# What's the point of doing high accuracy spectroscopy calculations?

I am currently reading Dickenson et al. (2013) The Fundamental Vibration of Molecular Hydrogen. I am trying to understand why this calculation is important for the field beyond basic scientific curiosity.

Should we expect researchers to keep pushing the accuracy?

Apologies for this extremely stupid question.

• While I gave an answer, this question probably fits better on academia.stackexchange.com ? May 6 at 7:22
• BTW, I am not dissing on the work. I am genuinely impressed and, as an outside to the field, trying to understand the impact. May 6 at 12:21
• @nickpapior This question would very likely get closed if it were on Academia.SE May 6 at 18:10
• @NikeDattani ok. You are probably right. :) May 9 at 8:13
• I think you misunderstand this paper - it's not producing a calculation, it's performing a very high precision measurement and then is comparing that measurement with the computed theoretical value. This is really textbook science - testing models with experiment. It's the core of what science is all about.
– J...
May 9 at 14:55

The paper in your question currently has 159 citations and was published in one of the most prestigious journals (Physical Review Letters). It is about high-precision spectoscopy on $$\ce{H2}$$, which is the simplest neutral molecule, and is therefore of fundamental interest as a building block to our understanding of all molecules, just as understanding $$\ce{H}$$ is a building block to understanding bigger atoms. You are basically asking "what value is there to beyond scientific curiosity?".

#### Story time:

4 years before that $$\ce{H2}$$ paper I made high-precision $$\ce{Li2}$$ potentials here (for the singlet states) and here (for the triplet states).

Kirk Madison's group needed these to be extremely accurate in order to do some experiments. They wanted to make ultra-cold optical lattices using $$\ce{Li2}$$, because these can be used for quantum computing. But how do you make $$\ce{Li2}$$? It's not done the way you make glucose, for example. Photoassociation (using photons to associate two atoms) is the only way that ultra-cold $$\ce{Li2}$$ has been made, and it requires knowing the molecular energy levels to extremely high precision. You shine a laser at the atoms, and adjust the wavelength of the light until the photons exactly match the energy difference between the "atomic" and "molecular" states. If you know what the molecular energy levels are to within $$\pm 1 \times 10^{-4}$$ cm$$^{-1}$$ and your laser's wavelength is being adjusted by $$10^{-5}$$ cm$$^{-1}$$ for each measurement (any bigger and you could miss the signal that you're seeking), then you would have to do about 20 measurements. If you only know the energy level to within $$\pm 1$$ cm$$^{-1}$$, then you would have to 200,000 measurements.

One of the eternal questions in computational modeling is whether we truly understand all the relevant contributions.

I believe the combination of experiment and theory in the paper suggest that if there's unknown physics, the effects are very small in this system.

From the paper:

In view of this development, the high level of agreement between the most accurate theory and experiment for the molecular hydrogen level energies may be interpreted to constrain effects of possible long-range hadron-hadron interactions. … In this sense precision molecular spectroscopy opens an avenue to search for new physics.

In a more general sense, there are often advantages to pursuing precision spectroscopy. The development of atomic clocks led to accurate GPS systems.

Certainly, I can imagine the work in this paper can lead to improved accuracy of quantum chemical methods, improved molecular spectroscopy, etc.

Generally, when you apply for grant funding, one must indicate potential impacts both to the broader scientific field, and to society. In the US, the National Science Foundation calls this "Broader Impacts" and it's specifically a criteria for reviewer evaluation. (The other main NSF criteria is "Scientific Impact".) Thus, grant agencies and reviewers already balance such concerns.

• Even more fundamentally than GPS, measuring the spectrum of atomic hydrogen led to the Rydberg formula which led to the Bohr model which led to quantum mechanics which led to the ability to do almost everything discussed on this stackexchange May 9 at 20:36

Your arguments can be said about numerous other articles (if not all but a very few ones).

What seems negligible in scientific impact at the publication time might be heavily influenced by other developments in the future.

As such any small step along a given scientific direction is in-significant in its sole entity, but by combining different scientific contributions they might lead to significant advances. It might also be the paper that spurred interest in author X in year Y which led to the discovery of the property Z which allows anti-gravity boots, who knows?

What's the point of doing high accuracy spectroscopy calculations?

I think there's a more fundamental answer.

But I'm going to argue from the experimental side. Of course implicit in my answer is the idea that these higher accuracy experiments will then require higher accuracy calculations, which will then demand higher accuracy experiments...

How does science progress?

We:

1. look at the world
2. spot some thing interesting
3. make a model
4. test the model
5. despair when it works perfectly, rejoice when it breaks down
6. revise the model or throw it out and build a new one
7. lather, rinse, repeat (i.e. back to step #4)

The more accurate the measurement is, usually the more it challenges a model. Most models these days include implicit or explicit approximations, and the deviations between models and accurate measurements challenge the models limits.

Talk about the very fundamental The Standard Model which has continued to fit new measurements in high energy particle physics. What has bothered at least some physicists is that predictions of this model has continued to agree with new experimental results better than it should. Some might say better than it "has a right to."

It makes some folks at least uncomfortable.

Suddenly there is news:

Contrary to popular headlines, there is much rejoicing!

Finally sufficiently accurate measurement has been made that disagrees with the best model available. This is gold for theorists, a chance to find either a refinement/adjustment of the current model or a new model (or perhaps new particle or new effect).

Another example is Eric Adelberger's (also here) and the The Eöt-Wash Group's insistence on super high accuracy of gravitation attraction between two objects in his lab.

Who else would stack lead bricks around their experiment to cancel the gravitational quadrupole moment of the hill behind the physics building?

These super-duper accurate torsional pendulum measurements have put serious constraints on theories of gravity and space.

Science often advances by measuring the next few digits of a quantity that models can predict. Nobody knows when and where the surprise will happen, so we simply pursue higher and higher accuracy wherever we can.

If you want to test how good your theory is, you need a precise calculation produced using that theory, and you need a precise measurement to compare it against.

Spectroscopy is generally the best way to make very precise and accurate physical measurements, so often it is the case that more precise spectroscopic results are what motivate the hard work required to do more precise spectroscopic calculations. The electron g-2 measurement, which is the most precise match between theory and experiment in all of physics (as mentioned in the abstract of the paper you reference), is a type of spectroscopy. Doing the equivalent in helium can probe a whole host of potential extensions of the standard model, see the 2nd paragraph of this paper for specific examples.