# Quantum Mechanics Fails Its Relativity Exams

When people talk about quantum mechanics, they’re usually referring to applying the principles of quantum mechanics to particles which are moving with non-relativistic energies. That’s fine, and quantum mechanics (or really, non-relativistic quantum particle mechanics) is extremely useful for huge ranges of problems, but there are also whole fields of physics for which we must take special relativity into account. Further, we know that particles are created and destroyed all the time—particle accelerators produce showers of daughter particles, which themselves decay into still other particles, and so on. So there is a definite need for some quantum framework which can account for Einstein’s special relativity, as well as for particle creation and destruction. This encompassing quantum framework is known as Quantum Field Theory.

In developing a relativistic quantum theory, it turns out that we can’t just quantize relativistic particles the way we can quantize non-relativistic particles, as I’ll detail below. Rather, we will need to construct a quantum field in order to take quantum mechanics into the relativistic regime. Here, we’ll take it for granted that a quantum field $\phi(x)$ can be constructed which satisfies certain fundamental requirements.

In this notation, $x$ is a 4-vector $x = \langle{t}; \vec{x}\rangle$  representing a point in spacetime, $\vec{x} = \langle{x}_{1}, {x}_{2}, {x}_{3}\rangle$ is a spatial vector in $\mathbf{R}^3$, and I’ll use boldface for operators (like the Hamiltonian, $\textbf{H}$). In the end our quantum field ($\phi$) will be operator-valued at each spacetime point—I just won’t use boldface for the fields themselves, even though they are operators. So $\phi$ associates each spacetime point $x$ with an operator called $\phi(x)$.

So, why doesn’t familiar quantum mechanics play well with relativity? Continue reading Quantum Mechanics Fails Its Relativity Exams

# Seeing Without Looking: The Quantum Bomb

Some of the most dramatic and unintuitive experimental results in quantum mechanics have come from dedicated physicists’ insistence on pushing the bounds of what should be physically possible (but not all, as Henry Becquerel’s serendipitous discovery of radioactivity reminds us). Dedication to probing the strangeness of quantum physics has been paying off for over a hundred years.
One of the more recent and striking successes of quantum theory, first posited in 1993 by Avshalom Elitzur and Lev Vaidman of Tel Aviv University, is the idea that we can actually detect an object without using photons or any other particles to look at it. What in the world does that mean? Well,

Imagine you’re tasked with determining whether a new (highly classified) special “quantum bomb” is operational or is a dud. This quantum bomb has two characteristics that make it extremely volatile:

1. If the bomb is operational, it will explode when a single photon of light strikes it;
2. If the bomb is a dud, it will not interact with photons in any way.

This may be an extremely strange and dangerous bomb, but you’ve found yourself before a problem which seems impossible: any light you shine on the bomb, perhaps to test it, will just cause an explosion. How can you possibly test that the bomb works without causing it to explode?

You need to perform an interaction-free measurement.