Gravity isn’t equal to Everthing April 8, 2017 Authored by: Hans van Kessel Crenel Physics © Hans van Kessel [email protected] Abstract. Normalizing the velocity of light ‘c’ to a non-dimensional 1 generates a simple system of units of measurements. All other natural constants will still have their unique unit of measurement, and thus no information will be snowed under. Instead, nature appears more transparent. Besides Planck’s 퐸 = ℎ. 휐, Boltzmann gives an alternate way of defining ‘content’: if the entropy of an object is expressed in e.g. J/K, multiplying that objects entropy with its (inherent) temperature delivers ‘content’ in Joules. This route delivers an enhanced Planck equation, applicable to binary particles (particles that have a discrete number of states). This alternate Boltzmann route must meet the conservation principle. This demands a relationship between natural constants. From that relationship, the gravitational constant between smallest observable binary particles is calculated. Photons are not binary particles. It will be argued why photons are not subject to gravity: the frequency drop we measure if they climb in a gravitational field is the consequence of the local clock running faster while climbing (time dilatation). Therefore, gravity isn’t equal to everything. Crenel Physics © Hans van Kessel [email protected] Table of contents: 1. Consolidating Units of Measurement. ........................................................................................................... 1 2. Boltzmann. ................................................................................................................................................... 4 3. Observability: the entropy atom. .................................................................................................................. 7 4. Conversion factors and G. ............................................................................................................................. 9 5. Various options for G. ................................................................................................................................. 10 6. Consequences of normalizing c.................................................................................................................... 13 7. Streamlined UoM. ...................................................................................................................................... 14 8. Verification and discussion. ......................................................................................................................... 15 Crenel Physics © Hans van Kessel [email protected] number indicates that the equation applies to the Crenel Physics system. 1. Consolidating Units of Any other velocity will be expressed as a fraction of light velocity ‘cCP’. Thus, within Crenel Physics, velocity ranges Measurement. from 0 to 1. Physics describes nature in terms of Units of Measurement, for In Metric Physics velocity is expressed in m/s. In Crenel which we will use symbol ‘UoM’. Thereby the Metric S.I. Physics, in order to arrive at the now required dimensionless system is used. It presumes the meter, second, kilogram and measure for velocity, the UoM for distance must be equal to the Joule as ‘base’. These are however not ‘base’. This UoM for time. That measure will be named ‘Crenel’ (symbol presumption blurs the fundamentals of physics. To illustrate ‘C’): both distance and time will be expressed in ‘Crenel’. The 2 this, consider Einstein’s equation 퐸 = 푚. 푐 . It can be rewritten Crenel will be our measure for whereabouts in terms of space 2 퐸 as: 푐 = ⁄푚. and time. 퐸푛푒푟푔푦 푈표푀 퐽 Per this equation: 1 푐2 = 1 = 1 . Memory aid: the name Crenel is associated with crenels as found on 푀푎푠푠 푈표푀 푘푔 top of castle walls. That shape has a pattern that can be associated 퐽 with both ‘distance’ as well as ‘frequency’ (and thereby ‘time’). The light velocity 푐 (in vacuum) then equals 1 √ ⁄푘푔. Let’s explore the UoM of some other physical properties. In 2 퐽 Metric Physics acceleration ‘푎’ is expressed in m/s . Therefore, However, in the S.I. system c is not expressed in √ ⁄ , but in 2 푘푔 in Crenel Physics acceleration is expressed in C/C which can 푚 -1 m/s: c = 299.792.458 ⁄푠. be simplified to C . Based on Newton’s law 퐹 = 푚. 푎, in Metric Physics force F is measured in kg.m/s2 (note the overlap 퐽 푚 Therefore: 1 √ ⁄푘푔 ≡ 299.792.458 ⁄푠. with the ‘N(ewton)’, the typically used measure). In Crenel Physics the force in kg.m/s2 converts to P.C/C2 = P/C. From the This illustrates overlap between UoM in the S.I. system. Per his 푀 .푀 gravitational equation 퐹 = 퐺. 1 2 we find the value of the G above equation, Einstein un-blurred one of these overlaps. 푑2 퐹.푑2 In the following we will produce a consolidated system of being equal to: 퐺 = . In this equation we substitute the 푀1.푀2 UoM, eliminating all overlap. It is based on Einstein and associated Crenel Physics UoM: Planck. In chapter 2 we will embed Boltzmann. To avoid 푃 .퐶2 confusion we refer to our consolidated system as Crenel 퐶 퐶 퐺 = = ⁄푃. Thus: Physics as opposed to ‘Metric Physics’. 푃.푃 푪 푮 ≡ ퟏ (CP1.2) Because ‘c’ is a universal natural constant, the equation 푪푷 푷 퐸 = 푚. 푐2 describes a universal (thus non-relativistic) conversion between mass and energy. This is a decisive In Planck’s equation 퐸 = ℎ. 휐 energy ‘E’ is expressed in -1 argument for both properties to share a common basis. That Packages and frequency ′휐′ is expressed in Crenel (the Crenel -1 shared basis is associated with content. All physical objects Physics counterpart of seconds ). This gives the Crenel have content, which can be expressed in the mass UoM as well Physics version of Planck’s constant ‘h’: as in the energy UoM. Therefore we can do with one (and no 풉푪푷 ≡ ퟏ 푪. 푷 (CP1.3) more than one) measure for content. Within the Crenel Physics model we will name it ‘Package’ (symbol ‘P’). With three natural constants cCP, GCP and hCP defined, we now have the following three equations: By expressing both E and m in ‘P(ackages)’ we implicitly normalized the conversion factor 푐2 in 퐸 = 푚. 푐2 to unity (the For light velocity c: dimensionless 1). And therefore ‘c’ is also equal to unity: 1 (dimensionless) = c (m.s-1) (1.4) For Planck’s constant h: 풄푪푷 ≡ ퟏ (CP1.1) 1 P.C = ℎ (N.m.s) (1.5) Note: in the following the subscript ‘CP’ indicates that this is the Crenel Physics version of some property. The ‘CP’ in the equation For the gravitational constant G: 1 C.P-1 = G (Nm2kg-2) (1.6) Page | 1 Crenel Physics © Hans van Kessel [email protected] The left sides in the above equations express the natural 풉.푮 ퟏ 푪풓풆풏풆풍 = √ ퟑ (풎풆풕풆풓) (1.12) constants (cCP, hCP and GCP respectively) in Crenel Physics 풄 UoM whereas the right sides express these in Metric Physics =4.0512x10-35m UoM. From these three equations we can extract P and C, and And, because one meter corresponds to c-1 seconds: express these in Metric UoM as follows: In equation (1.5) the symbol ‘s’ in the UoM can be replaced by 풉.푮 ퟏ 푪풓풆풏풆풍 = √ (풔풆풄풐풏풅풔) (1.13) c meters because 1 second corresponds to c meters. This results 풄ퟓ -43 in: =1.3513x10 s 2 Equations (1.9) through (1.13) show resemblance with the 1.P.C = ℎ.c (N.m ) (1.7) well-known Planck’s natural UoM, albeit that the above Based on Einstein’s E=m.c2, 1 kg corresponds to c2 Joules or c2 equations hold Planck’s constant ‘h’, whereas Planck’s UoM (N.m). In equation (1.6) the kg-2 in the UoM can therefore be hold the reduced Planck constant ‘h/2.’ (symbol ‘ℏ’ ). Had for replaced by c-4 (N-2.m-2): Planck’s equation E = ℎ. 휐 the alternate version E = ℏ휔 been used in the above, this would have led to full consistency with 1 C.P-1 = G.c-4 (N.m2.N-2m-2) = G.c-4 (N-1) (1.8) Planck’s units of measurement. Dividing equation (1.7) by equation (1.8) gives: Crenel Physics is frequency based, whereas Planck’s UoM are based on angular frequency. ℎ. 푐5 ℎ. 푐5 푃2 = (푁2. 푚2) = (퐽표푢푙푒2) The above demonstrates how a consolidated system of UoM – 퐺 퐺 based on Crenel and Package only- nevertheless delivered a set Or: of measures for mass, energy, frequency, time and distance, based on universal natural constants only. And moreover: these 풉.풄ퟓ ퟏ 푷풂풄풌풂품풆 = √ (푱풐풖풍풆풔) (1.9) are consistent with the historically known Planck UoM. 푮 =4.9033x109 J With c normalized to dimensionless 1, in Crenel Physics we can simplify the found measures: Because 1 Joule equals c-2 kg: 풉 ퟏ 푷 = √ 풄풑 in 푒푛푒푟푔푦 푈표푀 (CP1.14) 풉.풄 푮 ퟏ 푷풂풄풌풂품풆 = √ (풌풊풍풐품풓풂풎풎풆풔) (1.10) 풄풑 푮 -8 풉 =5.4557x10 kg ퟏ 푷 = √ 풄풑 in 푚푎푠푠 푈표푀 (CP1.15) 푮풄풑 Based on 퐸 = ℎ. 휐, equation (1.9) can be converted to -1 ퟏ frequency (in seconds ): ퟏ 푷 = √ in 푓푟푒푞푢푒푛푐푦 푈표푀 (CP1.16) 풉풄풑.푮풄풑 ℎ. 푐5 1 푐5 1 푃푎푐푘푎푔푒 = √ × (푠−1) = √ (푠−1 ) 퐺 ℎ ℎ. 퐺 ퟏ 푪 = √풉풄풑. 푮풄풑 in 푑푠푡푎푛푐푒 푈표푀 (CP1.17) or: ퟏ 푪 = √풉풄풑. 푮풄풑 in 푡푚푒 푈표푀 (CP1.18) 풄ퟓ Note that –as indicated- these equations are valid in the Crenel ퟏ 푷풂풄풌풂품풆 = √ (푯풆풓풕풛) (1.11) 풉.푮 Physics system of UoM (or for that matter: in any other system =7.4001x1042 Hz of UoM in which light velocity ‘c’ has been normalized to a dimensionless 1). Multiplying equation (1.7) with equation (1.8) gives: Equation (CP1.16) universally converts Packages to frequency ℎ. 퐺 -1 2 2 units, thus to Crenel . Consequently, there is a universal 퐶 = 3 (푚푒푡푒푟 ) 푐 relationship between both. To see the implication of this Or: equation, we first review the mathematical procedure to Page | 2 Crenel Physics © Hans van Kessel [email protected] convert content (per (CP1.14) or (CP1.15) ) to whereabouts The above equation shows how an increase of content can be (per (CP1.17) or (CP1.18) ). compensated by a decrease of whereabouts. That conversion procedure consists of two steps: This exchangeability will be further addressed later.