Time, Space, and Gravity: How Should Creationists Think About General Relativity?

I discussed special relativity in a previous article. In this article, I take up general relativity. In my previous article, I raised the question of what is moving and what is not moving. From the standpoint of physics, it usually doesn’t matter if one is moving or not, for the formulation of physics is the same within inertial reference frames. Even if one chooses to use a non-inertial reference frame, it is straightforward to transform either from an inertial reference frame to a non-inertial reference frame or from a non-inertial reference frame to an inertial reference frame. Hence, as far as physics is concerned, it doesn’t matter what is moving and what is not moving. That is why physicists sometimes are quoted about the equivalence of geocentrism and heliocentrism, for either one can be treated as valid, as far as physics is concerned, depending on the chosen frame of reference.

Mach’s Principle

Still, the perception remains that there ought to be a standard of absolute rest in which we can express all motion. The problem is, even if such an absolute standard of rest exists, how would one recognize it? We may feel like we are at rest, but how can we be sure that we are at rest? Physicists have wrestled with this conundrum for a very long time. The answer most physicists have settled on is more philosophical than scientific. But why should that be a problem? All systems of studies, such as philosophy, mathematics, and science, must begin with several axioms, postulates, and definitions. That is, all sciences, including physics, begin with certain assumptions that amount to philosophical presuppositions. Therefore, it ought not to be a surprise that the nature of what is moving and what is not moving is more philosophical than scientific.

Consider a pail of water suspended by a cord attached to its bail. If the cord is spun, the pail will begin to spin. At first, the water will not share in the pail’s rotation, but eventually, viscous forces in the water will cause the water to spin in synchrony with the pail. As the water begins to spin, one will notice that a concavity develops on the top of the water, with the concavity reaching its maximum depth once the water is fully rotating in sync with the pail. It is as if the water knows that it is spinning. But how does the water know that it is spinning? Consider another example. Stand outside on flat, level ground with your arms hanging limply at your side. Close your eyes and begin to spin around. You will notice that your arms rise upward. In fact, it will take effort to prevent your arms from rising. The faster you spin, the more your arms will rise. How do your arms know to rise? Like the water in the pail, it is as if your arms know that you are spinning, but again, how do your arms know that you are spinning?

As explained in my previous article, we would attribute these observations of the concavity of water in the spinning pail and our rising arms as we spin to the action of centrifugal forces within non-inertial reference frames. But how does the water or our arms know that we are spinning and that it is not the rest of the universe that is spinning? Again, as far as physics is concerned, the two situations are equivalent. Whether we explain what we observe by application of Newton’s laws of motion (in an inertial frame of reference) or if we appeal to centrifugal force (in a non-inertial frame of reference), something must be spinning, but which is it—the universe or us? As far as physics is concerned, we cannot say for certain which is spinning. (Yes, you read that right!)

In the latter nineteenth century, Ernst Mach addressed this question in depth, and so, his proposed resolution became known as Mach’s principle. If we spin around in a field on a clear, dark night, we will see the stars spin in the opposite direction. Meanwhile, a person standing next to us will not see the stars spin, nor will they see their arms rise. It is as if the stars represent a nonmoving (fixed) reference frame against which we can ascertain whether we are in motion. That is, we can assume that space is at rest with respect to the stars. Are the stars really at rest? Individual stars move, so even the stars are moving with respect to this hypothesized standard of rest. However, we could average the motion of all the stars to establish a standard of rest. Mach assumed that the average motion of the matter of the universe is zero and hence is at rest with respect to space. It is this standard of reference defined in terms of the matter of the universe that dictates what is moving. Hence, when we spin around, the matter in our arms rises upward due to the centrifugal force imposed by Mach’s definition of the standard of rest because as we spin, we are in a non-inertial reference frame. One way to state Mach’s principle is “local physical laws are determined by the large-scale structure of the universe.” A more informal statement would be “mass out there influences inertia here.” It’s important to note that Mach did not prove his principle. Rather, he took it as axiomatic (taken for granted or self-evident1) and a philosophical assumption, not a derived theory. As I previously stated, all systems of study require starting with a set of assumptions, principles, axioms, and definitions. Mach’s principle is simply one of those starting principles. It is Mach’s principle, when properly understood, that establishes the standard of rest in the universe.

The Twin Paradox Resolved

It is Mach’s principle, when properly understood, that establishes the standard of rest in the universe.

Mach’s principle played a key role in Einstein’s development of general relativity. While Mach’s principle is more obviously tied to general relativity, it also plays a more subtle role in special relativity. Consequently, Einstein assumed an absolute standard of rest for the universe in both versions of modern relativity theory—special and general relativity. This opposes the common misconception that modern relativity assumes exactly the opposite, that there is no absolute standard of rest. Many criticisms of modern relativity theory are built upon this misunderstanding. One of the most commonly heard objections to modern relativity theory is the so-called twin paradox, which arises from an incorrect understanding of modern relativity.

What is the twin paradox? According to special relativity, an object traveling at very high speed experiences time dilation compared to objects that are not moving at high speed. The twin paradox considers a set of identical twins, one who travels at nearly the speed of light to a star that is say 20 light-years away and the other who remains on earth. Upon traveling to the star, the astronaut then returns to the earth. To the twin that remained on earth, the round trip took more than 40 years. But to the astronaut, because of time dilation, the trip took less than a year. Upon the astronaut’s return to earth, he discovers that his twin on earth has aged more than 40 years, but the twin on earth is astonished that his brother has aged very little. If all motion is relative, why shouldn’t it be the other way around? From the reference frame of the astronaut, it is the twin on earth that has moved, not the astronaut. So why isn’t it the twin on earth that has aged very little while the astronaut is the one who has aged more than 40 years?

Of course, the flaw in the reasoning behind the twin paradox is the false assumption that modern relativity theory states that all motion is relative. Following Mach’s principle, we know that the astronaut accelerated four times with respect to the mass of the universe. First, the astronaut accelerated to nearly the speed of light to travel to the distant star. Second, once the astronaut approached the star, he had to decelerate to visit the star. Third, the astronaut had to accelerate to return to earth. Fourth, the astronaut had to decelerate as he approached the earth to land on the earth. Meanwhile, following Mach’s principle, his twin on earth did not experience any of these accelerations. Hence, there is no ambiguity as to which twin experienced motion and which twin remained at rest. With a proper understanding of modern relativity, the paradox disappears.

How did the false notion that all motion is relative come about? Perhaps it came from improper reporting and incorrect popular discussion of modern relativity ever since modern relativity was propounded more than a century ago. Or perhaps it was the fault of proponents of moral relativism a century ago—who sought scientific justification for their worldview—by appropriating the language of modern relativity theory to justify their morally dangerous teachings. The phrase “all motion is relative” is an accurate description of Galilean relativity, not modern relativity theory. As I discussed in my previous article, special relativity posits that there is an absolute standard: the speed of light. Add to that the absolute standard of space posited by Mach’s principle upon which much of general relativity relies.

General Relativity

While Mach’s principle influenced Einstein in developing his theory of general relativity, that does not get to the meat of what general relativity is about. I discussed the equivalence principle in my previous article. Why is it that gravitational and inertial masses are the same? As I said in my previous article, there is a strong implication of design in the equivalence principle. But what are the other implications of the equivalence principle? The only situations where forces are equal to inertial masses are the fictitious forces we must invoke in non-inertial reference frames (e.g., centrifugal forces in spinning reference frames). Could it be that gravitational acceleration is a fictitious force as well? That would suggest that when we experience gravitational acceleration, we are in a sort of non-inertial reference frame. (Note: When physicists use the term “fictitious” force, they don’t mean imaginary or nonexistent—these forces have real, measurable effects within non-inertial frames.)

When we are in non-inertial reference frames, there usually are clues that we are in a non-inertial reference frame. For instance, in a rotating reference frame, we notice that the universe appears to spin around us. When we are in a vehicle that is accelerating in a straight line, such as an airplane that is taking off, we see the universe appear to accelerate the opposite direction. This is Mach’s principle again. Do we see this when under the influence of gravity? Yes, as anyone who has ridden an amusement park ride that drops passengers from some height (usually more than 100 feet) to experience free fall would attest. To the passengers, it feels as though the ground (as well as the rest of the universe) is rushing upward (thankfully, the brakes engage to prevent a collision with the ground). Again, this is Mach’s principle. But there is a difference between free fall and the other two examples. In free fall, Newton’s laws of motion work with no need to invoke fictitious forces. Therefore, surprisingly, free fall is actually considered an inertial reference frame—a key insight behind general relativity. That is, the essence of the equivalence principle: Free fall, under the influence of gravity, is the sole example of an accelerating reference frame that is an inertial reference frame.

It was these thoughts about the equivalence principle that led Einstein to formulate general relativity. To treat gravity as a fictitious force, Einstein introduced time as a fourth dimension of space. This may sound odd, but we frequently express distance in terms of time. For instance, if asked how far Chicago is from Cincinnati, one may reply, “About four hours.” To make sense of such an answer, one must assume an accepted average speed as one travels from one city to the other, typically by automobile. When it comes to time being a fourth dimension of space, the assumed standard of speed is the speed of light. By multiplying the speed of light (c) by the time (t), one gets ct that has the same units as the other three dimensions of space, usually denoted by x, y, and z. Expressed this way, time is not that different from the other dimensions of space. In algebra, we often use ordered pairs (x,y) to express position in a two-dimensional Cartesian plane. Similarly, we can describe where things are in four-dimensional space-time with four coordinates, (x,y,z,ct). However, there is a fundamental difference between the three normal spatial dimensions of space and time. In normal spatial dimensions, one can move forward, backward, or remain at rest. But one cannot remain at rest or go backward in time—one must continually move forward in the positive direction in time.

How can one plot these four dimensions? It’s not easy because we can only perceive three spatial dimensions. Diagrams often simplify this by using two dimensions: one spatial and the time dimension, typically labeled (x,ct). While we may have difficulty visualizing more than three dimensions, mathematically, we can generalize the familiar two-dimensional and three-dimensional cases to describe any number of dimensions. For instance, in statistical mechanics, physicists often make use of four, five, and even six dimensions. These dimensions are often referred to as degrees of freedom.

Einstein described the motions of objects in a four-dimensional space-time manifold. Even objects that we perceive to be at rest continually, or seem stationary in space, still move forward in time. Whether we perceive objects to be at rest or in motion, in space-time, objects travel along what’s called geodesics. Simply put, a geodesic is the shortest distance between two points. Euclidean geometry (the geometry you likely studied in high school) is flat, so geodesics in Euclidean space are straight. But geometry can be curved, and such non-Euclidean geometry is well understood. Einstein proposed that the presence of mass curves space-time, leading to curved geodesics. It is the motion of objects along curved geodesics in space-time that we perceive as gravitational acceleration. This was one of the most important conceptual shifts in modern physics.

Within general relativity, gravity is considered a fictitious force, an effect of space-time curvature, not a true force acting at a distance. This has led some physicists to call gravity an emergent force. So is gravity a force, as described in Newton’s theory, or is gravity not a force, as described in general relativity? I will defer discussion of that until later. In the meantime, is there evidence for this different way of looking at gravity? Yes.

Evidence for General Relativity

The first evidence for general relativity offered was the perihelion advance of Mercury’s orbit.

The first evidence for general relativity offered was the perihelion advance of Mercury’s orbit. By the nineteenth century, astronomers had worked out the details of Newtonian gravity. For instance, in the general case, the planets orbit the sun in ellipses, not circular orbits. Consequently, each planet’s orbit has a perihelion, the point closest to the sun. Considering each planet’s motion around the sun individually gives a good fit to the observed motion of each planet, but there are small discrepancies. We can explain these discrepancies by small perturbations, small gravitational tugs, that the planets exert on one another. It is easy to solve orbital motion with Newton’s law of gravity when there are only two masses considered (the sun and a single planet). We call this the two-body problem. However, when we consider any additional masses (like all eight planets, not just one planet), the problem becomes intractable. This is known as the n-body problem, which can’t be solved in a neat, closed form. Instead, astronomers use a series of approximations that gradually converge toward an accurate solution.

Within a century of Newton formulating his law of gravity, astronomers used perturbation theory to accurately describe the motions of the planets. William Herschel accidentally discovered the planet Uranus in 1781, and he was able to quickly compute an orbit for it. After 60 years of observations, astronomers found that Uranus was not following its computed orbit. The deviations between the observed and predicted positions of Uranus were not large, but perturbations of the known planets could not account for the discrepancy. Was Newton’s theory of gravity wrong after all? Most astronomers thought not. To solve this problem, two astronomers working independently considered the possibility that there was an eighth planet beyond Uranus that was perturbing Uranus. Based on its assumed distance from the sun, the two astronomers both independently predicted the location of this hypothetical eighth planet. A search of the predicted position of the eighth planet confirmed that planet’s existence. Astronomers eventually named that planet Neptune. This successful prediction provided strong confirmation of Newton’s theory of gravity.

A couple of decades later, astronomers noticed a similar unexplained discrepancy in Mercury’s orbit. In the case of Mercury, the discrepancy was in the advance of Mercury’s perihelion2 position—the perihelion point of Mercury’s orbit was slowly revolving (shifting) around the sun over time. This is called perihelion precession. The observed perihelion precession of Mercury’s orbit was 574 arc seconds per century. Application of perturbation theory within Newtonian mechanics could account for only 541 arc seconds per century, leaving 43 arc seconds per century unaccounted for. Buoyed by the discovery of Neptune, astronomers thought that there might be a small, unseen planet orbiting closer to the sun than Mercury that was perturbing Mercury’s orbit. Astronomers named this hypothetical planet Vulcan. From the amount of perihelion precession of Mercury, astronomers predicted the position of Vulcan, but searches for Vulcan were fruitless. When Einstein published his general theory of relativity, he showed that his new theory of gravity accounted for the additional 43 arc seconds per century in the perihelion advance of Mercury’s orbit—delivering a satisfying “eureka!” moment when his theory provided the missing solution. This was the first direct evidence for general relativity.

A good theory must explain known phenomena, such as the previously unexplained observed perihelion precession of Mercury. But it is also important for a good theory to predict new things. Using his theory of general relativity, Einstein showed that during a total solar eclipse, the light of stars passing close to the sun would bend toward the sun, with the amount of bending being greatest for those light beams passing closest to the sun. This bending would cause the observed positions of stars to appear farther from the sun than their actual positions. To test this prediction, one would need to obtain two photographs of the stars, one taken during a total solar eclipse and the other taken at night months before or after the eclipse. Comparison of precise measurements of the positions of the stars on the two photographs would result in the amount of deflection observed. Astronomers attempted this during the June 8, 1918, total solar eclipse, but cloudy weather interfered. Astronomers tried once again during the May 29, 1919, total solar eclipse. The sky was clear during this second attempt, and the results were consistent with the prediction of general relativity. This was the first test of a prediction of general relativity. It is important to note that Newtonian gravity also predicts a bending of starlight as the light passes close to the sun. However, the amount of bending predicted by Newtonian gravity and general relativity is not the same. Therefore, observation of the amount of bending is an excellent test to determine which of the two competing theories is correct. The results were consistent with the prediction of general relativity, not Newtonian gravity.

This raises a good question: Are Newtonian gravity and general relativity competing theories? Not really. In most cases, the predictions of Newtonian gravity and general relativity are the same. It is only in very extreme conditions where the predictions of the two theories disagree, and even then, the differences between the two theories often are small. In both the precession of Mercury’s orbit and the deflection of starlight during a total solar eclipse, the extreme condition is being close to the sun’s huge mass. For the orbits of the other planets, the difference between the predictions of the two theories of gravity are much smaller than our ability to measure. Therefore, Newtonian gravity is sufficient to explain and predict planetary orbits. Most real-world situations fall within what scientists call the Newtonian limit, in which Newtonian gravity precisely describes what we see. In fact, it is easy within general relativity to show that in the Newtonian limit, general relativity converges to Newtonian gravity.3 Hence, Newtonian gravity is a special case within the broader framework of general relativity. The mathematics of Newtonian gravity is much easier than the mathematics of general relativity, so physicists and astronomers use general relativity only when Newtonian gravity fails to work. That is, we use Newtonian theory much more often than we use general relativity.

The predictions of general relativity have been tested many times since 1919. For instance, there have been repeated measurements of the amount of bending starlight passing near the sun during total solar eclipses since 1919, each time with increasing precision. Many tests of general relativity escape much reporting in news broadcasts, but one stands out for the ample news coverage that it received. In 1971, physicists flew atomic clocks around the world in opposite directions on commercial flights. When the clocks were compared, they showed time differences consistent with the prediction of general relativity. With its many successful tests over more than a century, general relativity stands as one of the most thoroughly verified theories in all of science.

Is Gravity a Force?

In Newtonian theory, gravity is a force. However, in general relativity, gravity is not a force; at best, gravity is a fictitious force. Does this mean there’s a contradiction? Before answering that question, consider the other pillar of modern physics—quantum mechanics. As I explained in an earlier article, in quantum mechanics, there are four fundamental forces: gravity, weak nuclear force, electromagnetic force, and the strong nuclear force. According to quantum mechanics, the fundamental forces are mediated by special particles called gauge bosons. For instance, photons are the gauge bosons that mediate the electromagnetic force. When two particles interact via electromagnetic force, they exchange photons between one another. This swapping of photons between the particles informs either particle of the location of the other particle (i.e., allowing each particle to “sense” the presence of the other). The W and Z bosons mediate the weak nuclear force, and gluons mediate the strong nuclear force. All these gauge bosons have been detected. According to quantum mechanics, gravity is mediated by gravitons, but gravitons have not yet been detected. Physicists are confident that gravitons exist, but so far, there is no fully agreed upon theory of quantum gravity. For now, gravitons remain hypothetical, and some are skeptical of ever detecting them (due to their extremely weak interaction). Physicists hope that one day all four fundamental forces will be unified into a single theory of everything (TOE). But one of the main impediments to unification of the fundamental forces is the incompatibility between general relativity and quantum mechanics. Any resolution must also address the question of whether gravity is truly a real force or something else entirely.

This ought not to be a surprise. In physics, we must accept what may appear to be contradictory conclusions. For instance, in the early nineteenth century, abundant evidence emerged showing that light behaves like a wave. But by the end of that century, physicists found abundant evidence that light also behaves like a particle. In classical physics, this was a contradiction, which indicates that there must be something wrong with classical physics. Shortly thereafter, physicists found that things we think of as being particles, such as electrons, have a wave nature as well. This realization caused physicists a century ago to abandon classical physics in favor of quantum mechanics, at least for exceedingly small systems, such as electrons. What about large systems? As we consider ever larger systems, quantum mechanical features converge to classical mechanical properties. Niels Bohr called this the correspondence principle. It is analogous to the Newtonian limit as one goes from systems best described by general relativity to systems best described by Newtonian gravity. There is a similar kind of convergence in our understanding of light. At long wavelengths, the wave nature of light is dominant, but at the short wavelengths, the particle nature of light dominates. Physicists reluctantly have come to accept the wave-particle duality of light, even though these two approaches contradict one another. Is there a way out of this conundrum? Perhaps our understanding of light is incomplete—that what we know is a special case of a more general theory of light yet to be discovered.

I suspect that the answer to the question of whether gravity is a real force or not will be similar to the correspondence principle and the Newtonian limit. But do we really need complete closure on such questions? Consider our understanding of heat. A couple of centuries ago, physicists thought that heat was a fluid that flowed from a region of excess (high temperature) to a region of deficit (low temperature). Physicists had a name for this fluid: caloric. Much of classical thermodynamics still treats heat as a fluid, even though we now know that the caloric theory is incorrect. We now understand that heat is kinetic energy due to motion of the particles making up matter. Statistical mechanics, a subdiscipline of thermodynamics, treats heat this way. Common formulations of the second law of thermodynamics treat heat as a fluid, but the statistical mechanical view of the second law of thermodynamics treats heat as the kinetic energy (collective motion) of particles. Why are there two diverse ways of viewing heat? It’s because they apply at different scales. The “fluid” view of heat is a macroscopic model, while the kinetic view of heat is microscopic. While we think that the kinetic theory of heat is correct, it often is far more difficult and complicated to use in real-world situations. Consequently, when considering macroscopic situations, it is useful to apply the older model—even though it is not technically true.

Physicists often look at a situation from more than one angle. A good example is mechanics. One can solve problems using forces and accelerations, but those quantities involve vectors, in which one must consider both magnitude and direction of the vectors. This can get complicated. On the other hand, one can often solve the same problems more easily by using energy constraints. Since energy is a scalar, having only magnitude, this approach often simplifies the math. These are two different ways of looking at the situation, force-based and energy-based, that result in the same solution—this isn’t a flaw. Some problems in mechanics are wholly intractable using a force-based approach but can be handled effectively using an energy-based approach. Physicists are comfortable looking at physical situations in different ways. However, non-physicists seem to want closure with a single approach to every situation. When critics of physical theories (such as modern relativity) seize upon what they think are contradictions, it is probably because those critics do not understand the theories.

Conclusion

And most importantly, our touchstone is the authority of Scripture. If ideas do not oppose what the Bible teaches, then we are free to entertain those idea.

For a long time, many creationists have opposed both special and general relativity. There may be different reasons for this rejection of modern relativity. Some creationists may think that the tenets of modern relativity contradict Scripture. Other creationists may still think that modern relativity theory gives support to moral relativism—it doesn’t. For one thing, modern relativity theory insists on some absolutes, such as a preferred standard of rest via Mach’s principle and the invariance of the speed of light with respect to inertial reference frames. Still other creationists may have discomfort with the non-absolute nature of space and time. But what if that’s simply how God designed the universe to work? The more that I contemplate Newton’s third law of motion,4 the more it baffles me, leaving me wondering why the world works this way. Still other creationists may have an overly suspicious view of mainstream science, thinking that if many scientists are wrong about the origin and age of creation, then those scientists must be wrong about far more. That amounts to an ad hominem argument—assuming that if someone is wrong about one thing, then that person must automatically be wrong about other things too. Instead, our arguments must be based upon proper reasoning, logic, and evidence. And most importantly, our touchstone is the authority of Scripture. If ideas do not oppose what the Bible teaches, then we are free to entertain those idea. Modern relativity theory is one of the most rigorously tested theories in all of science. I encourage creationists to understand and accept it.

The fact that many creationists do not properly understand modern relativity theory remains a problem. I hope that my two articles about relativity can help creationists come to a better understanding of this theory and appreciation for one of the most fascinating—and God-honoring—theories in modern physics.