Understanding Virtual Particles: Real or Mathematically Real?
Virtual particles are a fascinating concept in quantum field theory, often misunderstood due to their abstract and theoretical nature. While they represent disturbances in fields and are not physically real, they play a crucial role in our understanding of particle interactions.
Defining Virtual Particles
Virtual particles are theoretical entities that 'pop' into existence around real particles, carry momentum, and then vanish. These particles are not physically real, but rather mathematical constructs that have a profound impact on our calculations of particle interactions in high-energy physics. They appear in Feynman diagrams as intermediary steps in the process of energy and momentum transfer.
These diagrams, developed by Richard Feynman, are a graphical representation of the interactions between particles. Each line represents a particle, and the vertices represent the points where particles interact. Virtual particles are shown as loops within these diagrams, representing the exchange of energy and momentum between real particles.
Mathematical Representation
Virtual particles are associated with mathematical objects that simplify the calculation of subatomic processes. One such example is the 'virtual photon,' which is a term that represents the photon propagator in the equation:
u3σ3|v4σ4 iegμ|(-igμν)/
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Where u and v are wavefunctions of the incoming particles, σ represents the spin, and gμν is the Minkowski metric tensor.
Putting these terms together, we get a formula to determine the momenta of outgoing particles in terms of the incoming ones. This is the essence of what Feynman diagrams do: they provide a clear, step-by-step method for calculating interactions.
The Slippery Concept of 'Physical'
The concept of 'physical' is not as straightforward as one might think. Is the equator of the Earth physically real? Perhaps not in the sense that one can directly see a line on the ground, but the concept of the equator is useful and coherent. This leads to the question of how to define 'physically real' in the context of virtual particles.
Philosophers and physicists weigh in differently on this question. Some, like Michael Dummett, argue that abstract objects can still have a real existence, even if not physically tangible. Others, like Richard Mattuck, suggest that Feynman diagrams are not strictly physical, but rather a useful representation of calculations.
Virtual Particles vs. Real Particles
Virtual particles are not to be conflated with real particles. Real particles are excitations in quantum fields and can exist in superpositions of states. However, the concept of a superposition introduces its own set of challenges in defining what is 'real.'
Richard Mattuck points out that while some authors view Feynman diagrams as simply graphical representations of terms in an expansion, he argues that they are "physical-looking" and should be treated as such, even if they are not true physical particles. The off-shell nature of virtual particles and their violation of the Pauli exclusion principle highlight the abstract nature of these entities.
Conclusion
Virtual particles may be mathematically real, playing a crucial role in our calculations, but they are not physically real in the classical sense. Understanding their role in quantum field theory is essential for anyone interested in high-energy physics and subatomic interactions. Whether they are viewed as mathematical constructs or as a useful visualization, virtual particles continue to be a fascinating aspect of theoretical physics.