Kicking the Sacred Cow
Page 16
And fringe shifts were observed—not only of a magnitude consistent with the "hypothesis of a fixed ether" (Michelson's words) within the limits of observational error, but from which the experimenters were able accurately to calculate the rotation speed of the Earth.
Beckmann's theory predicts this on the theoretical argument that if the gravitational field describes an outward propagation, the effect would "decouple" from the source as soon as it leaves, somewhat like bullets from a rotating machine gun still radiating outward in straight lines. In other words, the field's effects shouldn't share the source's rotation, and hence the speeds of the light beams in the two arms of the interferometer will be different. This doesn't contradict Einstein, though, where the General Theory is invoked to arrive at the same result on the grounds that each beam has its own idea of time. But whereas Beckmann's conclusion follows from Galilean principles and a few lines of high-school algebra, GRT requires multidimensional tensors in spacetime and non-Euclidian geometry.
Electromagnetic Mass—Increase Without Einstein
The law of inertia says that a mass tends to keep its momentum constant, i.e., it resists external forces that try to change that momentum. That's what the definition of mass is. The same is true of an electromagnetic field. A steady electric current produces a steady magnetic field. If the field is changed by changing the current, it will, by Faraday's law, induce an electric field that will seek to restore the current and its field to its original value—all familiar to electrical engineers as Lenz's laws of self-inductance, mutual inductance, and so forth. Similarly, a steady electric field is produced by a steady distribution of charge. If the charge sources are moved to change the field, the resulting "displacement current" gives rise to a magnetic field, and the changing magnetic field induces an electric field that opposes the movement of the charges. This is sometimes known as the "inertia" of the electromagnetic field, manifesting an "electromagnetic momentum."
It turns out that the electromagnetic counterpart to momentum also carries precisely its counterpart to mass. The electromagnetic mass of a charged body is an additional factor by which it resists physical acceleration beyond the resistance normally exhibited by the uncharged mechanical mass. This was known to the classical physicists of the nineteenth century. It comes out as a constant that multiplies velocity to add a further parcel of momentum in the same way that regular Newtonian mass does.
At least, it does when the electric (Coulomb) field carried by the charged body is spherically symmetrical, as would be the case when it's at rest—and near enough when it isn't moving very fast. The direction of the electric field at any point around a charged body—the line of voltage gradient—lies perpendicular (orthogonal) to the surfaces of equipotential. For a charge at rest the equipotential surfaces are concentric spheres like the skins of an onion, across which the field lines radiate straight and symmetrically in all directions like sea-anemone spikes.
However, Maxwell's equations and the relativity principle—and nothing more—indicate that when the body moves, the charge distribution will change as the charge begins to partly "catch up" with its own equipotentials, causing them to bunch up ahead and spread out behind. The result is that the orthogonal field lines are no longer straight but become curves. (This was what prompted Lorentz to conclude that electrons contract in the direction in which they move.)
Now it gets interesting. The expression for the electromagnetic mass of a body depends on the distribution of its electric field in space. When the rearrangement that takes place with increasing velocity is taken into account, the electromagnetic mass increases from its value at rest. The formula that the classical physicists of the nineteeth century derived to describe it is the same as the SRT equation for mass increase. The difference is that instead of rearranging the field distribution, SRT rearranged space and time, then applied the result to all masses, electromagnetic or mechanical, charged or neutral. It would appear that SRT's way of getting there wasn't necessary.
Page, for example showed in 1912 76 that Coulomb's law of electrostatic attraction and the Lorentz transforms are sufficient to derive Maxwell's equations—from which everything supporting SRT follows. But Coulomb's law is formally identical with Newton's law of gravitation. Hence, Page's method must lead to formally identical results—a "Maxwell" law that holds for mechanical, electrically neutral mass. By this argument all mass is shown to be velocity-dependent from classical principles, invoking none of the observer-dependence of SRT. (Objection. "But it's right there in the textbooks. Force equals mass times acceleration. F = mždv/dt. Mass is a constant. You can't get away from it." Answer: "True, that's what most textbooks show. But Newton never said it. His force was always given by the change in momentum: d(mžv)/dt. It allowed for the possibility of mass being velocity dependent. Mark of a careful scientist.") And since both masses, neutral and electromagnetic, respond to velocity in the same way, they can be combined into a single inertial reaction—a force that resists changes in momentum—increasing with velocity. There's nothing especially remarkable about velocity-dependent forces. Hydraulic friction and aerodynamic drag are everyday examples.
When the mass expressed as a function of c is used to calculate the work done in accelerating a body from rest to velocity v, the resulting expression for kinetic energy reduces to the familiar 1/2mv2 when v is small. At rest, a residual energy E0 remains that's related to the mass m0 by, yes, you've guessed, E0 = m0žc2. You can do it without Einstein.
In his book Einstein Plus Two Beckmann goes on to show that all of the experiments usually cited as confirming the Einsteinian formulas for mass, energy, and momentum are equally consistent with the field-referred theory. Similar arguments were presented following the publication of Einstein's original SRT paper in 1905—see, for example, Lewis, 1908, which derives the velocity-dependent relationships showing mass tending to infinity as its velocity approaches that of light, from considerations of conservation when a mass is accelerated by radiation pressure.
From the theory based on the real, physical deformation of forces in motion through the locally dominant field, Beckmann is also able to derive from first principles the line spacing of the spectrum of the hydrogen atom, a first approximation to the Schrödinger equation of quantum mechanics, and the Titius-Bode series giving the distances between planetary orbits, which relativity must simply accept as given. Doesn't this make it a more powerful candidate predictively? In the latter connection, Beckmann also correctly deduces the precession of the perihelion of Mercury's orbit, usually cited as one of the decisive tests for GRT, and shows that a German by the name of Paul Gerber was able to do so using purely classical considerations in 1898, seventeen years before publication of the Einstein General Theory in 1915.
In fact, it was more in connection with the General Theory that the word "relativity" caught the world's attention. SRT didn't really create that much of a stir—as mentioned earlier, Einstein's Nobel Prize was awarded for a different paper also published in 1905, on the photoelectric effect. But in 1919 it was announced that observations of the solar eclipse in the western Pacific by a team headed by the British physicist Sir Arthur Eddington had confirmed the GRT prediction of the bending of rays of starlight passing close to the Sun, which elevated Einstein to instant fame and retroactively the SRT, too, by association. Whether it was really a triumph of the magnitude popularly depicted has been questioned. Ian McCausland, for example, 77 shows that the measurements were not particularly accurate, the standard error being about 30 percent, while the various displacements ranged from half to twice what the theory predicted, and a lot of fudging went on to come up with an average of the order that was needed. But in any case, if the local gravitational field is effectively the propagating ether, the speed of a traveling disturbance will vary with its density, and the same result can be arrived at by treating it as a refractive medium in uncurved space. 78
Gravity and Electromagnetics
Why have we been postulating the l
ocal gravitational field as the possible propagating medium, when everything we've been talking about refers to electromagnetics? Well, the reference frame that Beckmann's theory actually postulates is the dominant local force field. For most practical purposes it reduces to the same thing. The magnetic force between moving charges is so small compared to the electric force between them (one of those relationships like that of mass with energy, involving c2) that it can't even be measured unless the electric field is neutralized.
The example Beckmann gives to illustrate this is two lines of negative charges—electrons, say—moving past a stationary observer like parallel columns of soldiers. The moving charges constitute currents moving in the same direction, which accordingly generate a magnetic attraction between them. But this attractive force will be completely overshadowed by the electrostatic repulsion of the charges. To reveal the magnetic effect, it's first necessary to neutralize this repulsion, which could be achieved by adding a row of stationary positive charges like fence posts along the line of march of at least one of the columns. This is exactly what happens with the ionized atoms inside a conductor. What this says is that to demonstrate a magnetic force, at least one of the currents must flow in a normally neutral conductor such as a wire.
In the macroscopic world of neutral matter that we live in and build instruments out of for investigating electromagnetic phenomena, therefore, the dominant force field that's left after the electric fields have been eliminated by positive and negative charges that neutralize each other is that of gravitation. Or perhaps we should say "almost neutralize each other." Some fascinating work is going on that interprets the gravitational force as a residual effect of electromagnetism—see, for example, Assis, 1992 and 1995. So certainly it might be the case that in other parts of the universe not dominated by neutral matter, some other definition of the local reference frame should apply.
Dr. Carl Zapffe in his A Reminder on E = mc2 interprets the phenomena usually cited as relativistic in a field-referred theory using the magnetosphere, which also defines the local frame moving with the Earth—and in the process he provides three derivations using classical physics of the sanctified formula contained in the title. Plots derived from space probe data and other sources show the Earth's magnetopause—the boundary of the magnetosphere—as a huge, teardrop-shaped bubble compressed to a bowshock front on the sunward side and extending outward more than ten Earth radii, around which the solar wind streams like the airflow around the body of a plane. On our planet deep inside this bubble, we've been trying assiduously for over a century to measure our airspeed with our instruments inside the cabin. Zapffe offers a model of
successively embedded domains in which the terrestrial magnetosphere riding with the Earth inside a "heliosphere," similarly formed by its motion through the larger "galactosphere," and so on.
We can conduct a conversation effortlessly with another passenger in a plane because our entire acoustic environment is moving with us. Trying it sitting out on the wing would be a different matter, swiftly disposing of any notions we might have formed that air doesn't exist. It might be revealing to perform experiments along the lines of Michelson-Morley on a space platform outside the Earth's magnetosphere, under conditions that have never been tested before, in motion relative to the local frame as defined by the Sun.
Does "Time" Dilate? Or Do Clocks Run Slower?
When we're assured of something to the effect that "relativity is confirmed routinely in laboratories all around the world thousands of times every day," one of the instances usually cited is the verifying of time dilation. The example given earlier was of muon decay, where more muons from the upper atmosphere survive long enough to reach the ground than should be able to. According to relativity, it's because time in the muon's moving frame runs slower than the time in the observer's frame, which includes the ground, the atmosphere, and the whole of the path followed in the particle's flight down. But a crucial question isn't being asked about another possible state of affairs that would produce the same result.
Is some semi-abstract quantity called "time" actually being dilated? Or is it simply that a difference in the internal dynamics (increased mass, for example) of moving clocks—meaning time-varying processes in general—makes them run slower? What's the difference? The difference is fundamental if by "moving" we mean with respect to some privileged reference frame such as a general Lorentzian ether, the local gravity field, or whatever. Simply put, a clock moving in that frame runs slower—a physical reality, not some trick of appearances or mathematical acrobatics—than a clock that's at rest in it. The laboratory is at rest in the Earth's frame while the muon isn't, and so the muon's clock actually runs slower.
As an illustration of the principle (one which has nothing to do with relativity), consider an ordinary pendulum clock being flown around the world in an eastbound direction. The rate of a pendulum clock depends on g, the acceleration due to gravity. The Earth's rotation generates an upward centrifugal force that acts against g, reducing it slightly. Since an eastbound clock is adding to the Earth's rotation speed, this effect will be increased, causing the airborne clock to run marginally slower. This isn't due to time in the aircraft "dilating," but a real, physical effect arising from its motion. Hayden discusses this distinction and provides references to relevant experiments. 79
This is also the answer that LET or field-referred-type theories give to the famous "twins paradox," where two young twins are separated by a motion that can be regarded as symmetrical and then reunited, upon which one or the other or neither is found to be older, depending which argument you buy.
"One's frame had to be accelerated somehow in order to bring them back together again, and therein lies the difference," runs one line. Response: "But the difference in ages increases with the time that the traveling one has been traveling. Yet exactly the same process of stopping and reversing will eventually return him whatever the duration of the trip. How can the same acceleration sequence cause different results?"
"It's the reversal of direction of one of them that does it. Even with the ingenious arrangements that have been proposed for effectively synchronizing oppositely moving, constant-speed conveyors." 80 Response: "But the SRT equations don't anything about direction. They only involve velocity."
"Acceleration is involved one way or the other, so SRT doesn't apply. You need to go to GRT." Response: "So why was it given as an example of an SRT effect in the first place?"
And so it goes. The debate has gone on for as long as the theory of relativity has existed. Careers have been toppled by it. 81 According to LET and its equivalents, the twin who does the most moving through the preferred reference frame (or the local preferred frames at the places he passed through) will age more, and that's the end of it.
In principle there is a way to resolve this. Going back to the muon, relativity says that only the velocity with respect to the observer matters, so the muon is just as entitled to argue that it's the laboratory that's moving. Thus, by the muon's frame of reckoning, the laboratory's time should be running slower. What we need is an observer sitting on the muon as it passes through the lab to tell us once and for all if the laboratory clock runs faster (Lorentz, Beckmann, field-referred) or slower (Einstein). This has never been done, of course. But eventually the ingenuity of experimenters will no doubt come up with an equivalent.
Perhaps the closest that anyone has come to actually testing this is the Hafele-Keating experiment in 1972, where cesium atomic clocks were transported east and west in commercial jets and their rates compared to a standard on the ground at the U.S. Naval Observatory in Washington, D.C. It's not uncommon to hear the result dismissed blandly with, "The moving clocks ran slower, just as relativity says they should." And it's true that they did—referred to a fictitious standard that didn't figure anywhere in the experiment. And they did so at different rates. The fact was that relative to the stated ground reference in Washington, D.C., the westbound clock ran faster, gaining 273 nan
oseconds, whereas the eastbound one lost 59 nanoseconds. In a fast-foot shuffle to accommodate this awkward state of affairs, the relativists decided that everything should be referred to a nonrotating Earth-centered frame, relative to which everything was moving east, and hence it was possible to describe the three clocks as moving "slow" (westbound), "slower" (Washington, D.C.), and "slowest" (eastbound). But that still doesn't rescue the theory, which says, clearly, that as far as Washington, D.C., is concerned, as with any observer, lightspeed is constant and moving clocks are slowed irrespective of direction. Those who regard the clocks as moving with regard to an absolute local reference have no problem. Apparently, R. L. Keating himself was surprised by the result 82 but accepted the explanation that astronomers always use the Earth's frame for local phenomena. But they use a solar barycentric frame for other planetary phenomena in order to get results that agree with relativity. Interesting, eh?
The Famous Faster-Than-Light Question
So what about the consequence that comes out of it all that "nothing"—no kind of energy or other causal influence—can travel faster than light? It's probably the most popularly quoted line whenever relativity is mentioned, and so some words on it wouldn't be out of order here, although they are necessarily speculative.
The limit follows from the form of the equations that express velocity as a fraction of the speed of light—you can't have anything greater than a hundred percent of itself. Put that way it sounds a bit trite, rather than expressing anything especially profound. The same fraction forms the basis of all the velocity-dependence equations, such as that for mass, which increases to infinity as velocity approaches lightspeed, and time, which tends to a standstill. So accelerating a massive object to lightspeed would require an infinite input of energy, and since that's impossible the implication is you can't get there. All experiments on fast-moving particles confirm the predictions, and as far as some kinds of minds are concerned, those that seem to need limits and restrictions to guide their lives, that closes the subject. If all of the human race thought that way we'd never have bothered trying to build flying machines because the eminences who knew better had proved them impossible.