Conducting experiments in space has been a great adventure in my career. In the early 1990’s we were growing crystals from fluid solution in the microgravity of space and we needed to observe the fluid motion around the crystal. I suggested an old trick of placing neutrally buoyant particles in the fluid and observing their motion. Needing the help of a fluid mechanics expert who could tell us exactly how well the particles could track the fluid movement, I called on an old friend, Roger Rangel, a professor at the University of California, Irvine (Now a department head). The movement of particles in fluids can be predicted from the so-called Navier Stokes equations. The problem is that these equations have never been solved exactly, and scientists employ approximations and what are known as numerical solutions provided by long computer runs to get answers. An exact solution would look somewhat like the following, which is essentially Newton's second law of motion, every action has an equal an opposite reaction.

Newton's Second Law of Motion

The primary problem with such a solution is that it still has a lot of mathematical terms in it that so not provide a clear physical meaning. That is, it is not yet a usable solution without further work and approximations to break it down to more usable form. Specifically solutions to the Navier-Stokes equations contain an extremely complicated “history” term that look roughly like the last terms in the above equation..

Carlos Coimbra, a brilliant, young Brazilian student of Roger’s (now a professor at the University of Hawaii), was assigned to work with us on the program. Carlos, in addition to being a mechanical engineer, is also a very adept mathematician, and was familiar with fractional differential equations, a little-known branch of mathematics. After working with the problem for some time and running a series of numerical computer solutions, Carlos suggested that he might be able to solve the equations exactly, using fractional derivatives. Not withstanding the fact that scientists have been trying to do this for more than a century, Roger encouraged Carlos to proceed.

To make a long story short, by rewriting the equation in the language of fractional derivatives, Carlos transformed it into a standard equation type that is easily solvable. As often happens when a scientific equation is solved exactly, many doors are opened and new knowledge and phenomena are discovered. In fact, this new solution described, very simply, a new force in nature that would be proportional to a one half derivative, a very exciting finding for physicists, who love finding and labeling new forces.

The new solutions provided us a new and better understanding of the Navier-Stokes equations, especially how they operated in the absence of gravity. In fact, they alerted us to a number of rather astonishing phenomena that would be observable in the microgravity of space, phenomena that had never been seen on earth because gravitational effects had masked them. If Carlos’ solutions were correct, then we would, indeed, have a handle on all parts of the Navier-Stokes equation.

With great enthusiasm, I proposed to NASA a series of spaceflight experiments that would allow us to look for these phenomena in space, to observe this new force in action, and to further test the validity of the famous Navier-Stokes equations. NASA scientists, being equally enthralled, agreed in the scientific importance of the quest and recommended that such experiments be conducted on the Space Shuttle. The project SHIVA was born. SHIVA (Spaceflight Holography Investigation in a Virtual Apparatus) would apply holography in space to track the movements of particles in a fluid in three dimensions, and would uncover the effects of the famous history term. The acronym, SHIVA, had a second meaning. Shiva, the Indian god, is known as the destructor, destroying the old and making room for the new. We were going to do that as well.

Many obstacles to making such critical measurements in space had to be removed. We had to prove that the equipment would survive launch, be acceptable on the Space Shuttle, and produce the necessary measurements without taking up excessive amounts of astronaut time. Over the next five years, the SHIVA team of scientists and engineers from three universities and NASA designed, constructed, and tested the required apparatus that would fly on the Space Shuttle. After many experiments, design projects, conference calls, and reviews, we satisfied all of criteria set by NASA for flying an experiment in space, and we were ready to build the flight apparatus.

Our first major setback was the Columbia accident, which put all experiments on hold. And then a year later President Bush made his “New Space Initiative” announcement that we would go to Mars, changing the entire NASA apparatus and goals. Effectively, money needed for such an adventure killed all other space flight experiments. SHIVA was one of the last cancelled to provide money for the Mars venture. Fortunately, we were given another year to close down SHIVA. In that year we continued to work in our ground laboratories, improving our measurement accuracy more and more until we were finally able to observe and to measure many of the effects that would have been easily seen in space.

Terminating SHIVA was devastating to the many scientists, engineers, and technicians who had devoted years of their careers in preparing for the experiments and who were hoping to see the results of their labor.

Several years after SHIVA had been terminated I was working at the National Academy of Sciences in Washington D.C. on a committee to provide advice on spending $150,000,000 to commercialize technology. During a break I wandered into the academy gift store and came face to face with a mannequin wearing the T-shirt shown in the figure. My first impression was that it was a cute take off on the normal saying of “What part of ‘no’ don’t you understand?” And then I looked at the equation more carefully. In words I saw the T-shirt asking me “What part of the Navier-Stokes equation don’t you understand?” The universe had just presented me once again with the question SHIVA answered, this time on a fifteen-dollar T-shirt. And I can answer categorically there is NO part of the equation that the SHIVA team doesn’t understand, and we have proven it……….sorta. Moreover, I know a Brazilian guy out in Hawaii who can tell you even a lot more about it.