Limits on Space-Time

The dimensions of space and time stand as foundations of our physical world. But we discover that these were dramatically altered in the Beis Hamikdash.

The Aron Hakodesh housed within the Kodesh Hakodoshim experienced neither the dimension of space or of time. In the words of the Gemara, “Aron ein lo middah — the Aron was not subject to any measure.”¹¹ In other words, the 5.625-cubic-amos volume of the Aron occupied zero space.

Similarly, the Rogatchover Gaon states that the dimension of time was also nonoperative in and around the Aron.¹² This idea explains the inclusion inside the Aron of both the flask of mahn and the almond blossom on the Mateh Aharon. These were preserved like an everlasting time-capsule, totally transcending the dimension of time.

In the Heichal, further away from the Kodesh Hakodoshim, we likewise see the weakened impact of the workings of natural time and space. Here time was not completely annulled but rather dilated. In other words, time slows down and space can hold more than its usual volume. Regarding time: the Show Bread — Lechem Hapanim — remained warm and fresh for an entire week,¹³ and the Western Light — Ner Maaravi — remained alight for the entire day, despite having only enough oil for half that. Rav Yitzchak Isaac Chaver¹⁴ highlights that next to the Heichal, both in the Chatzer (courtyard) and further afield in Yerushalayim, we see a “space dilation” — mu’at machzik merubah — a large mass was able to miraculously fit into a small volume. This is famously noted in Pirkei Avos:¹⁵ “they stood cramped but prostrated with ample space,” and “no one complained of insufficient lodging space in Yerushalayim.”

Mishkan as Microcosm

If we analyze the Zohar we quoted above, we find a fundamental relationship between the form and structure of both the upper and lower worlds together with the Mishkan. In fact, Rav Saadiah Gaon,¹⁶ among many others, writes that “kulam hiskimu,” everybody agrees, that the Mishkan is a microcosm — a faithful detailed representation in miniature — of the macrocosm, the universe.

This axiom demands that those very entities, structures, and forms that exist in spiritual form in the upper worlds will also be found in a more physical form in our lower world, the universe, and vice versa. Likewise, there will also be parallel representations found in the Mishkan.

Let us analyze the unusual miracles described above in greater depth and suggest some deeper meaning behind them in the light of modern science.

Black Holes and Trampolines

In February 2016, over 1,000 scientists announced that they had detected the existence of “gravitational waves” using the brand-new Laser Interferometer Gravitational-wave Observatory (LIGO). In order to explain why this breakthrough was so momentous, we need to first understand the concept of a “black hole.”

In 1915, Albert Einstein published his General Theory of Relativity. Here he explained that space and time are not static background objects like the stage of a play upon which actors perform. Rather, space and time are dynamic and can change and contort into different shapes like a flexible fabric. This principle, which has been scientifically proven beyond reasonable doubt, is far removed from our normal sense of space-time.¹⁷

Let us explain the concept using the following simple illustration. Imagine the elastic fabric of a trampoline. It is flat and smooth if no one is on it. But when a child starts bouncing on it, the trampoline’s elastic fabric will be stretched into a different shape. Similarly, space-time becomes distorted by the objects “sitting” on it. This distortion gives rise to what we perceive as the force of gravity. Incredibly, this affects the shape and characteristics of the space-time dimensions.

It turns out, based on Einstein’s formula, that it is possible for there to be places where extreme conditions prevail, and space and time stop entirely. These are known as “black holes.” In our aforementioned trampoline metaphor, a black hole would be in the place where a supersized Japanese sumo wrestler jumps, causing huge waves in the fabric until it eventually ruptures completely beneath him. At the point of the tear, time and space cease to be, entirely.

On September 14, 2015, the highly accurate LIGO was able to measure a change in the space dimension of one million-million-millionth of a centimeter. This was due to gravitational waves (like waves on the “trampoline” of space-time) emanating from a cosmic clash of two black holes so violent that its shock waves rippled through the fabric of space and time across the entire universe. This was the first ever direct evidence for gravitational waves and enabled verification of Einstein’s formulae to utmost precision. Einstein described space and time as a flexible fabric — now we know that this is not a metaphor but reality.

A black hole results from the collapse of a star in on itself, which creates a “point of singularity” — the rip in the trampoline fabric from the sumo wrestler. According to Einstein’s theory, this point of singularity has a zero space dimension (a “virtual point”¹⁸), and a large amount of mass (the entire ex-star) is contained in this virtual point. It therefore has infinite density. This is truly unique, because there is nothing else in the entire physical universe that has a measure of infinity! The very name “black hole” points to this object’s powerful gravity (due to the infinite density of the point of singularity), so strong that not even light can escape. We will never be able to “see” inside a black hole, since no light can ever escape from inside.

It can be deduced mathematically that at the surface of a black hole (called the “event horizon”), some distance away from the point of singularity at its center, all time ceases. But at the surface of a black hole, space remains, although it is severely affected. The further one travels away from the black hole, the more its effect on space and time are reduced. At some point far away, space and time revert back to normal.

In summary, the black hole is a unique object — the extreme of physicality. Its source is the point of singularity at its center — a zero-dimensional point of infinity that dramatically affects space-time in its locality, including the most exceptional possible alteration where there is zero space and zero time at the point of singularity itself.

Black Holes and Torah

I had the privilege over the past few years of discussing the theories of relativity and quantum mechanics, which are the foundation of physics and cosmology, and their interface with chochmas hanistar, together with Rav Moshe Shapira ztz”l. We touched upon the concept of the black hole, especially the source and power of the black hole — the zero-dimensional point of singularity at its center, with its unique measure of infinity.

Referring to kabbalistic concepts in the Sefiros, Rav Moshe described this point as the mystical sefirah/emanation of Keser — the Crown — which is the highest sefirah possible.

An entire sefer can be written on the meaning behind this statement, from the perspectives of both the chochmas hanistar (Kabbalah) and also the chochmas habriah (creation), but this essay has neither the space nor time available. Nevertheless, let me take the liberty to touch on two aspects that are relevant to our discussion. Keser is the highest sefirah, closest in a metaphorical sense to HaKadosh Baruch Hu and therefore possessing the greatest “infinite-like” quality. Furthermore, Keser is represented by the kutzo shel yud (of the Sheim Hameforash, the explicit four-lettered Divine Name) — a virtual point contained within the letter yud, which has zero dimensions, beyond any direct physical representation. In many respects, this parallels the point of singularity, an infinite and unperceivable object.

With this background, we can present a deeper understanding of the miracles that occurred around the Aron.

The Luchos and Hashem

The Zohar writes that “Kudesha Berich Hu v’Oraisa chad Hu” — HaKadosh Baruch Hu and the Torah constitute a unified entity.¹⁹ Chazal interpret the letters of the word “anochi,” the first word in the Aseres Hadibros, to mean “Ana Nafshi kesavis yehavis — I have given of Myself in writing.”²⁰ This means to say that some representation of G-dliness is contained within the Torah, and thus, kiveyachol, inside the Luchos in the Aron.

It is therefore unsurprising to find that the highest sefirah, Keser, is associated with the Luchos. The Gemara refers to an angel named Achasriel — derived from the word Keser — appearing in the Kodesh Hakodoshim.²¹ Similarly, the Shelah Hakadosh refers to the Aseres Hadibros as the “Keser Torah.”²²

Perhaps we can suggest that, kiveyachol, as a metaphor of a metaphor, that Keser, being the sefirah closest to HaKadosh Baruch Hu, the Infinite and Perfect Oneness, is best represented by a point of singularity (yichud), zero physical dimension (beyond any physical representation), and also infinity. Thus, the Aron — the place of the Luchos — is associated with Keser, and, with its intimate oneness to Hashem, would be almost a physical expression of that Ultimate Point of Singularity.²³

Consequently, it follows that the impact on space-time around the Aron would echo that of another singularity: a physical singularity, the point of singularity in the center of a black hole. There, the closer to the point of singularity, the greater is the effect on space-time. And this will culminate in it vanishing at the point itself.

The nissim described above followed this pattern: in the Aron itself, space-time ceased to exist; it had contracted to nothing. Further afield, in the Heichal, space-time existed, but was still noticeably affected. The closer it was, the greater effect on the time dimension as demonstrated by the Ner Maaravi and Lechem Hapanim. The more distant it was, the lesser the impact, as seen in the space dimension for the Chatzer and, further afield, Yerushalayim.

White Holes

This is, of course, not to say that the Aron is a black hole. In fact, it is quite the opposite: a black hole is the most extreme physicality and absorbs all light. The Aron, on the other hand, contains the greatest concentration of spirituality and emits the light²⁴ that sustains the entire universe. What they have in common is that they are both points of singularity, though at opposite ends of the spectrum.²⁵

An interesting parallel to this is that, surprisingly, Einstein’s equations also allow for another extreme object. It has the same point of singularity, with infinite density and similar impact on space-time — except it is the total reversal of a black hole! It can only emit light (and not absorb anything), and is known as a “white hole.”

The science world has not yet discovered any, but perhaps we have…

Conclusion

This essay is merely a proposed insight into the amazing connections between the foundations of the physical world (maaseh Bereishis) and the foundations of the spiritual worlds (maaseh Merkavah). There is so much more still to explore. The increasing knowledge of modern science, especially in fundamental physics — the basis of our entire universe, will surely help us fulfill the mitzvos of ahavas Hashem and yichud Hashem, enabling us to be ever more ready for the future, when “ki mal’ah ha’aretz dei’ah es Hashem — the world will be filled with knowledge of Hashem.” At that point, we will understand the true achdus and the perfect unity of HaKadosh Baruch Hu, which encompasses the entire creation, from the upper worlds down to our physical universe: “V’yadata hayom v’hasheivosa el levavecha ki Hashem Hu haElokim baShamayim mima’al v’al ha’aretz mitachas, ein od.” n

Rabbi Eli Katz learned at Gateshead and Mir and holds a first-class honors degree in computer science from Imperial College, London. He is the author of Va’Ani Avorechaim: A Guide to Birchas Cohanim (2004); Easy Giving (second edition, 2016) on hilchos tzedakah and maaser kesafim; and Emor El HaKohanim: A Guide to Tree Enclosures (2015), on halachos of tree ohalos as they relate to taharas Kohanim. His new sefer on Torah and science, The Unity of the Spiritual and Physical Worlds, is planned to be published in 2018. He can be contacted at eli@familykatz.co.uk.

Endnotes

[1] The inspiration for delving into the unity of Torah and science, especially from the perspective of chochmas hanistar and the foundation of modern science (namely, the theories of relativity and quantum mechanics), came from the writer’s discussions with Rav Moshe Shapira ztz”l, Rav Eliyahu Zion Sofer (rosh hayeshivah, Rechasim), Rav Avrohom Gurwicz (rosh hayeshivah, Gateshead) and Rav Moshe Schatz (author of Ma’ayan Moshe). Additional motivation came from his chavrusa, Amos Wittenberg, and also an article by Stephen Greenman linking the Aron and special relativity.

[2] Meshech Chochmah (Bereishis 12:7) takes a similar approach in explaining the meaning of the pasuk “from my flesh [creation] I will perceive My G-d” (Iyov 19:26).

[3] Nefesh HaChaim, sha’ar 4, perek 10, quoting the Zohar in Terumah — chelek beis 161a

[4] Hakdamah of Ramban al HaTorah. Also see Chofetz Chaim, Sheim Olam, Shaar Chezkas HaTorah, perek 12 and his haga’ah.

[5] Sefer Hakdamos U’she’arim, sha’ar 1, perek 4, by Rav Shlomo Elyashiv ztz”l, 1841–1926, grandfather of Rav Yosef Sholom Elyashiv ztz”l.

[6] Zohar, parshas Pikudei (231a)

[7] Sefer Haklalim, (Klalim Milchemes Moshe; klal 15, yediah 4), p365 (published together with Daas Tevunos, 5758) by Rav Moshe Chaim Luzzatto (1707-1746) , author of Mesilas Yesharim and over 40 seforim, mainly on chochmas hanistar.

[8] Shir Hashirim 86b

[9] See also Shiurei Daas, by Rav Yosef Yehuda Leib Bloch ztz”l (1860-1930, Telsher rosh yeshivah) in chelek beis, shiur 6, paragraph beginning “B’eis ha’acharonah ..”

[10] Rambam, Hilchos Yesodei HaTorah, chapters 2-4

[11] Yoma 21a

^[12] Tzafenas Paneiach, parshas B’shalach 16:33. The Rogatchover explains how a flask of mahn, despite being forbidden to leave out overnight, was able to be stored in the Aron. A similar idea is found in Siach Yitzchak (drashah beis nunin, siman 19), by Rav Yitzchak Isaac Chaver, stating that the Aron transcended both space and also time.

[13] A great miracle was performed with the Lechem Hapanim — as it was laid [on the Shulchan and warm] so was it removed [remaining warm a week later] — Chagigah 26a

^[14] Afikei Yam (Bava Metzia 85a). Rav Yitzchak Isaac Chaver (1789–1852) is known as the “peh shlishi” of the Vilna Gaon, as he was a talmid of Rav Menachem Mendel of Shklov, who was a talmid of the Gra.

[15] Pirkei Avos 5:5

[16] This is quoted in Ibn Ezra (Parshas Terumah).

^[17] Einstein showed that time is just another dimension — we have up-down, right-left, forward-back and before-after. Hence the use of the hyphenated phrase space-time.

^[18] However, with the introduction of quantum mechanics, a point of singularity is possibly undefined and may be as close to zero dimension as physically possible — i.e., the smallest unit of quantum space-time, one one-hundred quintillionth the size of a proton. This is for a separate essay.

[19] Zohar, Acharei Mos 73a

[20] Shabbos 105a

[21] Berachos 7a

[22] Shelah Hakadosh, parshas Yisro

^[23] Rav Y. I. Chaver (Afikei Yam ad loc) — The Luchos of the Torah have the attributes of a virtual point with zero dimension, indicating that they are above all physicality.

^[24] The word aron is derived from ohr (light) of nun (50th level of kedushah) — referring to the Ohr Haganuz.

^[25] This is a separate topic for another time, dealing with the concept of the debatable 50th level of tumah, which is likewise closely associated to Keser (see Rav Moshe Shapira in Afikiei Mayim, Pesach, belekutim, v’lo yuchlo l’hismameiah).

(Originally featured in Kolmus Issue 39)