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NEWSCIENCENEWSCIENCENEWSCIENCE the body's density or material, can occur _ physical effect of a phase shift in space— Node points of a standing wave in loga- only in the exact node points of the global termed a "propagating wave"—will arise. rithmic space, however, are particular scales standing density wave. The rate of this phase shift (phase velocity) is which have different frequencies assigned to So far, systematic measurements to verify always finite and dependent on the medium. them. In order to calculate these frequen- this postulate of Global Scaling Theory have In contrast, phase velocity of a standing cies, it is necessary to acquaint oneself with not been carried out. However, the Institute wave between two adjacent node points is _ the mathematical foundations of Global of Solid State Physics at Friedrich Schiller zero because all particles oscillate in phase. Scaling Theory. University is preparing freefall experiments This gives rise to the impression that the (pseudo Galileo tests) at the Bremen gravity wave "stands". In each node point, the phase The Physics of the Number Line tower in order to determine the possibility of actually bounces 180 degrees—so phase The world of scales is nothing else but the material-related violation of the equivalence _ velocity is theoretically infinitely high. Itis logarithmic line of numbers known to rinciple, with a hitherto unmatched preci- precisely this property that makes standing mathematics at least since the time of Napier sion of < 10°. waves so attractive for communication. (1600). What is new, however, is the And the Satellite Test of fundamental recognition that the Equivalence Principle (STEP), number line has an harmonic structure lanned for 2004, aspires to an obser- which is itself the cause for the vational limit of c. 10'*. Ata height of standing pressure wave. 550 kilometres, comparisons will be The existence of a standing Leonard Euler (1748) had already made of acceleration velocities of shown that irrational and transcenden- four different pairs of test masses density wave In logarithmic tal numbers can be uniquely repre- moving onan almost creular or space explains, for the first sented as “oni! Fractions in which synchronous orbit (see website P A F 4 all elements (numerators and denomi- ttp://einstein.stanford.edu/STEP). time In the history of physics, nators) will be natural numbers. In 1928, Khintchine succeeded in pro- viding the general proof. In the theory of numbers, this means that all numbers can be constructed medium in which they propagate is from natural numbers, the universal bounded. Consequently, the existence of principle of construction being the a standing density or pressure wave in the Standing Waves as Carrier Waves for continued fraction. All natural numbers 1, 2, universe means that the universe is limited Information Transmission 3, 4, 5, ... in turn are constructed from prime by scale. At the universe's lower horizon of Standing waves do not transmit energy; numbers, these being natural numbers which scale, density of matter reaches amaximum; they merely pump energy back and forth cannot be further divided without remainder, at its upper horizon, it reaches a minimum. within half a wavelength. Half a wave- suchas 1, 2, 3,5,7, 11, 13, 19, 23, 29, 31, The two horizons constitute the universe's length is completely sufficient—even for _ ... (traditionally, 1 isn't classed as a prime "sound barrier". At precisely these phase interplanetary communication—if we are number, although it fulfills all criteria). The transitions, pressure waves are reflected; dealing with standing waves in logarithmic distribution of prime numbers on_ the they will overlap and form standing waves. _ space. number line is so irregular that no formula A standing wave can only exist for any The wavelengths of standing density had been found which would perfectly length of time if the medium is permanently _ waves in logarithmic space are 2 x 3k,i.e., describe their distribution—until the Theory provided with energy from outside. This 6, 18, 54, 162 and 486 units of the natural of Global Scaling was able to solve this means that our universe is in aconstant logarithm. Half a wavelength, therefore, mystery. energy exchange with other universes. corresponds to 3, 9, 27, 81 and 243 units. The distribution of numbers is indeed Standing waves are very common in These are relative scales of 1.3 and 3.9 and __ very irregular, but only on the linear number nature because every medium is limited or 11.7 and 35.2 and 105.5 orders of line. On the logarithmic number line, large bounded, be it the water of the oceans, the magnitude. gaps of prime numbers recur in regular air of the Earth's atmosphere or the radiation Exactly in these intervals, node points intervals. Gauss (1795) had already noticed field of the Sun's atmosphere. Standing occur. Hence, node points mark scales relat- this. Thus, the set pi(n) of prime numbers waves excite the medium into natural oscil- ing as 1:20, 1:8103, 1:5.32 x 10", 1:1.5 x up to the number n can be approximated by lations and, due to the fact that the ampli- 10* and 1:3.4 x 10". Within the scope of the simple formula, pi(n) =n/ Inn. The "Sound Barrier" of the the origin of gravitation. Universe Standing waves can only form if the tude of a standing wave is no longer time these scales, communication between two The reason for this phenomenon is the dependent but only space dependent, these —_ adjacent node points is possible. existence of a standing density wave on the eigenvibrations will move in sync across the The ability to modulate a standing wave is _ logarithmic number line, the node points of whole medium. confined to its node points, because it is this density wave acting as number attrac- A wave occurs whenever an oscillating only in the immediate proximity of the node tors. This is where prime numbers will particle in a medium excites adjacent points that energy can be fed into or taken "accumulate" and form composite numbers, particles into vibrations so that the process from a standing wave. If itis a standing i.e., non-primes, such as the seven non- propagates. Due to the viscosity or elasticity wave in linear space, the node points are _ primes from 401 to 409. Hence a "prime of the medium and the inertia of the particles, simply locations in which attachment of an number gap" will occur in this place. their oscillation phases differ and the external oscillatory process is possible. Precisely where non-primes (i.e., prime Node points of a standing wave in loga- rithmic space, however, are particular scales which have different frequencies assigned to them. In order to calculate these frequen- cies, it is necessary to acquaint oneself with the mathematical foundations of Global Scaling Theory. The existence of a standing density wave in logarithmic space explains, for the first time in the history of physics, the origin of gravitation. Standing Waves as Carrier Waves for Information Transmission mystery. The distribution of numbers is indeed very irregular, but only on the linear number line. On the logarithmic number line, large gaps of prime numbers recur in regular intervals. Gauss (1795) had already noticed this. Thus, the set pi(n) of prime numbers up to the number n can be approximated by the simple formula, pi(n) =n / Inn. The reason for this phenomenon is the existence of a standing density wave on the logarithmic number line, the node points of this density wave acting as number attrac- tors. This is where prime numbers will "accumulate" and form composite numbers, i.e., non-primes, such as the seven non- primes from 401 to 409. Hence a "prime number gap" will occur in this place. Precisely where non-primes (i.e., prime NEXUS + 51 AUGUST —- SEPTEMBER 2004 www.nexusmagazine.com