This is a radical view of quantum behavior that many physicists take seriously. Said “I think it’s totally real” Richard Mackenziea physicist at the University of Montreal.
But how does a myriad of winding roads become a straight line? and energy) from which we get a number called the amplitude. Amplitude indicates the likelihood that a particle will travel that path. Then sum all the amplitudes to get the total amplitude (the integral over all paths) as the particle moves from here to there.
Simply because the amplitudes of the individual paths are the same size, the tortuous path looks the same as the straight path. But the important thing is that the amplitude is a complex number. Real numbers mark points on a line, while complex numbers act like arrows. The arrows point in different directions for each path. Also, two arrows pointing in opposite directions sum to zero.
The bottom line is that for particles moving through space, the amplitudes of more or less linear paths all point in essentially the same direction and amplify each other. However, the amplitude of the tortuous paths points in all directions, so these paths act in opposition to each other. Only linear paths remain, showing how a single classical path of minimal action emerges from infinite quantum options.
Feynman showed that his path integral is equivalent to Schrödinger’s equation. The advantage of Feynman’s method is that it provides a more intuitive prescription for how to deal with the quantum world. That is, sum up all possibilities.
sum of all ripples
Physicists quickly came to understand particles as: Quantum field excitation— an entity that fills the space with values at every point. If particles can travel from place to place along different paths, the field can ripple back and forth in different ways.
Fortunately, path integrals also work in quantum fields. “It’s clear what we have to do,” he said. Gerald Dunn, a particle physicist at the University of Connecticut. “Instead of summing all paths, sum all configurations of a field.” Identify the initial and final placements of a field and consider all histories that might tie them together.
The gift shop at CERN, which houses the Large Hadron Collider, sells coffee mugs with the formulas needed to compute known quantum field actions (key inputs to path integrals).Courtesy of CERN/Quanta Magazine
Feynman himself development In 1949, the quantum theory of the electromagnetic field was published. Others come up with ways to calculate field actions and amplitudes that represent other forces and particles. When modern physicists predict the outcome of collisions in Europe’s Large Hadron Collider, path integrals are the basis of many of their calculations. The gift shop there also sells his mug of coffee with equations that can be used to compute the action of known quantum fields, the key ingredient in path integrals.
“This is the absolute foundation of quantum physics,” says Dunne.
Despite its triumphs in physics, path integrals bore mathematicians. Even a simple particle moving through space has an infinite number of possible paths. Even worse is a field whose value can change in infinitely many ways in infinitely many places. Physicists have ingenious techniques for dealing with wobbly infinite towers, but mathematicians argue that integrals were not designed to work in such infinite environments.
