The Fifth Force

Now, therefore, write ye this song for you, and teach thou it the children of Israel.” (Deut. 31:19)

The four known fundamental forces are: gravitational force, electromagnetic force, strong (nuclear) force, and the weak force (beta decay). Newton first described the gravitational force in his famous universal law of gravity. Today, we use Einstein’s General Theory of Relativity to describe gravitation fields. Electromagnetism was described in the 19 c. by Faraday and Maxwell. Strong and week forces were discovered much later, in the second half of the 20 c. Since Albert Einstein started a search for unified field theory, unsuccessfully trying to unify (describe by a single theory) gravity and electromagnetism, the quest for a unified field theory – the “Theory of Everything” – became the holy grail of theoretical physics. Strong and week forces were unified in quantum chromodynamics and electromagnetism was unified with week forces as electro-weak forces. Today the Standard Model successfully describes in a single model three of the four forces: electromagnetic, strong, and weak. Only gravity resists unification, because of the difficulty in formulating the quantum theory of gravity. Presently, the string theory is considered the leading candidate for the Theory of Everything.

The four fundamental forces correspond to four letters of the Tetragrammaton Y‑H‑W‑H:

The letter Yud is a dot, akin to a nucleus of an atom. Hence the nuclear (strong) force is associated with the letter Yud (י).  The letter Heh (ה) is an expansion of this dot in all four directions – a dot “explodes” as it were – hence this letter is associated with the beta decay (weak force), because nuclear decay can be pictured as an “explosion” of the nucleus. The letter Waw (sometimes also spelled in English as “vav”) is a vertical line. Since the electromagnetic force is a vector force (the strength of the electromagnetic field is described by a vector – a mathematical quantity that has both magnitude and direction and depicted as an arrow), it is associated with the letter Waw. The last letter is the letter Heh (ה). The last Heh represents sephirah of Malchut. Earth is also Malchut. Before the universal law of gravity was discovered by Isaac Newton, gravity was associated with Earth (the force that causes everything to fall down on Earth). Malchut being a feminine sephirah – Nukva – is the “weakest” of the sephirot. So is gravity – the weakest of the four forces. Thus gravity is associated with the last letter Heh.

The belief in the four fundamental forces has been the cornerstone of theoretical physics for a number of decades.  …Until people start talking about the fifth force. People have very different ideas of what that mysterious fifth force might be.

One theory is Brans–Dicke theory of gravitation, developed by Robert H. Dicke and Carl Brans in 1961. This is a scalar-tensor theory of gravity, which replaces gravitational constant G with a scalar field Ø (1/G = Ø). Scalar field Ø (scalar, unlike vector, has no direction – only magnitude) plays the role of the fifth force. Brans-Dicke theory predicts the same effects on the scale of the Solar system and, therefore, on this scale is not distinguishable from Einstein’s general relativity, with which it competes. Experiments are underway to test the strong principle of equivalence that may distinguish between Einstein’s theory and Brans-Dicke theory. (In 1980, in my doctoral dissertation, Towards a Covariant Theory of Gravity, I developed a generalization of General Relativity Theory, in which I introduced a metric-affine space where in addition to the metric, there is an independent affine connection, instead of a scalar field, that provides even more degrees of freedom and can likewise be viewed as a source of the fifth force, which I interpreted as an inertial force.)

Quintessence, which is a form of dark energy postulated to explain an accelerated rate of expansion of the universe, is another potential candidate for the fifth force. Unlike the cosmological constant, it is a scalar field. Quintessence comes from Latin quinta essentia, meaning the fifth element (in addition to four elements – fire, air, water, earth – which fills the universe like an aether.

Kaluza-Klein theory uses five-dimensional geometry that affords an extra degree of freedom and, therefore, can be viewed as a source of the fifth force. This approach is near and dear to my heart because, as a teenager, unaware of Kaluza-Klein theory, I developed a naïve version of five-dimensional geometry only to be told later that I was about 50 years late… Unlike Kaluza and Klein, however, I used energy/information as the fifth dimension, which I still consider a better candidate for the fifth dimension. In any event, whatever the nature of the fifth dimension, the extra degree of freedom can lead to the fifth force.

Supergravity and string theory also predicts a fifth force, which is a Yukawa force (a generalization of the inverse square law). Any deviation from the inverse square law, found experimentally, would indicate the presence of the Yukawa force – the fifth force.

Despite many reported “sightings” of the fifth force, these results could never be replicated and the fifth force remains a hypothetical force still to be discovered in nature.

If the fifth force really exists in addition to four known fundamental forces, what are we to do with our table above mapping each of the four fundamental forces on the letters of the Tetragrammaton? The answer comes from the Arizal’s commentary on the Torah portion Veyelech that we read this Shabbat. Commenting on the verse, “Now, therefore, write ye this song for you, and teach thou it the children of Israel.” (Deut. 31:19) in Taamei HaMitzvot, the Arizal writes:

“Know that it is necessary to have in mind that the Five Books of Moses correspond to the five partzufim: The Book of Geneses corresponds to the apex or the upper thorn of the yud (י) of the name Havayah (Y‑H‑W‑H) and the partzuf Arich Anpin. The Book of Exodus corresponds to the yud itself and partuf Abba. The Book of Leviticus corresponds to the first hei (ה) and partzuf Ima. The Book of Numbers corresponds to the Waw (ו) and supernal number of Israelites. The Book of Deuteronomy, known as the ‘repetition of the Torah,’ reiterates and includes everything that was in the preceding books, and corresponds to the final hei and partzuf Nukva.”

In Kabbalah, partzuf (pl. partzufim) is a Divine Persona (visage or configurations) of the 10 Divine Emanations – sephirot. Whereas a sephirah is a specific Divine emanation, a monochrome light of a particular color, as it were, a partzuf is a configuration of all ten sephirot interincluded in each other and harmoniously interacting with each other, although a particular sephirah or a number of sephirot dominates. Thus, Arich Anpin (Long Face or Macroprosopus) is partzuf of Keter. Abba (Father) is the male partzuf of Chochmah. Imma (Mother) is the female partzuf of Binah. Zeer Anpin (Small Face or Microprosopus) is the male partzuf combining six lower sephirot: Chesed, Gevurah, Tiferet, Netzach, Hod and Yisod. It is also identified with Israel. Nukvah is the female partzuf of Malchut.

Based on this Arizal, we can map fundamental forces over the letters of the Tetragrammaton, Five Books of Moses and five partzufim as follows:

Based on this table, we should have called the fifth force the “zero force” as it precedes the other four fundamental forces.

Although despite many attempts, the fifth force has not been discovered yet, based on the Arizal’s commentary, I will go out on a limb and make a prediction that it will ultimately be discovered.