MIKDASH AND SHABBAT: A SPIRITUAL SPACE-TIME CONNECTION
(parts 3-4 of 8)by Akiva Bernstein
III. PHYSICAL SPACE-TIME: A LITERARY PRESENTATION
Until the year 1905 (5665 from Creation, according to the Hebrew Calendar), it was assumed in the world of physical dynamics that there was no connection between matter and energy. Even though these two energies are amongst the basic entities that make up the universe, that was their only connection -- that they existed as part of the same universe. Likewise, until 1908 (5668 from Creation), it was always assumed that space and time were unconnected entities co-existing in the same physical world. "Matter is matter, energy is energy, space is space, and time is time." Jews who are classified as "Torah observant" Jews do precisely the same thing with regard to the two mega-concepts of Mikdash and Shabbat, i.e. "Mikdash is Mikdash, and Shabbat is Shabbat," and the only connection is that they both belong to the same universe, the world of Torah. This sad state of affairs prevails to this day.
In 1905, Albert Einstein, publishing his famous equation E=mc2, showed, without actually knowing why, an intrinsic connection between matter and energy, thus showing the supreme style of unity through which G-d created the physical world. On September 21, 1908 (see supra, Introduction) Herman Minkowski presented to the world an even more astonishing concept prevailing between two more basic entities in the physical universe. This was the concept that space and time cannot be treated as two independent entities, but "only a kind of union of these two will preserve and independent (physical) reality." What can be shown is that the reason that matter and energy are connected is only because of the intricate connection between space and time. The mathematical formulas which Minkowski derived show the following:
(1) Time in its real sense is not to be regarded in terms of the motion of the hands on a clock, but rather as an actual dimension, similar to but not identical with any of the three dimensions of space.
(2) There exists a conversion factor, based on the speed of light, which enables one to convert between units of distance in space and units of duration in time.
(3) Minkowski's formula shows that there exists a general distance that is composed of both a component in space and a component in time. Thus, in Minkowski's picture of the world, there exist four actual dimensions, three of space and one of time, which are all necessary to describe the exact position of any object relative to any other object. Perhaps the most astounding words which Minkowski uttered were at the very beginning of his lecture: "Space by itself and time by itself are doomed to fade into mere shadows." Time and space in the ultimate sense cannot exist separately and must not be depicted as existing in this manner.
According to Minkowski's 4-dimensional distance formula, an object's traversing a distance in space produces not only a change in its position, but also a change in terms of the rate of motion of the hands on a clock next to it, relative to a clock that remains stationary while this aforementioned object is moving. Thus, the object's total space- time distance is affected. This, however, only becomes apparent for an object traveling at very high speeds relative to a stationary observer, and thus, at low speeds, no connection between space and time is apparent. Applying the Correspondence-Equivalence Principle, only at very high spiritual speeds is the connection between Mikdash and Shabbat apparent, but not for those individuals moving at low spiritual speeds.
IV. PHYSICAL SPACE-TIME: A MATHEMATICAL DESCRIPTION
(This section should be read only by a person with a fairly high level of understanding of both mathematics and physics.)In 1887, two experimental physicists, Michelson and Morley, in an attempt to discover the absolute speed of the earth in space, measured the speed of light in different directions. The results of the experiment showed that the speed of light was the same in every direction. Or, put more generally, the speed of light seemed to be the same in every inertial reference frame. Around the year 1900, two theoretical physicists, in an attempt to resolve this strange problem, proposed a set of equations which later became known as the Lorentz and Fitzgerald transformation equations. Both Lorentz and Fitzgerald considered these equations as only a mathematical model for the solution of this strange problem, and only mathematically was the speed of light to be considered a constant, but not in actual physical reality, and that the actual physical dynamics of the world operated only in accordance with Newton's laws. In 1905, Einstein made the astounding proposal, as part of his Special Theory of Relativity, that in physical reality also the speed of light is constant in all frames of reference, and that the Lorentz-Fitzgerald equations are the set of equations with describe physical reality.
However, even Einstein himself did not have a full understanding of the
total meaning of these equations. It was only in 1908 that Minkowski
explained their full content. The particular equation we will deal with
is the following one:
Imagine two observers, A and B, B is traveling at a constant velocity of magnitude V relative to observer A and is heading in A's direction. Both observers have clocks in their hands, neither of which is yet working. There comes a point at which B meets up with A, and passes alongside him. At this very point, both A and B turn their clocks on, oath of which (all hands on the two clocks) had been set to the number 12, i.e. at the "start" position. The above equation gives the movement of the hands on B's clock relative to A's clock. B's clock is represented by t and A's clock by t0. The difference is the transformation factor (1-v2/c2)1/2 called the Lorentz-Fitzgerald transformation factor. It appears constantly in relativity theory.
In 1908, Minkowski took the aforesaid equation and , writing it out in expanded form, came out with astounding results:
t=t0(1-v2/c2)1/2 => t2=(t0)2(1-v2/c2)
Since v=s/t0, where s is the distance B travels -- as measured by A -- in the given time period t0 as measured by A's clock, therefore:
t2=(t0)2(1-[s2/t2]/c2) => t2=t02-[t02s2 /t02]/c2
=> t2=t02-s2/c2
or c2t2=c2t02-s2
or -c2t2=s2-c2t02
Therefore:
i2c2t2=s2 + i2c2t02, since i2=-1
Since s as a distance, it can be expressed in terms of a coordinate system with 3 independent perpendicular coordinates x1, x2, and x3, as follows:
s2=x12 + x22 + x32
Therefore, the above equation can be rewritten as:
(ict)2=x12 + x22 + x32+(ict0)2
Instead of the usual 3-dimensional distance formula s2=x12 + x22+x32, we have a formula with four terms in it: x1, x2, x3, and ict0. The first result of the equation is that the universe is not 3-dimensional in nature, but rather 4-dimensional. The second result is that, for the first time in history of mankind, we have an actual mathematical definition of the concept of "time". Notice that in the expression ict0, the term ct0 represents a distance: c is the speed of light, and any speed multiplied by a measurement of time is terms of units of time (for us this means seconds) equals a distance. The term ict0 thus means an imaginary number distance. Thus time is imaginary number space, or, more precisely, time is that dimension in which distance is measured in imaginary number units of length.
At this point we will introduce the following terms: t0 is observer A's proper clock time, t is observer B's proper clock time, ict0 is observer A's proper dimensional time, and ict is observer B's proper dimensional time. The above equation
(ict)2=x12 + x22 + x32+(ict0)2
shows that time, in terms of a dimension, i.e. ict0 (and not in terms of motion on the hands of a clock), is perpendicular to the three dimensions of space. This perpendicularity, creating a 4-dimensional universe, is known in mathematical physics as hyperspace. The above equation shows that, "in relativity dynamics, time and space must cone into the equations in the same way, since by means of a Lorentz transformation (written in Minkowski's expanded form) one may mix space and time. Relativity dynamics treats the time variable in a manner which is very different from non-relativistic dynamics (Newtonian dynamics)" [from Morse and Feshbach, Methods of Theoretical Physics, McGraw-Hill (1953), p. 247]. It was the mixing aspect of space and time that led Minkowski to use the term space-time to describe the 4-dimensional hyperspace mentioned above. The path of any object in space-time he called its world-line. The length of any object's world-line is always an imaginary number, except for an object constantly traveling at the speed of light, in which case the length of its world line would be zero (stationary space-time).
Minkowski, as mentioned above, revealed these findings to the world on the 25th of Elul 5668. The 25th of Elul is regarded by a Jewish traditional opinion as the first of the days of Creation. Amongst the first things created were time, space, and matter-energy. Even though Minkowski did not know this, G-d had Minkowski reveal, on the anniversary of the first day of creation, the secrets of the time dimension, including the first mathematical dimension of time.
As mentioned above, when Einstein presented his mass-energy equation, E=mc2 to the world in 1905, he had no idea that the reason that matter and energy are related was because space and time are interrelated. There will now be presented a formal proof of this fact. As stated above:
(ict)2=x12 + x22 + x32+(ict0)2
or more simply:
Dividing the equation through by (t0)2, we then have:
(ict/t0)2=s2/t02+(ict0/t0)2
Since t=t0(1-v2/c2)1/2,
or (t/t0)2=1-v2/c2, this then
becomes (ic)2(1-v2/c2)=v2+(ic)2,
since s/t0=v.
Dividing through by (1-v2/c2) produces:
We will leave this equation alone for a while, and introduce the following new conditions into the above situation: for the purposes of discussion, we say that observer A and observer B are identical twins who, when stationary relative to one another, have identical rest mass denoted m0. Multiplying the above equation by m02, we get:
Rearranging the terms we get: (m0c)2/(1 -v2/c2)=(m0v)2/(1 -v2/c2)+(m0c)2 which can be written as [m0/(1 -v2/c2)1/2]c2=[m0/(1-v2/c2)1/2]v2+(m0C)2
Let us now ascribe to the term m0/(1 -v2/c2)1/2 the symbol m, and present in Appendix A a formal proof that m=m0/(1 -v2/c2)1/2 is the mass of observer B when he is moving at a velocity v relative to A. The equation then becomes (mc)2=(mv)2+(mc0)2, which is the 4-dimensional momentum equation of Spatial Relativity.
The term mc is the total momentum of observer B (as Einstein called it) or the space-time momentum (as Minkowski called it), with respect to A. The term mv is the kinetic, or spatial, momentum of B with respect to A, and m0c is the rest, or temporal, momentum of B when stationary with respect to A.
If we multiply the above equation by c2 we then have:
Einstein called the term "mc2" the total energy of B, and Minkowski used the term space-time entergy of B, relative to A. The term m0c2 is the rest or temporal energy of B, when stationary with respect to A. We will call mvc the kinetic or spatial energy of B with respect to A, as opposed to work energy which we define as
If we use the symbols E=mc2 and E0=m0c2, then the above equation becomes
It can easily be shown that the Lorentz Transformation factor
(1-v2/c2) can be expressed as
{[x12 + x22 +x32 +(ict0)2]/(ict0)2}.
Therefore, since
the ratio
Thus, the ratio of the energy of the two observers B and A is inversely proportional to the space-time distance of A, measured relative to himself, divided by the space-time distance of B as measured by a relative to B. It is the change in the space-time distance of B, relative to A, when moving at speed v with respect to A, as opposed to what the space-time distance of B would be, relative to A, were B to be stationary with respect to A, which produces a change in the energy of B with respect to A, as measured when B is moving at speed v relative to A, as opposed to B's being stationary with respect to A. A change of energy, due to an acceleration of B, relative to A, produces a change in the space-time distance of B, relative to A, as measured by A, and this change was first referred to by G. Nordstrom, in 1913, as space-time curvature. This concept is one of the pillars of General Relativity Theory.
Returning to the equation (E)2=(mvc)2+(E0)2, we introduce an equation first proposed by Louis De Broglie in 1922, which expands the concept of both matter and wave properties for all particles in the universe, mv=h/G, where m is the mass of the particle, v is the constant speed of the particle relative to a stationary object, h is Plank's constant, and G (gamma) is the wavelength of this particle.
Let us now change around observers A and B, and instead call A a
designated stationary electron, and B -- and electron moving at a
constant velocity of magnitude v relative to A. The above energy
equation
(E)2=(mvc)2+(E0)2
holds for the two electrons A and B.
This can be rewritten as
(E)2=(mc/G)2+(E0)2, since mv=h/G, as
above. This equation holds good for any particle in the universe.
Since for photons v=c, the equation mv=h/G becomes
mc2=hc/G, or E=mc2=hc/G.
This can also be derived from the equation E2=(hc/G)2+(E0)2, using the simple fact that photons, which in free space move at the speed c, are never at rest in their photon form. Therefore, in their rest mass, and thus rest energy, is zero, i.e., for photons
Thus, E2=(hc/G)2+02, or simply E=hc/G.
This formula for photon
energy was first introduce by Planck around the year 1900 as part of his
study of black body radiation, and was done independently of any other
considerations, such as the Michaelson-Morley experiment or the Lorentz-
Fitzgerald transformation equations. We see form the above that all the
laws of physical dynamics are totally integrated into one another, and
internally consistent. Really, now, would we then ever expect anything
less of Hashem, as we find in Tehillim 92:6
Apendix A: A FORMAL PROOF THAT m=m0/(1-v2/c2)^(1/2 )
In the equation
the term 1/(1-v2/c2) cannot be associated with the term v, i.e. v/(1-v2c2)1/2 cannot exist in physical reality, for the following reason: since there are only 2 observers, the stationary observer and the moving observer, and since the moving observer has in 3-dimensional space a constant velocity v, the velocity quantity v/(1-v2/c2)1/2 would be greater than c when v > 71% of c, and this is a physical impossibility since c (the speed of light) is a constant for all frames of reference.
And since the quantity 1/(1-v2/c2)1/2 is a pure number, it cannot be associated only with itself, i.e. 1/(1-v2/c2)1/2(m0v), since any pure number by itself, in a momentum equation, reflects no physical reality.
But 1/(1-v2/c2)1/2 must be associated with an actual physical reality, and by a process of elimination, we conclude that it must be associated with m0, i.e. m0/(1-v2/c2)1/2, and this quantity is mass-like in nature. And since there are only 2 observers, and the mass of the stationary observer is m0, therefore m0/(1-v2/c2)1/2 must be the mass of the moving observer. Thus, m0/(1-v2/c2)1/2=m, where m is used to denote the mass of the moving observer.
What follows is a derivation of the 4-dimensional momentum equation the way it was derived by Einstein. Our puropose is to show that, since Einstein's derivation does not include terms involving spatial distance, Einstein did not realize that the equivalence between matter and energy was due to the interconnection between space and time.
We start with:
t=t0(1-v2/c2)1/2 => t2=t02(1-v2/c2)
or, t2=t02-t02v2/c2 => t02v2/c2=t02-t2
or, v2 =(c2t02 -c2t2)/t02 => v2=c2-c2(1-v2/c2) since t2/t02=(1-v2/c2)
Multiplying m02 and dividing by (1-v2/c2) gives
m02v2/(1-v2/c2)=m02c2/(1-v2/c2)-m02c2
=> [m0/(1-v2/c2)1/2]v2=[m0/(1-v2/c2)1/2]c2-(m0c)2
As above, m0/(1-v2/c2)1/2=m, and thus m2v2=m2c2-(m0c)2
or, (mv)2+(m9c)2=(mc)2. Thus, spatial distance does not enter in
at all.
LETTER TO THE EDITOR
Dear Friends of Israel:
I am not Jewish, but worked on a kibbutz, learned Hebrew and have a keen ineterst in the progress of Isreal.
Since the red heiffer story broke, I've been on the web looking to see what people are saying regarding "real estate" problem surrounding the rebuilding of the Temple.
A web article I just read asserted the Temple might not be rebuilt on the exact same location as the former ones.
The argument stated that Ezekiel saw with his own eyes the Shekinah leaving the Temple on Mount Moriah and ascending directly to the Mount of Olives. The article went on saying that "the Mount of Olives is the highest in the Moriah mountain chain and technically could be called the Upper Mount Moriah. The word "Moriah" means "G_d sees". Moses explained the meaning of this word in Genesis as the place of G_d's singular attention. In Zechariah 14 "the footstool of G_d" is mentioned which was seen in the Mount of Olives. The symbol of the "footstool" represents the dwelling place of G_d on earth-the Holy Temple, etc.
I have never heard such an idea before. Do you think the notion that the temple could be rebuilt on a different location has any merit?
Sincerely,
Jamie
Jamie,
The building of the Temple and its service must be governed by Jewish law as received throughout the generations. In fact, when there was a sect called the Seduces, who believed their understanding of the Torah was more correct than the accepted Tradition, the High Priest was required to take an oath that he would perform the service according to Tradition, without changing anything.
Among the greatest codifiers of Jewish Law is the Rambam (Rabbi Moshe Maimonides). He writes (Hilchot Beit HaBechira 2:1)
"The Altar is in a very precise location, which may never be changed." He then goes on to tell that the Altars that Avraham, Noach, Kayin, Hevel, and Adam sacrificed on were all on this exact location. Offering a sacrifice on any other location is considered to be a grave sin and a desecration.
We are not required to build the Beit HaMikdash according to Yechezkel's vision. Even the prophets who lived in his time, Chagai, Zechariah, and Malachi, did not build the Beit HaMikdash like Yechezkel. Rather, unless a prophet instructs us otherwise, we are to build according to the Tradition that we have received, and only in its proper place.
All the best,
yirmi
HaTenu'ah LeChinun HaMikdash
Gathering en masse to arouse consciousness among the People,
its rabbis, and its leaders to rebuild the Beit HaMikdash
and return the Kohanim to their Service
Telephone: +972-2-5371904
Email: Yirmiyahu Fischer
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