By Victoria Hristova, Year 12
Two equally good theories. Equally tested. Equally valid. Relativity, a product of Einstein’s savoir-faire in the early 20th century, has been widely credited as the most revolutionary theory of our times, overturning centuries of Newtonian physics in a single blow. Every notion from simultaneity to the speed of light and the very essence of motion was reformulated. Quantum physics preceded Einstein’s first theory, that of special relativity, by only a couple of years, the concept of energy as being quantized packets of energy, like photons, introduced by Max Planck as a solution to the black-body radiation problem scientists had been faced with thus far. The branch of quantum evolved radically throughout the 20th century, opening the doors of the infinitely small and granting new, probability-based ways of describing reality. Well if both theories work and have been tested, then what’s the problem, you may wonder? The issue stems from the fact that one theory cannot be applied to the workings of the other: quantum mechanics can’t be applied to the formation of galaxies on the largest scales of the Universe, as well as relativity can’t be used to describe the movement of particles. Physicists have been trying (which includes a lot of arguing with the opposite party) to fix this fundamental incompatibility between the two, but to absolutely no avail. From this once again arises the question of why? Why do our most mathematically sophisticated theories simply not work together, even though they are describing the exact same reality?
Relativity, both special and general, are simply too complex to explain in a couple of paragraphs, so take my words at face value here. The fundamental idea behind special relativity is, as its name suggests, that motion and time are relative between different observers. There is no fixed rate of movement, because we speak about the movement of an object in comparison to the standpoint of another object. If you take a third one placed differently relative to the one in movement, then the latter’s motion will appear in another way. Hence, there is no “absolute” notion of motion. Taking that a step further, there is no absolute notion of constant velocity motion. If you are sitting in a train carriage, moving at a perfectly uniform speed, and another train passes yours, moving in the opposite direction, for those split seconds in which you have no other frame of reference, it is impossible to tell whether the other train is moving, stationary, whether you are stationary, or both are moving. Another step farther, imagine you’re in that same carriage, moving at the same constant speed, also assuming you feel no jolting or shaking, and your blinds are down (you cannot see outside); in that case, you won’t be able to make the difference between being at rest or moving because you will have no frame of reference to indicate your state of motion. Hence constant velocity force-free motion has to be relative because it can only be found as such through the direct or indirect comparison to “outside” objects; only comparisons will have physical meaning. Moving on (pun unintended), this idea of relative motion has a startling effect on time, and this can be entirely credited to the fundamental law of nature in our Universe that the speed of light is constant and nothing can go faster. In a perfect vacuum, 300’000 m/s is the fastest anything will ever be able to go, which has some interesting implications for time. Imagine a light clock, where a single photon travels between two parallel mirrors as shown in the picture linked. Each time the photon makes a round-trip, the clock “ticks”. You’re watching this clock, set on a table, tick idly, and suddenly a second light clock appears and slides past the first one at constant speed. You notice that the path the photon travels in this second clock appears to be longer, because a double diagonal is in fact longer than a simple up-and-down path. In the time, for lack of a better word, the second clock travels the length of the table, it has therefore ticked less times than the stationary light clock, meaning that in a sense less time has passed for it; from our observer point of view, its passage of time has slowed down. This whole idea can be generalized to the statement that time elapses more slowly for an individual in motion than it does for a stationary individual. From that, using the simple calculation of distance = velocity x time elapsed, it can also be derived that objects in constant motion also undergo an apparent “shortening” from the point of view of an observer. These are incredibly mind-bending and counterintuitive discoveries, and rest assured that these changes can only be felt at high speeds (nowhere near anything we’ve ever achieved), but when studying the Universe, it is precisely this relativity which explained phenomena Newtonian physics had previously not been capable of.
The key takeaways thus far are: motion is relative, time is relative, space is relative, and the speed of light is the only absolute constant. Until now, we’ve been explaining these phenomena through simplified versions of constant-velocity force-free motion occurrences, which is in essence what special relativity is: the laws of physics appear identical to observers undergoing constant velocity motion, although their measurements of space and time may differ. But there is a crucial part of the puzzle missing: gravity. In Newtonian physics, gravity is an attractive force which tethers two objects together, dependent on their mass and the distance separating them. For what it was worth, Newton’s theory of gravity, albeit not explaining what gravity actually is, predicted spectacularly well the movement of celestial bodies. The only caveat comes from the fact that it allowed simultaneity, because to Newton, time was absolute. If there was a sudden change in mass or separation in our two-body system, it would be felt immediately. If the Sun were to suddenly explode, then Newton states that the Earth would feel the gravitational pull disappear instantaneously before the last light of the Sun reaches us eight minutes later. This alone violates the principle of the constancy of the speed of light. Nothing can be instantaneously transmitted, not even information, because nothing outruns photons. Great, so now we know the Newtonian description of how gravity works is wrong. But then what exactly is gravity? Let’s first establish what “Einstein’s happiest thought” was. In his patent office in Bern, Einstein was conducting one of his Gedankenexperiments (German for “thought experiment”), and came to the astounding realization that gravity and accelerated motion are in fact indistinguishable from one another. Acceleration can mimic gravity just like gravity can mimic acceleration. At just the right calibration, there is no difference between a situation with no gravity but acceleration (how spaceships work) and a situation with gravity but no acceleration. That is what’s called the equivalence principle. After another thought experiment, Einstein realised that acceleration, much like constant-velocity motion, warps space, and therefore, by definition, warps time as well. And since acceleration is comparable to gravity, then gravity also warps space and time. Space and time are inseparably interwoven in every possible scenario, and from then on this indivisible entity became known as spacetime. Think of it as a fabric which bends and warps in the presence of mass: that is what we call gravity, the curvature of spacetime. The greater the mass we place on this fabric, the deeper down it will sink, hence the greater its gravity. This fabric is the mechanism which transmits gravity, so our dilemma with the instantaneous transmission of the gravitational effects of the Sun exploding is resolved: gravitational disturbances keep pace with light, but do not outrun it. If this is too convoluted, just remember the words of the very quotable physicist (I’m not kidding, look it up) John Wheeler: “Mass grips space by telling it how to curve; space grips mass by telling it how to move.”
What is the significance of general relativity, you may ask? After its formulation, we have been able to take a huge leap forward in matters of cosmology and astrophysics. Suddenly, the existence of black holes became irrefutably possible, and somewhere in the trenches of WWI, physicist Karl Schwarzschild was the first to derive the mathematical explanation for the formation of these dark behemoths with the help of Einstein’s field equations. The very shape of the Observable Universe was determined with the help of general relativity and the curvature of spacetime (along with the earlier maths of a certain Bernhard Riemann), which by extension later explained Hubble’s discovery of the origins of the Universe in the Big Bang. Not bad for the work of a single man.
Due to the absolute and unfortunately unchanging length of this article regardless of the speed you are moving at, it is in the second part that you will find the answers as to why there is a fundamental inconsistency between the seemingly perfect at-first-glance general relativity and quantum mechanics. If you try not to move over the summer, then the time until I write the follow-up will pass much faster. Here’s a good application of physics if ever there was one.
Image credit: Spacetime curvature simulation by ESA
