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Force-Fields - 3 books:  What if you could create an impenetrable force-field shield? What if you could compress distances a million times? What else could you do? Dr. Jack Kelly and Dr. Jane Kamakahi met at a physics conference in Hawaii. They decided that by working together, they could create the force-fields of science fiction … or something like them. Jack: Jack Kelly went to Hawaii for a conference and a mini-vacation.  He found much more. Jack Kelly was attending a conference in Hawaii for two reasons.  First, the venue allowed him to present some speculative thoughts on physics and, second, it allowed him to go to Hawaii on official travel from the Oak Ridge National Laboratory – the Lab.  However, Jane Kamakahi, the woman who presented just before him, described an experiment in modifying tensors.  They discussed their ideas over lunch and what Jack had planned as a mini-vacation became the start of a collaboration in physics that would reshape the world. Jack enlists Sandy McNeill, an engineer at the Lab, to help and Jane does likewise with her chief technician, Keola Parker.  As they worked together, Jack discovers that he wants more than a professional relationship with Jane.  Because she also has a side job as singer/songwriter, Jack decides to learn the guitar to have something in common with her besides physics. As they begin to achieve important results, they are noticed by both Chinese and Russian intelligence agents.  And in Beijing, the spy-masters plot to obtain this new technology. Jane: Roadways in the skies present opportunities and problems. Jack Kelly and Jane Kamakahi have created tubes that act as roadways in the sky, allowing vehicles to drive across the country in less than an hour and from Oak Ridge, TN, where Jack lives to Hawaii, where Jane lives, in just over an hour.  Jack wanted something much shorter so he and Jane could be together more easily, but that was the best they could do – so far.  Together with, Sandy McNeill and Keola Parker, they had incorporated Tensors Unlimited to exploit their technology. As their company continues to create new applications, Russia and China continue their efforts to obtain the technology and applications that Jack and Jane have invented.  The two countries are also competing with each other, which leads to problems. Keola: Steam-powered spaceships seemed like something from pulp fiction, but they were close to a reality. Jack Kelly and Jane Kamakahi have gotten married.  Russia and China have just conducted a brief war using Jack and Jane’s technology, which each country stole.  However, these aren’t the only countries in the world with warlike plans; the world is not a peaceful place.  Further, Jack and Jane’s roadways in the sky are disrupting the economic world and ambitious countries must make adjustments. At the same time, Jack, Jane, and their friends continue to invent new applications.  Their latest is a steam-powered spaceship.  They believe that with the right design, they can build a single-stage spaceship that will take them to the Moon and back.  Actually building such as spaceship is beyond the capability of Tensors Unlimited, so they are working with the Oak Ridge National Laboratory to finish the design and start the construction. Sciences used and abused:  Physics and mathematics - tensor and spinor fields.

Jack and Jame Keola

Addendum:

These novels are science fiction. That means they are stories with some connection to science, particularly speculative science.

Physics and Mathematics

Scalars, vectors, tensors, and spinors are all mathematical terms for rather straightforward ideas. 

Think of a scalar as a thing with one slot that can be filled with a number.  It can represent anything, but for example let's create a scalar for height.  A scalar field is just a construct that contains a scalar for each point in some space.  For example, we could have a scalar field for the height of the grass on a golf course.  On the greens, the height will be nearly uniform and very short.  On the fairways, the height will be fairly uniform and higher.  In the rough, the height will be extremely variable and even higher.

A vector is a thing with two slots.  For example, wind speed and compass direction.  A weather map often shows a vector field of wind speeds and directions.  In the figures below, two patches show uniform vectors within the patch but differences between the patches.  In a real weather map, the vectors near a given point will not be uniform but will have similar directions and speeds, but the values will change smoothly as you change position.

A tensor is a generalization of a vector and usually has three or more slots, but there are also tensor fields.  On example of a two-dimensional tensor field is the stress on the ground just prior to an earthquake.  At each point, there are forces pushing on the point and if you look at each direction, the amount of forces is different.  You might represent this on a map as different sizes and shapes of elipses, one elipse for each point.

Note that a scalar is a tensor of order 0, a vector is a tensor of order 1, and a general tensor has higher order.  However, each of these can be applied to spaces of different dimensions.  Thus, you can have an order-0 scalat field on a 2-dimensional plane or the 2-dimensional surface of a sphere, but you can also have an order-0 scalar field on the 3-dimensional volume of a sphere.  Similarly, a tensor of any order might be applied to a space of any dimension.  For nice situations, you can think of representing each slot in one of these things by a set of coordinate values, with the number of coordinates being equal to the dimension of the space.  Therefore, the number of components of a vector field a three dimensional space would derive from three coordinates times three coordinates (for the two slots) = 9.  In a 2-dimensional space, there would only by 2 times 2 or 4 components.  But that stress tensor on a 2-dimensional surface would have 2 times 2 times 2 = 8 components.  On a 3-dimensional space, it would have 27 components.

A spinor is another generalization in which the component values can be complex numbers or real numbers.  This makes them much more complicated.

Fiction

In these books, our heroes are modifying the component values of tensors.  They use the short-hand and say they are modifying the component values.  However, rather than meaning that they just change the numeric value of the tensor that is written on paper, they are modifying a property that causes the tensor to have that numeric value.  In general, we don't know how to do this.

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