Tag Archives: Albert Einstein

Kefitzat HaDerekh: Wormholes in the Torah

This week’s parasha, Vayetze, begins with Jacob setting forth towards his mother’s hometown in Haran. We read that on his way he suddenly “bumped into” a special place (Genesis 28:11) that turned out to be Beit El, the “House of God”. Jacob was surprised to find himself there (28:16), presumably the site of the future House of God, the Temple in Jerusalem. The Sages (Sanhedrin 95b) explain what happened:

“And Jacob went out from Be’er Sheva, and went to Haran…” is followed by “and he happened upon the place, and tarried there all night, because the sun was set.” For when he reached Haran, he said: “Shall I have passed through the place in which my fathers prayed, without doing so likewise?!” He wished therefore to return, but no sooner had he thought of this than the earth instantly contracted and he “happened upon” that place.

Our Sages state that a miracle occurred after Jacob had reached Haran. He regretted not stopping by at the site of the future Temple Mount, where Abraham and Isaac had prayed, so the earth beneath his feet seemingly “contracted” and he was suddenly teleported to Jerusalem. In fact, the Sages state that such a miracle occurred for three people in the Tanakh: first was Eliezer, Abraham’s servant, then Jacob in this week’s parasha, and finally King David’s general Avishai. There is Scriptural proof for each one. For instance, when Eliezer had arrived in Haran he declared “I came today to the well” (Genesis 24:42), implying he had set out on his journey that same day. Eliezer was miraculously able to go from Be’er Sheva to Haran, a significantly long journey, in under a day.

This phenomenon would later become known as kefitzat haderekh, “jumping the path”, and would appear in Rabbinic narratives as well. Angels have a similar ability to seemingly teleport across vast distances. In one story, Rav Kahana was once selling some wares and a female customer tried to seduce him (Kiddushin 40a). He quickly fled in distress and ran to the nearest window and jumped! The angel-prophet Eliyahu appeared and caught him, complaining that he had to instantly travel a distance of “four hundred parasangs” to save him. A parasang, or parsa, is the average distance a person walks in 72 minutes—generally thought to be about 5 kilometres. So, Eliyahu flew some 2000 kilometres in a flash to catch the rabbi. Rav Kahana apologized and lamented that due to his poverty he had to resort to being a salesman. Eliyahu gave him a vessel full of money to free him from his job.

Meanwhile, the Zohar (I, 4b-5a) states that the malevolent angel Samael can traverse as much as 6000 parsas in a single moment. This number is not arbitrary, for the Talmud calculates that the Earth’s circumference is 6000 parsas (Pesachim 94a). This is an incredible piece of Talmudic science, considering how little of the globe was known then. Today, we know that Earth’s exact circumference is 40,075 km at the equator, a value close to that of our Sages. In fact, if making the correct assumption that the Sages must have been exact in their knowledge, we might be able to properly identify the length of a Talmudic parsa.

Although it is generally calculated in halakhah that a parsa is between 4 and 5 kilometres, by dividing 40,075 km by 6000 we can conclude that a parsa must be closer to 6.68 kilometres. This is also more in line with the notion that a parsa is a distance of 72 minutes: The average walking speed of humans is 5 km per hour (1.42 metres per second, according to the most precise measurements), so defining a parsa as 6.68 km is much closer to the scientific reality.

Jacob’s Ladder through Spacetime

The Talmud (Chullin 91b) calculates that the distance of the Heavenly Ladder that Jacob saw in his vision was a whopping 8000 parsas, which would be over 50,000 km. The word used by our Sages is rochav, meaning “width”. A superficial reading of the Talmud suggests that each angel is 2000 parsas wide (based on Daniel 10:6), and since Jacob saw four angels, the width of the Ladder must have been 8000 parsas. However, this does not make sense if taken literally, for why would an angel’s form be 2000 parsas wide? And if it was, how could Jacob even capture the sight of an angel in his limited field of view? The Talmud must be teaching something else. The big question here is why use the language of width as opposed to length or height, as might be expected?

When it comes to understanding the cosmos, we always speak of a “fabric of spacetime”. Perhaps the greatest achievement of Albert Einstein is pioneering the science behind it, proving that the three dimensions of space and the dimension of time are not separate, but interwoven together. With this, he was able to explain gravity a lot more accurately, demonstrating that larger bodies make a bigger “dip” in the fabric, pulling objects towards them kind of like a penny rolling around a funnel. And because they are integrated, strong gravitational effects can warp both space and time. We typically visualize spacetime as a flat “fabric”, with celestial objects scattered all over it. In fact, today we know that the universe does indeed appear to be flat (with a margin of error of about 0.4%). This is of tremendous significance.

In the Torah, the term aretz can refer to both Earth proper, and the wider physical universe at large. When we read that in the beginning God created et shamayim v’et ha’aretz, we do not define it simply as the “sky” and the “earth”, for those were not created until Days Two and Three. Rather, God created the entire spiritual realm (shamayim) and the entire physical universe (aretz). Our Sages noted long ago that the root of aretz (ארץ) is the same as ratz (רץ), “running”, since everything in this universe is in perpetual motion. More incredibly, today we know that the universe is constantly expanding, and we see distant stars “running away” from us. As such, when the Tanakh uses an idiom like kanfot ha’aretz, the “corners” or “edges” of the universe, it may be read quite literally. For a long time, there were people who understood these Torah statements as implying a flat Earth, when in reality they could have been alluding to a deeper scientific understanding regarding the “flatness” of the entire universe.

And that brings us back to the precise Talmudic language of rochav, “width”, in a place where we might have expected height. Of course, we do have a dimension of height. However, when zooming out to a “flat” universe, we really only visualize it in terms of width, as if on a two-dimensional plane. Going further, Einstein later showed, together with another Jewish scientist named Nathan Rosen, that it would be theoretically possible to “bend” spacetime and connect two points that are vastly far apart. It would be like folding over the fabric and then poking a hole through both layers. Such an “Einstein-Rosen bridge”, better known as a wormhole, would allow travel across extremely vast distances in a very short period of time. In other words, it would be very much like kefitzat haderekh!  

A wormhole shortens the trip by bending spacetime and forming a bridge.

So, what our Sages may have been secretly implying in describing the width of Jacob’s Ladder is that this wormhole (of sorts) spanned 8000 parsas, or over 50,000 km. This is a distance even wider than the Earth and, scientifically, we would expect wormholes to be very large like this. Such a wormhole was accurately depicted in the film Interstellar, allowing the protagonists to instantly travel to a distant solar system to find a new home for mankind:

It is worth noting that when our Sages described the teleportation of Jacob, they said that kaftzah ha’aretz, again using that term aretz, and implying that it “jumped” or “contracted” for him. So, another term for this phenomenon, truer to the language of the Talmud, would be kefitzat ha’aretz, the warping of the spacetime fabric of this universe. Kefitzat haderekh is accurate, too, implying that one “jumped the path”, finding an alternate shortcut from one point in the universe to another. This appears to have happened at Sinai, as well. Our Sages likened Jacob’s Ladder to the Sinai Revelation, and the Zohar (I, 149a, Sitrei Torah) even notes that the numerical value of “ladder” (סלם) and “Sinai” (סיני) is the same—130. At Sinai, too, a “wormhole” opened up allowing 22,000 angelic “chariots” to descend upon the mountain (Bamidbar Rabbah 2:3).

Theoretical physics aside, can we actually create such wormholes? In 2017, scientists succeeded in producing tiny, microscopic wormholes for the first time. It is certainly possible that in the near future we will have the technology to open up larger wormholes, making rapid travel across God’s vast universe feasible. It appears that God’s angels already employ such a wormhole-style system of travel, traversing thousands of parsas instantaneously. It might help explain the Tower of Babel episode which, as we’ve mentioned in the past, was not simply a tower but meant to “lift off” and “conquer” the Heavens.

Our Sages long ago taught that the people who built the Tower knew the wisdom of the angels and were using angelic powers to accomplish their plans (see, for instance, Zohar I, 76a). God “came down” to confound them. He wiped their memories and jumbled their languages so that they wouldn’t be able to collaborate in such a megalomaniacal way. Today, we live in a world that is once more getting real close to being “of singular language and singular words” (Genesis 11:1), and once again we see science stepping into the dangerous territory of “playing God”. Hopefully this time humanity will get it right and use the astounding abilities that God made possible in His universe only for the good.

The Meaning and Power of “Amen”

In this week’s parasha, Ki Tavo, the Israelites are presented with a list of curses that they would bring upon themselves if they did not fulfil God’s commands. In the first set of curses, the Israelites answer each statement with “amen”, a term connoting agreement and acceptance. The now-ubiquitous term is actually quite rare in the Tanakh. In the Torah itself it appears in only one other context with the same meaning (Numbers 5:22). What does “amen” really mean, and why is it recited at the end of blessings? Why does it have the power to include its reciter in another person’s mitzvah? Continue reading

Torah on the Big Bang and the Age of the Universe

The Torah begins with Beresheet, the famous account of Creation.  In recent times, many have questioned the validity of this narrative in light of the findings of modern science. In reality, the Torah’s account is quite accurate in scientific terms, and the Jewish tradition described the origins of the universe and its age with stunning precision centuries before modern science caught up.

According to Science

The current scientific model holds that 13.7 billion years ago, the entire universe was compacted into a super tiny point with infinite density. For some unknown reason, this point suddenly burst in a massively vast and rapid expansion of energy and radiation. As the early universe cooled and expanded, particles began to form, and then whole atoms, starting with hydrogen. Hydrogen atoms fused into helium atoms, and later on heavy elements formed from further fusion in the cores of stars and their explosions. Everything that we see today—the entire universe and all matter within it—emerged from that initial expansion, “the Big Bang”.

The evidence for a Big Bang is extensive. In fact, you can see some of it when you look at the “snow” on an old television that is not tuned to any channel. The antenna is picking up some of the cosmic microwave background radiation, the “afterglow” of the Big Bang. The entire universe is still glowing from that initial expansion! Popular physicist Brian Greene writes in his bestselling The Hidden Reality (pg. 43):

…if you were to shut off the sun, remove the other stars from the Milky Way, and even sweep away the most distant galaxies, space would not be black. To the human eye it would appear black, but if you could see radiation in the microwave part of the spectrum, then every which way you turned, you’d see a uniform glow. It’s origin? The origin.

The universe is glowing, it’s just that most people cannot see it because human eyes perceive only a very narrow part of the electromagnetic spectrum, which we call “visible light”. Light of a higher energy and frequency includes dangerous x-rays and gamma rays, while light of lower energy and frequency includes microwaves and radio waves. The seeming blackness of the universe is actually radiating with light—we simply cannot see it. Incredibly, this is precisely what the Torah states.

The electromagnetic spectrum. Visible light makes up just a tiny sliver of the spectrum. Some living organisms can see in UV or infrared wavelengths.

Zohar haRakia

We read in the Tanakh (Daniel 12:3) that “they who are wise shall shine as bright as the rakia…” The Torah tells us that God established a rakia (wrongly translated as “firmament”) on the second day of Creation, and this is where all the stars and planets are suspended (Genesis 1:15). The Talmud (Chagigah 12a), composed over 1500 years ago, further elaborates that above the earth is the vilon, the atmosphere that stretches over the planet, and beyond the vilon is the rakia, a vast expanse within which are all the stars. Beyond the rakia is a region called shechakim, the interface between the physical and spiritual realms, and further still are the highest levels of the Heavens, inhabited by angels and transcendental beings. From this, and other ancient sources, it is clear that rakia refers to outer space.

Daniel tells us that the wise will shine like the rakia, and goes on to state that “they who turn the many to righteousness [shall shine] as the stars”. We can understand how people might shine bright like stars, but why would Daniel say the rakia is shining? Outer space is totally dark! Of course, as Brian Greene described, today we know that the universe is indeed glowing.

One of the most ancient Jewish mystical texts is Sefer HaBahir. According to tradition, it dates back some two thousand years, and was first published at least seven hundred years ago. This book gets its name from another verse in the Tanakh (Job 37:21), which states “And now, men do not see the light that is bright [bahir] in the skies.” Once again, Scripture tells us that the universe is glowing with a bright light that humans are unable to perceive. Science has found that this glow comes from the Big Bang, and this too is accurately described by the most famous of Jewish mystical texts, the Zohar.

Cosmic Microwave Background Radiation, the glow of the universe, discovered in the 1960s by Robert Wilson and Jewish physicist Arno Penzias.

The Secret of Beresheet and the Big Bang

Like Sefer HaBahir, the Zohar was first published around seven hundred years ago, with its teachings dating back two millennia. The Zohar is a parasha-by-parasha commentary on the Torah, and naturally begins with the first section in describing Creation. The book gets its name from the above verse in Daniel which speaks of Zohar haRakia, the glow of the universe. It elaborates (I, 2a, 15a):

בְּשַׁעְתָּא דִּסְתִימָא דְכָל סְתִימִין בָּעָא לְאִתְגַּלְּיָא, עֲבַד בְּרֵישָׁא נְקוּדָה חֲדָא, וְדָא סָלֵיק לְמֶהֱוֵי מַחֲשָׁבָה. צַיֵּיר בָּהּ כָּל צִיּוּרִין חָקַק בָּהּ כָּל גְּלִיפִין… וְרָזָא דָא, בְּרֵאשִׁית בָּרָא אֱלֹהִים. זֹהַר, דְּמִנֵּיהּ כָּלְהוֹ מַאֲמָרוֹת אִתְבְּרִיאוּ בְּרָזָא דְאִתְפַּשְׁטוּתָא דִנְקוּדָה דְּזֹהַר סְתִים דָּא

When the Most Concealed One [God] began to create, He first made a singular point, with which he then brought forth all thought, drew all blueprints, and carved out all things… And the secret of “In the beginning, God created…” [Genesis 1:1] is radiance [zohar], from which all Utterances were created, in the secret of the expansion of that point of radiance.

Many centuries ago, the Zohar accurately and elegantly sums up the findings of modern science. God first created a tiny singular point which burst forth in light, and from which He “carved out” all things in existence. All of God’s Utterances (since the Torah says God created by speaking: “And God said ‘Let there be light.’”) came forth from the expansion of that initial primordial radiance.

Time is Relative

All that remains is the seeming contradiction in time. Science estimates 13.7 billion years, while the Torah speaks of six days. Of course, the nature of a “day” in the account of Creation is flexible, considering there was no Earth, sun, or moon until the third and fourth days (so how could there be a 24 hour day as we know it before this?) There were also no humans at this point, and the Torah describes Creation from the perspective of God, for whom “a thousand years is like one passing day” (Psalms 90:4). The fact that time runs differently for man and God actually highlights another scientific principle, as revealed by Albert Einstein.

Einstein’s theory of relativity holds that the passing of time varies depending on an entity’s speed. A person who could board a spaceship and fly near light-speed would experience very slow time. A few days for this person would be equivalent to many years on Earth. (This theme has been explored in countless science fiction books and films, including 2014’s Interstellar.) The Lubavitcher Rebbe often cited this fact to conclude that arguing about apparent space-time contradictions is therefore quite pointless. Meanwhile, physicist Gerald Schroeder has mathematically calculated that six days could be equivalent to 13.7 billion years when factoring in the universe’s expansion. After all, we are looking back in time at an ancient universe through human eyes, while God was looking forward in time from the universe’s first moments.

An infographic explaining the relativity of time. Note the conclusion: “there is no meaning to the concept of absolute time.” The whole debate of 6 days vs 13.7 billion years is therefore quite meaningless.

Physicist and Rabbi Aryeh Kaplan explored this issue extensively and cites multiple ancient Jewish texts that support the notion of a very ancient universe (see his book Kabbalah and the Age of the Universe). In multiple places, the Midrash states that before creating this world, God was creating and destroying many previous worlds (see, for example, Kohelet Rabbah 3:14), while the Talmud calculates that “there were 974 generations before Adam” (Chagigah 13b, Shabbat 88a).

On this last point, it has been shown that a generation according to the Torah is forty years (Numbers 32:13), and as we saw, a day for God is likened to 1000 human years (Psalms 90:4), therefore:

            974 generations × 40 years/generation × 365 days/year × 1000 human years/divine day =

14.2 billion years

Compared to the current best estimate of science at 13.7 billion years, it is amazing that one can come to a very similar number by simply putting together a few Torah verses.

What we see from all of the above is that ancient Jewish texts describe the universe’s origins in absolutely perfect detail. And it is only in recent decades that science has finally caught up. In many other ways, too, science has a lot of catching up to do.


The above is an excerpt from Garments of Light: 70 Illuminating Essays on the Weekly Torah Portion and Holidays. Click here to get the book!