Ground States and the Zero-Point Field


The electromagnetic zero-point field (ZPF), a sea of background electromagnetic energy that fills the vacuum, is often regarded merely as a curious outcome of the quantum mechanical requirement that the lowest allowable energy level in a harmonic oscillator mode is not zero but ħw /2, where w is the characteristic frequency of the oscillator. However, there is a growing body of evidence that the ZPF may play a causal role in some important fundamental processes. For example, it has been demonstrated[1] experimentally that the familiar spontaneous emission process in atoms can be regarded as stimulated emission by ZPF radiation. Of particular pertinence to this experiment, we have shown[2] that a dynamic equilibrium with the ZPF can explain the electronic ground state of the hydrogen atom. Unfortunately, this particular hypothesis has resisted our efforts to design a practical experimental test. However, there is a closely related hypothesis that is much easier to test.



It has been shown[3] that a charged harmonic oscillator immersed in the zero-point field (ZPF) will reach dynamic equilibrium with the ZPF when the oscillator energy is equal to ħw /2, where w is the oscillator frequency. Diatomic molecules have vibrational modes that closely approximate those of a harmonic oscillator at low energy levels. The ground state energy of such molecules is also given by ħw /2, where w is the molecular vibration frequency. We hypothesize that these molecular ground states are not fixed and immutable, as suggested by quantum theory, but are a result of dynamic equilibrium with the ZPF. We tested this hypothesis by measuring the vibrational ground state energy of H2 molecules placed into a Casimir cavity that suppresses the ZPF frequencies at the corresponding molecular vibration frequency (1.32 X 1014 Hz, 2.2 micron wavelength).


Experimental Strategy

We measured the vibrational ground state energy of H2 molecules indirectly by measuring the molecular dissociation energy. If the ground state energy were reduced, the dissociation energy would necessarily increase correspondingly.

The dissociation energy of H2 has been accurately measured[4] by observing the location of the absorption edge that occurs at about 84.5 nm (14.7 eV – EUV). This edge corresponds to photodissociation of the molecule into one ground state H atom and one H atom in the 1st excited electronic state (+10.2 eV). The difference, about 4.5 eV, is the dissociation energy.

We employed a parallel-plate Casimir cavity made from two 1/20 wave optical flats (aluminized for conductivity) placed face-to-face with 1 micron thick spacers to hold them apart. This spacing is slightly less than half the wavelength of the pertinent radiation so it was largely excluded from the cavity interior in two of the three spatial dimensions. The cavity was filled with H2 gas via a hole drilled in the center of one of the flats. EUV radiation entered the cavity, propagated through the H2 gas there, then through a subchamber behind the cavity and into a scintillation detector. The subchamber, normally kept evacuated, was employed for reference purposes. Using an external valve manifold, it could be filled with H2 gas (and the cavity evacuated) to obtain the ordinary absorption spectrum for comparison to the absorption spectrum of the H2 gas in the Casimir cavity.

This is a 500X enlargement of the entrance to the Casimir cavity. At this scale, the spacing between the walls is ½ millimeter. However, your screen is not nearly large enough to complete the drawing. The other end of the cavity should be shown 1 meter to the right of the entrance! With this perspective it is easier to understand why most of the light has to bounce off the walls of the cavity many times in order to propagate through it.

Because of the path length in the cavity (2 mm), the fact that the aluminum surfaces were slightly oxidized, and the fact that the cavity spacing is only ~10x the wavelength of the UV radiation, a relatively severe attenuation of the incident light (~10-4) occurred during transit of the cavity. As a result of this attenuation, it was necessary to conduct this experiment using the very bright EUV radiation available from the Alladin synchrotron at the University of Wisconsin in Madison, WI.



This diagram shows the layout of the Alladin synchrotron. We were graciously granted 3 weeks of beamtime on the Undulator NIM line in the upper left corner. This beamline provides the highest photon flux in our energy range (14-15 eV) and features the best monochromator at the SRC, a 4-meter normal incidence monochromator (NIM) than can provide up to 0.3 milli-eV energy resolution.

Dr. Ralf Wehlitz, a staff member at the synchrotron facility, provided invaluable support, advice, and assistance throughout our experimental program.

The above photograph shows most of the apparatus in its assembled form. The brass box (called the subchamber) hanging beneath the 6” Conflat flange houses the photodetector that will measure the intensity of the UV light propagating through the Casimir cavity. The cavity blocks are visible just in front of the subchamber, clamped together by a C-shaped piece of Al. Note the black bellows-sealed micrometer screw protruding from the top of the Conflat flange (on the left). This device permits fine adjustment of the vertical position of the cavity.

The plumbing system above the Conflat flange permits us to fill with H2 or evacuate either the Casimir cavity or the subchamber.

The above photograph shows the entire apparatus housed in the 6” Conflat cross that serves as a vacuum chamber. The UV beam from the synchrotron entered the cross from the left.

Note the two capacitance manometers (top) which provide absolute pressure measurements for the cavity and the subchamber.

The above photo shows the corner of the synchroton ring where our beamline is located. In the lower right corner, you can see the solid steel upper surface of one of the twelve bending magnets around the ring. Two more of them (yellow sides) are visible in the distance.

Only two beamlines come off the ring at this magnet and ours is the leftmost one that disappears under a platform.

This photo shows our beamline emerging from under the platform (lower foil-covered tube) and heading for the monochromator. Hal is sitting at the desk where we set up our data acquisition computers and part of our experiment is barely visible on top of the platform to Hal’s upper right.

The entrance and exit slits of the monochromator are located just beside the massive steel support column (blue).

This photo shows most of the 4 meter normal incidence monochromator on our beamline. The entrance and exit slits are just beyond the edge of the photo to the right.

The grating housing is mounted on a massive granite slab engraved with “McPherson.” Judging by the price of their smaller monochromators, the cost of this massive ultra-high vacuum instrument must have been astronomical.

Here is our apparatus installed on the elevated platform provided for users of this beamline.

In the tubing leading off to the right is a very fragile In window that is only 1600 Å thick. This window transmits about 30% of the 14 eV photons used in our experiment, but effectively blocks the relatively poor (10‑6 torr) vacuum in our apparatus (caused by the H2 gas continuously seeping from the Casimir cavity) from contaminating the 10-10 torr vacuum routinely maintained in the beamline.

Here is the view of the synchrotron vault from our experiment platform (our apparatus is on the left).

You can see one of the yellow bending magnets in this photo and portions of about 5 of the ~30 beamlines at this facility.

We spent the first week of our 3 week beamtime getting set up and learning to recognize the important parts of the H2 absorption spectrum. We spent the second week coming to the realization that the original detector scheme (a photodiode) had insufficient sensitivity and then scrambling to modify our apparatus to use a detector composed of a phosphor screen and photomultiplier tube (as depicted in the drawing earlier in this document). We spent the third week collecting usable data.



In short, we did observe a small but reproducible change in the absorption spectrum when the H2 gas was moved from the subchamber to the cavity.

This plot shows the change we found. For both the cavity (purple) and the subchamber (cyan), the detector signal is plotted on the vertical axis versus photon energy on the horizontal axis. The plot covers a very narrow range of energies centered on the dissociation absorption edge of the H2 molecule (14.66 eV).

Both spectra show the basic shape of the dissociation edge…i.e. a transition from low absorption to high absorption with increasing photon energy. However, the vertical size of the edge is smaller when the gas is in the cavity.

This absorption edge is caused by transitions from the normal ground state to the dissociated (i.e. free) state of the molecule. The observed reduction in edge height is therefore indicative of a dilution of the H2 gas in the cavity with a few percent of something that absorbs the EUV photons uniformly with no absorption edge in this narrow energy region. For example, H2 molecules in an excited vibrational state would suffice.

Importantly, H2 molecules with significantly suppressed ground states would also suffice to create the observed effect. Such molecules would require more energy to dissociate and thus their photodissociation absorption edge would be found at higher energies, probably somewhere off scale to the right in the plot above. Recognizing this, we spent a considerable amount of time scanning the region to the right of the 14.66 eV edge in search of a displaced absorption edge…without success. For various reasons, the absolute intensity of our photon beam was not perfectly stable. In view of this problem and the likelihood that the displaced portion of the absorption edge would be diffuse…i.e. that not all of the ground states would be suppressed by precisely the same amount… it is not surprising that we were unable to find any evidence of it.

Lacking positive identification of a displaced absorption edge, our observation of a reduced contrast at the 14.66 eV edge cannot be construed as proof of our original hypothesis. Almost any diluent would create the observed effect.

Further, it is not promising that only a small percentage (~5%) of the H2 molecules appear to be affected when the gas is placed in the cavity. Our latest calculations predict that all of the H2 molecules should be significantly affected by the cavity. Only a 3.7% reduction in the ground state energy would move the 14.66 eV dissociation edge to 14.67 eV (i.e. all the way to the right side of the spectral plot above). From the appearance of the plot, we can therefore conclude that the majority of the H2molecules in the cavity were negligibly affected by the cavity.

Unfortunately, our experimental results therefore neither prove nor disprove our hypothesis. The small size of the observed effect seems to tip the scales in favor of disproof…. but we cannot be certain without further experimentation. We are presently engaged in evaluation of new approaches to this experiment.



[1] See, e.g. S. Haroche and J.-M. Raimond, “Cavity Quantum Electrodynamics,” Sci. Am., pp. 54-62 (April 1993). Also H. Yokoyama, “Physics and Device Applications,” Science 256, pp. 66-70 (1992).
[2] H. E. Puthoff, “Ground State of Hydrogen as a Zero-Point-Fluctuation-Determined State,” Phys. Rev. D 35, pp. 3266-3269 (1987).
[3] T. H. Boyer, “Random Electrodynamics: The Theory of Classical Electrodynamics with Classical Electromagnetic Zero-Point Radiation,” Phys. Rev. D 11, pp. 790-808 (1975); M. Ibison and B. Haisch, “Quantum and Classical Statistics of the Electromagnetic Field,” Phys. Rev. A 54, pp. 2737-2744 (1996).
[4] G. Herzberg, J. Mol. Spectrosc. 33, pp. 147-168 (1970)