Will Quantum Physics Ever Replace the Theory of Relativity?

The quantum theory and relativity theory are not in conflict.

Is it possible that one day, quantum physics will subsume the theory of relativity? originally appeared on Quora, the place to gain and share knowledge, empowering people to learn from others and better understand the world. You can follow Quora on Twitter, Facebook, and Google Plus.

Is it possible that one day, quantum physics will subsume the theory of relativity?

I think this question was triggered by a common misunderstanding about quantum physics and relativity theory, promoted by popular science media.

So let me begin with an important statement: The quantum theory and relativity theory are not in conflict.

In fact, the very first attempt to formulate a modern quantum theory, which later became known as the Klein—Gordon equation, was relativistic. Erwin Schrödinger first formulated the theory in this form, but its prediction of negative probabilities deterred him; instead, he opted to publish a nonrelativistic version, which became known as the Schrödinger equation.

Dirac took the next step, then, when (using astonishing mathematical insight) he constructed another equation, the Dirac equation, which we now know as the equation that describes a relativistic fermion. The insights offered by the Dirac equation led us to understand the Klein—Gordon equation as well, reinterpreting negative probabilities as antiparticles.

And then, in the 1940s, quantum field theory was born, addressing the main shortcomings of quantum particle theories, such as their inability to account for particle creation and annihilation, and the subtle violations of causality. Quantum field theory has been fully relativistic from the onset. It is, in fact, possible to formulate quantum field theory on the curved spacetime background of general relativity.

You might wonder, then, why you keep hearing about a presumed “conflict” between quantum physics and relativity. The reason is simple: gravity.

The usual route of turning a classical field theory (like electromagnetism) into a quantum theory involves some formal steps of replacing dynamical quantities with corresponding quantum operators, working out the interactions of the theory, and last but not least, applying mathematical procedures to get rid of unwanted infinities.

It is this last step that fails for gravity. We understand why… but we have not been able to devise a convincing scheme to get around this problem.

But then, here is something interesting: the theory almost works. That is to say, it is possible to formulate a hybrid theory, so-called semiclassical gravity, in which the gravitational field itself is treated classically, but everything else is treated as quantum fields. This hybrid theory works very well, a little too well, perhaps: in every regime accessible to us through observation, its predictions are accurate. Which means that there are no experiments, no observations to offer insight, or to validate or refute new, quantum theories of gravity. So we are a little bit stuck here, with a theory that works but is rather inelegant and feels “unfinished”.

But “subsume” relativity? What for? Apart from the gravity issue, quantum field theory and relativity theory happily go hand-in-hand, together describing accurately just about every physical phenomena that we can observe. There is no conflict, no tension between the two, hence no need to “subsume” anything.

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