Virtual particles may be real particles out of phase with our reality

Isaac Newton introduced the concept of “force” as a well-defined mathematical concept into physics. Most forces we know are between physical objects. Critical to our modern understanding of forces is the concept of a virtual particle, a form of every well-known particle that cannot be detected directly and yet must exist. Some dismiss virtual particles as an artifact of how we calculate interactions while others see them as just temporary field states. In this article, I talk about how a 5-D theory might interpret them as “out of phase” with our reality (defined as a 4-D slice of that 5-D spacetime).

The vast majority of forces we experience day to day are electromagnetic. At a molecular level, when I push against the wall with my hand the electromagnetic force connecting electrons to their host atoms and atoms to their neighboring atoms to form molecular bonds in my hand and in the wall also resist the penetration of my hand into the wall. In that sense, I never actually “touch” anything.

Classical physicists tied Newton’s force to the universal concept of energy. A force occurs because all systems — a block on an incline plane or a weight attached to a pulley — are seeking a lower energy state, their ground state. Objects accelerate and decelerate when they have a net force on them which means that they can exchange potential energy for kinetic.

In classical physics, fields mediate forces. A positive charge creates an electric field that induces negative charges to experience a force towards it. Their ground state is to be on top of one another (other forces can prevent that from actually happening but it can happen in the case of a class of particle called bosons).

Quantum physics replaced the concept of a force field with a field of particles (or more precisely wave packets). The force between a magnet and an iron bar occurs because the molecules in the magnet and the bar are exchanging force carrying bosons — photons in this case. These photons, while not visible, cause the coupling of force field to matter of the magnet and iron system to decrease in energy when they move closer together. The calculation that showed that force carrying boson exchanges cause the forces was a major achievement of the mid-20th century.

One sticky point here is that the photons exchanged in electromagnetic interactions turn out not be real particles. You can’t see them like real photons. They are virtual particles.

Richard Feynman deserves a lot of credit for these being called “particles” at all. You could just call them field excitations. His Feynman diagrams, as they are now called, describe force interactions as if particles are being exchanged, but those apparent exchanges emerge from perturbation theory, a mathematical approach to making calculations possible by only including those parts that would produce a measurable effect.

Their interpretation as particles is dubious because, unlike real particles, their amplitudes are imaginary. They also don’t obey the correct relationship between their mass and momentum and energy. They are said to be “off mass shell”. Thus, you could just think of them as computational objects that don’t actually exist.

Unfortunately, because they are indirectly measurable, it is hard to say that they don’t exist at all. (Unlike, say, ghost particles, which are computational objects.)

In a paper I published in Physical Review D a couple years ago, I took on the concept of virtual particles. In this paper, I used the old idea that quantum theory in four dimensions of space and time can be interpreted as a classical theory in space, time, and one more dimension.

When you do that, virtual particles disappear because they don’t exist in classical physics. Every interaction has a definite input and a definite output. Feynman diagrams look like tree structures with lots of particles, i.e., field excitations, coming in and interacting and new particles exiting, but there are no loops that would represent virtual particle interactions as in quantum physics.

The way you go from a 5-D classical universe to a 4-D quantum one is by averaging over the fifth dimension. When you average particle interactions together like that, virtual particles pop out as loops. Those loops actually turn out to be statistical correlations between different particle interactions that match outputs to inputs.

If you interpret the universe to be a five dimensional one, then, virtual particles are in one sense real in that they are not loops.

On the other hand, they still have imaginary amplitudes if they are off mass shell.

The way that the 5-D approach handles this problem is using a mathematical trick that dates back to the 1940s called a Wick rotation that turns time into imaginary time. All the particles become completely real. You do all your calculations, then once you have an answer you return to real time.

The concern with that is that, if our 5-D universe only seems to make sense if time is imaginary, how can the fifth dimension be real?

It turns out that a lot of topics use imaginary numbers in them to describe real things. They tend to describe waves. Imaginary and, by extension, complex numbers (a real added to an imaginary number) are indeed extremely useful for describing wave-like behavior.

The reason is mathematical. Any pure wave (a single tone) has three describing numbers: amplitude, frequency, and phase. Amplitude is the intensity of the wave, how high it is. Frequency is how frequently the up and down motion appears. Phase is how much a wave is offset from another one in terms of its crests.

A single complex number has two numbers, magnitude and direction, which correspond to the amplitude and phase. The magic happens when you start moving a complex number around a circle.

When you move a complex number around a circle in the complex plane at a fixed rate, it has a frequency. The magnitude stays the same, the radius of the circle, and the phase, which is your initial offset, stays the same. This becomes important when you combine pure tones with one another to make a complicated waveform.

Another way to look at it is by looking at digital signals. Sound and other signal digitizers tend to gather or produce signal data by sampling or synthesizing signals that are offset from one another by 90 degrees in phase. These are the in-phase and quadrature (I/Q) of the signal. The in-phase is your real part while the quadrature is the imaginary. With that information and sufficiently rapid sampling, you can perfectly reproduce the sound or signal with whatever phase and amplitude you want. If you only had the in-phase data, you would lose phase information from the signal.

If the sound of your voice can be represented as a series of complex numbers, then certainly reality can be.

In quantum physics, we know that amplitude relates to the probability of something happening, like a particle appearing in particular location, but what do the frequency and phase mean?

In classical waves, phase and frequency along with polarization relate to their orientation and configuration in space and time.

In quantum physics, rather than being orienting in time and space these waves are orienting in a space called a configuration space which contains all possible configurations of a set of fields. In standard theory, these are superimposed on one another in superposition so that you get one huge wave that contains all possible realities. These realities interfere with one another just as real waves do. Phase and frequency determine when they destroy and when they build on one another.

In the 5-D theory, these configurations are 4-D configurations that evolve stochastically (with random noise) in a fifth dimension. In this case, they are not superimposed on one another but evolve like complicated and sometimes turbulent propagating waves through the fifth dimension.

If you look at a simple 5-D wave of massive particles, as I showed in my paper, it is always “on mass shell” in five dimensions. But it is only on mass shell in four dimensions when its momentum in the fifth dimension is a constant, meaning that all its momentum minus some fixed amount is contained within a 4-D slice. (This constant might be zero, but it is one fixed, unchanging constant.) These are what appear as “real” particles to us. This may be because only those waves interfere with one another only constructively in our slice and, therefore, have persistence in our universe.

From this, it is clear that virtual particles have two main characteristics: they are not on mass shell potentially because they are out of phase with our 4-D slice of the 5-D universe and second they influence real particles through their statistical behavior.

That means that virtual particles are just as real as “real” particles. They exist within the fifth dimension as waves but because they are out of phase they interfere destructively with each other and so cannot exist within it.

This does not impact predictions at all until we bring gravity into the mix. Because gravity is both a force carrier and a theory of space and time, it must have “virtual” particles, i.e., gravitons, and define a 5-D spacetime. How is that possible?

Well, it turns out that you need some symmetry breaking in order to achieve this. You have to break the 5-D theory of space and time into three components. A gravity force carrier acts as the metric of our 4-D spacetime. Two other force carriers, a vector force carrier (similar to electromagnetism), and a scalar force carrier (like the Higgs field), must also exist. These latter two have not been, as far as we know, measured but do feature in relativistic MOND-style dark matter theories. So, we may be detecting their influences right now.

This means that what we think of as gravitons would come in three varieties and all would have virtual particles propagating through the fifth dimension.

Because the 5-D theory depends on having these three varieties, if it could be shown that such a theory leads to what we see with dark matter and potentially dark energy as well, that would be a strong vote in favor of the theory.

Andersen, Timothy D. “Quantization of fields by averaging classical evolution equations.” Physical Review D 99.1 (2019): 016012.

Andersen, Timothy D. “Chaotic deterministic quantization in a 5D general relativity.” arXiv preprint arXiv:2110.05180 (2021).