Bioelectromagnetics 22:200^204 (2001)
Why Arguments Based on Photon Energy may be Highly Misleading for Power Line Frequency Electromagnetic Fields Arnt Inge Vistnes* and Kristoffer GjÎtterud Department of Physics, University of Oslo, Oslo, Norway When evaluating possible mechanisms by which low frequency electromagnetic ®elds may have a biological effect, arguments based on photon energy have often been used in a misleading way. For visible light the concept of photons has proved to be very useful in explaining experimental ®ndings. However, the concept of photons cannot be used without major modi®cations in describing phenomena related to near ®eld problems at power frequency (50 or 60 Hz) electric and magnetic ®elds. For this regime, the photon description is very complex. A very high number of highly coherent photons must be used in a quantum electrodynamic description of low frequency electromagnetic ®eld phenomena. Thus, one-photon interaction descriptions must be replaced by multiple-photon interaction formalism. However, at low frequencies, a classical electromagnetic ®eld description is far more useful than quantum electrodynamics. There is in principle no difference in how much energy an electron can pick up from a low frequency electric ®eld as compared to from a high frequency photon. Thus, the total gain in energy is not limited to the energy carried by a single photon, which is E hn, where h is Planck's constant and n is the frequency of the radiation. However, the time scale of the primary event in a mechanism of action is very different for ionizing radiation compared to power line frequency ®elds. The advice is to consider the time scale given by the inverse of the frequency of the ®elds, rather than photon energy, when one use physics as a guidance in evaluating possible mechanisms for biological effects from low frequency electromagnetic ®elds. Bioelectromagnetics 22:200±204, 2001. ß 2001 Wiley-Liss, Inc. Key words: classical ®elds; quantum electrodynamics; near ®eld photons; coherent photons
INTRODUCTION Basic physics can give useful guidance in evaluating possible mechanisms by which low frequency electromagnetic ®elds may have a biological effect. On the contrary, physics used in an improper manner may mislead to wrong conclusions. The purpose of this paper is to present a kind of visual picture that may help to ``explain'' why one particular concept in physics should not be used when discussing low frequency electromagnetic ®elds and biological effects. In what way may low frequency electromagnetic ®elds yield a biological effect? Both low frequency electric and magnetic ®elds lead to induced electric currents in the body. However, the currents are small, and the total energy absorption rate is far less than the metabolic rate [Seto and Cronvich, 1979]. Thus, the low frequency ®elds are highly unlikely to yield a thermal effect. But that does not disprove a possible biological effect. Even though ionizing radiation from radioactive sources may give a quite negligible thermal effect, they may result in severe biological damage. We explain ß 2001Wiley-Liss, Inc.
this by using the concept of photonsÐsmall energy packages that may deliver enough energy locally so that chemical bonds may be broken and molecules ionized. In physics we learn that individual photons have an energy E given by the famous equation E hn, where h is Planck's constant and n is the frequency of the ``radiation.'' If we simply plug in frequencies, we may get a list like the one presented in Table 1 [see, e.g., Persson, 1997]. In order to ionize an atom or a molecule, a minimum energy of approximately 4 eV per electron is needed. This means that UV, X-rays, and g-radiation may ionize atoms or molecules, while visible light, infrared radiation, microwaves, and radio-frequency ÐÐÐÐÐ Ð Contract grant sponsor: Norwegian Research Council; Contract grant number: 130715/212. *Correspondence to: Arnt Inge Vistnes, Department of Physics, P.O. Box 1048, Blindern, N-0316 Oslo, Norway. E-mail:
[email protected] Received for review 21 October 1999; Final revision received 7 June 2000
Photon Energy Arguments TABLE 1. Photon Energy Contents for Various Forms of Energy Source X-rays (l 0.4 nm) UV light (l 200 nm) Visible light (l 450 nm) Radio frequency (GSM telephone, 900 MHz) Power line frequency (50 Hz)
Photon energy E 3.1 103 eV E 6.2 eV E 2.7 eV E 3.7 10ÿ6 eV E 2.1 10ÿ13 eV
waves ``do not ionize.'' Thus, we can discriminate between ``ionizing'' and ``nonionizing'' radiations. This chain of arguments seems ®ne at ®rst. However, a second thought reveals that it cannot be completely valid. We know that 50 Hz electric ®elds lead to ionization of molecules in air near most of the high voltage power lines, at least on rainy days (when there are drops on the conductors). The corona effect is nothing but ionization of molecules in the air. Even ``static'' electric ®elds, with a frequency very close to zero and a corresponding in®nitesimally small ``photon energy'', lead to a massive ionization of molecules in air into so-called ``ionizers'' used in electrostatic air ®lters or in the management of static electricity e.g., in printing machines. The fact that both UV and power frequency electric ®elds lead to ionization, demonstrates clearly that the concept of ``photon energy'' alone is not suf®cient to explain the experimental ®ndings. On the other hand, it is clear that ionization in the presence of UV and in the presence of 50 or 60 Hz electric ®elds, are based on quite different mechanisms. For UV, X-rays, and g-rays it seems reasonable to use a model where an energy package in one shot leads to a broken chemical bond and ionization. We can call this a direct ionization. For the corona effect on the other hand, charged particles (electrons) are accelerated in the electric ®eld so that they eventually gain high energy. When such a particle hits a molecule, it may have suf®cient energy to break a chemical bond. We may describe this as an indirect ionization. In biological tissue, charged particles such as electrons or ions may be accelerated by electric ®elds, but even the indirect ionization is unlikely to occur. The reason is partly that the mass density in tissue is much higher than in air, so that a charged particle will collide with particles/molecules so frequently that it will have too short a time to gain velocity. Furthermore, the strength of the electric ®eld is far too small to lead to a major acceleration. Are we then left with no possibility for any biological effect? By no means. We know that even low frequency electromagnetic ®elds can lead to very
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convincing biological effects like the ``magnetophosphenes'' described by Lùvsund and co-workers many years ago [Lùvsund et al., 1980] or other kinds of ``acute effects.'' The induced currents in the body lead to displacement of charges, but the human body is far more complex than a ``salt water bag'' model. The presence of biological membranes and various tissues with very different electrical parameters will lead to inhomogeneities in the charge distribution. This is partly re¯ected in the very high electric permittivity of biological tissue observed at low frequencies [Grimnes and Martinsen, 2000]. Thus, local voltage differences may be created across biological membranes that eventually may trigger nerve cellsÐaction potentials may be initialized as an indirect effect of the external ®eld. And that is the acute effect. What happens when the external ®eld is insuf®cient to create acute effects? This is the real challenge we are faced with. But in principle a biological effect is still possible, taking into account the mechanisms mentioned so far. WHY THE CONCEPT OF PHOTONS MAY LEAD TO MISCONCEPTIONS As discussed above, low frequency electromagnetic ®elds may result in both (indirect) ionization (as exempli®ed by the corona effect) and triggering of nerve activity, inspite of a quite negligible photon energy, as given by E hn. Why does the concept of photons mislead us so much in this case? The purpose of this paper is to present a ``visualization'' of the physics involved. The hope is that the incorrect use of photon energy arguments, with which we too often have been presented until now, when discussing possible biological effects of low frequency electromagnetic ®elds, will disappear. Quantum electrodynamics (QED) is the theory that gives the most comprehensive quantal description of the interaction between charged particles and electromagnetic radiation. The static interaction between charges is described as an exchange of virtual photons, including all possible polarizations (transverse, longitudinal, and timelike). The electromagnetic radiation is composed of a huge number of transverse photons whose amplitudes have highly correlated phases and are thus very coherent. The coherence is required if the quantum electrodynamic description is to correspond to the macroscopic ®elds described by classical electromagnetism. It should be pointed out, however, that the description of extremely low frequency electromagnetic ®elds in the near ®eld regime is extremely complicated, and it might even be that in some respects the theory is hitherto not fully
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explored for this frequency band. For electromagnetic radiation ful®lling the strength criterion,1 a description by classical electromagnetic ®elds is both suf®ciently accurate and practical. We want to illustrate one major difference between photons at frequencies corresponding to visible light and higher frequencies on one hand, and power frequency ®elds at 50 (or 60) Hz on the other hand. The demonstration is based on an estimate of the ``photon density'' under conditions that are not strictly physical, but even so, the results indicate a very important point. A photon can, according to quantum electrodynamics, not be described by a quantal wave function in coordinate space. As a consequence there is no meaning to localizing a photon to a region smaller in order of magnitude than a wavelength [Akhiezer and Berestetskii, 1965, p 11]. The minimum possible volume a photon may occupy is, therefore, of the order of l3 where l is the wavelength associated with a photon. The following rough estimations describe some common physical conditions: 1. Visible light: The ``radiation'' from the Sun reaching the upper atmosphere of the Earth. The irradiance or ¯ux is about 1.4 kW/m2, covering all visible light including some UV. 2a. Power frequency electric ®eld at the ground level beneath a high voltage power line: the electric ®eld is 10 kV/m and the frequency chosen is 50 Hz. 2b. Power frequency electric ®eld of 1 mV/m inside a human body, which may correspond to the ®eld in a human body exposed to an external electric ®eld e.g., from power lines. According to standard physics the energy density for the visible light from the Sun can be estimated by dividing the irradiance by the speed of light. Similarly, the time-averaged energy density U below the power line is given by U 12 "E2 where e is the electric permittivity and E is the effective electric ®eld. From this the density of photons, each with an energy of E hn, can be estimated. Finally, we estimate the number of photons inside a volume of the ÐÐÐÐÐ Ð 1 In a particular quantum mechanical model based on so-called ``oscillators,'' it can be shown that it is meaningful to treat the electromagnetic radiation ®eld classically electric ®eld p if the strength satisfy the criterion jEj hc="=
ct2 where the time interval over which the ®eld is averaged is of order of t 1=n where n is the frequency of the oscillators [Berestetskii et al., 1982 p 15]. From this it is clear that the static ®eld can always be treated classically. For 50 Hz the limiting value would be of the order 1:7 10ÿ21 V=m, which is the electric ®eld from a single electron at a distance of 930 km.
order of l3 where a photon may be localized. The results can then be summarized as follows: 1. The light from the Sun have a photon density of about 1013/m3 (combining all wavelengths in the spectrum) and the number of photons inside l3 is about 10ÿ6. 2a. The 50 Hz electric ®eld below the power line would have a photon density of about 1028/m3 and the number of photons inside l3 is about 1048. 2b. The 50 Hz electric ®eld inside a human body below a power line would have a photon density of about 1014/m3 and the number of photons inside l3 is about 1034. Notwithstanding the crudeness of these estimations, they nevertheless give a hint that there are substantial reasons to expect that physics may be very different for visible light and electromagnetic waves at 50 Hz. For visible light, the photons come as individual packages with plenty of empty room between the photons, and one-photon interactions are the normal situation. At 50 Hz an enormous number of photons are present simultaneously at every point in space, even at the realistic ®eld strength found in a human body, and multiple-photon interactions will be common. At 50 Hz there are well-de®ned electromagnetic ®elds with well-de®ned phases. As we have seen from the point about the photons the classical ®eld results from a coherent superposition of quantal amplitudes of a great number of photons. It can be shown that the more precise the de®nition of the phase of the classical ®eld, the less precise is the number of photons involved. There is a quantal uncertainty relation giving the mutual dependence of the precision of the phase and the number of photons that does not involve the Planck constant.2 Because of the complexity, both mathematical and conceptual, of the quantum electrodynamic description of near ®eld extremely low frequency electromagnetic ®eld phenomena, it is highly advisable to base discussions of 50 Hz ®eld effects on classical electrodynamic ®elds rather than on photons.1 The ionization of air molecules at corona discharges is then easily understood as an interaction of charges with a strong electric ®eld. Thus, a molecule or an electron can eventually gain high enough kinetic energy in the electric ®eld so that a molecule, with which it collides, ÐÐÐÐÐ Ð 2 It should be remarked that the interference seen in Young's double slit experiment at low intensity also involves coherence in the relative phases of the individual photons. But this coherence should be distinguished from the coherence at work in establishing a classical electromagnetic ®eld.
Photon Energy Arguments
can be ionized. This can create an avalanche leading to a corona discharge [Encyclopaedic Dictionary of Physics, 1961, p 435]. If the same phenomenon would be explained by photons in a quantum electrodynamical theory, the description would be almost impenetrable due to complexity. This example demonstrates that the concept of photons is not useful in this regime. And not only is it of no bene®t, it can even lead to misconceptions and arguments that assume that interactions are based on one-photon reactions only. FURTHER CONSIDERATIONS A main difference between ionizing radiation and low frequency electromagnetic ®elds is, in our view, not the energy that a system can pick up from the radiation, but the difference in time-scale of the possible mechanisms. In order to ionize a hydrogen atom, one needs an energy of at least 13.6 eV, corresponding to the absorption of a photon with a frequency of at least 3.3 1015 Hz. In a classical model the revolution frequency of an electron in a circular motion around the proton in a hydrogen atom at the Bohr radius is estimated to be about 1.2 1016 Hz. This is of the order of the frequency of a photon required to ionize the atom. Thus the inverse frequency may be used as a rough measure of the time-scale characteristic for ionizing atoms or molecules by absorption of photons. If the electric ®eld component changes direction in a time-scale much shorter than the time-scale associated with the electron's movement in the atom/ molecule, the electric ®eld will only lead to a timedependent polarization of a neutral atom/molecule, or it may lead to a macroscopic displacement of (more or less) free charges. The polarization of neutral atoms/ molecules is not likely to destroy the atom/molecule. That will only happen if the electric ®eld is suf®ciently strong so that it leads to dielectric breakdown, which for air happens for a ®eld greater than approximately 3 106 V/m and for many materials a much higher ®eld. On the other hand, the polarization may add up to macroscopically important charge separations and apparent surface charges at various interfaces. The macroscopic separation of free charges may lead to changes in electrical potentials that certainly can lead to a biological effect. It is well-known that exposure to a strong 50 Hz magnetic ®eld leads to activation of nerve ®bres, for example in ``magneto-phosphenes.'' We think it might be wise to have the approximately 20 ms time period in mind when one looks for possible processes where an extremely low frequency ®eld may have a biological effect. It is not the energy, but the time aspect that might turn out to be the best
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guidance in evaluating possible mechanisms whereby low frequency electromagnetic ®elds may have a biological effect. SUMMARY This paper is written as a reaction to the use of photon energy arguments when discussing possible effects of low frequency electromagnetic ®elds. Some take the very small photon energy as a proof that 50 or 60 Hz electromagnetic ®elds cannot cause any biological effects at all. The photon energy, however, does not tell the whole story, but we have not yet seen any good explanation for this in the literature. In a review paper by Valberg and co-workers [1997], a subchapter is entitled ``60 Hz EMF energy cannot break chemical bonds.'' The authors apply photon energy arguments a lot. On the other hand, they write that photon energy is not relevant to interactions in the ``near ®eld'' of sources. However, they fail, to state and explain that photon energies are not relevant, even for ``radiative'' interactions, at these frequencies. The purpose of the present paper is to give an explanation of this. A system like an electron may pick up just as much energy from a power frequency electromagnetic ®eld as from ionizing radiation. This may in the ®rst place seem to contradict the quantum mechanical concept of photon energy, but on second thought it does not. The key to solving the apparent contradiction is to remember that energy is exchanged by ``independent'' (noncoherent) single photons at visible light and higher frequencies. At radio waves and lower frequencies, however, energy is exchanged by a very large number of highly coherent photons that act together (additively) in a constructive way, which is manifested as classical electromagnetic ®elds. There is in principle no difference in how much energy an electron can pick up from a low frequency electric ®eld as compared to a high frequency photon. There are, however, very different time-scales associated with ionizing and power-line frequencies. Ionizing radiation may lead to electron expulsions directly from an uncharged atom/molecule, while that is highly improbable (at least as a primary event) for low frequency ®elds. On the other hand, low frequency ®elds may lead to polarization of neutral atoms/molecules, and the polarization may lead to an apparent surface charge at interfaces. Low frequency ®elds may also lead to separation of (more or less) free charges, e.g., ions in the intercellular ¯uid. The corresponding electric currents may set up electric potentials that may initiate action potentials in nerve ®bers or stimulate other electrically dependent processes. Thus, it is
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important to appreciate the importance of the time scale given by the inverse of the frequency when we seek explanations for various observed biological effects caused by low frequency electromagnetic ®elds. Power line and radio frequency ®elds should be treated as classical electromagnetic ®elds rather than as ®eld quanta. Classical electromagnetism can handle the difference between ``near-®eld'' and ``far-®eld'' and the difference between static ®elds and timevarying ®elds. On the other hand, at visible light and higher frequencies, a quantal description cannot be avoided. ACKNOWLEDGMENTS One of the authors (AIV) thanks The Norwegian Research Council (contract 130715/212) for ®nancial support to this work.
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