Failure of Quantum Mechanics without Relativity

 Philosophical questions aside, in the 1930s and 1940s quantum mechanics was like an unstoppable Mack truck barreling down a highway, flattening all the problems that had puzzled physicists for centuries. One brash young quantum physicist, Paul Dirac, ruffled the feathers of many chemists when he had the nerve to say that quantum mechanics could reduce all of chemistry to a set of mathematical equations.

However, as successful as quantum mechanics was in explaining the properties of the chemical elements, by itself it was not a complete
theory. We should be careful to point out that quantum mechanics worked only when physicists used it to analyze velocities much lower than the speed of light. When attempts were made to include special relativity, this Mack truck hit a brick wall .

In this sense, the spectacular success of quantum mechanics in the 1930s and 1940s was a fluke. Electrons in the hydrogen atom typically
travel at speeds one hundred times less than the speed of light. If nature had created atoms where the electron traveled at velocities near the speed of light, special relativity would become important and quantum mechanics would have been much less successful.

On the earth, we rarely see phenomena approaching the speed of light, so quantum mechanics is valuable in explaining everyday phenomena such as lasers and transistors. When we analyze the properties of ultrafast and high-energy particles in the cosmos, however, quantum mechanics can no longer ignore relativity.

Imagine, for a moment, driving a Toyota on a race track. As long as you drive the car slower than, say, 100 miles per hour, it will perform well. However, when you try to speed fast 150 miles per hour, the car might break down and spin out of control. This doesn’t mean that our understanding of car engineering is obsolete and must be thrown away; rather, for speeds beyond 150 miles per hour, we simply need a drastically modified car that can handle such high velocities.

Similarly, when dealing with velocities much lower than the speed of light, scientists have found no deviations from the predictions of quantum mechanics. At high velocities, however, the theory fails. Quantum mechanics must be married to relativity.

The first marriage of quantum mechanics and relativity was a disaster, creating a crazy theory that for decades produced only a series of meaningless results. Every time physicists tried to calculate, for example, what happens when electrons collide, quantum field theory would predict infinite values for the collisions.

The complete union of quantum mechanics and relativity-both special and general-has been one of the great scientific problems of
this century, which only the superstring theorists claim to have solved .

Quantum mechanics alone is limited because, like nineteenth-century physics, it is still based on point particles, not super strings.

In high school we learn that, force fields such as gravity and the electric field obey the “inverse square law” – that is, the farther one
distances oneself from a particle, the weaker the field becomes. The further one travels from the sun, for example, the weaker its gravitational pull will be. This means, however, that as one approaches the particle, the force rises dramatically. In fact, at its surface the
force field of a point particle must be the inverse of zero squared, which is 1/0. Expressions such as 1/0, however, are infinite and illdefined. The price we pay for introducing point that all our calculations of particles into our theory is physical quantities, such as
energy, are riddled with 1/0s. This is enough to render a theory useless; calculations with a theory plagued with infinities cannot be made because the results cannot be trusted.

The problem of infinities would haunt physicists for the next half century. Only with the advent of the superstring theory has this problem been solved, because superstring banish point particles and replace them with a string. The original assumption made by Heisenberg and Schrodinger-that quantum mechanics should be based on point particles-was simply too stringent. A new quantum mechanics can built on a theory of superstrings.

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