Tag Archives: Einstein

Miracles and Einstein, Part 2

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Albert Einstein in 1947

Last week, I went over how Albert Einstein’s theories of relativity were a more comprehensive model of the universe than previous theories, and how a worldview that can acknowledge the possibility of miracles is likewise more comprehensive than the atheistic worldview. Apart from whether God exists or miracles do occur, the worldview that can handle those possibilities without breaking is, all else being equal, the more robust model. Today, I want to conclude that investigation with a look at one of Einstein’s more unique “thought experiments”.

Einstein was famous for his thought experiments, and for good reason. He worked as a clerk in the Swiss Patent Office, without access to laboratories and expensive equipment to conduct physical experiments. Moreover, some of his ideas were beyond the ability to experimentally verify for years. But throughout his life, Einstein carefully reasoned his way through the implications of different ideas via these thought experiments. He published 4 papers in 1905 (while still a clerk!) that revolutionized  science. Ten years later the world would get his general theory of relativity, and Einstein’s name would become synonymous with genius. Among his though experiments about lightning flashes and clocks and measuring rods on moving trains, he presented an interesting example in his book, Relativity, that I want to look at. To illustrate one implication of his theory of general relativity to the question of whether the universe is infinite or finite, he postulates a world of 2-dimensional “flat” beings living in a  2-dimensional “flat” world with “flat” tools for measuring their world. To the 2-D beings, depth is a foreign concept. Says Einstein, “For them nothing exists outside of this plane: that which they observe to happen to themselves and to their flat ‘things’ is the all-inclusive reality of their plane.” [1]  While he proceeds to build on this to look at the finitude of our universe,  what caught my eye was his point that only what happens in-plane is observable by the 2-D beings. This got me thinking of my own little thought experiment.

Suppose their flat universe is a region contained in a 3-dimensional universe. Maybe their entire existence is contained in a “tabletop universe” in your study. You, being a 3-D being, are able to look down on their universe and observe them in ways they cannot observe their own world.  For them, they might not be able to see past an obstacle in their path, but would have to go around it to see what was on the other side. You can simply see over the obstacle to know whether trouble awaits them on the other side or not. In some sense, you can see how their choices will play out before they can. But what if your relation with their world wasn’t simply limited to observation, but could also include interaction? While they could move and observe things in the x- and y-axes of their world, you would be able to approach them from the z-axis — “out of the blue”, so to speak. With their observations limited to a plane, your interactions with them would surely be mysterious. If you moved an obstacle out of their way, they would be able to see the effect of your interaction, certainly, but the origin of it? Probably not. It might, from their point of view, appear to defy their laws of physics.

Could you communicate with them? Possibly, though maybe not with the sound waves produced by your vocal chords. But you might be able to communicate with them in ways possible in their plane frame of reference. For instance, if they communicated with each other in flashes of colored light, and you wanted to give them a message, you could do so by translating your thoughts into flashing colored light instead of spoken or written words, in order to put your message in their terms. If you really wanted to interact with them in a way they could understand, though, entering their world would be the ultimate move. Of course, this is the stuff of sci-fi stories, but that’s why this is a though experiment, so let’s keep going. Suppose you could transform yourself to a 2-D being like the ones in the tabletop universe. Your interactions and communications with them would be more direct and personal in such a case. They would be able to relate to you better as one of them, rather than simply a mysterious source of messages and the occasional intrusions of solid geometry into their plane geometry world.  Even if you fully understood the limitations of living in a 2-D world beforehand, having endured those constraints yourself would make your interactions with them more meaningful for them.

Now, I’m not saying that spiritual reality is simply a higher physical dimension, or an alternate/parallel dimension, but I do think this analogy can show the plausibility of miracles. The skeptic often claims miracles are impossible, and yet we can think of scenarios where a completely naturalistic system could have events that would appear miraculous to one set of observers in the system. So to the skeptic, I would ask:

  • Is it really that much of a stretch to say that God exists in a way that transcends our observable universe such that He can be “outside” it, but still interact with it?
  • Would it be such a surprise that God might exist in a way that is like nothing else in our frame of reference? The idea of the Trinity, one Being with 3 personal centers of consciousness, is probably as different from our life experience as a 3-dimensional man would be to the 2-dimensional  creatures of Einstein’s thought experiment.
  • Should it be a shock that He could have knowledge of future events in ways we don’t understand? Some see omniscience as equating to deterministic control and negation of our free will, but knowledge of the future is not the same as causation of that future. Now the Bible does leave us with a tension between God’s sovereignty over us and our free will, but I would say this falls into the category of mystery rather than contradiction as some assume.
  • Is it so unbelievable that He would condescend to communicating with us in ways we could comprehend? The Bible records some of the different ways God has communicated with us: by direct speech to Adam and Eve [Ge 3:9], mediated speech through other humans (any of the prophets), inspired writing (like Paul’s epistles), angelic messengers [Lk 1:26-38], visions [Is 6:1-3], dreams [Mt 1:20-21], His Spirit indwelling us and speaking directly to our spirit [Ac 20:22-24], or even speaking through a burning bush [Ex 3:2-4:17] and a donkey [Nb 22:21-39].
  • Lastly, is it impossible that an omnipotent Creator could even enter His creation, taking on our limitations of physical existence and be one of us – “truly God and truly man” as the Creeds would say? That is the miracle of the Incarnation, and the most amazing demonstration of love for us. Some eschew this as arrogance on the part of us measly humans inhabiting this speck of dust in a vast cosmos, to think we are so important. But it’s not about some amazing worthiness on our part that warrants cosmic attention, but rather the amazing, mind-boggling extent of God’s love.

Perhaps, the skeptic’s problem is that they have too small a view of God. They are like the 2-D creature saying that the concept of “depth” is unintelligible and that there is nothing outside their plane. A world beyond their imagination breaks in to our world, and yet it doesn’t fit in their small, simplistic model of how the world works, and so they ignore it. Do you want to be open-minded, a real freethinker? Then free yourself from the constraints of atheism, and be open to the bigger view of reality. But I’ll warn you, when you do that, you’ll discover an added dimension to your world that Christianity best explains. Then you have a choice: do you turn your eyes back down to your flat world, or do you follow the evidence straight to Christ? Choose wisely, my friend.

[1] Albert Einstein, Relativity: The Special & The General Theory (NY: Barnes & Noble, 2004, original 1920), p. 93.

Miracles and Einstein, Part 1

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Albert Einstein’s official portrait on award of the 1921 Nobel Prize in Physics.

Miracles are often mocked by skeptics as impossible, but I would like to suggest here that the skeptic is not seeing the big picture, and is, ironically, being somewhat close-minded.

Now, it’s always good to define our terms, so first, what is a miracle? Nelson’s Bible Dictionary defines it as “A sign, a special manifestation of God. Miracles set forth God’s character, and are used to accredit His messengers” [1]. C.S. Lewis, in his classic work, Miracles, gave a good working definition as “an interference with Nature by supernatural power” [2]. We can gather from this two key points: a) miracles are the exception to the norm, and b) miracles have specific purposes. Indeed, the rarity works to highlight their significance and the purpose behind them. But can miracles “fit” into any modern view of the world? We live in a science-loving society, and our world is often (but not always) made better by scientific advances. Yet science is the study of the natural world around us, and miracles are supernatural, by definition. So where can miracles fit in our model of reality? Let’s work through that today.

Albert Einstein actually made some comments in his 1920 book, Relativity, that can shed some light here.  In it, he attempted to explain to the layman his theories of special and general relativity. Classical, or Newtonian physics had been an excellent framework for scientific inquiry since the time of… Newton. But some phenomena appear to break the laws of physics in a purely Newtonian framework. They are rare, but when they are observed, accounting for those puzzling phenomena requires more and more complicated, ad-hoc theories. The beauty of Einstein’s special and general relativity were that they explained the cases where Newtonian physics was deficient, but then both  simplified to Newtonian mechanics under the vast majority of conditions (namely weak gravitational fields and travel speeds much slower than the speed of light) [3]. As the speed of an object approaches the speed of light, or gravitational fields get very strong,  observations framed in classical terms tend to make less sense and physics appears to “break down”. Not breaking down in those cases, Einstein’s theories therefore had more explanatory power than Newton’s. And in fact, we’d already seen this subsuming of previous theories by more comprehensive theories with an example Einstein himself used: the laws of electrostatics were thought to be the laws of electricity until electrodynamics was developed by Einstein’s hero, James Clerk Maxwell. Said Einstein:

“Should we be justified in saying that for this reason electrostatics is overthrown by the field-equations of Maxwell in electrodynamics? Not in the least. Electrostatics is contained in electrodynamics as a limiting case; the laws of the latter lead directly to those of the former for the case in which the fields are invariable with regard to time.  No fairer destiny could be allotted to any physical theory, than that it should of itself point out the way to the introduction of a more comprehensive theory, in which it lives on as a limiting case.” [4]

What does any of this have to do with miracles? Well, a naturalistic methodology can explain our observations of the world the vast majority of the time. But we have to recognize that there are times it may not explain things. These cases of miracles, where we get intervention from outside the natural world for a specific purpose, won’t make sense to us until we enlarge our frame of reference to include the possibility of that. We are often reminded that methodological naturalism is the mandate of science, and there is no room for God in that. But then the skeptic making this response often proceeds not to a stance of methodological naturalism, but philosophical naturalism. The first is a method of investigation that assumes an event happened without supernatural intervention; the second assumes such intervention is not even possible. The distinction is significant. We cannot recognize effects from outside the system if we don’t recognize even the possibility of there being anything outside the system. It would be like coming home from work to find my grass wet, and puzzling over such an extremely isolated rain shower that didn’t get the house or driveway wet, and never acknowledging the neighbor’s sprinkler as a potential cause. An assumption of rain may be correct most of the time, but if don’t allow for the actions of free agents outside the “system” of my property lines, some explanations will forever elude me.

Despite the claims by atheists of being freethinkers, the Christian is actually in the more open-minded position here. The Christian acknowledges the validity of searching for natural causes to events (for God created an orderly and comprehensible universe governed by uniform, rational laws), but also acknowledges the possibility in rare situations (lest they become meaningless) of intervention by God when He deems appropriate and has a specific purpose in mind. In this way, the Christian actually has the more general theory of the world that can encompass the atheist’s smaller view of the world just as electrodynamics encompasses electrostatics, or relativity encompasses Newtonian physics. Maybe you’re a skeptic reading this right now. Understand, I’m not expecting you to instantly believe the miracles recorded in the Bible now, but in the final analysis, Christianity is a more comprehensive worldview than atheism. Now look at the big picture and follow the evidence where it leads. Till next week, S.D.G.

[1] “Miracle”, Nelson’s Foundational Bible Dictionary (Nashville: Thomas Nelson, 2004).
[2] C.S. Lewis, Miracles: How God Intervenes in Nature and Human Affairs, (NY: Macmillan, 1978), p. 5.
[3] For those interested , the kinetic energy formula according to special relativity would be the series mc² + mv²/2 + 3/8mv^4/c²+… where v equals the velocity of the particle considered. At velocities << c, mv²/2 becomes the dominant velocity-dependent term, while mc² is a constant of the particle. Therefore, the relativistic kinetic energy reduces to the classical KE=½mv² formula. Regarding his general relativity, Einstein said, “If we confine the application of the theory to the case where the gravitational fields can be regarded as being weak, and in which all masses move… with velocities which are small compared with the velocity of light, we then obtain as a first approximation the Newtonian theory. ” –  Relativity, p.39, 87.
[4] Albert Einstein, Relativity: The Special & The General Theory (NY: Barnes & Noble, 2004), p. 65.

“Hard Evidence”

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Lab Experiment“I don’t think there’s anything he could say that would convince me – I need hard evidence,” said an atheist friend when I invited him to come with me to  a presentation on the reliability of the Bible. That got me thinking about evidence and our desire for more of it. After all, “seeing is believing,” right?

This November marks the 100th anniversary of Albert Einstein publishing his theory of general relativity. Only 10 years earlier, in 1905, Einstein had published not one, but four, paradigm-shifting papers, including his special theory of relativity and his proposal of mass-energy equivalence, from which we get the famous equation E=mc². Since then, his theories have been repeatedly confirmed. Special and general relativity did not simply provide a competing theory compared to classical Newtonian physics; they encompassed Newtonian physics. In relatively weak gravitational fields, special relativity reduced to Newtonian formulas at speeds much slower than the speed of light (our typical earthbound experience). General relativity expanded on that to provide an explanatory framework that could account for objects travelling at all speeds and through any gravitational field. It explained what Newtonian physics could and couldn’t explain. That’s powerful.

How did Einstein develop this powerful theory? Can you tour the lab where he huddled over a workbench full of special scientific equipment, or see the telescope he tirelessly spent long nights peering through, looking for evidence of gravitational lensing, or examine his lab journals of dutifully recorded experimental results? Not really. Einstein worked as a simple patent clerk in his “miracle year” of 1905, and was still doing “thought experiments” when he developed general relativity. He was short on evidence, but long on problems to think through. He proposed 3 scenarios unexplained by Newtonian physics that relativity would need to correctly explain for it to be true: 1) the slight changes in Mercury’s orbit around the sun already observed by others, 2) the deflection of light by the sun that Newtonian physics predicted, but not accurately, and 3) the color change (redshift) of light passing through a gravitational field that was completely unverifiable at that time.[1] While he could compare his theory’s predictions to  Mercury’s orbital changes measured by others, he had no way to confirm the other 2 tests. In fact, the evidence to support his theory only trickled in over many years, the most conclusive confirmations  of it after his death in 1955. Sir Arthur Eddington confirmed the deflection of light by the sun’s gravity in 1919 when he measured the slight curvature of starlight bending in the gravitational field of the sun during a solar eclipse. But it was decades before sufficiently precise measurements could confirm gravity’s miniscule color-shifting effect on light here on earth. In the years since, though, several other effects have verified Einstein’s unproven theory.

In fact, Einstein’s general theory of relativity touches most of our everyday lives  in one very real, but surprising way. Our cars, planes, cellphones, and even wristwatches now have the ability to tell us where we are because a of wonderful cold-war invention called GPS. But engineers designing the GPS satellites originally didn’t think they would need to account for gravitational redshift in the signal timing. This change in color of visible light is actually an effect of time dilation; time actually runs faster in a weaker gravitational field. And so the clock on a GPS satellite will run 38 microseconds faster, per day, than the same clock on earth, which is enough to produce invalid location results. This would also handicap our cell phones that use this precise timing to handle transferring calls to new cell towers seamlessly.

So did the lack of hard evidence in any way detract from the truthfulness of his theory? No, that’s because we don’t create truth, we only discover it. If something is true, it’s true whether we know it or not, and whether we understand it yet or not. The GPS clocks ran faster whether the original engineers admitted it or not, and whether you and I fully understand it or not. Can Christianity be true without measurable, scientific evidence? Absolutely.[2] But there’s a deeper question here. Is experimental observation the only way we come to know truth? No. In fact, the “thought experiments” Einstein relied on were simply exercises in sound reasoning that scientists, mathematicians, and philosophers have used for millennia. As Einstein understood, there are many times where it is impossible to obtain “hard evidence” for something. It may be a unique, non-repeatable event, or it may be something infeasible to test at the present time, but that doesn’t have to stop us from investigating. Albert Einstein didn’t limit himself to experimental evidence, but rather used his mind to go where science couldn’t yet, and he changed the world. Don’t let your desire for a certain type of evidence keep you from investigating the truth of Christianity and changing your world.

[1] Albert Einstein, Relativity: The Special and the General Theory (New York: Barnes & Noble, 2004), p. 87-88.
[2] Not that there isn’t a wealth of evidence for the truth of the Bible, but that’s a subject for another day.