hand advances through the 12th part of a circle while the minute hand completes a full circle. This insures that every twelve hours the three hands will momentarily line up at twelve again. Even if the clock does not keep perfect time, the hands must come together at 12 unless they have slipped on their shafts, because the gears hold them in a fixed relationship. Setting the initial conditions achieves the result. The three hands move at different speeds, but they eventually come back to their initial alignment, and then repeat the same movement cyclically.
The relative motions of different clock parts are completely deterministic. This means that the clockmaker has predetermined how the different parts will move in relation to one another. Human clockmakers are not able to predetermine everything about the motion. Especially they would like to determine the rate of movement, so that a revolution of the hour hand would require exactly 12 hours. If they could do that, the clock would keep time perfectly. Clockmakers would achieve the purpose of their design.
Many intelligent people of antiquity tried to find simple relationships in the speeds of the Sun, planets, and stars to make the movement of the celestial bodies cyclical also. The Sun returns to nearly the same position high overhead in 24 hours, but the stars appear to move faster. They rise, pass overhead, set, and rise again in about 23 hours 56 minutes and 3.45 seconds. The Moon appears to move still faster. It rises, passes overhead, sets, and rises again in about 23 hours and 13.5 minutes. We now understand that the difference in speeds arises from three distinct motions. The rotation of the Earth on its axis makes the stars appear to rise periodically. The revolution of the Earth around the Sun makes the Sun’s period of rising different from that of any other star. The Moon circles around the Earth while the Earth moves around the Sun. The three periods, 24 hours exactly, 23 hours 56 minutes and 3.45 seconds, and 23 hours and 13.5 minutes, are incommensurate. There is no simple relation between them.
The motions of the Earth, Moon, and planets are like the motions of the hour, minute, and second hands on a clock. However, there are no gears to hold the Sun, Earth, Moon, and planets in a fixed relationship. We do not know if there was an initial alignment, or if they will all come together again to the same alignment after a long time. We do know that the Earth is not a perfect sphere. The Moon’s gravity acts on the Earth’s equatorial bulge and makes the Earth wobble as it rotates. The crashing of the ocean tides against the Earth’s continents dissipates the Moon’s orbital energy. Over the course of many centuries the Moon moves farther from the Earth, and the lunar month becomes longer. Therefore the analogy to a clockwork machine is doubtful. We can describe the wobbles and slowing, but we cannot solve all the equations exactly. No one has ever even proved that the solar system is stable over the long term. The long-term stability of the universe is even less certain.
If the universe is unstable then it cannot have existed forever in its present condition. Einstein had explored various models of the universe.
In some, the universe remains compact for an infinite time, from the infinitely remote past to the recent past, and then, at a crucial moment, it begins to expand. There was no physical way to define either the crucial moment or the cause that triggered the expansion.
If the universe was not static, forever approximately the same, then there had to be a nonphysical cause that initiated change. Someone or something had to cause the beginning, if there was one.
A Fully Deterministic Universe
Though we cannot solve exactly all the equations of physics, an omniscient creator presumably can. The creator of a fully deterministic universe can set the initial conditions with infinite precision and thus control all things. In such a fanciful place there is no need for miraculous intervention at crucial times because all things, including the thoughts and intentions in the hearts of people, can be traced back to the beginning. No human effort could ever make sufficiently accurate measurements and back-solve the equations of physics well enough to solve a typical whodunit, but then nobody would be responsible even for murder except the one who set the initial conditions. Einstein always believed in full determinism, and therefore said that the god of his concepts would not be justified in judging. If an omnipotent being predetermined our thoughts then our thoughts would really be his thoughts. If he judged us for our thoughts then he would really be judging himself. Einstein wrote:
Nobody, certainly, will deny that the idea of the existence of an omnipotent, just, and omnibeneficent personal God is able to accord man solace, help, and guidance; also, by virtue of its simplicity it is accessible to the most undeveloped mind. But, on the other hand, there are decisive weaknesses attached to the idea in itself, which have been painfully felt since the beginning of history. That is, if this being is omnipotent, then every occurrence, including every human action, every human thought, and every human feeling and aspiration is also His work; how is it possible to think of holding men responsible for their deeds and thoughts before such an almighty Being? In giving out punishment and rewards He would to a certain extent be passing judgment on Himself. How can this be combined with the goodness and righteousness ascribed to Him?[i]
[i] Einstein, Albert, Ideas and Opinions, based on Mein Weltbild edited by Carl Seelig, and other sources, new translations and revisions by Sonja Bargmann (New York: Wing Books, 1954), pp. 46–47, from Science, Philosophy and Religion, A Symposium, published by the Conference on Science, Philosophy, and Religion in Their Relation to the Democratic Way of Life, Inc. (New York: 1941).
[i] Einstein, Albert, Ideas and Opinions, based on Mein Weltbild edited by Carl Seelig, and other sources, new translations and revisions by Sonja Bargmann (New York: Wing Books, 1954), pp. 46–47, from Science, Philosophy and Religion, A Symposium, published by the Conference on Science, Philosophy, and Religion in Their Relation to the Democratic Way of Life, Inc. (New York: 1941).
In Einstein’s way of thinking, if there was a creator, then the creator was responsible for everything that went on at any time in the universe. Even intelligent organisms would only seem to have free choice. The laws of physics and the initial conditions would really determine their actions. Since the creator had made the laws and set the initial conditions, he would ultimately be responsible for prejudice, hatred, oppression, murder, and war. Einstein did not want to live in a universe set up that way. He was happy to find a way to make the universe uncreated, so the creator would not be responsible for human inhumanity.
The god Einstein rejected is not the God of the Bible. God disclaims our thoughts.
The god Einstein rejected is not the God of the Bible. God disclaims our thoughts.
Let the wicked forsake his way and the evil man his thoughts. Let him turn to the LORD, and he will have mercy on him, and to our God, for he will freely pardon. “For my thoughts are not your thoughts, neither are your ways my ways,” declares the LORD. “As the heavens are higher than the earth, so are my ways higher than your ways and my thoughts than your thoughts” (Isaiah 55:7‑9)
We know, though perhaps Isaiah did not, that there is no limit to the height of the heavens above the Earth. We can know God’s thoughts only if He reveals them to us. The God of the Bible takes no responsibility for our thoughts. He is justified in judging us.