Test of Special Relativity Confirmed - ScienceMag.org

[sander69]

On the following link it is mentioned that this experiment tests special relativity. Can someone please explain how it does that? http://www.sciencemag.org/news/2016/12/deep-probe-antimatter-puts-einstein-s-special-relativity-test

 

[mathman]

From article:
Explaining exactly why special relativity requires antimatter to mirror matter involves a lot of math. But in a nutshell, if that mirror relationship were not exact, then the basic idea behind special relativity couldn’t be exactly right, Kostelecky says. Special relativity assumes that a single unified thing called spacetime splits differently into space and time for observers moving relative to each other. It posits that neither observer can say who is really moving and who is stationary. But, that can’t be exactly right if matter and antimatter don't mirror each other.

 

[Dale]

It looks like they are talking about CPT invariance (charge parity time). I don't know the mathematical derivation, but apparently if a theory is the same when you swap charge parity and time then it follows special relativity and vice versa.

That said, I am unclear how this experiment tests that. As far as I know antihydrogen is just a charge reversal compared to regular hydrogen. So this should be only a test of C invariance, not CPT.

 

[Herman Trivilino]

Doesn't it go back to the Dirac equation? I don't understand the details, but isn't that a relativistic quantum theory that predicts the existence of antimatter.

 

[PeterDonis]

As far as I know antihydrogen is just a charge reversal compared to regular hydrogen.

Antiparticles are CPT conjugates of particles, so antihydrogen is the CPT conjugate of hydrogen. The charge reversal is the one that's obvious, but strictly speaking, if you look at the quantum wave functions, you have to take into account P and T reversal as well.

(The actual atoms and antiatoms are not states with definite parity either, which also complicates things in the detailed analysis.)

 

[Dale]

strictly speaking, if you look at the quantum wave functions, you have to take into account P and T reversal as well

Oh, I didn't realize that. That makes sense.

 

[vanhees71]

There's a famous theorem that any local relativistic QFT with a stable ground state, where relativistic means that the QFT leads to an S matrix that's invariant under special orthochronous Lorentz transformations must (a) for each particle also contain its antiparticle (where particle and antiparicle can be the same in the case of strictly neutral particles like the photon) and (b) the theory is also invariant under the combined CPT symmetry: If there's a process described by such a QFT there must be possible also a process, where all particles are interchanged with their antiparticle (C), space is reflected (P), and the time-reversal of the original process is (T) considered.

So, strictly speaking, ever more precise tests of this CPT theorem do not test just special relativity but also the restricting assumption that relativistic quantum theory is correctly described by a local relativistic QFT with a Hamiltonian bounded from below. So far CPT has been confirmed with all available experiments today.

 

[Ibix]

...so CPT says a hydrogen emitting a photon in the +x direction should look like an anti-hydrogen absorbing a photon (which is the same as an anti-photon) coming from the -x side? Which implies that the absorption and emission frequencies of a hydrogen and an anti-hydrogen must be identical. So testing that they are identical tests CPT symmetry, which is an implication of quantum field theory, which requires relativity. So testing for identical frequencies is a test of relativity.

...right?

 

[vanhees71]

It's a test of relativity under the additional assumption that the postulates underlying the Standard Model of elmentary particle physics hold true. Although I'm not aware of any consistent formulation of relativistic QT which is not a local relativistic QFT with a Hamiltonian bounded from below, in principle there could be such a theory, and then you could have a relativistic QT (i.e., a QT which is invariant under proper orthochronous Poincare transformations) but for which CPT is not a symmetry. As I said, that's however very speculative since against all efforts to find a violation of the predictions of the standard model (including tests of CPT symmetry) so far no such violations have been found. So far the Standard Model thus survived all tests ever done.

 

[Herman Trivilino]

From the article in the current (February) edition of Physics Today, speaking about the transition between antihydrogen's 1s and 2s states ...

The ALPHA experiment implies that if there’s any fractional difference between the transition frequencies of hydrogen and antihydrogen, it’s less than $2 × 10^{−10}$. In a way, that null result is reassuring. The symmetry between particles and their antiparticles is underpinned by the theories of both quantum mechanics and general relativity, so any observed difference between matter and antimatter spectra would require major changes to most of what we think we know about the laws of physics.

The nature of those changes remains to be seen. “In the search for a new effect, it’s useful to identify all possible types of signals, and indeed a general theory of all possible signals exists,” says Alan Kostelecky of Indiana University Bloomington. “But until an effect is discovered, predictions from specific models shouldn’t be taken too seriously.”

Still, it’s possible to make some educated guesses about what a matter– antimatter difference might look like. Because the revamping of quantum mechanics and general relativity could lead to unification of the two theories, one might expect the telltale spectroscopic difference to be on the natural size scale for unification effects: the ratio of the energy of electroweak processes to the Planck energy, or somewhere between $10^{−17}$ and $10^{−23}$. It’s conceivable that spectroscopic measurements could eventually chip away at that range. But that would require progress not just in antihydrogen spectroscopy but also in hydrogen spectroscopy. The latter’s precision is currently around $10^{−15}$.

Would I be correct to conclude that orders of magnitude improvements will need to be made before we can even hope to see any differences between the spectra of hydrogen and antihydrogen?