WILDERWIND
A page for philosophy, aerodynamics, physics and other fun stuff
by
Edmond S. Miksch
ed_miksch@yahoo.com
Copyright: June 26, 2007
Contents
A funny story about negative mass
It was springtime in 1952 at Reed College in Portland, Oregon. After long months of darkness and the gloom of winter, the sun was out, the air was warm, little birdies were singing in the treetops, and, the morning classes being over, I had spring fever. I knew that if I sat down in a library to study, I would soon be asleep. I decided to go into an empty classroom and do some calculations on the blackboard so I would stay awake.
I thought it would be a good idea to calculate the energy density of the gravitational field. Nobody had told me what it was, and it seemed like something I ought to know.
To calculate the energy density of the gravitational field, I did a thought experiment in which I started with a spherical shell of mass particles having a greater radius, RG and contracted the shell of mass particles to form a spherical shell having a lesser radius, RL. The two spherical shells have the same center. The experiment was to be out in space somewhere, where there was no gravitational field except the field due to the mass particles. The mass particles could be gold dust, buckshot, sand, etc.
Figure 1 shows the configuration when the mass particles are located at the greater radius, RG, and Figure 2 shows the configuration when the mass particles are disposed at the lesser radius, RL. In Figure 1, the heavy circle shows the mass particles at the greater radius, RG and the lesser radius is shown in phantom.
In Figure 2, the heavy circle shows the mass particles at the lesser radius, RL, and the greater radius is shown in phantom. In both figures, R denotes the distance from the center of the spheres to any point in space, either inside the spheres, or outside.
We now look for regions of space in which the gravitational field has been created or eliminated as a result of moving the mass particles from RG to RL. It is well understood that inside a massive spherical shell having a uniform surface density, the gravitational field due to the spherical shell is zero. Hence, for both the configuration shown in Figure 1 and the configuration shown in Figure 2, the gravitational field inside the smaller sphere having radius RL is zero. Therefore, there is no change in the gravitational field inside of RL.
It is also well understood that, anywhere outside of a spherical shell having a uniform surface mass density, and a total mass M, at a radius R from the center of the sphere, the gravitational field is given by:
(Equation 1 resembles Newton's law of gravity, where G is the gravitational constant.) In MKS units, G = 6.672*10-11. Hence, for both the configuration shown in Figure 1 and the configuration shown in Figure 2, the gravitational field outside the larger sphere having radius RG has the value given by Equation 1. Therefore, there is no change in the gravitational field outside of RG.
It is only in the region between the two spheres, where RL < R < RG that there has been a change. For the configuration shown in Figure 1, the field in that region is zero because that region lies inside the spherical shell of mass particles at RG .
However, after the spherical shell of mass particles is contracted to the configuration shown in Figure 2, that region lies outside the shell of mass particles. The field strength then has the value given by Equation 1. The gravitational field in the three regions is summarized in the lines at the bottom of the figures.
So, then I did some algebra, and I found that the energy density of a gravitational field of strength g is:
Then, I noticed the minus sign. I thought "Huh, I wonder where I made a mistake". So I went through my algebra and couldn't find a mistake. Then, I thought "Well, I created a gravitational field in the region of space between the two spherical shells, and I got energy out as a result. I guess the gravitational field really does have a negative energy density. I wonder why noboby told me."
Of course, the next thought was, well, energy = mass times c 2. Hence, the mass density of the gravitational field is:
So, I concluded that the gravitational field has a negative mass density. Why didn't somebody tell me?
A few weeks went by, and, during a discussion in physics class, I wanted to look smart and noted that the gravitational field has a negative mass density. The professor asked "Where did you get that idea?" I decided that nobody knew but me. I was pleased that I was so wise. I was a sophomore.
The following year, I was the editor of the Reed College Science Bulletin, which was a weekly listing of events in the science departments. I had some white space at the bottom of the page and started writing about negative mass. Well ...
I got censored!
Apparently, negative mass was just too far out. I was directed to eliminate the negative mass writings from the copies that left the campus.
The next year, my senior year, I was expected to write a thesis, which was to be an original contribution to knowledge. I thought that negative mass would be a good topic. There was some consternation among my professors, but they read my thesis. They didn't believe it, but couldn't find anything wrong with it. They decided that I had used valid scientific reasoning, even if they disagreed with the conclusions. They approved the thesis, although they disagreed with it.
A couple of years later, I was frustrated that nobody believed my theory of negative mass. I thought that if I supplied a hint, maybe someone would independently come up with negative mass, and, since he thought it up, he would believe it.
John Campbell, the editor of Astounding Science Fiction was asking readers to send in laws attributed to the Great Dr. Finnagle (otherwise known as Murphy) These are laws such as "In any laboratory experiment, if something can go wrong, it will." I saw an opportunity to supply a hint about negative mass. I sent in the law "If a string has one end, then it has another end." I also stated that the law had broad cosmological consequences provided the terms "string" and "end" have sufficiently broad definitions. I was thinking that the "string" would represent a tube of flux of the gravitational field, and that one end would be on a positive mass (such as Earth) and the other end would be in a region of space having a negative mass density. Somewhere out there in the wild black yonder. It was published as one of Finnagle's laws, and I was very pleased.
So, then, a couple of decades went by. I found a wife, started a family, found the Lord, we landed on the moon and I was working at the Westinghouse R&D Center. A friend handed me a scrap of paper with printed words "Miksch's Law: If a string has one end, then it has another end." Well, that was interesting. Apparently, it was from a desk calendar. That was fun, but I lost the scrap of paper and thought that was the end of it.
So, then, a couple more decades went by. The Berlin wall came down, somebody invented the microchip and packet switching, and the internet came into being. Our kids grew up, went to college and got married. One of our sons-in-law set up his computer to get fortune cookies in his email. One day, his cookie said "Miksch's law: If a string has one end, then it has another end."
I discovered that I was world-wide famous! Miksch's law is all over the internet, even translated into other languages. I was very pleased.
Well, let's see now. It has been over half a century and there is still no comprehensive theory of negative mass that works consistently with relativity and cosmology. And what about quantum mechanics? To see what we have so far, click the following link.