Motion couplers and momentum converters
( Please see previous section about Motion Cancellers before reading this one)
Electromagnetic science is full of non-intuitive conceptsthings that seem contrary to common sense and what you were taught in high school physics. Consider, for example, how two charged particles interact when one is moving and the other is not (or when they are on perpendicular trajectories):
"We pointed out in Section 26-2 the failure of the law of action and reaction when two charged particles were moving on orthogonal trajectories. The forces on the two particles don't balance out, so the action and reaction are not equal; therefore the net momentum of the matter must be changing. It is not conserved. But the momentum in the field is also changing in such a situation. If you work out the amount of momentum given by the Poynting vector, it is not constant.. However, the change of the particle momenta is just made up by the field momentum, so the total momentum of particles plus field is conserved." (The Feynman Lectures on Physics, Vol. 2, p. 27-11)
Newton's law of action/reaction does not apply in certain situations in electromagnetics, because the "force" is actually canceling a motion instead of producing one. This allows other motions to become manifest. To get the total picture, you have to look at what happens not only to the particles, but to the rest of the situation, something we currently call the "electromagnetic field". And because we live on a gravitationally bound reference system that is actually moving multidimensionally at the speed of light, things get even weirder when particles move at high speeds. See The Feynman Lectures on Physics, Vol. 2, section 13-6 "The relativity of magnetic and electric fields" and chapter 26, Lorentz Transformation of the Fields.
In the previous section you saw how motion of the wire in space produces mechanical energy. I further proposed that motion of space in the wire also produces energy, but of a different sort, namely electrical energy with an attendant magnetic field. Let us suppose now that we replace linear motion with rotational motion for these cases. Do we still get a picture that is self-consistent? Can we still extract energy from either system? More particularly, can we extract momentum? Energy has only a magnitude, but momentum has both a magnitude and a direction. Seeing what is going on with momentum would be even more illuminating than seeing what is happening with the energy.
To illustrate the issues, consider the behavior of the device shown in the illustration below. The marbles are revolving at high speed in a frictionless tube which is anchored to a turntable. The turntable is initially stationary, but is able to rotate freely. The system clearly has angular momentum, but if the tube is opaque, this is not obvious to an external observer. The observer can command the gate valve to close however. When it suddenly closes, the marbles will stop "flowing" in the tube and collide with the gate valve, which is securely mounted on the turntable. This rotational equivalent of "water hammer" will cause the turntable to start rotating.
Now suppose we have a coil of wire (a solenoid) with current circulating through it instead of a tube with marbles. According to the "Motion Cancellers" discussion on the previous page, this system will likewise have angular momentum, but in this case, it is caused by space rotating in the wire, instead of the wire rotating in space. Suppose we command the battery to disconnect. The electric current must suddenly stop. The space revolving in the wire (electric current) comes to a halt. What then happens to the alleged angular momentum of the system? Does it just disappear? Or does it cause the turntable to rotate as in the previous (mechanical) example?
I can tell you from personal experience what will happen. You'll see a big, fat spark when the battery disconnects, but the turntable will not rotate.
As a kid I used to play with inductors and batteries. I would connect a battery to a couple of wires from an old audio transformer, or a couple of wires from an old fluorescent light ballast. I noticed that some hookups would produce a little spark, some would produce a big, fat snappy spark, and others would produce nothing. When I got a couple of fingers across the terminals and disconnected the wire, I would sometimes get one heck of a shock. How could a little 6 volt battery and a little coil of wire produce such a high voltage?
Years later I would learn about V = L(dI/dt). This says that the voltage across an inductor is proportional to the time rate of change of the electric current. Disconnecting the wire caused the current (I) to change very suddenly. The time derivative of this is numerically large, and this causes the high voltage and fat spark. The energy which is stored in the (now) collapsing magnetic field suddenly returns to the wire.
Electrical engineers will tell you that inductors act like an electrical flywheel and capacitors act like an electrical storage tank Either can store considerable energy. When you disconnect a capacitor from a battery, you leave it with a "full tank of electric fluid" (so to speak). The energy remains stored, and does not have to go anywhere. But when you disconnect an inductor, the "flywheel" suddenly stops, and you get the electrical equivalent of water hammer. This is usually not desirable, and protective devices are inserted into circuits to dissipate the high voltage pulse. A diode, or a small lamp, for instance, will allow the current to circulate momentarily and come to a gradual stop even when the battery is disconnected suddenly.
So this little experiment demonstrates that an inductor stores energy, but does not specifically demonstrate storage of angular momentum. Mechanical momentum and electrical momentum still seem to be rather separate concepts. Yet according to the Motion Cancellers discussion (which you read previously) these should be equivalent. We should be able to show, without "cheating", that the electrical angular momentum can be turned into mechanical angular momentum by using fundamental electromagnetic principles directly, and without interposing some sort of energy conversion device.
This is NOT an intuitively easy problem to solve. However, the Poynting vector, and Feynman's comments about it, will serve to educate our intuition:
"Suppose we take the example of a point charge sitting near the center of a bar magnet, as shown in [the figure]. Everything is at rest, so the energy is not changing with time. Also, E and B are quite static. But the Poynting vector says that there is a flow of energy, because there is an E X B that is not zero. If you look at the energy flow, you find that it just circulates around and around. There isn't any change in the energy anywhereeverything which flows into one volume flows out again. It is like incompressible water flowing around. So there is a circulation of energy in this so-called static condition. . . .
You no doubt begin to get the impression that the Poynting theory at least partially violates your intuition as to where energy is located in an electromagnetic field. . . . The circulation of energy around a magnet and a charge seem, in most circumstances, to be quite unimportant. It is not a vital detail, but it is clear that our ordinary intuitions are quite wrong." (The Feynman Lectures on Physics, Vol. 2, p. 27-8)
With that in mind, consider a little gizmo Feynman describes. It is very similar to our problem, except that it includes some spheres that are charged with static electricity:
actual space. The presentation so far has included the following concepts:
"Do you remember the paradox we described in Section 17-4 about a solenoid and some charges mounted on a disc? It seemed that when the current turned off, the whole disc should start to turn. The puzzle was: Where did the angular momentum come from? The answer is that if you have a magnetic field and some charges, there will be some angular momentum in the field. It must have been put there when the field was built up. When the field is turned off, the angular momentum is given back. So the disc in the paradox would start rotating. This mystic circulating flow of energy, which at first seemed so ridiculous, is absolutely necessary. There is really a momentum flow. It is needed to maintain the conservation of angular momentum in the whole world." (p. 27-11)
Of course, this is not a good way to make an electric motor. Motors must operate continuously. The illustrations simply show that motion of mass through space, and motion of space through mass have analogous behavior.
The physics of electromagnetism has a lot of concepts that seem strange and awkward on first encounter. The physics of space/time ratios and the concepts of multidimensional motion will, hopefully, allow you to become more comfortable with these concepts.
The various discussions above have been based on the premise that an electron acts like a unit of
1. Space moving through a wire partially cancels one dimension of gravitational motion and leaves a magnetic field as a residual effect.
We can now mention evidence for another concept:
Adding more space to a wire reduces its material density. In other words we would expect the wire to expand. If this could be done with extreme suddenness, the ordinary forces that keep the atoms of the wire together will be overcome, and the wire will be blown apart. However, the effect would be mechanical, rather than thermal; the wire does not melt or vaporize. Evidence for just such an effect comes from experiments of Dr. Peter Graneau, Dr. Jan Nasilowski and others. They found that in electrodynamic wire explosions, the breaks were due to tensile stress (which act longitudinally) rather than pinch-off forces (which act radially). The wire seems to pull itself apart into discrete fragments in these experiments. A similar experiment was done with segments of a copper rod stacked vertically in a glass tube. When an enormous current pulse was sent through this stack, the copper segments moved apart. Photos showed multiple electric arcs between the segments. Explanations for railgun recoil effects have led to similar conclusions. In these experiments the rails are securely anchored and have no freedom to expand. Sometimes the rails crumple back upon themselves as though there were tremendous unrelieved expansion forces. It is an effect similar to an asphalt road "washerboarding" on a hot summer day. In conclusion:
4. Enormous electric current in a wire adds physical space between the atoms of the wire and may even cause the wire to tear apart. If the ends of the wire are securely clamped, the wire may buckle back upon itself.
"We have thus seen how solid conductors can bend and buckle, and even shatter, if subjected to high current pulses. The discussion indicates that some kind of longitudinal stress is present." http://www.df.lth.se/~snorkelf/Longitudinal/node3.html , http://www.df.lth.se/~snorkelf/Longitudinal/node5.html
If more space can be added to a material aggregate and result in a decrease in density, then it is natural to also ask: "Can more time be added to a material aggregate and result in an increase in density?" If this can be done, then the possibility of producing materials with ultrahigh densities and attendant useful properties might become a reality. Ultrahigh density diamond, for example, should be able to easily cut through normal diamond.The possibility of making "high energy density materials" is of great interest to the military. Chemical explosives have specific energies of 5 MJ/kg. Thin film batteries and superconducting rings have about 1 to 50 MJ/kg. In chemical explosives the energy comes from chemical bonding, which is about 10eV per molecule. Superdense materials would have bond energies MUCH higher than this.
Conventional high explosives, for example, have specific energies on the order of 5kJ/g and maximum mass densities of 2 g/cm3. This corresponds to an energy density of 10 kJ/cm3. So-called "metallic hydrogen" is believed to have an energy density of about 270 kJ/cm3 which would be about 35 times more energetic than TNT. It could be used as a powerful "conventional" (non-nuclear) military explosive. A bomb containing one ton of metallic hydrogen would then be equivalent in destructive potential to 35 tons of ordinary TNT. It could also be used to make nuclear weapons much more compact, possibly even obviating the use of a fission trigger (fission makes the bomb radioactively dirty, and the materials required for the fission trigger are very expensive and hard to obtain; a design with no fission trigger would make cost proportional to explosive power, but could also prove to be a proliferation nightmare). As a rocket fuel, metallic hydrogen would have high specific impulse, say, 1400 sec compared to 400 sec for JP4 + liquid oxygen. As an aircraft fuel it would have 300 times more energy than the best available, which implies a flight range 300 times normal.
Astronomers are well aware of the existence of extremely high density matter, such as that in white dwarf stars. They also know about high density structures, such as compact, high velocity jets, and even compact galaxies. There is no generally accepted comprehensive theory explaining the "compactness" features of the universe. With tongue in cheek I can say that it might just be a matter of time.
For more information see:
Fourth Generation Nuclear Weapons, Andre Gsponer, Jean-Pierre Hurni, 1999, 6th ed., p. 101 to 121;
Science News, Vol. 157, Jan 22, 2000, p. 54 (octanitrocubane);
We saw previously that energy is t/s, that mass and inductance are both t3/s3, and that electrical current is s/t. It is possible to use these dimensions to derive other dimensions for electrical quantities. Power (energy per time), for instance, is 1/s. The less obvious dimensions can be derived from common electrical formulas. The voltage across and inductor, discussed above, is V = L(dI/dt) and we can use it to find the dimensions of voltage ("electric potential"). Hence, V [=] t3/s3 (s/t)(1/t) or t/s2. We can also readily see that the formula is analogous to F = ma, where a = dv/dt. Voltage even has the same space/time dimensions as mechanical force. Electric field intensity (E) is measured in volts per meter and therefore is t/s3. This can also be derived from formulas found in college level textbooks on electromagnetic science:
In a similar way we can find the space/time dimensions for a magnetic field:
But there are some troubling inconsistencies in electrical space/time dimensions. The Poynting vector is usually interpreted as power per area which comes out to 1/s3. The literature also expresses it as S = gc2
Does E = cB agree with these dimensions? We can readily see that it does.
where g is the momentum density (momentum per volume) and which has the dimensions of t2/s5. According to this formula then, S works out to be 1/s3, exactly as expected. But we are not so fortunate when expressing S in terms of E and B as in this formula:
S = e0c2E X B
The permittivity, e0, is expressed in coulombs per volt per meter. Charge is the one-dimensional analog of mass, and so permittivity is probably (t/s)(1/(t/s2))(1/s), which appears to be dimensionless. The dimensions for the remaining items have been given previously, and with those, S works out to be (s2/t2)(t/s3)(t2/s4) or t/s5. That is obviously NOT the same as 1/s3 which is what we were expecting. Did we mess up something when we used the vector cross product? Does S have some alternative interpretation which would account for the discrepancy? Has a term inadvertently been left out of the formula? Is a profound insight lurking here somewhere?
Perhaps the guess on the dimensions for permittivity were wrong. Simple inspection shows that they would have to be (s2/t) for the Poynting formula to work out correctly. Permittivity is used in formulas for capacitance, so maybe we can look at some capacitance formulas, explore the dimensions, and see if our new guess for the e0 dimensions is reasonable. Here is a good formula (Electrical Engineering Circuits, H.H. Skilling, 2nd ed., p. 18) to start with. It has obvious space/time dimensions and little else:
C is the capacitance, e0 is the permittivity of free space (vacuum), A is the area of the plates, and s is the separation between plates. Plugging everything in, we find that the dimensions for capacitance (C) are (s2/t)(s2)(1/s) which is just (s3/t) .
We now must find out if these dimensions for capacitance make sense. If they do, then the new choice for the permittivity dimensions is probably correct as well. Let's try the formula for current through a capacitor (note that v is voltage here, not velocity):
This is perfect. We were hoping that the space time dimensions of capacitance would work out to be (s3/t) and that is exactly what we got. We can now confidently check other capacitance formulas and see if they to give the same dimensions for capacitance. Here is one that relates the charge on the capacitor plates to capacitance and voltage:
And we find . . . that it doesn't work. Instead of getting (s3/t), we get just (s).
Let's go back to the original capacitor formula: C = e0 (A/s). If permittivity were dimensionless as originally supposed, the formula above, charge = CV, would be dimensionally correct. In other words, capacitance is just a space unit.(s). If we take that value and plug it into the formula for current, we find that current is (s/t) instead of (t/s). This seems to be trying to tell us something.
Rather than have two kinds of capacitance, it is more reasonable to believe that there are two kinds of electric current. This has already been discussed elsewhere. One type of electricity, the so-called "static electricity", is based on coulombic charge which has the dimensions of (t/s). Ordinary electric current, however, is just space per time (s/t), like a velocity, as discussed above and in the previous section. Maybe "storing current" in a capacitor is equivalent to stuffing it with space units. Or maybe is it equivalent to stuffing it with coulombic charge units. Which is it? The formula for force exerted on a charge by an electric field between the plates of a capacitor is F = QE . Force is (t/s2) and electric field is (t/s3). It is obvious that the kind of Q (charge) we are looking at here must have the dimensions of (s) and not (t/s). In contrast to the inductor, what the capacitor stores is a "stopped" version of (s/t) or, in other words, just (s). And unlike the inductor, the electricity does not "squirt back out" when the battery is disconnected; a capacitor acts more like a storage tank than a pressurized accumulator (especially when the dielectric is a vacuum).The conceptual problems here can be illustrated by thinking about a capacitor storing electrons as though it were a jar that stores marbles. Note that the marbles are stored throughout the jar's volume, not just on the jar's surface, and that the jar has limited capacity. If we want to store more marbles, we need to have a jar with more space. However, the marbles (electrons) represent space units (rotational space). Putting space units into the jar, and then asserting that the jar is running out of space does not make any sense. We need a jar that has temporal volume instead of spatial volume. That way, adding more electrons creates a space/time (or time/space) ratio. This ratio also implies a limited capacity. But how do we put more temporal volume into a capacitor? As explained previously, matter itself is a temporal structure (t3/s3). Putting a slab of matter between the two plates, creates more temporal volume, more "capacity". Some materials work better than others for this purpose, and this in turn leads to concepts like "capacitivity"something that is today called "permittivity".
Permittivity is thus an actual physical characteristic, and therefore should NOT be a dimensionless quantity. The second guess on the dimensions for permittivity (s2/t) is probably correct.
Anyway, the point here is that space/time dimensions for electrical and mechanical quantities can be worked out, despite some obvious difficulties and long standing misconceptions. Ultimately, everything in physics can be expressed in terms of space/time ratios of some sort. This can lead to new insights about the true nature of these entities and their relationships with other entities.
The Feynman Lectures on Physics, Vol. 2, Feynman, Leighton and Sands, 1964
Basic Properties of Matter, Dewey B. Larson, 1988
New Light on Space and Time, Dewey B. Larson, 1965
Nothing But Motion, Dewey B. Larson, 1979
The Reciprocal System, http://www.rsystem.org
The Collected works of Dewey B. Larson, http://www.rsystem.org/dbl/index.htm
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Copyright 2004 by Brian Fraser