What are virtual particles?
- kieronconway
- Apr 28
- 4 min read
Updated: 3 days ago
Virtual particles are a conceptual and mathematical tool, used in quantum field theory (QFT), to describe the three fundamental forces;
strong nuclear.
Electromagnetic
weak nuclear.
Unlike real particles, virtual particles are not directly observable.
If they're not real particles, then what are they?
Force interactions are complex processes and are expanded into a series of simpler contributions in the mathematics.
Each contribution can be represented by a Feynman diagram.
A Feynman diagram representing the repulsion of two electrons is shown here;
In the typical Feynman diagram;
Lines represent real, measurable particles entering and leaving the interaction.
The internal line represents intermediate mathematical objects called propagators.
These propagators are often interpreted as virtual particles.
Many Contributions to a single outcome
In QFT, an interaction does not have a single pathway.
Instead;
There are many possible interaction pathways that contribute.
Each contribution has a probability amplitude of occurrence.
The final result comes from combining all the contributions.
Each contribution is defined by a Feynman diagram and the simplest diagram usually defines the most probable contribution.
The more complex contributions provide smaller corrections. The following diagram illustrates this concept.
Virtual particles represent “off-shell” excitations in a force field, the underlying mechanism by which force interactions are achieved.
What are “off-shell” excitations?
Real particles obey the energy-momentum relationship, defined by the equation:
E² = (pc )² + (mc² )²
where m is the particle's rest-mass, E is the total energy of the particle, p is the momentum and c is the velocity of light.
This is a fundamental relationship between energy and momentum.
Real particles adhere to this relationship and are referred to as “on-shell”.
Virtual particles do NOT adhere to this relationship and are termed “off-shell”.
Their energy and momentum is not constrained in the same way as real particles.
Virtual particles exist only within the mathematical structure of the interaction and are often referred to as “book-keeping” entities in QFT.
A “book-keeping” Analogy
Think of adding up a large set of numbers to achieve the sum of all the values. Along the way, you constantly create intermediate values of the final sum.
On their own, these intermediate values are meaningless, but they assist in getting to the end result.
They can be described as “book-keeping” artefacts of the end result.
In a similar manner;
Virtual particles are contributions to a mathematical framework that uses real fields to define real interactions.
Virtual particles can be considered as representatives of “book-keeping” artefacts.
Why do Different forces have different virtual particles?
In QFT, modern particle physics is built on what's called “gauge symmetry”.
Gauge symmetry requires the introduction of gauge fields to maintain symmetry under certain transformations in the maths.
Why Photons for the Electromagnetic Interaction?
Imposing gauge theory on charged particle fields, using what's termed U(1) symmetry, requires the presence of an additional field to preserve gauge symmetry.
This additional field is the electromagnetic field that mediates the electromagnetic interactions using virtual photons.
Why Gluons for the Strong Nuclear Interaction?
The strong nuclear interaction involves SU(3) gauge symmetry, more complex than U(1), requiring an additional eight separate gauge fields to preserve gauge symmetry.
Each of these additional fields is quantised by a different type of gluon, of which there are eight types.
Virtual gluons carry the colour charge to mediate colour exchange between two participating quarks, the main mechanism that creates powerful quark containment in hadrons.
Unlike photons, gluons can even interact with themselves.
What about the weak interaction?
The weak interaction arises from SU(2) gauge symmetry, which requires three additional gauge fields.
Unlike the photon and gluon, the weak force mediators (Z, W+ and W- bosons) have mass due to electroweak symmetry breaking.
This allows them to change the flavour of charged and uncharged particles. For example, in neutron decay a DOWN-quark (charge = -1/3) is converted to an UP-quark (charge = +2/3) through the mediation of a W- boson.
Despite this symmetry breaking, gauge symmetry prevails in the mathematics of the weak interaction.
The vacuum energy of the Higgs field, (the Mexican hat potential) is where the broken symmetry manifests itself.
Key Takeaways
Virtual particles are not real, “on-shell” particles that pop in and out of existence to mediate a fundamental force.
They are mathematical elements in QFT calculations, representing intermediate pathways to interactions between real particles using virtual, “off-shell” excitations.
For each pathway contribution there is a Feynman diagram, the simplest diagram of which is the one used to represent the interaction as a whole.
Virtual particles reflect the behaviour of the underlying quantum fields and provide a powerful way to calculate and understand the fundamental forces of nature.
The simple way to look at a fundamental force is to consider it as an interaction between real fields mediated by virtual, off-shell excitations in a force field.
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