"Dad?" said the Nine-Year-Old.
"Yes?" I said.
"Why do people think that going faster than light is the same as going backward in time?"
"Look, we're at your school already," I said. "We'll talk about it after school."
Clearly it's time for me to do some remedial reading...
So I downloaded and read Albert Einstein's "On the Electrodynamics of Moving Bodies." And I discovered something interesting. The conventional history of science, which says that Relativity Theory was impossible before and a direct consequence of the failure of Michelson and Morley's experiment to find differences in the speed of light resulting from the movement of the earth through the luminiferous aether, is wrong.
Instead, "On the Electrodynamics of Moving Bodies" says something very different. It doesn't say that Einstein's Relativity Theory theory is a solution to the problem raised by the Michelson-Morley experiment. Instead, it says that his theory is a solution to deeper problems in the way that Maxwell's Theory of Electrodynamics was formulated. Maxwell's formulation introduces "assymetries which do not appear to be inherent in the phenomena" that need to be smoothed away. I found myself wowed by Einstein's first two paragraphs:
It is known that Maxwell’s electrodynamics—as usually understood at the present time—when applied to moving bodies, leads to asymmetries which do not appear to be inherent in the phenomena. Take, for example, the reciprocal electrodynamic action of a magnet and a conductor. The observable phenomenon here depends only on the relative motion of the conductor and the magnet, whereas the customary view draws a sharp distinction between the two cases in which either the one or the other of these bodies is in motion. For if the magnet is in motion and the conductor at rest, there arises in the neighbourhood of the magnet an electric field with a certain definite energy, producing a current at the places where parts of the conductor are situated. But if the magnet is stationary and the conductor in motion, no electric field arises in the neighbourhood of the magnet. In the conductor, however, we find an electromotive force, to which in itself there is no corresponding energy, but which gives rise—assuming equality of relative motion in the two cases discussed—to electric currents of the same path and intensity as those produced by the electric forces in the former case.
Examples of this sort, together with the unsuccessful attempts to discover any motion of the earth relatively to the “light medium,” suggest that the phenomena of electrodynamics as well as of mechanics possess no properties corresponding to the idea of absolute rest. They suggest rather that, as has already been shown to the first order of small quantities, the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good. We will raise this conjecture (the purport of which will hereafter be called the “Principle of Relativity”) to the status of a postulate, and also introduce another postulate, which is only apparently irreconcilable with the former, namely, that light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body. These two postulates suffice for the attainment of a simple and consistent theory of the electrodynamics of moving bodies based on Maxwell’s theory for stationary bodies. The introduction of a “luminiferous ether” will prove to be superfluous inasmuch as the view here to be developed will not require an “absolutely stationary space” provided with special properties, nor assign a velocity-vector to a point of the empty space in which electromagnetic processes take place.
If I understand this, Einstein didn't need the Michelson-Morley experiment to derive and believe in relativity. His argument was much simpler. If I understand it, it went like this:
Phrased this way, special relativity becomes inescapable: it explodes in your mind with the force of a bomb as you read the subsequent paragraphs of "On the Electrodynamics of Moving Bodies."
I am left myself wondering about all those people who moved magnets near wires and moved wires near magnets in college physics classes in the second half of the nineteenth century. Each time they conducted such experiments--and interpreted them as the results of two different processes--nature was telling them, "Hey King Stupid! It's relative motion that matters only!"
But no one caught even a glimpse of what was going on save (for Lorentz and Fitzgerald, and they caught only a glimpse) until A. Einstein had a conversation with M. Besso in Zurich in 1905.
Posted by DeLong at October 30, 2002 04:52 PM | TrackbackI had this revelation in high school, while thinking about some textbook problem involving induced currents on a wire, trying to think about it in terms of the Newtonian relativity we had been taught. I asked my physics teacher, who had a master's in physics, about the apparent contradiction, and he was stumped. A few days later he came back to me and said it had something to do with special relativity. I was shocked; special relativity wasn't something we were supposed to have to learn about until college. That night I went home and reverse engineered the Lorentz contraction formula on my own. If only I had been born a century earlier I could have beat Einstein to the punch.
Posted by: on October 30, 2002 05:15 PMThe insight of those regarded as "great thinkers" continues to astound me. Never mind complicated theory and deft mathematical sleights of hand, impressive enough; to draw such conclusions from such observations is nothing short of amazing. Makes one wonder how you could ever hope to really undestand what they're talking about, of whether you'll ever have anything meaningful to contribute to the converstation.
Posted by: Dennis O'Dea on October 30, 2002 06:35 PMIf I remember my university physics correctly, there are a couple of things that aren't quite right here:
- Maxwell's theory didn't need to be corrected for relativity. Maxwell's equations for electrodynamics (not just statics) are invariant to Lorentz transformations while Newton's are not. The surprising thing was that the new kid on the block was right -- Maxwell's equations had been around for less than 50 years -- and Newton's were wrong.
Having said that, the extract does read as if Einstein is claiming that Maxwell got it wrong. Perhaps someone can tell us why that is.
- There is a phrase at the beginning of the second paragraph, "the unsuccessful attempts to discover any motion of the earth relatively to the “light medium,” which is a reference to the Michelson Morley experiment, so it clearly was in Einstein's mind when he did his work.
Thanks for these posts Brad DeLong - continually interesting reading, no matter what your frame of reference.
Posted by: Tom Slee on October 30, 2002 07:08 PMThat's somewhat misleading. I'm not an expert on the history of these things, but my understanding of it goes like this. For years, before the understanding of electromagnetism, people only thought that relative motion mattered. This is now called Galilean relativity, sometimes. The problem everyone had is that the laws of electromagnetism don't obey Galilean relativity. So, people gave up on this idea of relativity because it was obvious that Maxwell's equations gave the right answer. In order to understand the failure to detect the movemeny of the Earth with respect to the aether, Lorentz (and others, probably) postulated all sorts of kludgy things to make it work. Einstein's great insight was to realize that all the formulae of these kludges could instead be interpreted as a new kind of relativity, one that included time in addition to space. It was only when this very unintuitive idea of relativity was postulated did Maxwell's equations remain invariant.
Note that the different interpretations of effects in different frames still remained. The electric and magnetic fields are not vectors and they transform into each other when you change frames. Really, the fit into a different object, a 'tensor', that behaves very nicely under Einstein's relativity. So, Eistein's great insight wasn't that everything is relative -- people had already thought of that and postulated the luminiferous aether to get around it. Instead, Einstein's great insight is that everything was relative, but not in the way that everyone thought it was, thus relegating the aether to the historical dustbin of kludgedom.
Posted by: Aaron Bergman on October 30, 2002 07:35 PMThat's somewhat misleading. I'm not an expert on the history of these things, but my understanding of it goes like this. For years, before the understanding of electromagnetism, people only thought that relative motion mattered. This is now called Galilean relativity, sometimes. The problem everyone had is that the laws of electromagnetism don't obey Galilean relativity. So, people gave up on this idea of relativity because it was obvious that Maxwell's equations gave the right answer. In order to understand the failure to detect the movemeny of the Earth with respect to the aether, Lorentz (and others, probably) postulated all sorts of kludgy things to make it work. Einstein's great insight was to realize that all the formulae of these kludges could instead be interpreted as a new kind of relativity, one that included time in addition to space. It was only when this very unintuitive idea of relativity was postulated did Maxwell's equations remain invariant.
Note that the different interpretations of effects in different frames still remained. The electric and magnetic fields are not vectors and they transform into each other when you change frames. Really, the fit into a different object, a 'tensor', that behaves very nicely under Einstein's relativity. So, Eistein's great insight wasn't that everything is relative -- people had already thought of that and postulated the luminiferous aether to get around it. Instead, Einstein's great insight is that everything was relative, but not in the way that everyone thought it was, thus relegating the aether to the historical dustbin of kludgedom.
Posted by: on October 30, 2002 07:35 PMOops. Sorry about the double post.
Posted by: Aaron on October 30, 2002 07:37 PMI recall in my college introductory physics
course, the lecturer derived the speed of
light, c, from Maxwell's equations. So I
have thought for a long time that Einstein
was looking at a problem raised by the
theory. I believe Poincare almost got the
theory of special relativity before Einstein.
I also think from some history of science I
vaguely recall that either Michelson or Morley
when to their grave believing in the theory
of aether and disbelieving in the theory of
special relativity. Maybe that was in Against
Method?
Was Einstein the last scientist in human history to reach profound conclusions about physical reality using only brain, books, pencil and paper? Will every step forward from now on depend on enormous investment in experimental research?
Posted by: Jeffrey Kramer on October 31, 2002 04:51 AMThere's some debate as to whether Einstein relied on (or really even knew about) Michelson and Morely when he developed Relativity in 1905, but it's clear from his writing that he felt that the key was the unity of electric and magnetic fields. There's a pretty slick hand-waving argument using length contraction that lets you see them as the same thing, at least in the special case of two current-carrying wires...
This reminds me, though-- I started explaining this, but never posted the second half of the story. I'll have to fix that this weekend.
(I'm also interested to hear how you explain the FTL/time travel thing... Which, in turn, reminds me that I need to look for the Calvin & Hobbes cartoon where his father explains relativity in terms of time zones ("If you were moving east, time would speed up...")...)
The key idea is in the second paragraph-- " ... the phenomena of electrodynamics as well as of mechanics possess no properties corresponding to the idea of absolute rest." This concept is quite independent of the fact that Maxwell's equations are Lorentz-invariant. One consequence is that all physics is -local-.
This, to me, gives the strongest argument about why you can't go faster than the speed of light-- In any -local- reference frame (regardless of how fast that local frame may appear to be moving with respect to some fictional frame that's 'at rest') the velocity of a beam of light will always have -exactly- the same numerical value. So, not only is there no way to go faster than light, there is no way to 'catch up'-- light, in -all- reference frames, is -always- going 299,792,456 meters/second faster than you are.
Posted by: Matt on October 31, 2002 05:19 AMI'm a physicist, so I hope I don't botch this.
* Maxwell was awesome: he took seemingly unrelated experiments by Faraday, Ampere, and other, put them together in a consistent framework and then noticed that a piece was missing from Ampere's Law that would symmetrize the equations (the poorly named "displacement current" - via which a changing electric field creates a magnetic field). So he put this piece in "by hand" (later experiments were sophisticated enough to detect the effect and verify Maxwell's assumption), which was the crucial step for showing that electromagnetic waves could happen. He worked out the wave speed, which depended on physical constants derived from forces between current-carrying wires and forces between static charges, and he found this predicted that electromagnetic waves travelled at the speed of light. I can't believe that he slept that night, with the realization that he was the only person ever with the knowledge of what light was.
Did I mention I'm long winded?
* Einstein was awesome: indeed he did not derive his primary motivation from the Michelson-Morley experiment. One thing to keep in mind is that the ether-drag hypothesis had satisfied most physicists as the explanation of the MM experiment. Correcting a few comments above: Einstein by no means said Maxwell was wrong. In fact, Einstein was the truest champion of Maxwell's equations: by the turn of the century some physicists were aware that Maxwell's equations weren't consistent with Galilean invariance. But the usual viewpoint was that there were some more terms to be found in electromagnetism that would explain the problem. Maxwell's equations were seen as still incomplete, since Galilean invariance is so powerfully intuitive.
Einstein had the audacity to suggest that Maxwell's equations were complete and that Galilean invariance is wrong. He had the intelligence to pursue this line of reasoning and discover that a new and consistent mechanics could result from it, so he wrote it down.
Few people bothered to understand it, because they didn't accept the motivations for the work. In fact, when Max Planck was writing in support of Einstein's candidacy for a position in Berlin, he listed Einstein's many successes and said something along the lines of "the silly mistake with relativity shouldn't be held against such a great man".
* About faster than light speed travel and going back in time: a consequence of Einstein's special relativity is that two different observers in two different reference frames can disagree about the time ordering of two events. There's no inconsistency - it's just the shape of spacetime. And there's no sci-fi fantasy scenerios about lost causality (event A affects event B to one observer but event B affects event A to another observer) because it doesn't happen. The ordering of two events cannot be switched when their separation in distance and time is such that light or anything slower could have passed from the first event to the second (a "timelike" interval). The ordering can be reversed only when they are so far apart in space (or so close together in time) that not even light could travel from A to B (a "spacelike" interval). Therefore only "non causally connected events" have relative ordering.
Enter particles travelling faster than the speed of light (affectionally known as tachyons): they COULD get from A to B even if the interval between A and B is spacelike. So a tachyon could carry information from A to B (thus affecting something about B), and meanwhile, in someone's reference frame, B is before A, so the tachyon is travelling back in time.
Not my most lucid explanation (!) but I'm trying to finish before class....
Do tachyons exist? First, non-tachyonic matter, like us, can never go faster than the speed of light. No matter how much energy you give us, we just get closer and closer to 'c'. But there could be coexisting tachyons - nothing excludes it. However, if they do exist, they must be very weakly interacting, because we don't (yet) see their influence in any way. So the answer is, for now, that we don't know if tachyons exist, but we also have little reason to care.
A final point to be made as to why the MM experiment is usually cited as the source of relativity - it's got some justification but I'll have to write about that later today.
Einstein and Maxwell are, in my opinion, the #2 and #3 physicists of all time. Not just for this work - they both made other significant contributions. Did I mention that I'm long winded?
You have one precocious son there!
Posted by: JT on October 31, 2002 06:44 AMI am not a physicist so this may be poorly explained/understood, but here goes: Einstein's interpretation of Maxwell's equations in the 'light' of special relativity showed that the electrostatic force and the magnetic force were relativistic flip sides of the same phenomenon. His criticism of Maxwell's equations is not that they are wrong but that their form of expression leads to a misleading assymmetry arising from a resting observer's terminology, i.e. the existence of the magnetic field as fundamentally different from the electric field.
An earlier post mentioned the use of the example of two current carrying wires to show how this works. I think this example can help quite a bit. From a resting perspective, two parallel wires carrying current in the same direction attract one another. There is no electric field around the wires because the wires are electrically neutral overall. From our perspective, the overall charge density is neutral, although one type of charge is in motion. Because there is no electric field, there must be some other force than electric force at play. We can call this force the magnetic force, causing the wires to attract one another.
Let's apply special relativity to the problem then. Imagine we are moving along with the charges on one of the wires. Looking over at the other wire, we see like charges which appear stationary (having the same velocity on the other wire) and unlike charges moving in the opposite direction. Due to Lorenz contraction, space of the unlike charges in compressed, so the magnitude of electric field density of these charges appears greater in this relativistic frame. So while in our original 'resting frame' there is no net electric field, in the frame of the moving charges, there does appear to be a net electric field generated by the unlike charges on the other wire, which causes the wires to attract one another.
So Maxwell's equations are right insofar as they give the relationship between electric and magnetic fields. What Einstein is saying is that the magnetic field is just a convention. The difference between the electric and magnetic fields doesn't adhere in the phenomena but occurs to us because of our point of view.
Posted by: John Wetzel on October 31, 2002 07:35 AMmarvellous, brad! thank you!
:)
Getting back to the original question, any trip faster than light can be seen from various frames of reference as having an arrival time somewhat after the departure time, or somewhat before, or taking no time at all. This isn't time travel in the usual sense, because the movement in space has to be greater than the movement in time. This doesn't allow you to influence events in your past. However if you can make *two* FTL trips, which are instantaneous in two different reference frames, then you can cancel the movements in space, leaving you with a net movement in time.
Hence the saying, " Relativity, (unrestricted) FTL, Causality: choose two".
Posted by: Bill Woods on October 31, 2002 10:42 AMIn fact, your son is right to suspect that there is something up with this; the concept of "going backward in time" is in all probability incoherent.
Posted by: Daniel Davies on October 31, 2002 10:48 AMWell, I must say I'm finding this fascinating. One thing, though: what was the "ether drag" hypothesis, and how did it explain the MM experiment?
Posted by: Jimbo on October 31, 2002 01:21 PM"Ether drag" is the idea that the reason you can't see the motion of the Earth relative to the luminiferous ether is that some of the ether is dragged along with the Earth, and thus at rest with respect to it. Thus, when you do tests at the surface of the Earth to measure the motion relative to the ether, you see nothing, because the local ether is moving with the Earth.
It's a wonderfully baroque sort of idea, but not all that satisfactory, both because it is needlessly baroque, and because you would expect to see some odd effects on astronomical observations if ether drag were for real, and we don't see any of that. There's probably a Ted Chiang sort of SF story in the idea, though...
Wow. This discussion brings back haunting memories of college physics classes in Early Quantum and Relativity. I got a 24 out of 100, with the bell curve...I got a "B". My first test question was to derive E=mc2.
As for MM. Back in...1987 I think. I attended the MM Experiment 100 year celebration at Case Western Reserve in Cleveland. They had a working mock up of the experiment. Not that this gives me any added credibility mind you.
To answer Jimbo, I'll do my best.
They had a setup to split a beam of light into 2 parts. They split them off into right angles of each other. One part went off into the direction of the Earth's spin, (thus with the added velocity of the Earth's spin) the other perpendicular to that and therefore not with the added velocity. So they had a splitter, and a bunch of small mirrors arranged so that the beams went off in there directions and then returned back to a spot together. MM thought that the beam with the "push" from the Earth's spin would make that beam travel faster so that the 2 beams would come back together out of phase. The didn't, they always came back in-phase. To explain this, it was conjured that "ether" must be slowing the first beam down. Kinda like going into the wind. Ether was this...invisible cosmic stuff. As far as I know, no one conjured that the speed of light is constant and can't be pushed.
As for the time question. Clocks will slow down as you approach the speed of light. But, the traveller will not notice. Only until he compares his clock to another clock in a different frame of reference will the difference be noted. Experiments with atomic clocks show a clock at sea-level is "faster" that a clock on top of a tower. The clock on the tower has a slightly higher velocity from the Earth's spin.
Geesh...I'm done.
Posted by: BEM on October 31, 2002 01:56 PMI was a physicist at one point...so I will try to explain my view on it.
The idea of ether drag came from the genesis of the maxwell equations*. Maxwell built the edifice based on mechanical analogues of the processes occurring in the rest of the world. The div-grad-curl operators have very natural source-slope-vorticity analogues in liquid flow. To have a wave, however, one needs a medium.
Imagine you are travelling in a (slow flowing) river, and drop a rock. The speed of the waves measured from your position on the boat is uniform--the circles spread out. Measured by the person on the side of the river, the speed of the foreward and reverse travelling waves are different. Equivalently, if we are ina moving boat on the water, and drop a rock, the foreward ripple goes as v_ripple - v_boat (by our measurement) and the side ripples at v_ripple, while the reverse ripple moves at v_ripple+v_boat.
The michelson-morely experiment said "the earth is moving, and if there is a medium in which light moves, then the measured speed will be different in two directions. It will be c in one direction, and c-v_earth in the other". So if you measure velocity on the earth, we ought to see a measurable difference between the speed of light in perpendicular directions.
They didn't.
I think a better way of understanding Einstein is to first understand that his background with Minkowski (and thus, minkowski-spaces) gave him a perparation to understand the effects of multidimensional topology as measured in 3 dimensional systems. Second, he made the interesting, critical step to say "What if the math is correct." In many ways, this is THE innovation of the 20th century, where physics was finally freed from the shackles of our physical understanding, and became an object of pure math. This lead Planck to say "do I avoid the ultarviolet catastrophe if I make the ridiculous assumption that energy is partitioned into little chunks." And more critically, then Heisenberg said--well what if that is really true. Einstein did the same for electromagnetics and spacetime. Much of early 20th century physics is the struggle of people to believe that the math was more true than their intuition allowed.
So as everyone else has said, it isn't quite right to say that Einstein showed how Maxwell was wrong. I think it would be better to say that Einstein showed that Maxwell was correct, and that there were deep physical consequences to that.
*this is the source of a bad physics geek joke, which you see on the T-shirts of exceedingly geeky students. Essentially, the derivation of electromagnetic waves as light is a few step derivation from Maxwells laws. this is printed on the t-shirt, with thus, LET THERE BE LIGHT on the end. I wrote the sentence without that in mind, but I kind of like the pun....
Brad, you may be interested in a more advanced version of the same idea you raised here which goes by the name of gauge theory. This comes in many forms, but the basic idea can be shown in the context of the interaction of the electron field and the electromagnetic field.
Both of these fields can be described mathematically in a way that seems to leave unresolved a specific term in the equations describing the fields at particular points in space and time. (In the electron case this is the complex phase of the spinor fields, in the EM case the grad chi term that can be added to the (phi, A) field.) However when one puts the EM and electron fields together, these two terms magically result in a single common solution to the system---the degrees of freedom in the one field cancel out the degrees of freedom in the other field.
In many ways this is analogous to a much more sophisticated form of the relativity principle where, recall, one cannot define an absolute velocity but one can define the relative velocity between two bodies.
The "pick any two" statement about FTL, while clever isn't really correct. I wrote a lot about that here. I'm not sure it's at all coherent, though -- it's very easy to slip into jargon after all.
Posted by: Aaron on October 31, 2002 05:22 PMErm, my eyes slid over the "(unrestricted)" part. Ugh. That is correct. Anyways, I hope what I wrote is interesting anyways....
Posted by: Aaron on October 31, 2002 05:25 PMJust a few follow-up comments.
* Gauge theory is really beautiful. I'm still trying to learn how to explain it, so I won't try again here. Maynard gets kudos for the effort.
* It's not really correct to say that Einstein had useful knowledge from Minkowski to help him work out special relativity. True that Einstein studied with Minkowski - the two didn't really get on so well, primarily because Einstein was difficult - but Einstein worked out his special relativity with no 4-dimensional geometry in mind (for one reason: he was less mathematically sophisticated than Minkowski at this point in his life). Minkowski was one of the first to pay any attention to Einstein's work (to his credit, he took his difficult former student seriously) and he worked out the geometrical interpretation, now called Minkowski space. Einstein, rather than grateful, initially viewed the geometry as simply cute mathematics, but a distranction from the real point. Later, when Einstein was working out general relativity, he finally realized the great utility of Minkowski's geometry.
* MM and ether-drag is well explained above. So now why do people cite MM as important in establishing the correctness of relativity? First, it's worth distinguishing between what motivated Einstein (intersting, but ultimately unimportant) from what motivated the physics community to accept relativity (important). Relativity (special mixed with general) has today many direct confirmations, mostly due to precise clocks that detect that the rate of time depends on the gravitational field and velocity. The GPS, for example, simply wouldn't work without taking relativity into account. But these kinds of confirmations weren't available in the early 1900's. Once people started paying enough attention to Einstein's work, they could understand his motivation from Maxwell's equations, but elegance doesn't imply correctness: they still wanted something experimental to back it up. Up until the observed bending of light by the Sun's gravitational field, the main "direct" test of relativity was the MM experiment, so it gets cited as the evidence for relativity.
Another aside: a useful analogy to physics research is a hard crossword puzzle. Some clues you can only pencil in a guess for, and then later, when the perpendicular words get filled in, you begin to see the connections and either modify your guess or gain more confidence in it. Eventually you become confident enough to ink it. The MM clue got pencilled in with the (admittedly baroque) "ether drag" and nothing was there to contradict it. The Maxwell's eq puzzle got pencilled in by Einstein with special relativity. The overlap of the two lead people to fill in special relativity for both and gain confidence in it at the same time.
Ugh. Should read "the overlap of the two led people" .... though it's fun to picture "two lead people"
>>The electric and magnetic fields are not vectors and they transform into each other when you change frames. Really, the fit into a different object, a 'tensor', that behaves very nicely under Einstein's relativity.<<
Well, yes, that's the point. Maxwell thought he had two vector fields, electric charges, and four dynamic equations connecting them. Einstein realized that there was one electromagnetic field tensor.
Posted by: Brad DeLong on November 1, 2002 08:06 PM