How can quantum energy describe gravity

Gravity, quantum states and hopping neutrons

Gravity is probably the most common force we know. This article describes the principle of a trap experiment, as it was carried out for the first time by Galileo. Today, however, the object of choice is a low-energy neutron, the height of fall is only a few micrometers and quantum mechanics is necessary to describe the results. Because for the first time it has been possible to observe quantum states in the earth's gravitational field. The exciting experiment, which Hartmut Abele from the Physics Institute vividly describes here, examines superstring theories and is a contribution to the search for a union of forces.

Galileo Galilei would rub his eyes in amazement. According to his experiments, objects fall in the earth's gravitational field with the constant acceleration of gravity g, regardless of their mass. If you repeat your famous fall experiment with neutrons, however, the neutrons no longer fall. In any case, they do not do it if you fall below a height of 0.05 millimeters and use a neutron mirror for reflection. Due to the quantum nature of the neutron, only discrete energy levels on which the neutrons are located are allowed, and these energy levels are found as steps in the measurement data. This shows how quantum phenomena differ from classical physics. Such bound states of quantum mechanics are expected whenever the strength of the force field is greater than the energy of the particles. The states can then only take on very specific energy values. The hydrogen atom - the electromagnetically bound system of electron and proton - is an example of this. Classical physics is no longer sufficient to explain the structure of the atom satisfactorily, and the energy levels are calculated using quantum mechanics. We were the first to observe a gravitationally bound quantum system in which the neutron in the earth's gravitational field corresponds, so to speak, to the electromagnetically bound electron in the hydrogen atom. In our case, the quantum states have an energy of pico-electron volts, which is many powers of ten smaller than the energy of the electrons in the hydrogen atom. From a physical point of view, gravity plays a special role because it is much weaker than all other fundamental forces of nature. The experiments now make it possible to carry out new types of gravity experiments or to redefine fundamental constants in these energy ranges with unmatched accuracy. Further motivations for gravitation experiments come from modern superstring theories, in which the difference in forces between the extremely weak gravitation and the other fundamental interactions, i.e. electromagnetism, the strong and the weak force is canceled. In some of these theories, forces similar to gravity can then occur, which at short distances, say one to ten micrometers, could be billions to billions of times stronger than gravity without our noticing it. This article describes a gravitation experiment by our international research team in which these quantum states were observed in the earth's gravitational field. The experiment also enables statements to be made about the ranges and strengths of gravitational-like forces in an area in which no limits were previously known. The first results were published in the journal "Nature" last year.

The experiment took place in Grenoble at the Institut Laue-Langevin. Here is a European neutron source, in which the world's largest neutron fluxes are generated. Neutrons, together with protons, make up the components of the atomic nucleus. We ourselves are made up about half of neutrons and half of protons. The light electrons hardly matter. A neutron is neutral, which means that it does not carry any electrical force. In order to obtain large neutron fluxes for experimentation, two processes have become established. On the one hand, neutrons can be obtained through nuclear fission, for example at the Laue-Langevin Institute in Grenoble, the European neutron source. Alternatively, you can shoot at the atomic nucleus with a high-energy proton beam. During the subsequent so-called spallation process, the nucleus bursts and around 30 high-energy neutrons per proton are released.

The neutrons generated in the nuclear fission process are initially all very "hot" (more than ten billion degrees, which corresponds to an energy of two mega-electron volts). For the experiment, however, you need extremely slow, i.e. "ultra-cold" neutrons that are cooled down to a thousandth of a degree above absolute temperature and have a transverse energy of around one pico electron volt. The energy difference of 18 powers of ten is obtained through various cooling processes and a further selection of neutrons with too high an energy. The first seven orders of magnitude can be obtained practically for free without much effort. The fuel element in which the hot neutrons are generated by nuclear fission is located in a water tank that is filled with heavy water and is at room temperature. In this water bath the neutrons move like an ideal gas; the fast fission neutrons collide with the water molecules and the water transfers its temperature distribution to the neutrons. Now that the neutrons have reached room temperature, they can be used very effectively, for example as probes to study the structure and dynamics of solids. Numerous instruments are available for this at the Laue-Langevin Institute. This enables scientists to clarify questions from biology, chemistry, physics, medicine, technology or interdisciplinary issues. By tomography with neutrons it is now possible to examine technical objects and to visualize the internal structure on the computer and to reconstruct it in three dimensions.

Physicists from Heidelberg recently used thermal neutrons to take pictures of a motorcycle engine with a displacement of 1000 cubic centimeters. The penetration capacity of the neutrons is so good that it is possible to record a running engine in real time. In this way, combustion processes in engines can be better understood and there is hope of being able to optimize them further in the future.

Our gravitation experiment needs much colder neutrons. In the next step, the thermal neutrons pass into a second moderator stage, the "cold source", which consists of heavy hydrogen at a temperature of 20 K or -253 ºC. The neutrons in turn receive the temperature distribution of the cold source through collisions with hydrogen. One then speaks of cold neutrons. These cold neutrons can be guided very efficiently by so-called neutron guides to further experiments and instruments.

Neutron guides are made possible by an effect of quantum theory: matter represents a natural mirror for neutrons. If the energy of the neutrons is below a certain potential threshold, they are reflected, if it is above, the neutrons penetrate the matter and are absorbed and thus eliminated . Cold neutrons are still reflected up to an angle of incidence of around one degree.

In the Physics Institute of Heidelberg University, a new technology from neutron optics was further developed, with which neutron guides are equipped with multiple layers, so-called supermirrors. Graduates and PhD students have now become self-employed with this technology and run the S-DH company as a start-up company.

The neutron guide built by us at the Laue-Langevin Institute with the new technology has increased the number of neutrons tenfold through the use of these super mirrors. However, the proportion of usable neutrons for our experiment from the cold source is very low. For every ten million neutrons there is just one neutron that is slow enough. All other neutrons have to be selected out. The faster neutrons are eliminated by letting neutrons rise in the gravitational field and sending them through a curved neutron guide. The faster neutrons do not reflect and are absorbed, so that at the end of the conductor only neutrons with a speed of less than 50 m / s are available. Another collimation system supplies our experiment with neutrons that have a speed of less than 5 m / s. These neutrons are so slow that, in contrast to faster neutrons, they reflect off walls at all angles of incidence. These special neutrons are called ultra-cold neutrons. They have some properties of an ideal gas and are useful for our experiment.

The setup of the experiment is quickly explained: The neutrons are guided via a horizontal mirror in the earth's gravitational field to a detector that counts the incoming neutrons. Every neutron is reflected at least twice on this mirror. An additional absorber reduces the energy of the transverse component by a further factor of 100,000. The neutrons that hop too high penetrate the absorber and are absorbed, or they are scattered out of the experiment without reaching the detector.

If the neutrons have enough energy - for hopping heights above 50 micrometers above the mirror - a distinction cannot be made between classical description and quantum mechanics and the measurement data follow the classical expectation. If the hopping heights are limited from above by a neutron absorber, then the quantum regime becomes noticeable for the corresponding small neutron energies. In contrast to light, neutrons now show properties that can only be caused by gravity in interaction with quantum mechanics: the neutrons can only take on very specific energy values.

The reason lies in the nature of quantum mechanics. As mentioned at the beginning, only very specific energy values ​​are allowed in bound systems - this applies to neutrons that are trapped in gravitational potential as well as to electrons in the hydrogen atom. For the first permitted state, the ground state, it is exactly 1.4 pico electron volts, for the next state it is 2.4 pico electron volts. These energy values ​​correspond to a rise of 13 micrometers or 24 micrometers for neutrons in the earth's gravitational field.

Probability statements can be made about the location of a neutron about its quantum state. The first three states can be seen in the illustration on page 20 and explain the measuring principle: First of all, the absorber is lowered completely onto the mirror. No neutrons can reach the detector. Then the absorber is slowly raised. As long as the neutron "feels" the absorber, which quantum mechanically means that the probability of the neutron being located at the absorber is not zero, the neutron will still not be able to reach the detector because it is eliminated in the absorber by a nuclear capture reaction. The counting rate is still zero, apart from a small contribution that can be attributed to the floor of the hall.

If the absorber reaches a height of around 15 micrometers, neutrons that are in the ground state can cross the system and reach the detector, since the absorber no longer has any influence. These neutrons ensure an initial increase in the counting rate in the detector, which is noticeable in one step.

Neutrons in higher states will continue to be absorbed. This only changes again at an absorber height of around 24 micrometers, at which the second neutron state is opened for the detector and which is indicated in a further stage. From 35 micrometers, the neutrons of the next state can reach the detector and gradually the quantum mechanical measurement curve changes into a measurement curve of classical physics.

In this regard, our experiment has some similarities with the Franck-Hertz experiment, which demonstrated the energy levels in atoms many years ago. It is very fascinating that the occupation numbers of the ground state and the next state can be influenced by using two differently oriented neutron mirrors, for example the population of the ground state could be reduced by 80 percent.

It is the first time that gravitationally bound quantum states are detected. The experiment shows that under certain conditions the neutrons do not follow the classical Galilean expectation when they are reflected by a mirror. If the selected energy range of the neutrons is too low, no neutrons can be transmitted. If gravitation could be switched off, the signal in the detector would look completely different. Light that is not subject to the gravitational pull is transmitted undisturbed.

Gravitation is probably the most common force we know. In the meantime, it offers one of the greatest challenges for theoretical physics, since there is no quantum-mechanically consistent theory of gravitation. In addition, there is the big difference in strength between gravity and the other forces, which causes headaches. For example, the electrostatic repulsion of two electrons is 1042 Orders of magnitude stronger than their mass attraction. Nothing explains the weakness of gravity, a puzzle known as the hierarchy problem.

"Great theories of union" try to trace all elementary forces of nature back to a common basic principle from which all properties of the forces can then be derived. After all, the forces can be described within the framework of a quantum theory, the standard model of particle physics, which to this day describes all phenomena from particle, nuclear and astrophysics with great success. Unfortunately gravitation could not be included so far. The superstring theory is considered to be a very promising approach here. For experimental physicists, the fact that the Planck scale - the scale on which interesting string physics could be observed - is about 20 powers of ten smaller than the neutron diameter has been quite daunting so far. Even the Large Hadron Collider (LHC) at the C.E.R.N. will ultimately be able to resolve distances of a ten-thousandth of the neutron diameter.

This complication of string theories is due to the fact that it is only possible in a higher-dimensional geometric space. Our universe seems to have only four dimensions: three space dimensions (up / down, left / right and back and forth) and one time dimension. According to string theories, we normally do not feel any of these additional or extra dimensions, since it is assumed that these additional dimensions are compactized, that is, they have the topology of a circle, in this case with a radius on the order of the Planck scale.

According to new string theories, the compactification of some of these extra dimensions could take place on lengths that are far greater than the Planck length, and thus gravitation would reach the strength of the other interactions far above the Planck scale through a geometry effect. In this way, these string theories circumvent the hierarchy problem.

Within the framework of these theories, even gravitation-like, but repulsive, short-range forces are expected which, if they existed and if they acted on our massive neutron, would be billions to billions of times stronger than gravity. If this were true and forces existed in additional dimensions, then one should find deviations from Newton's law of gravitation at small distances. Deviations from the known 1 / r potential of gravity would then be allowed down to the millimeter range.

Amazingly, such enormous extra dimensions have so far not been experimentally refuted. This is where our experiment comes in again. The neutron is attracted to the total mass of our earth. According to Newton, the force on the neutron is proportional to the square of the distance to the center of the earth, which results in the known acceleration due to gravity g = 9.81 m / s2 leads. If the neutron now approaches the mirror, only the mass of the mirror could modify the acceleration due to gravity if there were the strong deviations from the Newton potential described above at small distances of less than a millimeter.

The hypothetical additional contributions can also be calculated easily, since essentially only the density of the mirror, the range and the strength of the additional force are important. For distances greater than 50 μm, we have full agreement with the classical expectation and in this area we can exclude deviations from Newton's law due to extra dimensions. Our informative value is not particularly good in this area, and now better limits of torsional pendulum experiments, such as those carried out by the University of Washington in Seattle, are known. In the range below 50 micrometers, however, we observed deviations from the classic expectation in our experiment. However, we do not attribute it to a deviation from Newton's potential, but to the described quantum states in the earth's gravitational field and on the basis of Newton's law of gravitation.

Nevertheless, we can check the predictions of superstring theories in this area.At such small distances, the law of gravity has not yet been checked. Our experiment does not find any deviations from Newton's law of force and it can meanwhile rule out the hypothetical trillion-fold stronger repulsive forces at small distances down to one micrometer.

In summary, the experiment shows that under certain conditions neutrons do not follow the classical Newtonian or Galilean expectation, at least not if their reflection is made possible by a mirror. For the first time, the measurements show the expected quantum states in the earth's gravitational field. Quantum mechanics has thus come closer to gravity. The observation of quantum gravity is not associated with this, but theories that predict deviations from the Newton potential can be restricted with narrower limits at ranges between one and ten micrometers.

In particular, the experiment restricts superstring theories that seek a solution to the hierarchy problem with the help of additional dimensions in an area in which no limits were known.

Priv.-Doz. Dr. Hartmut Abele,
Institute of Physics,
Philosophenweg 12, 69120 Heidelberg,
Telephone (0 62 21) 54 92 14, Fax (0 62 21) 47 57 33,
e-mail: [email protected]