Steven Dutch, Natural and Applied Sciences, Universityof Wisconsin - Green Bay
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The most elementary kind of relativity predates Einstein by centuries. If two ships pass each other at night on a calm sea, there is no way to tell, by observing anything on either ship, which of the two is moving, or even if both are moving. As long as they are traveling at constant speed in straight lines, no observation of the ships themselves will determine whether they are moving or standing still. We refer to this as Galilean Invariance or Galilean Relativity. (If you can think of ways to test, hold that thought.)
Frame of Reference is the viewpoint from which some observer sees the universe. Usually it requires measuring distances along a system of axes. For example, if you’re walking in Manhattan, you measure in terms of avenues parallel to the island (and they do not run north-south), streets perpendicular to it, and stories above ground. In Chicago you’d use a similar system, but the streets run north-south and east west, and “up” in Chicago is about 20 degrees different from “up” in New York thanks to the curvature of the earth.
Preferred Frame of Reference means one that is somehow special, or where observations somehow depend on your location. In space, you can orient your coordinate axes any way you like and put the origin anywhere, and set your clock however you like, and the laws of physics will still look the same. On the rotating earth, however, things appear different depending on how far you are from the rotation axis. The rotating earth does have a preferred frame of reference.
Inertial means a reference frame that obeys Newton’s First and Second Laws, that is, objects in motion remain in motion as long as nothing intervenes. There are two kinds of inertial frames:
Lots of reference frames are non-inertial. Anything that changes direction or velocity is non-inertial, so anything that is rotating is non-inertial. In a rotating reference frame you see forces that don't exist in inertial reference frames, like centrifugal force or the Coriolis Effect.
If the earth is rotating and moving around the sun, and we don’t feel it, it must be that motion, in and of itself, cannot be sensed. This was not at all obvious in an age when there was no smooth motion. The only motions anyone had felt in Galileo’s day were walking, riding a horse, riding a cart, or traveling by ship, all eminently sensible. In his Dialogue Concerning The Two Chief World Systems, Galileo argued that someone below decks in a ship sailing on a calm sea would not be able to tell, by any experiment, that the ship was moving. Since Galileo laid down the first clear description of this idea, it’s called Galilean Relativity.
Why below decks? Because if you can see outside, you can see whether the ship is moving relative to something else. In Galileo's illustration, there's nothing you can do, relative to your immediate surroundings, to tell if you're moving.
But if you're not moving in a constant direction and velocity, you can tell. Picture a big rotating space station like the one in 2001. Imagine you're in a closed room, feeling one g of apparent gravity, and to heighten the illusion of being in an ordinary room, the floor is flat and the walls are perpendicular to the floor. If you put a marble in the center of the floor, it will roll toward one of the end walls. Plumb bobs will hang toward the end walls. The apparent gravity you feel is actually due to "centrifugal force" - actually it's due to the fact that you want to keep moving in a straight line and the space station keeps sweeping you up - and this apparent force varies in direction from place to place. It also gets stronger as you move away from the hub of the space station.
Let’s imagine a spacecraft in deep space passes a space station where a second identical spacecraft is docking. Under Galilean Relativity, clocks on all the spacecraft will keep the same time. All the spacecraft will measure each other as being the same length. They will all measure the velocity of the docking spacecraft relative to the station as the same. If one spacecraft fires its engines to change speed, all observers will measure the same acceleration. In other words, space and time are absolute in the sense that everybody measures them the same way. A second is a second for everybody; a meter is a meter for everybody. If we take a clock to Pluto, we can assume that reads the same time as on Earth. But since everybody sees all the laws of nature in the same way, one frame of reference is no more or less correct than any other.
Astonishingly, a lot of the misconceptions about Relativity have to do with plain old Galilean Relativity and have very little to do with Einstain.
Reality: since the time of Galileo, there has never, ever, in any field of science, been a theory that required some particular point in space and time be the origin of everything. Just like there has never been a mathematics text that claimed that some particular point on a sheet of graph paper has to be the origin of every graph. In Galileo’s day it was a big deal, since people had assumed the center of the earth was the origin of everything. But once we got over that, nobody has ever had the slightest need for some unique origin. Does anybody really get seriously anguished over the fact that there’s no intrinsic definition of zero longitude? Apart from the French, who wanted it to run through Paris Observatory?
We have never seen a theory that requires absolute space and time. That’s a long way from proving that absolute space and time do not exist. Especially when this idea is so often used to argue that all ideas are relative. The argument, if it can be dignified as such, goes that since even space and time have no absolute frame of reference, nothing else can, either. Turn the argument backwards: if we do discover some absolute center for space and time, will that somehow mean there are moral absolutes? If so, how? If not, then what’s the philosophical relevance of this issue at all? If we ever do discover that some point in say, M51 is the actual center of the universe, it may have some very interesting implications for cosmology, but not for anything else. Here on earth we will still use latitude, longitude, and sea level. For Solar System navigation we will use the Sun; for the galaxy, we will use the center of the galaxy.
Galilean Relativity applies to measurements of motion relative to the immediate surroundings of the observer. It doesn’t preclude the existence of other ways of distinguishing among reference frames. Galileo’s hypothetical sea voyager need only come up on deck to see if he’s moving. If we imagined our the ship on a river instead of a calm sea, merely looking at the bank would tell you.
If a ships is drifting down a river, there’s nothing anyone can do on board to tell that the river is on a rotating earth, which is revolving around the sun, which is orbiting the center of the galaxy, which is being sucked in the direction of the Virgo Cluster of Galaxies, which is in turn being pulled toward the Hydra-Centaurus Supercluster. If you made a fuss about it, the sailors would deal with the issue by tossing you overboard, because all those astronomical motions are utterly irrelevant to their concerns. If there are two ships, one drifting and the other one at anchor, it is possible to tell which is which by observing the local frame of reference. Similarly, our entire visible universe could be moving in some direction at incredible speed without our being able to detect it. But this fact is utterly irrelevant in physics since the visible universe provides an eminently useful local reference frame. “Local” in this sense means something about 13.6 billion light years in radius. So if you were in a spaceship at rest with respect to the earth and compared notes with someone blasting by you at 90% of the speed of light, it would be possible to tell who was moving and who was standing still with respect to the visible universe. The moving spaceship would see stars bunch together in his forward direction. Stars behind would have their light red-shifted, those ahead would have their light blue shifted (contrary to innumerable bad illustrations, including the clunkiest episode in the whole Cosmos series, their color would not change dramatically). And if the moving spaceship didn’t have heavy forward shielding, he’d get a bad radiation dose from plowing into particles in space. Micrometeorites would be a problem since even a one milligram meteor would liberate about a kiloton of energy on impact. If we ever discover we’re part of a larger universe, we will certainly do our best to find out how we relate to it. We might well find that a spacecraft that appears to be zipping through our universe at close to the speed of light is actually standing still in his universe as we rush past him.
On the other hand, if the entire visible universe is moving, how fast, and in what direction? What's it moving relative to, and how did this motion originate? Until you can answer those questions, building some philosophy around the notion that our universe might be moving amounts to supporting a philosophy by postulating a large number of physical facts whose existence is completely unproven.
Even scientists can get tripped up by failing to distinguish "frame of reference" from "inertial frame of reference." Here is an example from a site that purports to correct misconceptions about meteorology. One reader took issue with the use of the term Coriolis force, which is an effect of the earth's rotation that makes hurricanes and ocean gyres rotate. The reader asked "Don’t you mean Coriolis effect?"
Answer: No, I don’t mean the Coriolis effect. While one can use the word, effect, in almost any context for something which happens, I am referring to the Coriolis force. The modern convention (nearly a century old now) is that there are no preferred coordinate systems and that once you adopt a coordinate system, one gets a set of forces along with it. When you shift coordinate systems, some forces vanish, others appear. In an inertial coordinate system, there is no Coriolis force. In a rotating coordinate system there is.
There are no preferred inertial coordinate systems, but a rotating system most definitely does have a preferred coordinate system.
Another reader wrote in to say "I was taught that the Coriolis force was not a real force, but a fictitious one…. " The response was no, the Coriolis Force is real.
My copy of the Berkeley Physics Series, volume 1, uses the term "fictitious." Although it’s a bit of an argument from authority, when a place with as many Nobel Prizes in physics as Berkeley says the Coriolis force is fictitious, I’d shut up and take notes.
If you spin a bucket of water, the surface will climb the sides of the bucket and assume a paraboloidal shape. The reason is that the water wants to keep moving in a straight line but the sides of the bucket keep forcing it into a circular path. The water piles up around the outside of the bucket, and when the slope of the water becomes steep enough for gravity to pull the water inward as strongly as the water tries to move outward, the surface reaches a stable shape. Or, in popular parlance, centrifugal force balances the pull of gravity downslope.
Some physics texts, in their zeal to get rid of privileged reference frames altogether, assert that we could picture the bucket being stationary and the universe revolving around it, and the gravity of distant objects, plus relativity, produces an attractive force that pulls on the water. For some strange reason, if you spin another bucket nearby, it too will develop a paraboloidal surface, and it will do it regardless of the direction the bucket is spinning, while the Pacific Ocean stays put. So if we adopt a reference frame that spins with one bucket, the universe revolving around us creates an outward pull that creates a paraboloidal surface on the water. A foot away is another bucket, spinning in the opposite direction, also with a paraboloidal surface. Now how did that happen? And a few feet away is a non-spinning bucket with a level surfaces. Now how can the same revolving universe make the water in one bucket spin clockwise, the water in another bucket spin counterclockwise, and in a third bucket not spin at all?
The problem with this approach is that a rotating system is not inertial. This particular system has privilege written all over it. First, the rotation axis is a privileged position and direction in space and second, gravity provides an additional privileged direction. If you did this experiment in a spinning cylindrical satellite the water would flatten out to cover the walls of the satellite. See Arthur C. Clarke’s Rendezvous with Rama for an example. This is a system with privileged directions so why try to pretend otherwise? More importantly, if the bucket spins once a second, and we imagine the bucket stationary with the universe spinning, anything more than 50,000 kilometers away will be moving faster than the speed of light.
Relativity, as formulated by Einstein, comes in two flavors: special and general. One might naively assume that Special Relativity was, well, special and that General Relativity was more basic, elementary, or generic. Actually, it’s the other way around. Special Relativity applies to inertial reference frames. It’s a special case, in the mathematical sense of limited or simplified in some way. General Relativity applies to all reference frames, even those that are subject to acceleration by gravity.
Special Relativity had been largely worked out before Einstein. The key event was an experiment done in 1887 by Albert Michelson and Edward Morley. In those days it was universally assumed that light, like sound, had to propagate through a medium, which was called the “ether.” Michelson and Morley devised an experiment to compare the speed of light moving head-on to the earth’s motion with that of light moving in other directions. To everyone’s amazement, they found no difference. It took several decades for physicists to scrap the concept of the ether, but it did become clear immediately that the speed of light was the same for all observers. Physicists Joseph Larmor, Hendrik Lorentz and Henri Poincar worked out the implications of the constancy of the speed of light and found all the most familiar effects of special relativity, including length contraction and time dilation. However, they derived all these results in terms of light propagating through an ether.
What Einstein did was to derive special relativity merely from the constancy of the speed of light, without invoking an ether at all. Physicist Ernst Mach, a no-nonsense unsentimental type, was the first prominent figure to ask, if we don’t need the ether to explain anything, why do we still believe in it? Later still, it was shown that special relativity is a consequence of the fact that physical laws are the same in all inertial reference frames. The reason everyone knows Einstein but only scientists know of Larmor, Lorentz and Poincar is that Einstein went far beyond the previous ideas. He showed that mass was equivalent to energy and went on to work out how relativity interacted with gravity. He also showed that reference frames in free-fall were inertial – if you were in a closed spacecraft falling straight down, you wouldn’t be able to tell if you were moving.
Much of the most atrocious pseudo-philosophical garbage put out about relativity actually applies to Galilean relativity, so what’s the big deal about Einstein? Until Larmor, Lorentz and Poincar, you could assume that if you sent a space ship to Pluto, it might take years to get there, but clocks on board would measure the same time as on earth. It was actually Poincar who pointed out that the only way to establish time conventions between distant locations is by convention, that we can't really assume that clocks keep the same time everywhere. We could send a radio message to Pluto announcing the time on Earth, calculate the travel time for light, and set a clock on Pluto to agree with the computed time on Earth, but there's no way to demonstrate directly that the two clocks are really keeping the same time.
The constancy of the speed of light for all observers was demonstrated by Michelson and Morley and its implications worked out by Larmor, Lorentz and Poincar. Einstein earned his place in the pantheon of science by streamlining their results and vastly extending their ideas. But it is just plain false that in relativity there are no absolutes. Before relativity, people had assumed time and space were absolute in the sense that everyone measured things the same. The absolute in relativity turns out to be something unexpected, the speed of light. In order to make the speed of light the same for all observers, no matter how they are moving, time and space must be "elastic."
From a page simply titled “Imponderables:”
Einstein's principle of equivalence says that you can't tell the difference between being in a stationary elevator in a gravitational field and an accelerating elevator in free space. However, if the stationary elevator is in a field that has the magnitude of that of a black hole, your temperature will increase due to Hawking radiation [black holes give off radiation]. If you are accelerating in free space (at a value equal to g of the black hole) your temperature will increase according to the Davies-Unruh effect [a subtle quantum mechanical effect of the vacuum]. However, the Hawking formula predicts a different temperature to the Davies-Unruh formula. So, we can imagine a thought experiment where we can measure this difference, and hence tell if the elevator is accelerating or not. Does this violate Einstein's principle of equivalence? Explain.
Duh, no. Equivalence only says you can’t tell the difference from experiments in your own frame of reference. Imagine two observers, one blindfolded in a room on earth, one blindfolded in a spaceship accelerating at one g. They can’t tell which is which. Now we tell them to take off the blindfolds and look out the window. Similarly, external heating because of your motion relative to some other frame of reference is perfectly consistent with relativity. If you're in a closed room falling into the sun, you will certainly be supplied with external clues about your frame of reference.
One of the favorite misconceptions about relativity is the famous "twin paradox." As our two ships pass by in black intergalactic space, we send timed laser pulses back and forth. But because of the motions of the ships, the travel times of the pulses are longer than they would be if the ships were standing still, and each ship sees the other's clock as running slow.
On the other hand, if we send an interstellar spacecraft on a long journey, the clock on the spaceship will seem to run normally. The pilot may see the trip taking five years of his time, but he returns to earth to find his identical twin brother is fifty years older.
This is about as paradoxical as flying from New York to San Francisco and having to set your watch when you land. The two situations are not the same. People on earth see the spaceship, and only the spaceship, traveling close to the speed of light. The pilot of the spaceship sees everything in the universe transformed. People on the earth feel nothing; the pilot feels acceleration; he has a way of knowing whether he's moving or not.
It's easy, and even many physics textbooks do it, to get the idea that time dilates because the ship accelerates, or because the ship exchanges time signals with earth, or whatever. The reality is that the spaceship runs on a different clock because that's the only way the pilot can see light traveling at the speed of light and that's how the universe is made.
But what's to prevent the pilot from thinking of himself as stationary, seeing the universe zip past at near the speed of light, and aging fifty years while his twin on earth only ages five?
There's nothing at the macroscopic level that is an exact analogue for atomic particles, which is why quantum mechanics is so perplexing. But a couple of analogies might help.
It's easy to get the impression that uncertainty exists because we are klutzy. We weigh something, get perspiration, dead cells, and skin oils on it that change the weight of the object, so we can't be perfectly sure what the object weighed before we touched it. Or we watch children at play, but they respond differently when adults are watching than when they're alone. We want to know how fast the wind is blowing, but our instrument perturbs the very flow we are trying to measure. In all these cases, we can imagine refining the technique to eliminate disturbances and thereby achieve perfect precision.
Another celebrated distortion is the statement that "1 + 1 = 2 in decimal notation but 1 + 1 = 10 in binary." No; one plus one equal two in all notations. The fact that two in binary notation looks the same as ten in decimal notation means nothing.
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Created 11 March, 2002, Last Update 18 January, 2020
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