The world is teeming with problems. Wherever man looks, some new problems crops up to meet his eye-in his home life as well as in his business or professional activity, in the realm of economics as well as in the field of technology, in the arts as well as in science. And some problems are very stubborn; they just refuse to let us in peace. Our agonizing thinking of them may sometimes reach such a pitch that our thoughts haunt us throughout the day, and even rob us of sleep at night. And if by lucky chance we succeed in solving a problem, we experience a sense of deliverance, and rejoice over the enrichment of our knowledge.

     But it is an entirely different story, and an experience annoying as can be, to find after a long time spent in toil and effort, that the problem which has been preying on one's mind is totally incapable of any solution at all --- either because there exists no indisputable method to unravel it, or because considered in the cold light of reason, it turns out to be absolutely void of all meaning - in other words, it is a phantom problem, and all the mental work and effort was expended on a mere nothing.

Back to COBE and MAP 

            Father George LeMaitre (1894-1966) and Alexander A. Friedman (1888-1925) were the first to postulate that the universe had been created under a Big Bang scenario [1]. As a Roman Catholic priest, Father LeMaitre expounded his idea from 1927-1933. For his part, Alexander Friedman published in 1922 [1].

            Prior to LeMaitre and Friedman, the universe had been widely regarded under a quasi-static model. Thus, the universe had been viewed as existing in a relatively constant state; being the same today as it had been and always will be. It was in this setting that Penzias and Wilson obtained the measurement that was to dramatically propel Big Bang cosmology forward and result in the downfall of the Quasi-Steady State theory [2].

            Thus, in 1965, A. A. Penzias and R. W. Wilson were working on a 20 ft horn reflector antenna at the Bell Laboratories in New Jersey. They intended to use this antenna for astrophysical studies. Soon, they discovered an excess antenna noise at a frequency of 4.08 GHz [2]. They tried to account for the noise, but simply could not determine its origin. Eventually, they would discuss their problem with Professor Dicke at Princeton. Dicke had predicted that the Big Bang should result in a thermal signature at about 10 K. As such, he was delighted to learn of Penzias and Wilson's discovery of unexplained antenna noise. Like Penzias and Wilson, Dicke and his colleagues at Princeton believed that this noise could be translated to a corresponding temperature if the source of the noise was assumed to be thermal in origin. Ultimately, Dicke et. al. would author a paper in The Astrophysical Journal on Cosmic Background Radiation [3] which would precede the Penzias and Wilson report of their experimental finding [2].

            In reporting their antenna noise, Penzias and Wilson would chose to assume that this noise power was thermal in origin. By making this assumption, Penzias and Wilson also inferred a source that could be treated as an ideal blackbody. Once this inference was made, it was possible for them to apply the Laws of Planck [4], Wein [5] and Stephan [6] to the problem. Thus, assuming an ideal blackbody, Penzias and Wilson were able to translate the noise power to a temperature. This temperature corresponded to a blackbody at 3.5 ± 1 K. At the time, of course, Penzias and Wilson had no idea whether or not the source could be considered as thermal in origin. That was because they were operating at a single frequency and could not be certain of the source of the noise. With time, however, the thermal nature of the noise was confirmed.

            The most recent and important confirmation of the thermal nature of the Cosmic Blackbody Radiation was provided by the COBE satellite. This satellite mapped the Cosmic Microwave Background at an elevation of roughly 900 km above sea level. Thus, data from COBE clearly indicates a source of thermal origin with a Wein's displacement temperature of 2.728±0.004 K [7]. Moreover, this measurement probably corresponds to the most perfect thermal radiation curve ever measured. The signal to noise on the FIRAS results from COBE is so high that the error bars are only a small fraction of the linewidth [7]. Indeed, the error bars have to be expanded by a factor of 400 just to be seen. Clearly, the temperature of the universe had been established without a doubt. This proved to be a fatal blow to the quasi-static model of the universe. That was because the quasi-static model had no means of explaining the thermal signature at 3.5 ± 1.0 K initially reported by Penzias and Wilson [2] and confirmed by COBE.

            With the COBE mission also came the realization that the Cosmic Blackbody Radiation curve was anisotropic. That is, the curve did not have exactly the same intensity in all directions. As such, the MAP (Microwave Anisotropy Probe) Satellite is now being launched by NASA in order to further refine the COBE measurements and more explicitly establish the nature of the anisotropy in the Cosmic Microwave Background. Unlike COBE however, the MAP satellite will not orbit the earth. Rather, it will travel 1.5 million miles from the earth towards Mars were it will orbit the sun in a manner synchronous with the earth.

            The Cosmic Blackbody Radiation curve has now become the central experimental proof for the Big Bang theory. However, it seems that little attention has been devoted in understanding what it means to say that an object can be treated as an ideal blackbody. Kirchhoff defines a blackbody as one which is in thermal equilibrium with an adiabatic enclosure.

CONCLUSION:

            When Penzias and Wilson used thermodynamic principles to set a thermal temperature of 3.5 K, they paid no attention to the phases of matter. They believed, like Planck, that Kirchhoff's law of emission was universally applicable. Kirchhoff's law states that for a blackbody, the emission spectrum is determined only by the temperature and the frequency in the presence of thermal equilibrium within an adiabatic enclosure. Penzias and Wilson assumed that they were looking at an ideal blackbody. However, they could never know if the source of their signal met the requirements for a blackbody as defined by Kirchhoff. Nonetheless, since the resulting curve did prove to be thermal in appearance, they assumed that the associated temperature was beyond question.

            As for the COBE team, they also made the same assumptions. They must have been surprised to note the tremendous signal to noise of their measurement. Indeed, the high signal to noise of Penzias and Wilson's curve posed a problem for a while since there was not enough known mass in the universe to account for this signal. But astrophysicists would solve this with the theoretical introduction of dark matter and black holes. Despite all of this, the prevailing theory of cosmology reached the brink of collapse near the end of the last century. Finally, this was salvaged through the introduction of dark energy.

            For astrophysics, the COBE signal could not be coming from the earth. After all, the signal did not change with the seasons and the earth was clearly not at ~3K. So much signal was present, yet no one advanced the concept that the receiver must indeed be very close to the source.

            It is clear from reading "The Little Heat Engine", that liquids and gases do not and cannot follow Stephan's Law of Thermal Emission. That is because, in gases and liquids, the total energy of the system is not contained purely in the vibrational degrees of freedom as required for Kirchhoff's law to be valid. Rather, in these two phases, energy is contained within vibrational, translational and rotational degrees of freedom.

            For gases, as more heat is added into the system, the translational and rotational degrees of freedom are utilized to deal with a proportionally larger and larger fraction of the energy. However, it is the density of the states associated with the vibrational degrees of freedom that are directly associated with thermal emission. From the experimental data on thermal emission in gases, it seems that the density of these states can actually decrease. Thus, for gases, total emission actually drops with temperature.

            Little is known about thermal emission in liquids.  However, in liquids, thermal emissivity does not increase with temperature. This may be simply a reflection that the vibrational degrees of freedom in liquids are not able to deal with as much energy as in the solid case. This is revealed by the weaker phonons in liquids. The vibrational degrees of freedom are likely to be the first to be filled in a liquid. In the liquid, as in the solid, thermal emission is determined exclusively by the density of states associated with the vibrational degrees of freedom. The densities of these states are likely to be much lower in a liquid. This is reflected in the behavior of the phonons. Consequently, a lower apparent temperature is likely to be found in the liquid.

            As energy is added to a liquid, it is primarily the translational and rotational degrees of freedom which are available. This is because the vibrational degrees of freedom are probably already full at the point the solid melted producing the liquid. With increased input of energy, convection increases and viscosity decreases. However, the energy associated with convection and increased viscosity is not available for thermal emission. That is why liquids could be predicted to report a lower than expected Wein temperature. That is also the reason why one might expect to see a lack of temperature dependence for thermal emission in a liquid.

            In closing, this is the reasoning that leads to the conclusion that COBE measured the thermal emission of the oceans. One should consider the possibility that the oceans are emitting at an apparent temperature T_app such that T_app=T/α and "α" equals ~100.  Alpha would have a slight temperature dependence.

          This T_app would corresponds to the ~3 K signature previously assigned to the Cosmos. Through this simple introduction of "α" and T_app, the Laws of Planck, Wein and Stephan can be reformulated for the liquid. In this case however, these laws will express an inaccurate temperature. However, the apparent temperature reported will reflect the relative distribution of energy in the vibrational degrees of freedom relative to the other degrees of freedom.

            It is clear that the signal to noise for the COBE measurements is extremely high. As such, the possibility that the oceans are the source should not easily be dismissed. The earth is primarily a liquid. The presence of convection currents in the oceans is well established. These convection currents require energy to be maintained. This energy is not available for thermal emission. As such, the oceans are expected to produce a Wein's displacement temperature much lower than expected from real temperature measurements. It is now proposed that the ocean is reporting an apparent temperature of ~3 K, namely the precise curve that Penzias and Wilson first detected and COBE mapped to great precision. Since the signal is in the microwave region, it is likely that the radiation shield on COBE cannot completely eliminate the possibility of diffraction.  The signal would thus originate from the ocean and Mie scattering in the atmosphere would be responsible for rendering it nearly isotropic.

            The temperature of the universe can never be measured. That is a limitation given to us by Kirchhoff. As such, there is a real possibility that Big Bang will die, should the day come that the MAP satellite fails to confirm the anisotropy detected by COBE and should the Planck satellite fail to detect a signal. At this point, we will all be re-examining quasi-steady state cosmology.

REFERENCES:

1. Berger A., An Introduction to the International Symposium George Lemaitre, in "The Big Bang and George Lemaitre", D. Reidel Publishing Company, Dordrecht, 1984, p. vii-xiv.

2. Penzias A. A. and Wilson R. W., A Measurement of Excess Antenna Temperature at 4080 Mc/s. Astrophysical J. 1: 419-421 (1965).

3. Dicke R. H., Peebles P. J. E., Roll P. G. and Wilkinson D. T.. Cosmic Black-Body Radiation. Astrophysical J. 1:414-419 (1965).

4. Planck M., Ueber das Gesetz der Energieverteilung in Normalspectrum. Annalen der Physik. 4(3):553-563 (1901).

5. Wien W., Uber die Energieverteilung im Emissionspektrum eines schwarzen Korpers. Annalen der Physik. 1896; 58:662-669.

6. Stefan J., Ueber die Beziehung zwischen der Warmestrahlung und der Temperatur. Wein. Akad. Sitzber. 79:391-428 (1979).

7. Fixen D. J., Cheng E. S., Gales J. M., Mather J. C., Shafer R. A. and Wright E. L. The Cosmic Microwave Background Spectrum from the Full COBE FIRAS data set. Astrophys. J. 473, 576-587 (1996).

8. Robitaille P-M.L., Abduljalil A.M., Kangarlu A., Zhang X., Yu Y., Burgess R., Bair S., Noa P., Yang L., Zhu H., Palmer B., Jiang Z.,Chakeres D.M., and Spigos D. (1998) Human Magnetic Resonance Imaging at Eight Tesla. NMR Biomed. 11, 263-265.

9. Robitaille, P-M.L. Magnetic Resonance Imaging and Spectroscopy at Very High Fields: A Step Towards 8 Tesla in "Proceedings of Physical Phenonema at High Magnetic Fields-III (Zachary Fisk, Lev Gor'kov, David Meltzer and Robert Schrieffer, eds), World Scientific, London, in press (1999), 421-426.

First Presented at the APS NW Section meeting in Seattle (May 2001)

Published Electronically on June 23rd, 2001.
Revised March 15, 2002