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Relativity of Manna
This is the thing which the Eternal hath commanded: ‘Gather ye of it every man according to his eating; an omer a head, according to the number of your persons, shall ye take it, every man for them that are in his tent.’ And the children of Israel did so, and gathered some more, some less. And when they did mete it with an omer, he that gathered much had nothing over, and he that gathered little had no lack; they gathered every man according to his eating. (Exodus 1618)
In the desert, Jewish people were given manna—one omer[1] (Biblical measure) per member of the household. Rashi explains:
Some gathered [too] much [manna] and some gathered [too] little, but when they came home, they measured with an omer, each one what he had gathered, and they found that the one who had gathered [too] much had not exceeded an omer for each person who was in his tent, and the one who had gathered [too] little did not find less than an omer for each person. This was a great miracle that occurred with it [the manna].
Some gathered more, some less… But when they measured, each got exactly one omer of manna. How can this be? Suppose, someone first gathered the amount of omer and then, decided to work some more and gathered an additional amount. Normally, we would expect that the total amount gathered would be the sum of the omer and the additional amount. Yet, this is not what happened—when the gathered manna was measured, it was exactly one omer. Similarly, if one worked less and gather an amount some quantity less than the omer, he did not bring home the difference between the omer and that lacking quantity, but exactly one omer. How can it be? This fact one can easily explained if we modify the formula for the amount of manna gathered but the Lorentz factor.[2]
Those who studied Special Theory of Relativity will immediately notice the uncanny resemblance of the formula for the addition of two quantities of manna[3] to the formula for addition of velocities.[4] Indeed, the analogy is clear. The velocity of light in the vacuum is a universal constant. That means that if one shoots a laser beam from a rocket flying at half the speed of light, the velocity of photons will not increase by 50%. In fact, when we measure the velocity of photons in that beam of light, we will find they all moving with the same constant velocity c—the velocity of light in the vacuum. Similarly, if one shoots a laser beam from a rocket flying at the opposite direction at half the speed of light, the velocity of photons will not decrease by 50%. It will still be c—velocity of light in the vacuum.
The same is with manna. Those who worked more or worked less—when measured, everyone gathered the same amount, one omer of manna. The omer of manna is also a universal constant just as the velocity of light in the vacuum. Perhaps this is why one omer of manna was preserved for generations to come—for sure, to remind us of the miracle in the Sinai desert—but also, perhaps, to teach us the concept of relativity.
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Endnotes:
[1] Omer is a biblical measure used for grains and other dry goods. In the biblical system of weights and measures, One omer is equal to one tenth of an ephah. An ephah is equal to 72 logs. One log is equal to the Sumerian mina, which is defined as one sixtieth of a maris. Therefore, one omer was equal to twelve hundredth of a maris. In contemporary units, the value of the omer differs slightly according to various opinions. Thus, omer is 2.16 liter according to Maimonides, 2.49 liter according to Rabbi Abraham Chaim Noeh, approximately 3 liters according to the Tzemach Tzedek, and 4.3 litters according to the Chazon Ish.
[2] The Lorentz factor is a quantity expressing how much the measurements of time, length, and other physical properties change for an object while that object is moving. It appears in several expressions in special theory of relativity and was derived by the Dutch physicist Hendrik Lorentz. The Lorentz factor is written as γ = 1/√(1β^{2}), β = v/c, where v is the relative velocity, and c is the speed of light in a vacuum. In our case, β = m/o, where m is an extra amount of manna gathered in addition to (or less than) omer, and o is the omer.
[3] This formula can be written as m’ = (m_{1 }+ m_{2})/(1+ m_{1}m_{2}/o^{2}), where m_{1 }is the amount of manna collected initially, m_{2} is the additional amount of manna, m’ is the total amount of manna, and o is the omer. This formula can be easily derived from postulating the constancy of the omer (based on the biblical principle that nobody gather more or less than the omer): (o – m’)/(o + m’) = [(o – m_{2})/( o + m_{2})] [(o – m_{1})/( o + m_{1})].
[4] This formula is v’ = (v_{1 }+ v_{2})/(1+ v_{1}v_{2}/c^{2}). This formula is derived from a similar postulate of the constancy of the speed of lite c in the vacuum.
Originally published on QuantumTorah.com on 01/24/2016.
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