The theory of relative time arose through the six classic pillars of science: a field observation, supporting verifiable measurement, explained by a relevant theory (paradigm), a follow-up experiment, which, failing to support the relevant theory, led to its overthrow and replacement by another theory. See, measure, explain, test, refute, re-interpret.
And it all started with a failed field observation.
One wintry night in 1725 James Bradley and Samuel Molyneux aimed a 20 foot telescope at gamma Draconis in an attempt to discover stellar parallax. To their astonishment, the “image” of the star Eltanin was shifting in the OPPOSITE direction.
Story has it that Bradley was sitting on the banks of the Thames watching sailboats tacking across the river when the solution hit him.
The speed of light was known to be high, but finite, having been first measured in 1675 from the occultations of the Jupiter’s moons across a known distance of space. Olaus Roemer’s first calculation was off by a whopping 30 percent, but it had the advantage of having a correct and repeatable methodology.
Bradley realized that because of the Earth’s 30 km/sec (or 30 kps) speed around the Sun the telescope tube had to be leaned into the starlight, rather like motoring upstream at an angle against the current in order to travel dirtectly across a river. However small the angle (let a = 20.5 seconds of arc, or about .0057 degrees), it just happened to be the trigonometric ratio of the Earth’s speed (v) divided by the speed of light (c), tan(a) = v/c, so that by solving for c, Bradley calculated the speed of light to well within 1 percent.
The irony was that parallactic displacement was still outside their instrument error – Alpha Centauri, our second closest star 4.3 light years distant, requires the scope to be aimed at an accuracy well under .8 seconds of arc – so they never found what they were really looking for.
The effect of stellar aberration is not constant for every star in the sky – remember, we’re whizzing around the galaxy at over 270 km/sec yielding “stellar aberration” – but for the stars in our lane of the galaxy, the effect is constant enough to postulate one particularly interesting morsel of information: the speed of light is INDEPENDENT of the speed of the emitter.
That is, a speeding star does not “push” its light ahead of it; it will shorten the wavelength and increase the frequency of the light, but the star’s speed is not added to the light. We know this because all telescope tubes need to be pointed, not at the star itself but, rather, at its “image.” Indeed, the raises the thorny specter of scientific induction, but even if you can only catch the football in your own end zone, you’re still going to have to make a run for it.
For embedded in this observation is a really useful and satisfactory theory of EVERYTHING. That is, if the speed of light is truly independent of the motion of the emitter, then it must transmit through space the same way that sound transmits through the air.
This means there must be some super-thin ultra-refined medium permeating all of space. Its eddies and whirlpools are responsible for magnetism and electricity, its pressure against the surface of the Earth would be a pretty good explanation for gravity, and organized ripples through it must surely be the mechanism for the transport of light. Good theory! No one check, though! We’re sure it’s right! Honest!
But in the 1880s, two scientists, Albert Abraham Michelson and Edward W. Morley, went looking for it.
Michelson, the son of German immigrants, was an Annapolis graduate recognized as a brilliant instrument builder, his specialty being optics. While an instructor at the U.S. Naval Academy between 1875-79, Michelson used a spindle of rotating mirrors to measure the terrestrial speed of light.
Now that I’ve hooked you with the gee-wiz element of the narrative, let’s backtrack to pick up a crucial, however nerdly, bit of information.
In the 1830-40s, engineers were encountering signal loss in telegraph cables. The longer the line, the worse the problem got. When they started studying submarine cable telegraphy, the problems seemed insurmountable. They needed to nail down the electrical characteristics of the system, ALL of them. They already knew that the electrical field set up in a wire at an appreciable fraction of light. And, by this time, they knew the speed of light through space with great accuracy. The question is, what is its speed on Earth?
It fell to a Parisian, Louis Fizeau, to carry out a clever way of measuring it in 1849. His apparatus was basic, simple, and easy to describe, and remains the basic paradigm of very fast signal detection and measurement equipment. So it is best to review the experiment here:
Fizeau used a toothed wheel with 720 notches capable of rapid uniform, but variable, rotation, attached to a tachometer. Behind the wheel was a light source aimed at a mirror 8.6 km away to the hill in Monmarte, Paris’ highest point. When the wheel spun, a pulse of light was sent through each notch to the mirror, which reflected back to the same notch, after having rotating one notch over, in front of the lens of a powerful telescope. In short, one pulse of the light signal, traveling over 17.2 km, should be caught within 1/720th of the wheel’s rotation. Done at night, the first image would be of a light flashing in the distance. When the wheel’s speed is adjusted so that when the light stops flashing and becomes steady, the tachometer is read, and the rest is simple arithmetic.
For the record, Jean-Bernard-Leon Foucault, Fizeau’s assistant, repeated the experiment the next year, only using rotating mirrors.
By the time Michelson was studying optics in Europe (1880-82), the speed of light across the Earth’s surface was known to such considerable degree of accuracy that it was considered “constant” everywhere, no matter what.
But it remained to be proved how it propagated through the ether.
The theory was that light propagates as rarefactions of the ether much the way sound travels through air, or waves travel on the ocean. If the ether exists, it will be distorted as a drag wake around the Earth as the Earth speeds around the Sun at such a considerable speed (30 kps) that the distortion of the ether should be measurable.
In 1881, Michelson used his first interferometer to look for the effect. He split one beam of light (he called them “pencils of light”) through a half-silvered mirror (in the center) into two perpendicular beams sent to two mirrors on each arm of the device, and back to another half-silvered mirror in the center, given focus through a microscope. The instrument was simple at first; two spindly brass arms on a tripod lightweight enough to set on the kitchen table without scratching the surface.
The difference between the light beam traveling ACROSS (transversely) the direction of the Earth’s orbit, to the light beam traveling PARALLEL (longitudinally) to the direction of orbit, should throw the two recombined light beams out of phase to produce a measurable interference fringe in the magnitude of:
2(v^2 + c^2) : ((c + v) + (c – v))^2
The amount of fringing predicted would be from the same mechanism that spoils conversation in the back of a speeding pickup truck.
When the device was rotated 90 degrees, the fringe shift should have been still more dramatic, albeit still on a microscopic level.
Instead, Michelson saw NOTHING. At least, nothing beyond the margin of instrument error.
Thinking the error might be caused by the shortness of the beam, heat variations, or even vibration in the room, Michelson’s successive interferometers became more and more elaborate.
Continuing his experiments with Ed Morley at the Case School of Applied Science in Ohio, the beams of light were reflected by an array of multiple mirrors (increasing the mirrored beams’ combined light path to over 32 meters); the mirrors were in turn set on a large granite (or concrete) block; and that was made to float on a pool of mercury (which they called a “bath”) to damp any extra vibration when the thing was rotated. I even have it by word of mouth that Michelson once ordered all carriage traffic and steam engines in Cleveland stopped one afternoon to further eliminate any local vibration through the Earth’s crust.
But, still, nothing.
This experiment, and its exotic variants (consider Sir Oliver Lodge’s efforts with his “ether machine”), have since been preformed hundreds of times – once by maser in 1958. In “Carrying the Fire,” Michael Collins wrote of repeating a version of it while in lunar orbit during Apollo 11 in 1969.
But even up to the 1960s the fringing effect was never more than .01 to .004 of the expected value.
As early as the 1880s, theorists started jumping on it. The “Titanic” that was the Theory of the Ether was sinking hard by the bow, leaving plenty of job openings for a new crew. The death of the old school left nothing but fertile opportunity for a fresh generation of scientific revolutionaries.
George Francis Fitzgerald and Hendrik Anton Lorentz speculated that the “pressure” of the passing ether was shortening the apparatus (and everything else on the planet, including the planet) to a degree that exactly cancelled out any interference fringing.
Even Albert Einstein considered this idea for a while in “The Electrodynamics of Moving Bodies,” until he realized that something else was going on.
But his was a rationalization you really need to make for yourselves if the conclusion of General Relativity is to make any sense. And, believe it or not, if you’ve followed me so far, you have all the evidence you need to form an opinion about relative time.
Let’s review:
(1) The speed of light is independent of the emitter’s speed. This is from investigations that proceeded after James Bradley’s initial 1725 observation. All that changes on the light beam is the Doppler shift of its frequency and wavelength, and these cancel, too. That is (let l be wavelength (as this system doesn’t do lambdas)), then f x l = f’ x l’ = c, no matter what.
(2) The speed of light through space is nearly the same as the speed of light on Earth – our atmosphere slows it down a bit – but in a laboratory vacuum it’s the same. This is necessary conclusion of the Michelson/Morley experiment.
(3) Though the Earth is moving 30 kps around the Sun (and in excess of 270 kps around the galaxy), any space alien measuring a beam of light from the Earth, no matter his position or motion on another planet, will measure our signal beam as having the speed of light. This is a extrapolation of review item (1).
So how does one reconcile the apparent contradiction between review items (2) and (3)?
Immediately, an ether drag can be ruled right out.
Apparently, the photon of light is traveling as if the apparatus is MOVING OUT FROM UNDER IT. The geometry of the movement would put the perpendicular mirrors along the periphery of an ellipse, with the emitter at one focus and the collator at the other. It’s a property of an ellipse that the length of any line drawn from one focus to any point on the periphery PLUS the length of a line from that point on the periphery drawn to the second focus is a CONSTANT. The distance between foci is how far the Earth moves in the time it takes for light to travel those two constant light paths.
The time (t’) it should take for light to travel the radius (R) of the apparatus round-trip (2R) should be:
t’ = 2R/c
But the greater distance that light needs to travel, using the standard geometrical axiom stated in the second paragraph above (the major axis of an ellipse is 2a), should require a greater amount of time (t”) according to the geometry of,
(2a)^2 = (ct”)^2 = (vt”)^2 + (2R)^2
which reduces to
(2R)^2 = ((t”)^2)(c + v)(c – v)
whence (multiplying (c + v) by (c – v) and dividing both sides by the speed of light and t” squared, or ct”^2)
(2R/ct”)^2 = 1 – (v/c)^2
or, taking the square root of both sides,
2R/ct” = (1 – (v/c)^2)^(1/2)
replace 2R/c with t’, and
t’/t” = (1 – (v/c)^2)^(1/2)
after rearranging, we get the more familiar…
t” = t’/((1 – (v/c)^2)^(1/2))
…expression for a time dilation effect.
t” should be the ACTUAL time that it takes for a light beam to travel round trip around Michelson’s interferometer; and since it’s traveling a longer distance IN SPACE, it is slightly longer in duration than laboratory time t’ which is indicated by the ABSENCE of interference fringing.
One possible way to reconcile this contradiction is either to consider that the light beam has INCREASED IN SPEED – a contradiction, since measurments of stellar aberration and terrestrial measurments coincide. The other explanation would be to realize that all the clocks in the laboratory (and, indeed, in the rest of the world) are wrong by the order of t”/t’. But does v represent 30 kps, or 270 kps, or something else entirely different?
So it would appear that for one inertial system going faster than another, time is as real as it gets, but also, indeed, relative.
In fact, it seems that by inserting c for v in our conclusion above (let v = c), laboratory time slows to zero, leading to the uncomfortable idea that if we were to ride along with a photon crossing 18 billion light years of the known universe, the trip would be instantaneous.
Lest we be disturbed by the philosophical implications of this, recall that some fringing effects were recorded by previous interferometry, albeit thought to be of a magnitude well below machine error. So perhaps we don’t know EVERYTHING yet.
But this led Einstein to formulate the fundamental postulate of Relativity, insisting that, “The Laws of Physics are the same in all uniformly moving reference frames.” In other words, if we’re all moving at the same speed, no matter what it is, there’s nothing to worry about.
But the worrisome dilemma of a photon experiencing zero trip time to cross the universe no doubt had even Einstein in awe…perhaps even in doubt…a shadow of it seems to surface briefly in his “Electrodynamics” when he wrote, cryptically, on page 12 of the paper:
“For velocities greater than that of light our deliberations become meaningless; we shall, however, find in what follows, that the velocity of light in our theory plays the part, physically, of an infinitely great velocity.”
Or as Carl Sagan liked to say, “There’s something strange about the speed of light.”
I would add that there’s SOMETHING STRANGE about space-time.
It is a strangeness that will take perhaps the next generation of scientific revolutionaries to figure out.
