When a scientist talks about work, he does not mean having a job and getting a paycheck. Work is when a force moves an object of some type over a distance.  Think of a ship bobbing up and down in a harbor. Work is being done because the force contained in the water is causing the boat to move over a distance, The formula for work is, well,  Work = Force multiplied by distance. W=F x D.  There are usually no problems with this straightforward approach to  figuring out how much work is done. We simply look at the motion of the boat, and when we compare the motion of two identical boats, if one of those boats is moving more than the other, more work is being done on the boat that is moving the greatest distance.  In the world we are used to living in, this all makes sense. But, we also have to account for work being done at the most minute scales, the scales of smallness where Quantum Physics dominates, and here we run into a small problem.

 

In the quantum realm, there are many kinds of particles. Scientists spend their entire careers classifying these particles, and trying to find new ones. One of the most basic classifications for all particles is whether they are real, complex, virtual, or imaginary. Huh? How can anything be 'imaginary'? Yeah, I know it sounds crazy, but there really are imaginary particles. To make an even bigger mess, for quantum physics to work at all, all these different particle classifications have to be treated seriously. So, to understand the concept of Work on the quantum scale of things, I need to backtrack and first explain just what the hell all these classifications are about. I'm going to stick with particles, but Fields can also be treated the same. No one said it was going to be easy, sigh.

Imaginary Particles, This particle does not contain any energy whatsoever. Like Barbara Eden blinking her eyes on the American television show "I Dream of Jeannie",  an imaginary particle literally pops into existence and hangs around for a while.  Then the universe realizes this particle should not exist because it was literally made from nothing at all, and so, it disappears. The lifespan governing how long an imaginary particle can 'hang around' is based on properties the particle would have IF  it were real and had real physical properties.  It is given by the Heisenberg uncertainty relation, ΔEΔt ≥ ħ/2 , discovered in 1927 by Werner Heisenberg (1901 - 1976). Within Heisenberg's uncertainty equation, there is a natural, and fundamental constant of nature called the reduced Planck's Constant, named after its discoverer Max Planck (1858 - 1947), and denoted as ħ (called h-bar). H-bar is just Planck's constant, h, divided by 2𝝅. Since Planck's constant is very small, the amount of time an imaginary particle can exist is very short - on the order of millionths of billionths of a second, and even less than that. However, it is important to realize, that even though imaginary particles don't technically exist in the way we mean the word, while they are here, they can and do make a lasting impression in the world -- more on this later.

Virtual Particles;  Virtual particles are much like the imaginary particles in the above paragraph.  Since imaginary particles are always popping up out of nowhere, many scientists use the term virtual when referring to a dynamic process where you have these imaginary particles continuously being created and destroyed a short time later, while at the same time they are actually doing work on the universe while they exist. Truthfully, though, many physicists see these classifications of particles as more of a nuisance and really wish they would just go away, or they view them as abstract mathematical ideas and then wish they would go away. But, if they did, we would be living in a universe that would look completely different from the one we presently inhabit. For example, virtual particles can act as a shield -- they get between us and the nuclear forces at work inside atoms. They absorb some of this energy and 'weaken' these forces that act only within atomic radii. If they did not, these forces would be stronger than they are, and that would really mess up how "real particles" look - they wouldn't be friendly anymore. A nuclear force even a tiny bit stronger than what we observe would have profound consequences on the lifetime of the elements in the periodic table. As a matter of fact, with a stronger nuclear force, only 3 or 4 elements would be able to exist at all -- today we know well over a hundred chemical elements. If the nuclear force was stronger than it is, if you tried to stick more than about 3 or 4 protons together to make more elements, you would wind up with a black hole. Without virtual particles doing their thing, our universe would be a black hole and we wouldn't be having this discussion...

Real Particles;   Ah, now we can get to the regular stuff, the matter we are all familiar with, the stuff you can grab in your hand, like rocks, cars, spouse, spousette, and...well you get the idea. Sorry. There is no such stuff as real particles. They just don't exist. What you are really dealing with are called  "Complex Particles".  Complex particles are actually an amalgam of the real and, you guessed it, the imaginary. There just doesn't seem any way to get around it, Imaginary is here to stay. The main difference with complex particles is the fact that even though they have an imaginary component, it is only half. The other half is made of real energy, which keeps the particle around for a long time - unlike imaginary particles, the lifetime of real particles is not governed solely by the uncertainty relationship. This is where the concept of energy is useful. It allows your toaster oven, your car, or even a common rock, to exist for a really long time. Still, your BMW is really only half real (and your Pinto even less so) - and so are you (along with everything else). The other half of what makes everything up is imaginary (hey, maybe you could try this ploy the next time you shop for a car: if you can convince the car salesman the product he is selling is only half real, maybe he will cut the price in half...okay, good try).

 

The relationship between the three particle types: imaginary, virtual, and real (complex) particles

Both imaginary and virtual particles exist only fleetingly.  Imaginary particles arise spontaneously from the vacuum, while virtual particles emerge during particle interactions. Neither can be directly detected in experiments. The connection between them is mostly mathematical. Imaginary particles are often used in setting up various QFT (quantum field theory) calculations to represent the behavior of virtual particles. Not seeing the forest for the toothpicks, there is another more conceptually easier way to think of both these particle types. Imaginary particles don't have an effect on the universe, because they have no way to manifest. They are the true ghosts in the machine. Mathematically describable, but never more than an echo of a reality. Virtual particles, on the other hand, are one step closer to reality. Physicists say that virtual particles are able to 'borrow' energy for a short time, based on Heisenberg's uncertainty relationship, at which time they can be useful before they disappear back into the sea of uncertainty. Virtual particles can be considered probabilitie's stepchildren. It is possible to turn a virtual particle into a real particle with the application of enough potential (read energy). This is the process that leads to black hole evaporation - a virtual particle pair spontaneously emerges in space close to the event horizon of a black hole. The black hole captures one of the particles which gets swallowed by the black hole, and the other particle of the pair escapes into space away from the black hole, stealing a tiny bit of the black hole's energy to remain in the universe permanently.   This is now called Hawking radiation, after the physicist Steven Hawking (1942 - 2018) who first proposed this process in 1974.  Over time, this process gradually causes the black hole to shrink and ultimately evaporate away. So what about imaginary particles? There is nothing in the literature I'm aware of that forces an imaginary particle to be created in pairs, so while the application of energy can make a virtual particle real, there is no way to apply energy to an imaginary particle to make it either virtual or real. This is why I called them 'ghosts'. However, this may not always be true... If there is a way to turn an imaginary particle into a virtual particle, then it too, can become real.  So is there a mechanism? Yes... but it involves thinking only of probability, not energy. I put forth a new way to look at things:

1. An imaginary particle is governed by a probability wave that is always less than 100%  If the probability wave defining its wavefunction reaches 100% it becomes:

2. A virtual particle, which at 100% means it has the ability to temporarily manifest.  It's lifespan is given by Heisenbergs' uncertainty relationship. If potential is given to the virtual particle, it becomes:

3. A complex particle, which is a permanent particle. It has both a real side defining its ability to make a continuing impression in the universe, as well as an imaginary side, defining its past existence.

The bottom line is that it is possible in the grand scheme of things for imaginary particles to do real work in limited circumstances - yeah, I know, crazy huh? I will have much more to say about this at a later time: Stay Tuned!

 

So, what does all this have to do with work , and by extension FTL communications? Glad you asked.

First, ask yourself just what is an imaginary 5 miles per hour? Like dividing by zero, there is no 'real' answer. Or there are an infinity of answers. One answer (at least one - I'm working on 2 or 3 right now)  will lead to FTL communications.

But, let me take care of work, first. Remember when I said energy is defined as a work function? In the macroscopic world we live in,  W=F x D works just fine. It doesn't do so well in the quantum world.  Virtual (or imaginary) particles do not have any energy  at all, remember? That's why they disappear. Virtual particles at least can do real work while they are here, though. Work that lasts after they are gone. This really makes no sense at all. How can a virtual particle perform real work? They shouldn't be able to. But they do. It gets even shadier if the virtual particle originated from an imaginary particle! A nice, tame example goes something  like this - if I used imaginary particles to build a virtual nutcracker to break a real walnut shell, then the nut cracker, being imaginary, vanishes, but it still leaves behind the work it has done in the form of the broken pieces of walnut shell. Real work has obviously been done, because it took something applied to the walnut shell to break it, moving around all those small parts of the once whole shell,  yet this real result was caused by an imaginary quantity. If imaginary particles only did imaginary work, this web page wouldn't exist, but they do real work, so this web page exists.  There really is no conventional solution to this dilemma, so it becomes just another item put in the 'ignored' category. Even so, there is no magic here -- the same basic formula for defining a work function still holds, whether for 'real' work or 'imaginary' work.  In reality, this is an in-your-face clue on how you can build a FTL communicator.