An article in March/ April 2018 MIT Technology Review magazine, The race to invent the artificial leaf, is an excerpt from a book by Varun Sivaram called Taming the Sun. The excerpt mentions the work of two scientists, Nathan Lewis at Caltech and Daniel Nocera at Harvard University, on creating an artificial leaf. If as it seems the 4/3 law partly explains the efficiency of photosynthesis, would connecting the 4/3 law be of any assistance in dealing with the practical hurdles to a commercially viable artificial photosynthesis?
Do you mean that the photosynthetic or metabolic rate is proportional to 3/4 of the mass of the leaf?
Dr. Andrew Paul McKenzie Pegman
No, though that is a good question and my question should have been clearer. The relationship appears to be that one dimensional energy distribution in the 3 dimensional plant (total 4 dim) has 4 degrees of freedom (DF) while the recipient part of the plant has mass proportional to volume: 3 dim. Therefore the ratio of DF of transmission system to recipient system (the ratio of their respective entropies in effect) is 4/3. In early February 2018 I posted an article about this question about photosynthesis on RG. George Gamow in a 1961 article mentions this in an incidental remark in his paper (cited in my RG article on photosynthesis). The efficiency (if the 4/3 law applies) arises this way: the same energy that has 4 DF in the 4 dim system has 3 DF in the 3 dim system with zero loss of energy, because the same energy occurs simultaneously in the 2 co-existing reference frames; the reference frames are different but the energy is the same. Additionally, what seems to occur is that there is a kind of pressure: the pressure of energy residing in 4 dimensions trying to "push" into only 3 dimensions, which creates "dimensional pressure", leading to the 4/3 ratio. I wonder, though I am not sure how to frame the problem, whether the 4/3 dimensional ratio somehow relates to or accounts for our concept of energy, since the 4/3 law is scale invariant and universal.
Thank you for your question and best wishes.
Bob Shour
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