Physics is the mother of all the sciences. It strives to describe characteristics of the physical universe with parameters that are unambiguous and measurable. Those measurements can’t depend on who makes them, where or when they are made, the orientation of the measuring apparatus or the thing being measured.
For models of the universe to be valid, they must use only parameters that are free of bias. Whether a measurement is made in one frame of reference — meaning location and time — or another, the result should be the same. This is called invariance.
The question becomes, “In making a measurement, do I get the same result in my current frame of reference as I would if I were doing the measurement in another location, traveling at a high speed, turned in different orientation in space or repeating the measurement at another time?”
Until the beginning of the 20th century it was thought distance and time measurements met these conditions. As such, the two parameters were thought to be reliable for use in descriptions of the physical universe.
But experiments on electric and magnetic fields by Michael Faraday and others in the 1800s ultimately forced physicists to abandon these intuitive notions. In 1864, James Maxwell used the results from these experiments to formulate a concise mathematical representation showing how oscillations in electric or magnetic fields gave rise to the other field.
Furthermore, these field oscillations propagated through space like waves. The ratio of the strengths of the two fields was shown to give the speed of their propagation. It was a constant value of nearly 300 million meters per second.
Countless experiments have confirmed that all electromagnetic radiation energies propagate at this same speed. Though the different energies (frequencies) have different names — radio waves, X-rays, gamma rays, microwaves, ultraviolet, infrared, and visible light — by convention their speed is referred to as the speed of light, symbolized by the letter ‘c’.
What does it mean that the speed of light is invariant? Maxwell’s equations specify that no matter what frame of reference I might use to measure the speed of light, I will always get the same result. I will get the same measurement if light from a flashlight is hurtling toward as I would if the light is receding away. Nor will it depend on my speed relative to that of the flashlight.
This has profound consequences for measurements of distance and time.
Imagine I measure the length of a stick or the time it takes for some event to happen. Someone traveling toward me in a spaceship at near the speed of light measures the length of my stick as I hold it. With simple geometry it can be shown that this independent measurement yields a length shorter than what I report.
Furthermore, the event I experience seems to the spaceship traveler to happen at a slower pace than what I report. One doesn’t usually think of having an inherent bias in measurements of distance. Neither does one think time is dependent on one’s frame of reference. Typically time is thought of as a kind of free flowing thing. It just happens as the backdrop to events.
Is it important that distance and time are not universal invariants, not absolutes? In a chemistry or biology laboratory, and for nearly everything we experience, deviations that arise from these relativistic effects are far too small to be of any consequence.
But, this is no consolation for physicists. Their representations of the physical universe must work under all circumstances. Only when the frame of reference of an observer has no effect on what is observed are physicists certain they are seeing something fundamentally true. Distance and time fail this criterion.
Albert Einstein and Hermann Minkowski showed the way to a more satisfying model. If time and distance are not invariant in ordinary three-dimensional space, could they be merged into a single entity and treated as equals in a four-dimensional space? Would there be something that would maintain invariance in such a space?
Constructing this 4-space took some doing. How can one merge distance and time when they have different dimensions? Spatial dimensions are measured in units of length (inches, meters) while time is measured in seconds, minutes, hours.
Distance and time are, however, related by speed. By multiplying all times in the time-dimension by the speed of light one gets a length. In doing so, one is no longer trying to combine apples with oranges.
Are there invariant parameters in 4-space that substitute for what we had thought distance and time did in 3-space? Just as one can use simple geometry in 3-space to demonstrate consequences of an invariant speed of light, one can use somewhat more abstract geometry in 4-space?
This yields an invariant parameter called an “event,” which serves as a good analog for distance and time. It also reveals that space is not “flat” in a mathematical sense, but is “curved.”
But trouble is brewing. There are several mathematically valid solutions. Some of them specify events occurring before their cause.
Physicists disregard these “aberrant” solutions by imposing the Law of Causality, which simply states event B cannot happen before A, if A caused B. Not everything in physics is so intuitive, but this one yields unambiguous and powerful results. The surviving solutions are the principle equations of special relativity relating distance and time for different frames of reference.
What about the other things that are familiar to us from 3-space, like momentum and energy? Having established a 4-space invariant analog to distance and time, it is possible with just a few more steps of mathematical reasoning to construct a 4-space vector that represents momentum.
From this, one derives the relativistic equations for conservation of momentum and energy. Furthermore, in this mother lode is the famous E= mc2. Voila, equivalence, a kind of symmetry, has been revealed between mass (m) and energy (E).
Our familiar conservation laws are now extended to work even at near the speed of light. The equations expressing these relativistic conservation laws collapse to the old conservation laws at low speeds.
Faraday opened the door a crack. Maxwell threw it open with his unification of electric and magnetic fields and its specification that the speed of light was invariant.
Finally, Einstein and Minkowski launched us into a model that revealed fundamental invariances in a 4-dimensional space. Each step required rigorous logic and acknowledgment that, regardless of what we might want or find easy to understand, nature is what it is.
Steve Luckstead is a medical physicist in the radiation oncology department at St. Mary Medical Center. He can be reached at firstname.lastname@example.org.