return to homepage WHY MILLIKAN GOT THE WRONG NUMBER
Millikan performed the famous oil drop experiment in 1909, finding a
value of 1.5924 x 10-19C for the elementary electric charge, or the
charge on the electron. We now think the number is a bit higher, the
current figure being 1.6022 x 10-19C. Millikan could never explain
to himself or to anyone else why he was off by about .6%, the
difference being more than six times greater than his standard
error. It has been assumed that the difficulty of the experiment was
the cause of the error, but Millikan always dismissed that. If we
study the set-up, we find that the experiment is indeed difficult and
expensive to prepare, but once it is correctly prepared, it should be
expected to give an answer without such a large error. This is what
Millikan's standard error is meant to tell us. We should have
expected an error of <.1%.
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IN HIS OIL DROP EXPERIMENT
Millikan
never identified the cause of the error, and no one else has done so
since then. The oil drop experiment was soon replaced by other
experiments, and the question of Millikan's failure has not been a
topic for many decades. Currently, the number is estimated from the
Josephson effect or the Hall effect, and neither effect is analogous
in any way to Millikan's experiment. And the actual number we use comes from no experiment. It comes from CODATA equations.
My
recent studies have allowed me to solve this longstanding mystery.
The crucial factor is that the oil drop experiment was performed
vertically, in line with gravity. In fact, Millikan arrayed his
electrical force to balance the gravitational force. The reason this
explains the error is that I have shown that what has been called
gravity up to this time is actually a compound force. Newton's
gravitational field is, in fact, a vector addition of two fields: the
gravity field of the Earth and the charge field of the Earth. The
charge field has been hidden up to this time in the compound field.
This
means that Millikan was not, as he thought, balancing two fields, his
electrical field up and gravity down. He was balancing three fields:
his electrical field up, gravity down, and the Earth's charge field
up. In another paper, I have derived a number for the Earth's charge
field: .009545 m/s2. In a different paper I have shown that this
charge field is the mechanical cause of the difference between the
Bohr magneton and the magnetic moment of the electron. The Bohr
magneton is a theoretical number and the magnetic moment is an
experimental number, found in the Earth's field. But since the Bohr
magneton does not include the Earth's field, the two numbers cannot
match. They are off by the amount of the Earth's charge field (roughly).
[My recent paper on the electron's magnetic moment forced me to return to this paper for a closer analysis. I found that my first analysis was both incomplete and, as a matter of vector additions, incorrect.]
Millikan's number is about .6% less than the current accepted number. Although there is not universal agreement on the cause of this error, Richard Feynman* thought it was because Millikan mismeasured the viscosity of the air. That is close to the truth, but we can now see it was not only the viscosity of the air that was mis-measured, it was also the buoyancy of the air. Millikan didn't realize that the Earth's charge field was a large factor there as well, so we find a second place the error creeps into the experiment.
The Earth's charge field is .0973% of its unified field, so we would expect an error of that much at first glance. But because the error is coming in in several places, we have to multiply that effect. First of all, we have to double the number, simply to find the first correction. In Millikan's math, the charge of the Earth is implicitly included in g, although Millikan didn't know it was there, of course. The current number which we give to gravity is actually a unified field number. So to bring the Earth's charge back into the equations explicitly, we have to reverse the vector. This reversal doubles the number, since it takes it from plus to minus. Then we do the same thing with the buoyancy. Every time we find the Earth's charge entering the experiment, we have to add two values of .000973. So far we have found just the two, so we multiply by four to get .0039, or about .4%.
Since I have recently found that the number for e should be 1.607 instead of 1.602, we must study Millikan's experiment for a third place the Earth's charge enters the experiment. We find it by realizing that Feynman was right: both the viscosity and the buoyancy have to be studied, since the oil droplets were measured at velocity. I had at first assumed Millikan balanced them between charge and gravity, but, as with Cavendish, that proved to be impossible. The droplets were always in motion. And even if they hadn't been, their masses were too difficult to measure, requiring a solution at velocity. At any rate, although buoyancy and viscosity are closely related, they aren't equivalent. The buoyancy would enter the equations even without velocity, but once we measure at velocity, the charge field enters a third time. This is because with buoyancy, we have the charge field of the Earth holding up the oil droplets directly. With viscosity, we have the charge field holding up the oil droplets via surrounding particles. The surrounding particles resist the oil droplet, and the charge field helps them do that. This is true whether the oil droplets are moving up or moving down, because the air molecules are energized by charge. Part of the air molecules' ability to resist or have a viscosity comes from charge. So we have our third entrance of the Earth's charge into this experiment. So we muliply by six instead of four, giving us .78%. Millikan's number varies from 1.607 by .92%, so we are getting close. We now have an unexplained error of only .14%.
However, my analysis tells us something else extraordinary. What we have found is that Millikan missed the current number because his equations left the charge field out of it. The current number includes the charge field of the Earth. But of course this means that Millikan was more accurately measuring the electron/proton charge field, without the Earth's influence. Since this is what we now think we are measuring, and what we wanted to measure, it could be said that Millikan did the job extremely well. His method—putting the experiment in the line of the Earth's field—actually took the field out of the math. That is why we had to put it back in to match data. Since we are in the Earth's charge field, all our data includes the Earth's field, and Millikan's experiment doesn't. He arrayed the numbers against themselves, you see, negating them. And in doing so, he appears to have found the electron/proton solo field, within .14%.
Now let us look at some of the newer methods of measuring e. The methods using the Faraday constant and Avogadro constant are shot with through with errors, and even Wikipedia admits1 that in practice the electron charge is not computed from the constants, but the reverse. The method called "shot noise" is admitted to be more imprecise than the oil drop method,1 so we need not deal with it here. With the
Josephson effect we are looking at voltage oscillations in
superconductors. As we saw with my analysis of the Podkletnov effect, superconductors increase the effect of the charge field of the Earth. If you freeze a portion of the atmosphere, the charge field must pass through it more easily, since it has less resistance. This increases the force of the field, and
adds to the margin of error in the experiment due to charge. With the Hall effect, we have a quantum effect of electrons at low temperatures in strong magnetic fields. Again, a magnetic field at a low temperature creates a superconducting effect which increases the error of the experiment.
This is why we still use CODATA equations to calculate e, instead of relying on these newer experiments. The newer experiments don't correctly or accurately give us either the field with the Earth's charge or without it. Because they do not set up in line with g, they cannot find the electron/proton solo field. And because they use superconductors or very low temperatures, they skew the existing charge field. They can't freeze the entire Earth, can they? Well, if both the electron/proton solo field and the Earth's field are involved, as we have seen, freezing one and not the other can only skew the experiment.
*Cargo Cult Science
1http://en.wikipedia.org/wiki/Elementary_charge