Changing Concepts of Light and Matter
Hänsch, Theodor W.
Observations in atomic, molecular, and optical physics have played a central role in reshaping our concepts of light and matter. The lecture will lead from historical milestones to modern frontiers, including spectroscopic precision tests of fundamental physics laws, ultraprecise clocks, and novel quantum matter. Large mysteries remain, and our concepts of light and matter are likely to undergo further dramatic changes in the future.
 Good morning. It's always a pleasure to be here in Lindau. And you know that I'm an experimental physicist working with lasers and light and with a passion for precise measurements, which have taught us much about light and matter in the past and which might teach us more in the future. So today I thought I would talk about how our concepts of light and matter have evolved over time and how they are still changing. Light and matter, of course, intertwined with the concepts of space and time. And these are essential not just to physics but to life. They're essential for survival. And so evolution has hardwired very strong intuitive concepts in our brain, which are so compelling that they can actually hinder scientific struggles. Let's look what was discovered in the scientific exploration of light, which started probably with when Sir Isaac Newton sent a ray of sunlight through a prison and he saw how the light is dispersed into a rainbow of colors. And he argued that these different colors must correspond to different kinds of light particles. Then came Thomas Young, who showed that light is a wave. Just like water waves going through a double slit, you can observe interference ranges to waves oscillating in phase, reinforce each other to waves oscillating out of phase, can cancel each other through interference. Frenel came up with a mathematical formulation of this kind of wave theory, even though at a time it was not known what kind of wave light is. But from interference experiments, Young was able to measure the wavelengths of light. And so he determined that in the visible spectrum, the wavelength ranges between 700 nanometers in the red and 400 nanometers in the violet. And once you know the wavelengths at the speed of light, of course you can calculate the frequency of light. So in the middle of the spectrum, we are talking about something like 5 times 10 to the 14 oscillations per second. Nowadays, of course, we know that light is an electromagnetic wave. There is a huge spectrum from radio waves to gamma rays. And these interferences can be used as a tool for very precise measurements. One important such measurement was made by Abraham Michelson in the late 19th century using his famous Michelson interferometer. He could show that the speed of light does not change with the motion of Earth. And of course, Einstein was the one who came up with his brilliant special theory of relativity to explain this, at least to model it. And then, as we heard yesterday, of course, also with general relativity, we thoroughly changed our understanding of space and time. And David Gross yesterday has, of course, already pointed out the latest triumph of this kind of interferometry is the detection of gravitational waves from two coalescing black holes using essentially a giant and sophisticated Michelson interferometry, the LIGO observatory. So much for waves, and so people were happy that they understood what light is. But there were some worrisome observations in the late 19th century. People in Germany, the PDB, it was at that time, not yet called PDB, but they in Berlin carefully measured the spectrum emitted by black hot bodies because they wanted to understand how to make more efficient electric light sources, and the spectrum measured could not be explained in any classical model. Planck was the one who showed that if you make the assumption that light is emitted only in packets, emitted and absorbed in light packets of quantity, Planck's constant times frequency, then one can model this type of black body spectrum very well. And Einstein then postulated 1905 that it's not just absorption and emission, but the nature of light itself is its quantize. The term photon was coined much later in the 1920s. But today we have position-sensitive photon detectors where you can watch how an interference pattern builds up photon by photon in a double slit experiment. So we know that light can act as if it were made of particles. It can act as if it was an electromagnetic wave. It can act as if it were made of particles. It's not classical particles, but particles that show these strange correlations over a distance called entanglement, which indicate that you cannot assume that a photon that you detect already has its properties before detection. This has become a tool for applications such as quantum cryptography, quantum information processing, quantum computing, and the pioneers here, John Clauser and Alan Aspey. And even more, more mentors, discovery or invention was that of the laser, that you can make a source of coherent light waves that acts much like a classical radiofrequency oscillator. The rays to build the first laser was triggered by Art Schollow and Charlie Towns with a seminal paper published in 1958. The first laser was realized by Ted Mayman in 1960. Here are the parts of his original laser that are right now in our Max Planck Institute of Quantum Optics in Garching, thanks to Kathleen Mayman, the widow of Ted Mayman. And what I find charming is that it's really very simple. It's a simple device that could have been realized much earlier, and it also shows that you can have, or the largest impact is not always from big and sophisticated instruments. It can be simple instruments that are game changers. Other examples, of course, are the transistors, the scanning, tumbling microscope. And so this is, I think, the kind of invention that I am really, very excited about. And of course, the impact in science is illustrated by the fact that there are now 26 Nobel Prizes around the laser were enabled by the laser and not counting yet the detection of gravitational waves that surely will be included in the future. Okay, so much for light. What about matter? The question, what is matter, of course, is a natural question to ask. Old philosophers speculate that maybe there's small, indivisible building blocks of matter atoms, but these ideas were soon forgotten, but they're revived in the 18th and 19th century by chemist Dalton, who showed that if he makes this assumption that matter consists of atoms, then one can naturally understand the proportion in which elements react to form molecules, and one can even determine relative molecular weights. And of course, we see low-schmidt numbers, even absolute atomic weights, but nobody had an idea how these atoms are composed. There were some hints that they must be complex, Fraunhofer, with his spectrographs, looking at the solar spectrum discovered the dark absorption lines due to atoms or ions in the solar atmosphere or Earth atmosphere. And this kind of spectroscopy soon became a tool to chemists like Bunsen or Kirchhoff used it to identify atoms by their spectrum, like a fingerprint, but how the spectral lines came about remained obscure. Very simplest of the atom and the very simplest of the spectra in the end provided the Rosetta stone for having a deeper look into how atoms work. There is the visible Balmer spectrum that was first observed in astronomy in the light of distant stars, and you know that Jacob, Johann Jacob Balmer was the first to come up with an empirical formula for the wavelengths of this very simple line spectrum that was later generalized by Rittberg, who introduced the empirical Rittberg constant, but still one didn't know how these lines could come about. One had even no idea what is going on inside an atom until radioactivity was discovered and until Rutherford used scattering of radioactive alpha rays from a gold foil to discover that all the mass, almost all the mass of an atom must be confined to very small heavy nucleus and the light electrons surrounding these nucleus like a cloud. So this is inside Bohr tried to model the hydrogen atom, the simplest atom with just a single electron as some sort of planetary system, and he tried to see what could give the Balmer spectrum and he realized that no classical model would work. He had to make some radical assumptions like Planck that there are only certain stationary orbits which are allowed and that radiation is emitted in transitions in jumps between these orbits, these early quantum postulates, they are hard to swallow, but they allowed Bohr to calculate the Rittberg constant in terms of the electron mass, electron charge, Planck's constant and the speed of light to fairly high accuracy so people realized there must be something to it even though it made no sense. Puzzling about it, Louis de Bois showed that if you make the assumption that electrons, particles can also have wave properties and if you wonder what would be the orbits where you have resonant waves, an integer number of wavelengths fits around, that you could reproduce the Balmer spectrum, Schrodinger came up with a wave equation for these matter waves which is perhaps one of the most successful and best tested equations in physics. As the Schrodinger equation for the hydrogen atom could be solved in closed form, one can draw pictures of orbit of orbitals, still it's a question that has not been definitely answered until today, what is it that this Schrodinger equation or the Schrodinger wave function describes? There is infinite room for speculation for philosophy, but if we want to stay on the solid ground of science, I think all we can say for sure is that this equation describes our information about the probabilities of clicks and meter readings. It doesn't say anything about the true microscopic world. This is the essence, the spirit of the Copenhagen interpretation which has been sharpened and made more consistent with the interpretation of cubism and minimal interpretation that interprets probabilities in the Bayesian spirit as we have heard from C.R. Scharosh. So in particular, different physicists can assign different probabilities dependent on the information they have. So this is still some frontier where we hope one of you maybe will have some insights how we can go beyond this phenomenological description. Nonetheless it works very well. DRR two years later was able to generalize the Schrodinger equation to include relativistic effects and this DRR equation was miraculous because it not only contained relativistic effects, it also predicted the existence of anti-electrons of positrons and it was so beautiful that people felt this must now be the ultimate truth. There were nagging uncertainties where DRR could really describe the fine structure of hydrogen lines very well and since the second world war we know that the DRR equation is not complete. It is not able to describe the fine structure of hydrogen lines because there are effects that were not included in particularly the effect of the vacuum fluctuations and vacuum polarization. LAMB was his discovery of the LAMB shift of the fact that there are two energy levels in hydrogen, the two S state where the electron comes close to the nucleus and the two P state where it stays away. Two levels that should be precisely the same, they should be degenerate according to DRR but in reality they are split by about a thousand megahertz and this was the beginning of quantum electrodynamics and modern quantum field theories in 65, the Nobel Prize for the developments in quantum electrodynamics was given to Tomor-Naghe, Schwinger and Feynman. Of course since then we have thanks to Gelman found that there is a scheme how we can classify the building blocks of all matter in terms of quarks and leptons and bosons and we believe that this is a complete description of matter as we understand it today. Of course it is eager to look beyond the standard model and new accelerator experiments at certain maybe one will discover new things but so this is considered a very successful model of matter and its interactions. According to the standard model the proton, the nucleus of the hydrogen atom is a composite system made up of quarks and gluons and there is a theory of quantum chromodynamics that attempts to model this but it is still at an early stage. We cannot for instance predict the size of the proton and this question how small is the proton is something that has become important experimentally partly because of lasers and precision spectroscopy. So my own encounter with hydrogen started in the early 1970s when I was a postdoc at Stanford University. Art Scholler, co-inventor of the laser was my host and mentor and he gave good advice to young people. He said if you like to discover something new try to look where no one has looked before and actually we had a tool where we could do this very nicely in the early 70s because we had the first tunable dialaser that was at the same time highly monochromatic so one could use it to study spectral lines free of Doppler broadening using non-linear spectroscopy saturation spectroscopy. And so we succeeded to for the first time resolve individual fine structure components of the red Balmer alpha line where before spectroscopists were dealing with a blend of unresolved lines due to the very large Doppler broadening of the light hydrogen atoms. And this has been the start of a long adventure studying hydrogen with ever higher resolution and ever higher precision in the hope that if we look closely enough maybe one day we will find a surprise and only if we find a disagreement with existing theory can we hope to make progress. And so over the years and this adventure is continuing today we have advanced the fractional frequency uncertainty with which we can study transitions in hydrogen from something like six or seven decimal digits in classical spectroscopy to 15 digits today. And to make progress beyond 10 digits we had to learn how to measure the frequency of light. So the motivation for doing this kind of work is we want to test bound state 2D look for possible discrepancies but we can also measure fundamental constants in particular the Whitberg constant and the proton charge radius. One can ask the question are constants really constant or might they be slowly changing this time. There is anti-hydrogen so one can hope to compare matter and antimatter and altogether maybe discover some new physics. And so this quest has motivated inventions in the 1970s techniques of Doppler free laser spectroscopy also the idea of laser cooling of atomic gases was inspired by this quest for higher resolution and accuracy in hydrogen. And in the 1990s finally a tool the femtosecond frequency comb that makes it now easy but had been impossible or extremely difficult before namely to count the ripples of a light wave. So at the turn of the millennium various newspapers and journals reported on these frequency combs because they had been cited when the Nobel Prize was awarded in 2005 to Schenhal and myself and so the frequency comb is for the first time a simple tool for measuring optical frequencies of hundreds or even thousands of terahertz it provides a phase coherent link between the optical and the radio frequency region and it's a clockwork mechanism a counter for optical atomic clocks. So how does the frequency comb work? Typically you have a laser or some kind of source that emits very short pulses with a broad spectrum. If you have a single such pulse you get a broad spectrum. If you have not a single pulse but two pulses in succession they interfere in the spectrum. So it's similar to the Young's double slit experiment but now interference in the spectrum or in the spectrograph and you get a fringe pattern. So in essence you have already a frequency comb, a comb of lines not very sharp, the more distant the pulses are the more comb lines you get and the frequency spacing between these comb lines is just precisely the inverse time interval between the two pulses. So if I have not two pulses but many pulses then they can interfere like we get interference in the diffraction rating. We have a multivave interference if we can build up sharp lines. The longer we wait the sharper the lines and they can be as sharp as any continuous wave laser but only if you have precisely controlled timing otherwise of course this doesn't work. So these are extremely elementary principles according to Fourier. Still most people didn't expect that this could actually work to measure the frequency of light. They didn't anticipate how far these principles could be pushed. That you could take a moduloc titanium sapphire laser, send its light through a non-linear fiber to broaden it by self-phase modulation through a rainbow of colors and still have a frequency comb. So you can get 100,000 or a million sharp spectral lines. They equally spaced by precisely the pulse repetition frequency. The only thing that was still a problem was that we don't know the absolute position of these lines. They are not really basic but the absolute positions depend on the slippage of the phase of the carrier wave relative to the pulse envelope, the so-called carrier envelope offset frequency. But once you have an octave spanning comb it's extremely simple to measure this offset frequency. You can take comb lines from the red end, send them through a non-linear crystal to frequency double, get the comb lines in the blue end, look at the collective beat note and you can measure it and if you measure it you can use server controls to make it go away or you can simply take it into account. And so now you can buy instruments, optical frequency meters and there are hundreds of these used in different laboratories. They are being miniaturized so one can have an instrument that was my dream 30 years ago, something that you put on a desktop or in a rack and you have an input for laser light on a digital display. You can measure the frequency, you can read out the frequency to as many digits as you like. There is work going on on miniaturized comb sources based on micro-toroids fabricated by lithography. And one of the reasons for growing interest in these combs is that there is an evolutionary tree of applications but we have no time. Looking at the clock and I see that I really need to speed up. But let's look at the original purpose, at frequency measurement. So there is this extremely sharp transition in atomic hydrogen, a two-photon transition from the ground state to the metastable 2S state which has a natural line of only 1 hertz or so. You can excite it with ultraviolet light. The earliest experiments were done in 1975 with Karl Weimann who is actually here at this meeting. I haven't seen him yet but I think he will arrive on Wednesday. And now we are able to measure the frequency of this transition to something like 15 decimal digits. For the measurement, we need a comparison. Our comparison was the national cesium fountain clock time standard at the PDB and we had a fiber link linking laboratories about 1,000 kilometers away. So if I have that frequency, can I determine the Rittberg constant? Yes, the comparison with theory but there is one problem. We don't know the proton size wave. And so that's why the frequency is known to 15 digits but the Rittberg constant only to 12 digits. So to make progress, we need a better value of the proton charge radius. How is the proton charge radius measured? The electron scattering experiments and accelerators and there is also the possibility to measure it by comparing different transitions in hydrogen. If you look at the energies of S levels, they scale with Rittberg constant over principle quantum number square plus length shift of the constant divided by the cube of the principle number and this length shift traditionally includes a term that scales with the root mean squared charge radius of the proton. So by comparing two different transitions, you can measure the proton size. You can do it much better by looking at artificial man-made atoms of meonic hydrogen where you have a, instead of the electron, a negative muon 200 times heavier that comes 200 times closer to the nucleus. In this case, the length shift is actually in the mid infrared at 6 micron but you can, by capturing muons in hydrogen gas, you can populate the matter stable to S state and induce transitions with a laser and look for Lyman alpha which in this case is a 2 kilo electron volt in the x-ray region. So this kind of experiment was done, was finally successful here. You see the part of the international team in front of the laboratory at the Paul Scherer Institute in Switzerland and so in 2010 and 2013, they could publish results with Randall Spohl really as the leader of the team at observing such resonances, length shift resonances in meonic hydrogen and the big surprise was that it wasn't where it was expected to be. Now, two positions where the resonance should be according to the official code data value and where it should be according to accelerator experiment. So it wasn't there. And if you look at the error bars, we see that the proton size determined from the meonic hydrogen is almost 8 sigma away from the size determined by scattering electrons or looking at electronic hydrogen. This is known as the proton size puzzle. It has not been completely resolved. Our suspicion is that the meonic hydrogen experiments are right and maybe the hydrogen spectroscopy wasn't right. This has to do with the fact that we have one very sharp transition. The one is too, but they're auxiliary transitions that are not so sharp and that are more easily perturbed by electric fields and other effect. So if one looks at all the hydrogen spectroscopic data that flow into the value of the proton radius, one sees that each individual one has big error bars and only if the average over all of them do we get this small error. But maybe one is not allowed to do that. So there are some new experiments carried out in our laboratory with Axel Bayer studying one photon transition in a cold beam of metastable 2S atoms from 2S to 4P. This is essentially Ballmer beta. And he went through great pains to eliminate any conceivable systematic error. So he now has some result, which is on the other side actually of the proton radius determined from meonic hydrogen. I don't know if this is really conclusive, but it suggests that maybe that would be the solution. We're not discovering new physics, but we are discovering old errors in spectroscopy of hydrogen. Nonetheless, so if we for a moment assume that the meonic hydrogen gives us the right proton size, then we can see how will this affect the Rittberg constant. And so here we have the official value of the Rittberg constant according to the most recent code data adjustment of the fundamental constant, and if we take the meonic hydrogen radius, we see that the error bars shrink quite a bit, almost in order of magnitude, which is a major step for a fundamental constant. But we also move the Rittberg constant, which has, of course, consequences in all kinds of precise predictions. I have to come to an end. Let me just briefly mention, very soon, maybe even this year, I expect to see the first results of laser spectroscopy of anti-hydrogen. And of course, the question whether hydrogen and anti-hydrogen are precisely the same, or if there is a tiny difference is very monumental for our understanding of nature. And even the tiniest difference would be important. Therefore, the more digits you can get in measurements, the better. Also in astronomy, frequency combs are now being installed in large observatories with highly resolving spectrographs. And there are a number of areas where maybe one can discover more about light and matter. So first, you can use it to search for Earth-like planets around sunlight stars. But of course, you can test for general relativity. You can maybe get observational evidence for possible changes in fundamental constants. There is also the question, are these cosmic redshifts that we observe, are they shifting, are they changing this time? Can we get earthbound observation evidence for the continuing accelerated expansion of the universe? And it looks like this might be possible. And of course, how little we know about the universe is illustrated here, where we assume that 68% is totally unknown, dark energy, and 26% is 6.8% are dark matter of unknown composition. So there is still a lot to be discovered. And the progress that we have made in our own lab was really not so much motivated by this important question, but more by curiosity and by having fun in the laboratory. Thank you.
 Good morning.  It's always a pleasure to be here in Lindau.  And you know that I'm an experimental physicist working with lasers and light and with a passion  for precise measurements, which have taught us much about light and matter in the past  and which might teach us more in the future.  So today I thought I would talk about how our concepts of light and matter have evolved  over time and how they are still changing.  Light and matter, of course, intertwined with the concepts of space and time.  And these are essential not just to physics but to life.  They're essential for survival.  And so evolution has hardwired very strong intuitive concepts in our brain, which are  so compelling that they can actually hinder scientific struggles.  Let's look what was discovered in the scientific exploration of light, which started probably  with when Sir Isaac Newton sent a ray of sunlight through a prison and he saw how the light  is dispersed into a rainbow of colors.  And he argued that these different colors must correspond to different kinds of light  particles.  Then came Thomas Young, who showed that light is a wave.  Just like water waves going through a double slit, you can observe interference ranges  to waves oscillating in phase, reinforce each other to waves oscillating out of phase, can  cancel each other through interference.  Frenel came up with a mathematical formulation of this kind of wave theory, even though at  a time it was not known what kind of wave light is.  But from interference experiments, Young was able to measure the wavelengths of light.  And so he determined that in the visible spectrum, the wavelength ranges between 700 nanometers  in the red and 400 nanometers in the violet.  And once you know the wavelengths at the speed of light, of course you can calculate  the frequency of light.  So in the middle of the spectrum, we are talking about something like 5 times 10 to the 14  oscillations per second.  Nowadays, of course, we know that light is an electromagnetic wave.  There is a huge spectrum from radio waves to gamma rays.  And these interferences can be used as a tool for very precise measurements.  One important such measurement was made by Abraham Michelson in the late 19th century  using his famous Michelson interferometer.  He could show that the speed of light does not change with the motion of Earth.  And of course, Einstein was the one who came up with his brilliant special theory of relativity  to explain this, at least to model it.  And then, as we heard yesterday, of course, also with general relativity, we thoroughly  changed our understanding of space and time.  And David Gross yesterday has, of course, already pointed out the latest triumph of  this kind of interferometry is the detection of gravitational waves from two coalescing  black holes using essentially a giant and sophisticated Michelson interferometry, the  LIGO observatory.  So much for waves, and so people were happy that they understood what light is.  But there were some worrisome observations in the late 19th century.  People in Germany, the PDB, it was at that time, not yet called PDB, but they in Berlin  carefully measured the spectrum emitted by black hot bodies because they wanted to understand  how to make more efficient electric light sources, and the spectrum measured could not  be explained in any classical model.  Planck was the one who showed that if you make the assumption that light is emitted  only in packets, emitted and absorbed in light packets of quantity, Planck's constant times  frequency, then one can model this type of black body spectrum very well.  And Einstein then postulated 1905 that it's not just absorption and emission, but the  nature of light itself is its quantize.  The term photon was coined much later in the 1920s.  But today we have position-sensitive photon detectors where you can watch how an interference  pattern builds up photon by photon in a double slit experiment.  So we know that light can act as if it were made of particles.  It can act as if it was an electromagnetic wave.  It can act as if it were made of particles.  It's not classical particles, but particles that show these strange correlations over  a distance called entanglement, which indicate that you cannot assume that a photon that  you detect already has its properties before detection.  This has become a tool for applications such as quantum cryptography, quantum information  processing, quantum computing, and the pioneers here, John Clauser and Alan Aspey.  And even more, more mentors, discovery or invention was that of the laser, that you  can make a source of coherent light waves that acts much like a classical radiofrequency  oscillator.  The rays to build the first laser was triggered by Art Schollow and Charlie Towns with a seminal  paper published in 1958.  The first laser was realized by Ted Mayman in 1960.  Here are the parts of his original laser that are right now in our Max Planck Institute  of Quantum Optics in Garching, thanks to Kathleen Mayman, the widow of Ted Mayman.  And what I find charming is that it's really very simple.  It's a simple device that could have been realized much earlier, and it also shows that  you can have, or the largest impact is not always from big and sophisticated instruments.  It can be simple instruments that are game changers.  Other examples, of course, are the transistors, the scanning, tumbling microscope.  And so this is, I think, the kind of invention that I am really, very excited about.  And of course, the impact in science is illustrated by the fact that there are now 26 Nobel Prizes  around the laser were enabled by the laser and not counting yet the detection of gravitational  waves that surely will be included in the future.  Okay, so much for light.  What about matter?  The question, what is matter, of course, is a natural question to ask.  Old philosophers speculate that maybe there's small, indivisible building blocks of matter  atoms, but these ideas were soon forgotten, but they're revived in the 18th and 19th century  by chemist Dalton, who showed that if he makes this assumption that matter consists of atoms,  then one can naturally understand the proportion in which elements react to form molecules,  and one can even determine relative molecular weights.  And of course, we see low-schmidt numbers, even absolute atomic weights, but nobody had  an idea how these atoms are composed.  There were some hints that they must be complex, Fraunhofer, with his spectrographs, looking  at the solar spectrum discovered the dark absorption lines due to atoms or ions in the  solar atmosphere or Earth atmosphere.  And this kind of spectroscopy soon became a tool to chemists like Bunsen or Kirchhoff  used it to identify atoms by their spectrum, like a fingerprint, but how the spectral lines  came about remained obscure.  Very simplest of the atom and the very simplest of the spectra in the end provided the Rosetta  stone for having a deeper look into how atoms work.  There is the visible Balmer spectrum that was first observed in astronomy in the light  of distant stars, and you know that Jacob, Johann Jacob Balmer was the first to come up  with an empirical formula for the wavelengths of this very simple line spectrum that was  later generalized by Rittberg, who introduced the empirical Rittberg constant, but still  one didn't know how these lines could come about.  One had even no idea what is going on inside an atom until radioactivity was discovered  and until Rutherford used scattering of radioactive alpha rays from a gold foil to discover that  all the mass, almost all the mass of an atom must be confined to very small heavy nucleus  and the light electrons surrounding these nucleus like a cloud.  So this is inside Bohr tried to model the hydrogen atom, the simplest atom with just  a single electron as some sort of planetary system, and he tried to see what could give  the Balmer spectrum and he realized that no classical model would work.  He had to make some radical assumptions like Planck that there are only certain stationary  orbits which are allowed and that radiation is emitted in transitions in jumps between  these orbits, these early quantum postulates, they are hard to swallow, but they allowed  Bohr to calculate the Rittberg constant in terms of the electron mass, electron charge,  Planck's constant and the speed of light to fairly high accuracy so people realized there  must be something to it even though it made no sense.  Puzzling about it, Louis de Bois showed that if you make the assumption that electrons,  particles can also have wave properties and if you wonder what would be the orbits where  you have resonant waves, an integer number of wavelengths fits around, that you could  reproduce the Balmer spectrum, Schrodinger came up with a wave equation for these matter  waves which is perhaps one of the most successful and best tested equations in physics.  As the Schrodinger equation for the hydrogen atom could be solved in closed form, one can  draw pictures of orbit of orbitals, still it's a question that has not been definitely  answered until today, what is it that this Schrodinger equation or the Schrodinger wave  function describes?  There is infinite room for speculation for philosophy, but if we want to stay on the  solid ground of science, I think all we can say for sure is that this equation describes  our information about the probabilities of clicks and meter readings.  It doesn't say anything about the true microscopic world.  This is the essence, the spirit of the Copenhagen interpretation which has been sharpened and  made more consistent with the interpretation of cubism and minimal interpretation that interprets  probabilities in the Bayesian spirit as we have heard from C.R. Scharosh.  So in particular, different physicists can assign different probabilities dependent on  the information they have.  So this is still some frontier where we hope one of you maybe will have some insights how  we can go beyond this phenomenological description.  Nonetheless it works very well.  DRR two years later was able to generalize the Schrodinger equation to include relativistic  effects and this DRR equation was miraculous because it not only contained relativistic  effects, it also predicted the existence of anti-electrons of positrons and it was so  beautiful that people felt this must now be the ultimate truth.  There were nagging uncertainties where DRR could really describe the fine structure of  hydrogen lines very well and since the second world war we know that the DRR equation is  not complete.  It is not able to describe the fine structure of hydrogen lines because there are effects  that were not included in particularly the effect of the vacuum fluctuations and vacuum  polarization.  LAMB was his discovery of the LAMB shift of the fact that there are two energy levels  in hydrogen, the two S state where the electron comes close to the nucleus and the two P state  where it stays away.  Two levels that should be precisely the same, they should be degenerate according to DRR  but in reality they are split by about a thousand megahertz and this was the beginning of quantum  electrodynamics and modern quantum field theories in 65, the Nobel Prize for the developments  in quantum electrodynamics was given to Tomor-Naghe, Schwinger and Feynman.  Of course since then we have thanks to Gelman found that there is a scheme how we can classify  the building blocks of all matter in terms of quarks and leptons and bosons and we believe  that this is a complete description of matter as we understand it today.  Of course it is eager to look beyond the standard model and new accelerator experiments at  certain maybe one will discover new things but so this is considered a very successful  model of matter and its interactions.  According to the standard model the proton, the nucleus of the hydrogen atom is a composite  system made up of quarks and gluons and there is a theory of quantum chromodynamics that  attempts to model this but it is still at an early stage.  We cannot for instance predict the size of the proton and this question how small is  the proton is something that has become important experimentally partly because of lasers and  precision spectroscopy.  So my own encounter with hydrogen started in the early 1970s when I was a postdoc at  Stanford University.  Art Scholler, co-inventor of the laser was my host and mentor and he gave good advice  to young people.  He said if you like to discover something new try to look where no one has looked before  and actually we had a tool where we could do this very nicely in the early 70s because  we had the first tunable dialaser that was at the same time highly monochromatic so one  could use it to study spectral lines free of Doppler broadening using non-linear spectroscopy  saturation spectroscopy.  And so we succeeded to for the first time resolve individual fine structure components  of the red Balmer alpha line where before spectroscopists were dealing with a blend of  unresolved lines due to the very large Doppler broadening of the light hydrogen atoms.  And this has been the start of a long adventure studying hydrogen with ever higher resolution  and ever higher precision in the hope that if we look closely enough maybe one day we  will find a surprise and only if we find a disagreement with existing theory can we hope  to make progress.  And so over the years and this adventure is continuing today we have advanced the fractional  frequency uncertainty with which we can study transitions in hydrogen from something like  six or seven decimal digits in classical spectroscopy to 15 digits today.  And to make progress beyond 10 digits we had to learn how to measure the frequency of light.  So the motivation for doing this kind of work is we want to test bound state 2D look for  possible discrepancies but we can also measure fundamental constants in particular the Whitberg  constant and the proton charge radius.  One can ask the question are constants really constant or might they be slowly changing this  time.  There is anti-hydrogen so one can hope to compare matter and antimatter and altogether  maybe discover some new physics.  And so this quest has motivated inventions in the 1970s techniques of Doppler free laser  spectroscopy also the idea of laser cooling of atomic gases was inspired by this quest  for higher resolution and accuracy in hydrogen.  And in the 1990s finally a tool the femtosecond frequency comb that makes it now easy but  had been impossible or extremely difficult before namely to count the ripples of a light  wave.  So at the turn of the millennium various newspapers and journals reported on these frequency combs  because they had been cited when the Nobel Prize was awarded in 2005 to Schenhal and  myself and so the frequency comb is for the first time a simple tool for measuring optical  frequencies of hundreds or even thousands of terahertz it provides a phase coherent  link between the optical and the radio frequency region and it's a clockwork mechanism a counter  for optical atomic clocks.  So how does the frequency comb work?  Typically you have a laser or some kind of source that emits very short pulses with a  broad spectrum.  If you have a single such pulse you get a broad spectrum.  If you have not a single pulse but two pulses in succession they interfere in the spectrum.  So it's similar to the Young's double slit experiment but now interference in the spectrum  or in the spectrograph and you get a fringe pattern.  So in essence you have already a frequency comb, a comb of lines not very sharp, the  more distant the pulses are the more comb lines you get and the frequency spacing between  these comb lines is just precisely the inverse time interval between the two pulses.  So if I have not two pulses but many pulses then they can interfere like we get interference  in the diffraction rating.  We have a multivave interference if we can build up sharp lines.  The longer we wait the sharper the lines and they can be as sharp as any continuous wave  laser but only if you have precisely controlled timing otherwise of course this doesn't work.  So these are extremely elementary principles according to Fourier.  Still most people didn't expect that this could actually work to measure the frequency  of light.  They didn't anticipate how far these principles could be pushed.  That you could take a moduloc titanium sapphire laser, send its light through a non-linear  fiber to broaden it by self-phase modulation through a rainbow of colors and still have  a frequency comb.  So you can get 100,000 or a million sharp spectral lines.  They equally spaced by precisely the pulse repetition frequency.  The only thing that was still a problem was that we don't know the absolute position of  these lines.  They are not really basic but the absolute positions depend on the slippage of the phase  of the carrier wave relative to the pulse envelope, the so-called carrier envelope offset frequency.  But once you have an octave spanning comb it's extremely simple to measure this offset  frequency.  You can take comb lines from the red end, send them through a non-linear crystal to frequency  double, get the comb lines in the blue end, look at the collective beat note and you can  measure it and if you measure it you can use server controls to make it go away or you  can simply take it into account.  And so now you can buy instruments, optical frequency meters and there are hundreds of  these used in different laboratories.  They are being miniaturized so one can have an instrument that was my dream 30 years ago,  something that you put on a desktop or in a rack and you have an input for laser light  on a digital display.  You can measure the frequency, you can read out the frequency to as many digits as you  like.  There is work going on on miniaturized comb sources based on micro-toroids fabricated  by lithography.  And one of the reasons for growing interest in these combs is that there is an evolutionary  tree of applications but we have no time.  Looking at the clock and I see that I really need to speed up.  But let's look at the original purpose, at frequency measurement.  So there is this extremely sharp transition in atomic hydrogen, a two-photon transition  from the ground state to the metastable 2S state which has a natural line of only 1 hertz  or so.  You can excite it with ultraviolet light.  The earliest experiments were done in 1975 with Karl Weimann who is actually here at  this meeting.  I haven't seen him yet but I think he will arrive on Wednesday.  And now we are able to measure the frequency of this transition to something like 15 decimal  digits.  For the measurement, we need a comparison.  Our comparison was the national cesium fountain clock time standard at the PDB and we had  a fiber link linking laboratories about 1,000 kilometers away.  So if I have that frequency, can I determine the Rittberg constant?  Yes, the comparison with theory but there is one problem.  We don't know the proton size wave.  And so that's why the frequency is known to 15 digits but the Rittberg constant only  to 12 digits.  So to make progress, we need a better value of the proton charge radius.  How is the proton charge radius measured?  The electron scattering experiments and accelerators and there is also the possibility to measure  it by comparing different transitions in hydrogen.  If you look at the energies of S levels, they scale with Rittberg constant over principle  quantum number square plus length shift of the constant divided by the cube of the principle  number and this length shift traditionally includes a term that scales with the root  mean squared charge radius of the proton.  So by comparing two different transitions, you can measure the proton size.  You can do it much better by looking at artificial man-made atoms of meonic hydrogen where you  have a, instead of the electron, a negative muon 200 times heavier that comes 200 times  closer to the nucleus.  In this case, the length shift is actually in the mid infrared at 6 micron but you can,  by capturing muons in hydrogen gas, you can populate the matter stable to S state and  induce transitions with a laser and look for Lyman alpha which in this case is a 2 kilo  electron volt in the x-ray region.  So this kind of experiment was done, was finally successful here.  You see the part of the international team in front of the laboratory at the Paul Scherer  Institute in Switzerland and so in 2010 and 2013, they could publish results with Randall  Spohl really as the leader of the team at observing such resonances, length shift resonances  in meonic hydrogen and the big surprise was that it wasn't where it was expected to be.  Now, two positions where the resonance should be according to the official code data value  and where it should be according to accelerator experiment.  So it wasn't there.  And if you look at the error bars, we see that the proton size determined from the meonic  hydrogen is almost 8 sigma away from the size determined by scattering electrons or looking  at electronic hydrogen.  This is known as the proton size puzzle.  It has not been completely resolved.  Our suspicion is that the meonic hydrogen experiments are right and maybe the hydrogen  spectroscopy wasn't right.  This has to do with the fact that we have one very sharp transition.  The one is too, but they're auxiliary transitions that are not so sharp and that are more easily  perturbed by electric fields and other effect.  So if one looks at all the hydrogen spectroscopic data that flow into the value of the proton  radius, one sees that each individual one has big error bars and only if the average  over all of them do we get this small error.  But maybe one is not allowed to do that.  So there are some new experiments carried out in our laboratory with Axel Bayer studying  one photon transition in a cold beam of metastable 2S atoms from 2S to 4P.  This is essentially Ballmer beta.  And he went through great pains to eliminate any conceivable systematic error.  So he now has some result, which is on the other side actually of the proton radius determined  from meonic hydrogen.  I don't know if this is really conclusive, but it suggests that maybe that would be the  solution.  We're not discovering new physics, but we are discovering old errors in spectroscopy  of hydrogen.  Nonetheless, so if we for a moment assume that the meonic hydrogen gives us the right  proton size, then we can see how will this affect the Rittberg constant.  And so here we have the official value of the Rittberg constant according to the most  recent code data adjustment of the fundamental constant, and if we take the meonic hydrogen  radius, we see that the error bars shrink quite a bit, almost in order of magnitude,  which is a major step for a fundamental constant.  But we also move the Rittberg constant, which has, of course, consequences in all kinds  of precise predictions.  I have to come to an end.  Let me just briefly mention, very soon, maybe even this year, I expect to see the first  results of laser spectroscopy of anti-hydrogen.  And of course, the question whether hydrogen and anti-hydrogen are precisely the same,  or if there is a tiny difference is very monumental for our understanding of nature.  And even the tiniest difference would be important.  Therefore, the more digits you can get in measurements, the better.  Also in astronomy, frequency combs are now being installed in large observatories with  highly resolving spectrographs.  And there are a number of areas where maybe one can discover more about light and matter.  So first, you can use it to search for Earth-like planets around sunlight stars.  But of course, you can test for general relativity.  You can maybe get observational evidence for possible changes in fundamental constants.  There is also the question, are these cosmic redshifts that we observe, are they shifting,  are they changing this time?  Can we get earthbound observation evidence for the continuing accelerated expansion of  the universe?  And it looks like this might be possible.  And of course, how little we know about the universe is illustrated here, where we assume  that 68% is totally unknown, dark energy, and 26% is 6.8% are dark matter of unknown  composition.  So there is still a lot to be discovered.  And the progress that we have made in our own lab was really not so much motivated by  this important question, but more by curiosity and by having fun in the laboratory.  Thank you.
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Good morning. It's always a pleasure to be here in Lindau. And you know that I'm an experimental physicist working with lasers and light and with a passion for precise measurements, which have taught us much about light and matter in the past and which might teach us more in the future. So today I thought I would talk about how our concepts of light and matter have evolved over time and how they are still changing. Light and matter, of course, intertwined with the concepts of space and time. And these are essential not just to physics but to life. They're essential for survival. And so evolution has hardwired very strong intuitive concepts in our brain, which are so compelling that they can actually hinder scientific struggles. Let's look what was discovered in the scientific exploration of light, which started probably with when Sir Isaac Newton sent a ray of sunlight through a prison and he saw how the light is dispersed into a rainbow of colors. And he argued that these different colors must correspond to different kinds of light particles. Then came Thomas Young, who showed that light is a wave. Just like water waves going through a double slit, you can observe interference ranges to waves oscillating in phase, reinforce each other to waves oscillating out of phase, can cancel each other through interference. Frenel came up with a mathematical formulation of this kind of wave theory, even though at a time it was not known what kind of wave light is. But from interference experiments, Young was able to measure the wavelengths of light. And so he determined that in the visible spectrum, the wavelength ranges between 700 nanometers in the red and 400 nanometers in the violet. And once you know the wavelengths at the speed of light, of course you can calculate the frequency of light. So in the middle of the spectrum, we are talking about something like 5 times 10 to the 14 oscillations per second. Nowadays, of course, we know that light is an electromagnetic wave. There is a huge spectrum from radio waves to gamma rays. And these interferences can be used as a tool for very precise measurements. One important such measurement was made by Abraham Michelson in the late 19th century using his famous Michelson interferometer. He could show that the speed of light does not change with the motion of Earth. And of course, Einstein was the one who came up with his brilliant special theory of relativity to explain this, at least to model it. And then, as we heard yesterday, of course, also with general relativity, we thoroughly changed our understanding of space and time. And David Gross yesterday has, of course, already pointed out the latest triumph of this kind of interferometry is the detection of gravitational waves from two coalescing black holes using essentially a giant and sophisticated Michelson interferometry, the LIGO observatory. So much for waves, and so people were happy that they understood what light is. But there were some worrisome observations in the late 19th century. People in Germany, the PDB, it was at that time, not yet called PDB, but they in Berlin carefully measured the spectrum emitted by black hot bodies because they wanted to understand how to make more efficient electric light sources, and the spectrum measured could not be explained in any classical model. Planck was the one who showed that if you make the assumption that light is emitted only in packets, emitted and absorbed in light packets of quantity, Planck's constant times frequency, then one can model this type of black body spectrum very well. And Einstein then postulated 1905 that it's not just absorption and emission, but the nature of light itself is its quantize. The term photon was coined much later in the 1920s. But today we have position-sensitive photon detectors where you can watch how an interference pattern builds up photon by photon in a double slit experiment. So we know that light can act as if it were made of particles. It can act as if it was an electromagnetic wave. It can act as if it were made of particles. It's not classical particles, but particles that show these strange correlations over a distance called entanglement, which indicate that you cannot assume that a photon that you detect already has its properties before detection. This has become a tool for applications such as quantum cryptography, quantum information processing, quantum computing, and the pioneers here, John Clauser and Alan Aspey. And even more, more mentors, discovery or invention was that of the laser, that you can make a source of coherent light waves that acts much like a classical radiofrequency oscillator. The rays to build the first laser was triggered by Art Schollow and Charlie Towns with a seminal paper published in 1958. The first laser was realized by Ted Mayman in 1960. Here are the parts of his original laser that are right now in our Max Planck Institute of Quantum Optics in Garching, thanks to Kathleen Mayman, the widow of Ted Mayman. And what I find charming is that it's really very simple. It's a simple device that could have been realized much earlier, and it also shows that you can have, or the largest impact is not always from big and sophisticated instruments. It can be simple instruments that are game changers. Other examples, of course, are the transistors, the scanning, tumbling microscope. And so this is, I think, the kind of invention that I am really, very excited about. And of course, the impact in science is illustrated by the fact that there are now 26 Nobel Prizes around the laser were enabled by the laser and not counting yet the detection of gravitational waves that surely will be included in the future. Okay, so much for light. What about matter? The question, what is matter, of course, is a natural question to ask. Old philosophers speculate that maybe there's small, indivisible building blocks of matter atoms, but these ideas were soon forgotten, but they're revived in the 18th and 19th century by chemist Dalton, who showed that if he makes this assumption that matter consists of atoms, then one can naturally understand the proportion in which elements react to form molecules, and one can even determine relative molecular weights. And of course, we see low-schmidt numbers, even absolute atomic weights, but nobody had an idea how these atoms are composed. There were some hints that they must be complex, Fraunhofer, with his spectrographs, looking at the solar spectrum discovered the dark absorption lines due to atoms or ions in the solar atmosphere or Earth atmosphere. And this kind of spectroscopy soon became a tool to chemists like Bunsen or Kirchhoff used it to identify atoms by their spectrum, like a fingerprint, but how the spectral lines came about remained obscure. Very simplest of the atom and the very simplest of the spectra in the end provided the Rosetta stone for having a deeper look into how atoms work. There is the visible Balmer spectrum that was first observed in astronomy in the light of distant stars, and you know that Jacob, Johann Jacob Balmer was the first to come up with an empirical formula for the wavelengths of this very simple line spectrum that was later generalized by Rittberg, who introduced the empirical Rittberg constant, but still one didn't know how these lines could come about. One had even no idea what is going on inside an atom until radioactivity was discovered and until Rutherford used scattering of radioactive alpha rays from a gold foil to discover that all the mass, almost all the mass of an atom must be confined to very small heavy nucleus and the light electrons surrounding these nucleus like a cloud. So this is inside Bohr tried to model the hydrogen atom, the simplest atom with just a single electron as some sort of planetary system, and he tried to see what could give the Balmer spectrum and he realized that no classical model would work. He had to make some radical assumptions like Planck that there are only certain stationary orbits which are allowed and that radiation is emitted in transitions in jumps between these orbits, these early quantum postulates, they are hard to swallow, but they allowed Bohr to calculate the Rittberg constant in terms of the electron mass, electron charge, Planck's constant and the speed of light to fairly high accuracy so people realized there must be something to it even though it made no sense. Puzzling about it, Louis de Bois showed that if you make the assumption that electrons, particles can also have wave properties and if you wonder what would be the orbits where you have resonant waves, an integer number of wavelengths fits around, that you could reproduce the Balmer spectrum, Schrodinger came up with a wave equation for these matter waves which is perhaps one of the most successful and best tested equations in physics. As the Schrodinger equation for the hydrogen atom could be solved in closed form, one can draw pictures of orbit of orbitals, still it's a question that has not been definitely answered until today, what is it that this Schrodinger equation or the Schrodinger wave function describes? There is infinite room for speculation for philosophy, but if we want to stay on the solid ground of science, I think all we can say for sure is that this equation describes our information about the probabilities of clicks and meter readings. It doesn't say anything about the true microscopic world. This is the essence, the spirit of the Copenhagen interpretation which has been sharpened and made more consistent with the interpretation of cubism and minimal interpretation that interprets probabilities in the Bayesian spirit as we have heard from C.R. Scharosh. So in particular, different physicists can assign different probabilities dependent on the information they have. So this is still some frontier where we hope one of you maybe will have some insights how we can go beyond this phenomenological description. Nonetheless it works very well. DRR two years later was able to generalize the Schrodinger equation to include relativistic effects and this DRR equation was miraculous because it not only contained relativistic effects, it also predicted the existence of anti-electrons of positrons and it was so beautiful that people felt this must now be the ultimate truth. There were nagging uncertainties where DRR could really describe the fine structure of hydrogen lines very well and since the second world war we know that the DRR equation is not complete. It is not able to describe the fine structure of hydrogen lines because there are effects that were not included in particularly the effect of the vacuum fluctuations and vacuum polarization. LAMB was his discovery of the LAMB shift of the fact that there are two energy levels in hydrogen, the two S state where the electron comes close to the nucleus and the two P state where it stays away. Two levels that should be precisely the same, they should be degenerate according to DRR but in reality they are split by about a thousand megahertz and this was the beginning of quantum electrodynamics and modern quantum field theories in 65, the Nobel Prize for the developments in quantum electrodynamics was given to Tomor-Naghe, Schwinger and Feynman. Of course since then we have thanks to Gelman found that there is a scheme how we can classify the building blocks of all matter in terms of quarks and leptons and bosons and we believe that this is a complete description of matter as we understand it today. Of course it is eager to look beyond the standard model and new accelerator experiments at certain maybe one will discover new things but so this is considered a very successful model of matter and its interactions. According to the standard model the proton, the nucleus of the hydrogen atom is a composite system made up of quarks and gluons and there is a theory of quantum chromodynamics that attempts to model this but it is still at an early stage. We cannot for instance predict the size of the proton and this question how small is the proton is something that has become important experimentally partly because of lasers and precision spectroscopy. So my own encounter with hydrogen started in the early 1970s when I was a postdoc at Stanford University. Art Scholler, co-inventor of the laser was my host and mentor and he gave good advice to young people. He said if you like to discover something new try to look where no one has looked before and actually we had a tool where we could do this very nicely in the early 70s because we had the first tunable dialaser that was at the same time highly monochromatic so one could use it to study spectral lines free of Doppler broadening using non-linear spectroscopy saturation spectroscopy. And so we succeeded to for the first time resolve individual fine structure components of the red Balmer alpha line where before spectroscopists were dealing with a blend of unresolved lines due to the very large Doppler broadening of the light hydrogen atoms. And this has been the start of a long adventure studying hydrogen with ever higher resolution and ever higher precision in the hope that if we look closely enough maybe one day we will find a surprise and only if we find a disagreement with existing theory can we hope to make progress. And so over the years and this adventure is continuing today we have advanced the fractional frequency uncertainty with which we can study transitions in hydrogen from something like six or seven decimal digits in classical spectroscopy to 15 digits today. And to make progress beyond 10 digits we had to learn how to measure the frequency of light. So the motivation for doing this kind of work is we want to test bound state 2D look for possible discrepancies but we can also measure fundamental constants in particular the Whitberg constant and the proton charge radius. One can ask the question are constants really constant or might they be slowly changing this time. There is anti-hydrogen so one can hope to compare matter and antimatter and altogether maybe discover some new physics. And so this quest has motivated inventions in the 1970s techniques of Doppler free laser spectroscopy also the idea of laser cooling of atomic gases was inspired by this quest for higher resolution and accuracy in hydrogen. And in the 1990s finally a tool the femtosecond frequency comb that makes it now easy but had been impossible or extremely difficult before namely to count the ripples of a light wave. So at the turn of the millennium various newspapers and journals reported on these frequency combs because they had been cited when the Nobel Prize was awarded in 2005 to Schenhal and myself and so the frequency comb is for the first time a simple tool for measuring optical frequencies of hundreds or even thousands of terahertz it provides a phase coherent link between the optical and the radio frequency region and it's a clockwork mechanism a counter for optical atomic clocks. So how does the frequency comb work? Typically you have a laser or some kind of source that emits very short pulses with a broad spectrum. If you have a single such pulse you get a broad spectrum. If you have not a single pulse but two pulses in succession they interfere in the spectrum. So it's similar to the Young's double slit experiment but now interference in the spectrum or in the spectrograph and you get a fringe pattern. So in essence you have already a frequency comb, a comb of lines not very sharp, the more distant the pulses are the more comb lines you get and the frequency spacing between these comb lines is just precisely the inverse time interval between the two pulses. So if I have not two pulses but many pulses then they can interfere like we get interference in the diffraction rating. We have a multivave interference if we can build up sharp lines. The longer we wait the sharper the lines and they can be as sharp as any continuous wave laser but only if you have precisely controlled timing otherwise of course this doesn't work. So these are extremely elementary principles according to Fourier. Still most people didn't expect that this could actually work to measure the frequency of light. They didn't anticipate how far these principles could be pushed. That you could take a moduloc titanium sapphire laser, send its light through a non-linear fiber to broaden it by self-phase modulation through a rainbow of colors and still have a frequency comb. So you can get 100,000 or a million sharp spectral lines. They equally spaced by precisely the pulse repetition frequency. The only thing that was still a problem was that we don't know the absolute position of these lines. They are not really basic but the absolute positions depend on the slippage of the phase of the carrier wave relative to the pulse envelope, the so-called carrier envelope offset frequency. But once you have an octave spanning comb it's extremely simple to measure this offset frequency. You can take comb lines from the red end, send them through a non-linear crystal to frequency double, get the comb lines in the blue end, look at the collective beat note and you can measure it and if you measure it you can use server controls to make it go away or you can simply take it into account. And so now you can buy instruments, optical frequency meters and there are hundreds of these used in different laboratories. They are being miniaturized so one can have an instrument that was my dream 30 years ago, something that you put on a desktop or in a rack and you have an input for laser light on a digital display. You can measure the frequency, you can read out the frequency to as many digits as you like. There is work going on on miniaturized comb sources based on micro-toroids fabricated by lithography. And one of the reasons for growing interest in these combs is that there is an evolutionary tree of applications but we have no time. Looking at the clock and I see that I really need to speed up. But let's look at the original purpose, at frequency measurement. So there is this extremely sharp transition in atomic hydrogen, a two-photon transition from the ground state to the metastable 2S state which has a natural line of only 1 hertz or so. You can excite it with ultraviolet light. The earliest experiments were done in 1975 with Karl Weimann who is actually here at this meeting. I haven't seen him yet but I think he will arrive on Wednesday. And now we are able to measure the frequency of this transition to something like 15 decimal digits. For the measurement, we need a comparison. Our comparison was the national cesium fountain clock time standard at the PDB and we had a fiber link linking laboratories about 1,000 kilometers away. So if I have that frequency, can I determine the Rittberg constant? Yes, the comparison with theory but there is one problem. We don't know the proton size wave. And so that's why the frequency is known to 15 digits but the Rittberg constant only to 12 digits. So to make progress, we need a better value of the proton charge radius. How is the proton charge radius measured? The electron scattering experiments and accelerators and there is also the possibility to measure it by comparing different transitions in hydrogen. If you look at the energies of S levels, they scale with Rittberg constant over principle quantum number square plus length shift of the constant divided by the cube of the principle number and this length shift traditionally includes a term that scales with the root mean squared charge radius of the proton. So by comparing two different transitions, you can measure the proton size. You can do it much better by looking at artificial man-made atoms of meonic hydrogen where you have a, instead of the electron, a negative muon 200 times heavier that comes 200 times closer to the nucleus. In this case, the length shift is actually in the mid infrared at 6 micron but you can, by capturing muons in hydrogen gas, you can populate the matter stable to S state and induce transitions with a laser and look for Lyman alpha which in this case is a 2 kilo electron volt in the x-ray region. So this kind of experiment was done, was finally successful here. You see the part of the international team in front of the laboratory at the Paul Scherer Institute in Switzerland and so in 2010 and 2013, they could publish results with Randall Spohl really as the leader of the team at observing such resonances, length shift resonances in meonic hydrogen and the big surprise was that it wasn't where it was expected to be. Now, two positions where the resonance should be according to the official code data value and where it should be according to accelerator experiment. So it wasn't there. And if you look at the error bars, we see that the proton size determined from the meonic hydrogen is almost 8 sigma away from the size determined by scattering electrons or looking at electronic hydrogen. This is known as the proton size puzzle. It has not been completely resolved. Our suspicion is that the meonic hydrogen experiments are right and maybe the hydrogen spectroscopy wasn't right. This has to do with the fact that we have one very sharp transition. The one is too, but they're auxiliary transitions that are not so sharp and that are more easily perturbed by electric fields and other effect. So if one looks at all the hydrogen spectroscopic data that flow into the value of the proton radius, one sees that each individual one has big error bars and only if the average over all of them do we get this small error. But maybe one is not allowed to do that. So there are some new experiments carried out in our laboratory with Axel Bayer studying one photon transition in a cold beam of metastable 2S atoms from 2S to 4P. This is essentially Ballmer beta. And he went through great pains to eliminate any conceivable systematic error. So he now has some result, which is on the other side actually of the proton radius determined from meonic hydrogen. I don't know if this is really conclusive, but it suggests that maybe that would be the solution. We're not discovering new physics, but we are discovering old errors in spectroscopy of hydrogen. Nonetheless, so if we for a moment assume that the meonic hydrogen gives us the right proton size, then we can see how will this affect the Rittberg constant. And so here we have the official value of the Rittberg constant according to the most recent code data adjustment of the fundamental constant, and if we take the meonic hydrogen radius, we see that the error bars shrink quite a bit, almost in order of magnitude, which is a major step for a fundamental constant. But we also move the Rittberg constant, which has, of course, consequences in all kinds of precise predictions. I have to come to an end. Let me just briefly mention, very soon, maybe even this year, I expect to see the first results of laser spectroscopy of anti-hydrogen. And of course, the question whether hydrogen and anti-hydrogen are precisely the same, or if there is a tiny difference is very monumental for our understanding of nature. And even the tiniest difference would be important. Therefore, the more digits you can get in measurements, the better. Also in astronomy, frequency combs are now being installed in large observatories with highly resolving spectrographs. And there are a number of areas where maybe one can discover more about light and matter. So first, you can use it to search for Earth-like planets around sunlight stars. But of course, you can test for general relativity. You can maybe get observational evidence for possible changes in fundamental constants. There is also the question, are these cosmic redshifts that we observe, are they shifting, are they changing this time? Can we get earthbound observation evidence for the continuing accelerated expansion of the universe? And it looks like this might be possible. And of course, how little we know about the universe is illustrated here, where we assume that 68% is totally unknown, dark energy, and 26% is 6.8% are dark matter of unknown composition. So there is still a lot to be discovered. And the progress that we have made in our own lab was really not so much motivated by this important question, but more by curiosity and by having fun in the laboratory. Thank you.
concepts of light and matter have evolved over strong intuitive concepts in our brain, which are included in the future. Okay, so much for light. What about matter? The question, what is matter, electrodynamics and modern quantum field theories for optical atomic clocks. So how does the sharp transition in atomic hydrogen, a two-photon transition from the ground state to the evidence for possible changes in fundamental