# Work

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, or virtual. I am going to further muddy the classification waters by introducing another classification: imaginary. Huh? How can anything be 'imaginary'? Yeah, I know it sounds crazy, but there really are imaginary particles. It is a special subset of virtual particles.  Because Schrodinger's wave equation is actually imaginary, and since it is possible for virtual particles to have imaginary properties, like mass, it makes sense to classify a totally imaginary particle and distinguish it from other virtual 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.

# Particle types

Imaginary Particles, This particle type is the easiest to describe, yet at the same time, the most difficult to visualize.  This particle does not contain anything real 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 as it does its thing. Then it goes away. No muss no fuss...  These are the class of particles that will look you in the eye, like an outlaw in a spaghetti western, and say "Rules? We don't need no stinking rules" (notice i didn't put a period at the end of that sentence?).  Particle types that have no relation to any particle we are familiar with can exist in this imaginary realm. Electrons with fractional charges or enigmatic quark-like particles that lack spin or color, if it can exist- even in an alternate universe- it qualifies as an imaginary particle. Remember, these many and various particles, being purely imaginary, can have no direct effect on or in our universe.  However, it is important to realize, that even though imaginary particles don't technically exist in the way we usually mean the word, they are still governed by Schrodinger's wave equation and can be assigned probability levels exactly like any other matter wave. 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, but better behaved.  Because virtual particles are one step closer to being real,  they naturally follow more of the rules.  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. The upper limit is defined 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 by ħ , called h-bar. H-bar is just Planck's constant, h, divided by 2𝝅. And since Planck's constant is a very small value, the amount of time a virtual particle can exist is very short: millionths of billionths of a second, and even less than that.

Unlike their close cousins, the imaginary particles, the only particle types that can exist virtually are the ones the we are already familiar with. No anti gravitating protons in this crowd, for sure. Virtual particles are always created in particle-antiparticle pairs, exactly like real particles and exactly unlike imaginary particles which are 'created' as isolated, lone structures. 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  and imaginary 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 these 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, money, and...well you get the idea. Sorry. There is no such thing as real particles. They just don't exist. What you are really dealing with are called  'Complex Particles'.  Complex particles display this complex behavior due to their wave-particle duality. They can be both localized like a real particle -  think 'object you can hold in your hand'. A baseball, a BB, or a sand grain, are all objects. They can also be spread out and interfere like waves. Remember, the wavefunction governing a physical system is given by the Schrodinger equation which is mathematically imaginary. This is the main reason I chose to include the whole new classification for imaginary particles. Schrodinger's equation demanded it.

# 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 mostly during particle interactions. Neither can be directly detected in experiments. The connection between them is mostly mathematical. Virtual particles are often used in setting up various QFT (quantum field theory) calculations when particle pair production is necessary.  When a single particle is needed, such as for shielding nuclear forces within atoms, imaginary particle representation is used. 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, using an undefined process somehow powered by and 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 probabilities' 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 and energy? Since imaginary particles are never created in pairs, there is no way to apply potential 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 indirectly convert 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 defined by a probability wave that determines its existence, similar to any other particle.  However, the probability of this matter wave never reaches 100%. As a result, imaginary particles cannot be meaningfully assigned potential energy.  Additionally, because they cannot contain energy, they can be created as single, isolated particles.  If the probability wave defining their wavefunction ever reaches 100% it transitions into:

2. A virtual particle, which can exist with a probability at 100%.  This particle resides in the transitional realm between the imaginary and the complex.  Unlike an imaginary particle,  a virtual particle has the potential to become complex. Virtual particles are always  created in particle pairs like complex particles, yet they are entirely governed by the uncertainty principle unless potential energy is added to their interactions. If  no potential is imparted to the virtual particle pair, it once again becomes imaginary. If potential energy is imparted to the virtual particle pair, it transitions into:

3. A complex particle, which is a permanent particle. It possesses a real aspect that defines  its ability to make a lasting impact in the universe, as well as an imaginary aspect that defines its past existence. It should also be noted that of the potentially infinite variety of particles available at the imaginary level, only those particles that are allowed by physical law may be expressed at either the virtual or complex levels.

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 of those answers (at least one)  will lead to FTL communications. And, possibly much more.

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. However, these 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  - or imaginary - particle perform real work? They shouldn't be able to. But they do. It is at least possible for the virtual particle to have the potential to perform real work.  A case might be made that a virtual particle may act as a mediator between two energetic systems: it accepts energy from a real particle thereby becoming real just long enough to transfer the potential it contains to another particle, then  becomes  virtual once again after its job is done. 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.  Invoking the uncertainty relation between time and energy as an explanation is a good try, but it isn't good enough. The uncertainty principle is not a mechanism. It doesn't outline a process. Philosophically, this is close to someone saying if he could write out all the thousands of differential equations that can describe a bird and place all those equations in a hat and shake it vigorously, a real bird will fly out. Sorry, but just no. 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.

If there is no conventional solution as to how imaginary and virtual particles are able to perform real work, then how can they?  Well, if you look at my 3 classifications of matter above in detail, the astute reader might see that the concept of energy is not actually present until you get to the third classification - the one for complex matter. Energy, or potential, can not be expressed at all for imaginary matter, and if it were involved with virtual matter it would instantly make the virtual mass complex.   So energy has mostly nothing to do with it, unless as I described in the above example, with virtual particles acting as force mediators between other complex systems. What is present in all 3 classifications is probability. What determines if a particle is able to do work is defined by its probability level alone. This is why virtual particles exist for only a short time, why they are governed solely by Heisenberg's Uncertainty Principle. They derive their potential to exist solely by the probability level of their wave equation, as stated by Schrodinger's equation. They exist only when their probability level is at 100%.  Imaginary particles can't even do this, because they are not mandated to appear in particle pairs.  If only a single imaginary fermion were to appear, several other conservation laws would be violated, and the universe doesn't break the rules it considers important, spin angular momentum being one of them. Complex particles, powered by energy , i.e. real potential, are the only classification of particle that gets to hang around in a stable form, because now, the uncertainty relation is not the deciding factor. The universe keeps complex particles around and stable because now that real potential is involved, it would cause more problems for the universe to disappear them.

Another point to bring up now, is that it is easy to assign probability levels of 100% to the wave equation, especially in homework problems at college. It simply means you have detected a particle somewhere.  A particle appears where the probability level is 100%. Sounds a bit like common sense, doesn't it? Remember, however, that there are literally an infinite number of pathways a particle can take to get from source to target. Which one is the lucky one where a detection event occurs? Quantum mechanics will not provide any clues in this area. You can decide where there is a high likelihood where the particle will wind up by looking at the geometry of your experimental set-up, but that is no guarantee you will choose correctly. It might instead bounce off your set-up and interact with the wall behind you. If so, then that is the 100% path the experiment chose. Heck, there will be many times where you will completely loose your particle! Where it winds up is anyone's guess. Lucky for you, particles are cheap and easily available so you may run your experiment as many times as needed. This is the basis for Feynman's Sum Over Path, also known as the Path Integral Formulation, developed by Richard P. Feynman (1918 - 1988). The approach describes an averaging of all the paths a particle can take from its starting point to its destination. That's an awful lot of paths, for sure. But only one path gets the prize - a particle collapse at 100%. But it does bring up an intriguing thought - what about all those failed paths? What happens to them - read on to find out!

Hint:  this is all an in-your-face clue on how you can build a FTL communicator.