Zachor and Shamor and the Wave-Particle Duality

In Parshat Va’etchanan, among other major favorite highlights and features, we read the second appearance of the Ten Commandments. It is no secret that there are easily noticeable differences between the text of the Commandments here (Deut. Ch. 5) and their first appearance in Exodus (Ch. 20.) Perhaps the most famous of these textual differences (due, surely in part, thanks to its appearance in Lecha Dodi which gets it mentioned every Friday evening) occurs in the fourth commandment: the Sabbath.

In Exodus 20:8:

Remember the sabbath day and keep it holy.                                        זָכ֛וֹר֩ אֶת־י֥֨וֹם הַשַּׁבָּ֖֜ת לְקַדְּשֽׁ֗וֹ

While in Deuteronomy 5:12:

שָׁמ֣֛וֹר אֶת־י֥וֹם֩ הַשַׁבָּ֖֨ת לְקַדְּשׁ֑֜וֹ כַּאֲשֶׁ֥ר צִוְּךָ֖֣ ה’ אֱ-לֹהֶֽ֗יךָ

Guard [alt. “Observe” or “Keep”] the sabbath day and keep it holy, as the LORD your God has commanded you.

The rabbis of the Talmud noticed this dichotomy long ago, of course.

With respect to actual Jewish law, they explain that the two words are distinct to categorize: “Remember” – zachor – refers to the positive mitzvot of shabbat (e.g. kiddush, enjoying three meals, etc.) and “Guard” – shamor – refers to the prohibitions of shabbat (i.e. work.)

But the rabbis also go beyond just categorizing. Although there are two versions in the texts, they both narrate the same event, which only happened once! Which one was actually said by God at Mt. Sinai, “Remember” or “Guard”? They explained it as both versions being the reality:

ראש השנה דף כז,א

ותרי קלי מי משתמעי והתניא זכור ושמור בדיבור אחד נאמרו מה שאין הפה יכולה לדבר ואין האוזן יכולה לשמוע

b. Rosh Hashanah 27a:

But can two distinct sounds be heard at once? Has it not been taught: ‘”Remember” and “observe” were spoken in a single utterance, something that is impossible for the mouth to speak and impossible for the ear to hear’?

The rabbis explain that God miraculously spoke both words — “Remember” and “observe” — simultaneously, something that seems physically impossible, at least for a human. Likewise, the assembled Israelites at Mt. Sinai all simultaneously heard (distinctly and clearly) both words, which also seems physically impossible.


However, despite this seeming to be physically impossible, to those familiar with modern physics, it may sound strangely analogous to a well established principle – which likewise seems completely counter-intuitive to the human mind – known as the Wave Particle Duality. This idea in quantum mechanics essentially says that particles are waves and waves are particles – sometimes.

This bears some explanation, of course. In the 19th century, scientists came to the understanding that light is a wave, and behaves according to equations that describe the propagation of waves (I’ll spare you the equations. You’re welcome!)

In 1801, Thomas Young did a famous classic experiment, known everafter as “Young’s Double Slit Experiment”, that demonstrated light’s wave nature: Waves (in general) have peaks and troughs and if two waves cross, they can interfere with each other by adding or subtracting the peaks and troughs. So if two waves have the same wavelength, i.e. the distance between their peaks (or troughs), they will have double the intensity when peaks add up and none at points where a peak and a trough add/subtract to make zero intensity. Young demonstrated this by shining light through double pinholes and observing the pattern of interference “fringes” that was produced on a screen.

Diagram of Young’s Double Slit Experiment (left) and the pattern produced (right)

Around the end of the nineteenth century, scientists began to make discoveries about subatomic particles that make up ordinary atoms, among them the electron. J. J. Thompson is credited with discovering the particle now known as the electron by experiments he conducted in 1897. Electrons are subatomic particles about 1000 times less massive than a single hydrogen atom (which usually consists of one proton and one electron) that are negative in electric charge. More colloquially, they make up electricity, flowing through wires and appliances that we use constantly in the modern world.

In the years following that discovery, much scientific attention was focused on these particles. One phenomenon which was difficult for scientists to explain was the Photoelectric Effect: If a light was shined on a(n appropriate) piece of metal, it produced an electric current, i.e. it emitted electrons which then flowed through a wire. This effect might be powering your home right now, if you have solar power panels providing your electricity. What happens, in brief, is that the electrons in atoms absorb energy from light, and once they have enough extra energy can break away from their atoms.

Diagram of the Photoelectic Effect: Light (in red) energizes electrons in the metal plate and ejects them.

However, the puzzling part of this phenomenon was that making the light brighter did not make the emitted electrons more energetic (but produced more of them), but changing the frequency (i.e. color or wavelength) of the incident light could make the electrons more energetic.

In 1905, Albert Einstein explained the Photoelectric Effect with a radical idea: That light was also quantized – i.e. came in specific discrete quantities. This essentially means that light is also a particle! We now call particles of light photons. Einstein explained that each photon had an energy proportional to its frequency:

E = h × f

where E is the energy and f the frequency. The constant “h” is known as Planck’s constant, having been discovered slightly before Einstein by Max Planck in his explanation of “Black-body Radiation.” (We’ll save that for another time…) When electrons absorb energy from photons, it can only be in those discrete quantities, which, for each photon, depend on its frequency. Although his Theory of Relativity may be more famous, this was the work that won Einstein the Nobel Prize (but not until 1921.) The radical idea that light was a particle, was difficult to explain according to classical (i.e. 19th century) physics, which had proven that light was a wave! But subsequent research continued to back it up.

What’s more, over the next decades, (quantum) physicists discovered that the reverse was also true: that particles behave like waves in many experiments!

In 1924 Louis deBroglie explained that matter (i.e. particles) also have a wavelength! This is expressed as λ= h / p, where p is the momentum of a particle (=mass times velocity), λ is the wavelength (now known as the “deBroglie wavelength”) and h is again the Planck constant.

One corroborating experiment of this idea is an updated version of the double-slit experiment that Young used to demonstrate that light is a wave: it can also be done (with 20th century technology) to show that electrons (and other particles) are waves!

What is more, with more recent technology, scientists can repeat Young’s experiment with a single photon going through the slits one at a time – and it still produces the wave-based interference pattern!

So now we know that waves are particles and particles are waves! How can this be? Sometimes, depending on the experiment, we measure behavior like one and sometimes like the other. But both are true! This is (in brief) the Wave-Particle Duality. Everything – all matter and energy in the Universe – is both wave and particle at the same time, however impossibly paradoxical that seems to us!

The idea of such a counter-intuitive paradox where both are true can provide a valuable lesson in studying Torah.

Zachor and Shamor“Remember” and “observe” – both true, both real, both spoken. They are two aspects of one Divine utterance. They are two different aspects of the shabbat experience.

Take another example, from the first two chapters of Genesis: There are two creation narratives, which, at least on the surface, seem quite different. But they are both true! (See Rav J.B. Soloveitchik’s awesome essay Lonely Man of Faith for more on that!)

As Bible students and scholars know, there are many such seemingly contradictory texts in the Torah. Explanations abound; some for limited specific instances or examples, others more general. The rabbis of the Talmud were well aware of these, and loved to expound on them.

In the Talmud Yerushalmi, we find a more comprehensive version of the “Zachor and Shamor” idea:

תלמוד ירושלמי – מסכת נדרים פרק ג הלכה ב, דף ט

דברים ה) שוא (שמות כ) ושקר שניהם נאמרו בדיבור אחד מה שאי איפשר לפה לומר ולא לאוזן לשמוע. (שם) זכור (דברים ה) ושמור שניהם בדבור אחד נאמרו מה שאי אפשר לפה לומר ולא לאוזן לשמוע. (שמות לא) מחלליה מות יומת (במדבר כח) ושני כבשים בני שנה תמימים נאמרו בדיבור אחד מה שאי אפשר לפה לומר ולא לאוזן לשמוע. (ויקרא יח) ערות אשת אחיך לא תגלה. (דברים כה) יבמה יבא עליה שניהן נאמרו בדיבור אחד. (במדבר לו) ולא תסוב נחלת בני ישראל ממטה למטה אחר. (במדבר לו) וכל בת יורשת נחלה שניהן נאמרו בדיבור אחד. (דברים כב) גדילים תעשה לך. (שם) לא תלבש שעטנז שניהן בדיבור אחד נאמרו. וכן הוא אומר (תהילים סב) אחת דבר א-ליהם בדיבור שתים זו שמענו. וכתיב (ירמיהו כג) הלא כה דברי כאש נאם ה’ וכפטיש יפוצץ סלע.

p. Nedarim 3:2, (p. 9):

“False” (Deut. 5) and “Lying” (Ex. 20) [i.e. in the 9th Commandment] both were spoken in a single utterance, something that is impossible for the mouth to speak and impossible for the ear to hear.

‘”Remember” and “observe” both were spoken in a single utterance, something that is impossible for the mouth to speak and impossible for the ear to hear.

“Those who profane it [i.e. shabbat] shall die” (Ex. 31) and “Two unblemished one year old sheep” (Num. 28) were spoken in a single utterance, something that is impossible for the mouth to speak and impossible for the ear to hear.

“Do not uncover your brother’s wife’s nakedness” (Lev. 18) and “Her brother-in-law [i.e. after the husband/brother’s death] shall come unto her” (Deut. 25) both were spoken in a single utterance.

“And the [inherited] portions of land of the Children of Israel shall not be turned from one tribe to another tribe” (Num. 36) and “Every daughter who inherits a portions of land” (ibid.) both were spoken in a single utterance.

“Make tassels [i.e. tzitzit] for yourselves” (Deut. 22) and “Do not wear shaatnez” (ibid) both were spoken in a single utterance.

And thus it says (Psalms 62) “One spoke God” – in utterance – “two of these we heard.” And it is written (Jeremiah 23) “Thus, is not my word like fire, saith the Lord, and like a hammer that shatters rock?”

This amazing text requires some explanation. The first example of a pair where “both were spoken in a single utterance” (similar to the second example of “Remember” and “Guard”) is also from the Ten Commandments (the ninth), and again where the parallel narratives have a (slightly) different word. So far, so good; pretty clear, same idea as above.

The other examples listed as pairs of verses where “both were spoken in a single utterance” however, are not all so obvious. They are examples of pairs of mitzvot that seem contradictory, not just a single word switched. Summarized in brief they are:

  • Not profaning the Sabbath vs. offering the required two sheep as sacrifices (which involves slaughtering, a prohibited action on Sabbath.)
  • The prohibition of having sex with one’s brother’s wife vs. the command of levirate marriage (if the brother dies childless.)
  • Tribal inheritance shall not pass to another tribe vs. daughters inheriting from their fathers (and possibly marrying someone from another tribe.)
  • Making tzitzit (of wool) on a garment (even a linen garment) vs. not mixing wool and linen.

Now, these are not particularly difficult “contradictions” to explain. The Torah itself explicitly explained the solution in the case of inheritance. (See Num. 36) The general Jewish legal principle that a positive command trumps a negative prohibition also resolves most of them.

I would suggest that the rabbis are trying to illustrate an idea rather than just point to specific contradictions. They are showing us that the Torah is full of “contradictory” dualities throughout its verses, narratives and commandments – but the two contradictory things are both true. Just like we now know is true for everything in the physical world, that everything is both particle and wave. They can both be true, because God is able to “utter” two contradictory things, unlike the human mouth and unlike human senses can perceive.

Perhaps another featured part of Va’etchanan can also shed some light on this. There is specifically one “thing” that is not a duality: God! As found later in the parshah in the Shema (Deut 6:4):

Hear, O Israel! The LORD is our God, the LORD is one.              שְׁמַ֖ע יִשְׂרָאֵ֑ל ה’ אֱ-לֹהֵ֖ינוּ ה’ אֶחָֽד׃

In all the universe, including the Torah, God’s unity is unique. Everything else is in our reality is part of duality.

God is uniquely one, but as the sugya finishes off God’s word is like fire and like a rock; like energy and solid matter; both wave and particle – full of seemingly contradictory duality, but all true.

The Yerushalmi is telling us that not only in the two versions of the Ten Commandments with zachor and shamor do we find such duality. God’s words are always multifaceted; like the rock broken by the hammer, there are always (seventy) multiple facets to the words of the Torah, seemingly contradictory but all true. And all coming from the same “rock” – who is One!


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