WO2021107789A2 - Time translation symmetry breaking electrical energy generation systems - Google Patents

Description

Description

Title of Invention : Time Translation Symmetry Breaking Electrical

Energy Generation Systems

[1] Thi s patent is for TTSBEEGS (Time Translation Symmetry Breaking Electrical Energy Generation Systems) which are essentially the configuration of SC (Superconducting) primary windings serving as energy generators inductively coupled to secondary windings serving as energy extractors; the primary and secondary windings form TTSBEEGS transformers which must be interconnected on the primary side either in series, in parallel, or a combination in series and in parallel to at least one current source so as to form a SC closed circuit. The extractor windings are inductively coupled to the generator windings thus preserving the integrity of the SC closed circuit. The energy yield is theoretically determined via transformer and circuit physics. Essential to TTSBEEGS are SC components with which TTS (Time Translation Symmetry) is broken and at the time of this patent SC components still required cryogenic cooling to maintain the SC state. The critical operating parameters are temperature, magnetic field density and the current.

Fig·1

[2] 1 current source.

[3]2, 3, 4, 5 SC primary windings or generator windings interconnected in series

[4]6, 7, 8, 9 SC or copper secondary windings depending on source current

[5] 10 power applications or transformer functions for power supply

[6] 11 junction of 4 phase supply rail

[7]The Helmholtz SC free energy density function is defined Δf = where the

critical magnetic field density is B_c = B_C(0)(1 — ). The generator windings 2, 3, 4, 5 have

the total free energy density ∑_fi f_i = f₂ + f₃ + f₄ + f₅ where the subscripts identify the corresponding generator windings in diagram 1; if ∑_fi f_i strictly satisfies the condition while the system is generating energy then in accordance with the TTSB (Time

Translation Symmetry Breaking) axioms the circuit is a TTSBEEGS. B_c is the manufacturer’s rated critical magnetic field density, T_c is the critical temperature, T < T_c is the operating temperature and B_c( 0) is the rated critical magnetic field density at T = OK.

[8]6, 7, 8, 9 are secondary winding inductively coupled to the respective generator windings. They are SC if the generators windings are energized by a direct constant current source and copper if the generators windings are energized by an alternating current source. The phase common supply rail is not essential, however theoretical phase investigations reveal the potential to alter the load characteristic which may be useful in managing peak loads of TTSBEEGS that have an alternating current source; see Fig.10.

[9]Fig.l is a circuit so in principle the power and potential energy of the generator windings can be calculated using Kirchhoff s 1^st law, Joules law, Faraday’s law and Ampere’s law applied to solenoids and transformers.

[10] Nomenclature for the double subscript format used in proofs and general statements; Let

differentiates each parameter in terms of the primary s = 1 & secondary s = 2 sides and i identifies specific transformers; i.e. is the magnetic field density generated by

the generator windings.

[11] Inductance L_{i, σ} relates to flux where L_{i σ} is the

length of the windings, A is the cross section area of the coil and N_{i, σ} are the number of winding turns. By Faraday’s law |ε| =

and extending Kirchhoff s 1st law for series resistance, the EMF of four series connected SC generator windings is

+

-

is a sum of the free energy contributions F_{/ .} Let F_c be the free energy maximum at temperature T given the parameters I_c, B_C,T: T < T_C for the SC wire used to build SC generator windings, then given the condition ∑_Fi F_i,1 < F_c is satisfied, the TTSB axioms are also satisfied and the system will operate as a TTSBEEGS.

[12] For all of the following proofs and empirical calculations, secondary windings are assumed to be copper and the current source alternating. The coupling configurations 2 & 6, 3 & 7, 4 & 8, 5 & 9 in Fig.l are generator transformers, therefore assuming the losses due to the individual transformers such as copper losses, iron loses, reluctance and flux leakage add as individual resistive loads, then these loses can be calculated using transformer physics.

[13] Theorem; I_i,1 = transformer currents scale proportional to the

quotient of the primary windings turns N_i,1 and the secondary windings turns N_{i ,2}

[14] Proof: Given transformer equation then

[15] In principle the effective impedance Z_{i, σ} = can be used to

determine the potential power of a TTSBEEGS.

[16] Theorem; transformer impedances scale proportional to

the squared quotient of the primary and secondary windings.

[17] Proof: Let X_L = 0,X_C = 0 thus Z_{i, σ} = R_{i, σ .} by Joules law l²R = P and by ohms law

[18] A SC current is expected to generate self inductance due to the phase displacement crossing the flux lines of the orbiting SC charge carriers, this is expected to be a limiting factor giving rise to I_c, B_c and T_c. However, the effective impedance doesn’t need to account for this; the consideration is limited to determine the potential energy and power yield.

[19] Let Z_i,1 = √(R_i,1)² + ( X_L + Xc)² _i,1 = 0 be the ideal impedance in the absence of a B field. By Joules law the potential peak power of 4 generator windings interconnected in series to a current source is P = I² _sZ_1,1 + I² _sZ_2,1 + I² _sZ_3,1 + I² _sZ_4,1 = I² _s ∑_zi Z_i,1; in terms of inductive reactance I² _s ∑_zi Z_i,1 = I² _s ∑_XiX_i,1 = 2πfl² ∑_Li L_i,1 = 2πfI² _s(L_1,1 + L_2,1 + T_3,1 + L_4,1)·

[20] Theorem: I² _si,1Z_i,1 = I² _si,2Z_i2∀i ∈ N ≥ 1 generator transformers have local 1 to 1 symmetry [21] Proof: let N_i,1 # N_{i ,2} & Z_i,1 # Z_{i ,2} Assume no local 1 to 1 symmetry. By Joules law

which is a contradiction, by extension P₁₍₁

thus = I² _si,2Z_i2∀i ∈ N ≥ 1 generator transformers have local 1 to 1 symmetry·

[22] Corollary: /_s = /_i,1Vt ∀i ∈ N due to local 1 to 1 symmetry it follows that the source current I_s flows equally through the generator windings connected in series.

[23] Proof: Assume I_i,1 # I_s therefore

which is a contradiction since the power of generator transformers has local 1 to 1 symmetry thus I_s = I_i,1∀i ∈ N ·

[24] The theory is sufficiently advanced to explicitly prove that not only is the circuit in Fig.1 a TTSBEEGS, but also show that the production of electricity over and above the input energy is physically possible by today’s superconductor manufacturing standards.

[25] The superconductor wire manufacturers Superpower have published the performance characteristics of enhance AP wire Ref.15 in which they published plots showing I_s as a function of B at various fixed temperatures. Each plot illustrates the maximum I_s for any given corresponding maximum B field and constant operating temperature. Making use of inductive reactance X = 2 πfL = 2πfNΦI_s ^-1 = 2πfNBAI_s ^-1 , power is generally stated in terms of the magnetic field density P and since there’s local 1 to 1

symmetry then it follows that given any constant operating temperature T < T_c, a SC transformer always has a maximum local power limit determined from the source current and the generated B field; see Fig.11 for the characteristic P verses B curve which illustrates the optimal ranges given T.

[26] To explicitly prove that the circuit in Fig.1 is a TTSBEEGS, let the source current I_s < I_c flow through n = 4 identical generator windings 2, 3, 4, 5 each having the number of windings N wound onto cores with the cross section area πr². Let the temperature be constant at T < T_C then the potential power is P_i,1 = 2π²r²fI_sN ∑_Bi P_i = 8π²r² fI_sNB_s. It also follows that given T & I_S there is a measured critical magnetic field density B_c that fails the SC state. However by construction each transformer satisfies the condition B_s < B_c thus the free energy condition F < F_c is never violated [27] Proof: let I_s < I _C, T < T_c, B_s < B_c then by local 1 to 1 symmetry

the power

due to /₅, P_s thus the free energy condition is always satisfied·

[28] Is there a global count that needs to be considered since nB_s > B_c → nF_s > F_C: F_S < F_c? A geometric argument is constructed to answer this question. Let F_k be the free energy used to generated peak power given the peak SC alternating current source /_s < I_c and

the constant operating temperature and the power extracted per windings is Let

lengths l_k = l_{i ,2} and the number of turns

so the magnetic density B_k = B_k nl_k = l_s,nN_k = N_s such that the SC

windings N_S are uniformly distributed preserving the magnetic field density B_k in any arbitrarily selected length l_k completely contained within the SC generator core’s length l_s. Since nl_k = nl_{i ,2} then nN_{i ,2} inductively coupled secondary windings can be compactly wound side to side and without overlap onto the rescaled generator coil of length l_s.

[29] Letting → denote the inductive coupling of secondary extractor windings with generator windings, the newly constructed magnetic circuit is nB_{i ,2 i} → B_s where the locally conserved B field always satisfy B_{i ,2} → B_s < B_c∀i ∈ N > 1. Thus n → 1: n ∈ N > 1 the number symmetry can be violated while preserving the local B field B_k = B_{i ,2} = B_s < B_c: nB_k > B_c.

[30] Proof: Let l_k = l_{i ,2} ∀i ∈ N, N_k # N_{i ,2} = N_1,2 Vi, nl_k = l_s, nN_k = N_s, by local 1 to 1 symmetry N_k2I_k2 = N_kI_s and by geometric construction nB_{i ,2} → B_s Thus nB_k doesn’t change the

magnitude of B_k so the condition B_k < B_c is satisfied while violating number symmetry·

[31] Number symmetry violation is a consequence of TTSB and due to the true cost of power generated by a superconducting current equalling zero as detailed by axiom 3 and subsequently proven. The size of a current may vary due to inductive reactance changes, temperature changes or changes to an applied magnetic field and by equivalence this may present as resistance; however it is only an apparent resistance if the current is truly SC. If a SC ring is left for a period of time where the operating temperature and the externally magnetic field density are constant then in principal the current will circulate endlessly and its magnitude will not change. The only way this can happen is if the resistance within the SC wire is truly zero since the alternative R > 0 dissipates energy.

[32] Theorem 0 = I² _sR the real cost of power produced by a SC current is always zero.

[33] Proof: 0 = I² _sR, let a SC current /_s > 0, R = 0 therefore P = I² _sR ↔ P = I² _s0 ↔ P =

0 ↔ I² _sR = 0·

[34] In conclusion, the circuit in Fig.1 can be physically built today and the potential power yield of such a TTSBEEGS scales linearly with the number of transformers. Since n is unbounded, the potential power yield is unbounded 2π²r²fI_snN_kB_k = nP_{k .}

[35] The following empirical exercise determines the power yield and some basic performance characteristic of a TTSBEEGS; the construction is designed so that two layers of

4mm 2^nd GEN HTSC wire exactly fit onto a core of length so that the cryogenic

coolant easily penetrates the windings. Note that these calculation can be done with respect to a direct current by determining the scale of / = s and assuming I_s = I_{p .} The core is selected to satisfy the relative permeability μ_{r .} Let B = 8 T, I_s = 200A, l = 2m, μ_r = 63.66NA^-1, r = 0.1m, / = 50 Hz, N_i,1 = 1000, N_{i 2} = 2786, T = 20 K. The values B = 8T and

4 = 2004 are consistent with the wire characteristics Ref.15, where strictly

Given r = 0.1m and N_i,1 = 1000 the optimised power yield is estimated by the P vs B curves in Fig.12, and the estimated yield limit for this system is 4 U = 90 MJ . →

ce can be restated

and since the primary side has no resistance, the impedance for an ideal inductor is Z_i,1 = 394.75Ωz90°. [40] Assuming no load losses of 2% per generator windings; (1 — 0.02)15.79 MJ =

15.47

local 1 to 1 symmetry Z_i,1 =

thus the no load impedance i Checking via the

imaginary form gives Z_i,1 = The transformers are identical thus the impedances across two is The Inductance remains 89° thus the sum of the four impedances must be

[41] Calculating the expected transformation of energy ready for high voltage power grid transportation; the voltage in the secondary windings per transformer is 220000V and therefore the current is /

which is approximately 71.24 and the sum total is 4 X 71.24 = 2874. This voltage setting satisfies NZ 220 kV transport grid specification and the power can be divided ready for transport. There are a number of assumptions built into these figures, however the governing formula is easily customised to meet any additional physical constraints not accounted for.

Fig-2

[42] 12 source current

[43] 13, 14, 15, 16 SC secondary generator windings & induced current sources

[44] 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28 sets of SC primary windings connected in series

[45] 29, 30, 31, 32, 33, 34, 35, 36 SC or copper secondary windings depending on source current

[46] 37, 38 Load applications or transformer functions for power supply

[47] 39 enclosed circuit

[48] 40, 41 duplicated circuits enclosed by 39

[49] 42 junction of 4 phase supply rail

[50] Fig.2 details a circuit that will generate an exponential increase in the total power yield. The circuit enclosed by 39 is identical in layout to the circuit detailed by Fig.2, however its current source is an induced current source induced by SC windings 13. The SC primary windings 17, 18, 19, 20 are coupled with SC secondary windings 13, 14, 15, 16 and in principle, couplings 19 & 16, 18 & 13, 17 & 14, 20 & 15 are ideal transformers. The behaviour and power yield of circuits of this type is expected to remain consistent with the physics of series connected generator windings. The material from which 29 to 36 are constructed depends on the current source selected to drive the system; again SC if the current source is constant and copper if it is an alternating current source.

Fig-3

[51] 43 source current

[52] 44, 45, 46, 47 SC primary generator windings connected in parallel

[53] 48, 49, 50, 51 SC or copper secondary windings depending on source current

[54] 52 Load application or transformer functions for power supply

[55] 53 junction of 4 phase supply rail

[56] Fig.3 details the layout of TTSBEEGS with generator windings 44, 45, 46, 47 connected in parallel. The inductively coupled secondary windings 48, 49, 50, 51 connect to a non essential four phase supply rail 53 ready to do work and other various useful functions 52. The current source may be alternating or direct; the choice determines the construction material of the secondary winding. With respect to an alternating current source, the phase supply rail has the property of altering the current drawn due to the difference in phase angles that results from loads applied asymmetrically across the parallel branches. Only when the phase angles are equal is the maximum current drawn equally, see Fig.10.

[57] The potential power of the generator windings connected in parallel are expected to obey normal circuit physics. Given proportional impedance is The total impedance

[58] The sum of parallel currents however given

then the free energy condition is always satisfied since by local 1 to 1 symmetry a variable current can’t exceed its source I_s.

[59] Due to the circuit geometry the current divides proportional to the inductive reactance given the primary side EMF is and the free energy is expected

N_i,1, l_s = l_i,1, 4 > /_{; i} Vi G N > 1, then the free energy limit of n identical SC primary windings is F_ma

dl and the condition VB_i,1: B_i,1 £ B_s < B_c is satisfied since AI_i,1 < 4 < 4^: 4_,i

Thus 4 is limited by design parameters JV_S, 4 to ensure the system remains SC while maximally loaded, unloaded, or a mixed state, since If F_t £ F_max then 4 < 4VF_{f .}

[61] The number symmetry, n_{k i}→ 1 is the numerical description of SC charge carriers having the same macroscopic wave function. However the topology of a parallel circuit is expected to constrain the underlying field (L X A) E Έ/2Έ thereby dividing a constant current |41 into parallel interconnected generator windings in accord with Kirchhoff s laws. The assumption is that the impedance to the perturbation of the C’pair harmonic oscillators is fundamentally different to the resistance that arises due to free electron collisions of normal current producing charge carriers; however the impedance is still a function of B. For direct current the function lim_{ΔF →0} F_t = nF_s must also be considered even though F_t = nF_t is the lowest energy configuration; this is because the changing electromotive force

may be driven by a constant current I_s while /,· < I_s, thus current may be driven into parallel branches.

[62] A direct current is expected to induce current in secondary SC windings due to conduction via phonon transport, therefore the generator windings can be replaced with a permanent magnet, see Fig.8. However while the net change in direct current remains zero, direct current cannot be induced to flow in normal conducting secondary winding without a governor; see Fig.6 Fig.7 Fig.9.

[63] An empirical exercise forFig.3 follows. Using values B = 8 T, l = 2m, T = 20 K,

394.8Ω → U_t = 394.8Ω X 200² = 15.79 MJ. Given an alternating current source, the power yield is significantly less than series interconnected SC generator windings.

Fig-4

[64] 54 source current

[65] 59, 60, 61, 62 SC dual purpose secondary generator windings & secondary current source

[66] 55, 56, 57, 58, 64, 65, 66, 67 sets of SC generator windings connected in parallel

[67] 68, 69, 70, 71 SC or copper secondary windings, depending on source current

[68] 63 enclosed circuit

[69] 73, 74, 75 duplicate circuits defined by 63

[70] 72 transformation functions for power supply

[71] 76 junction of 4 phase supply rail

[72] 54 is the source current, windings 55, 56, 57, 58 & 64, 65, 66, 67 are the primary generator windings. 59, 60, 61, 62 are secondary generator windings coupled with 55, 56, 57, 58 to form generator to generator ideal transformers and the primary generator windings 64, 65, 66, 67 are driven by the generator to generator coupled ideal transformers. Areas 73, 74, 75 are duplicate circuits detailed by the circuit enclosed by 63.

Fig.5

[73] 77 primary current source

[74] 78 SC secondary windings, generated secondary current source

[75] 82,83, SC primary windings connected in parallel with series connected 81 & 85

[76] 81, 85, SC primary windings connected in series

[77] 84 SC primary windings connected in parallel with 79 & 80

[78] 79, 80 SC primary windings connected in series

[79] 86, 87, 90, 91, 92, 93 SC or copper secondary windings depending on source current

[80] 88, 89 LA or transformer functions for LA or power supply [81] 94 junction of 3 phases current supply rail [82] The circuit is an example of a combination of parallel and series connected SC generator windings. 77 is the current source that energizes two distinctive circuits. However 78 is a secondary current source that is at most 90^° out of phase with the circuit driven by 77. The 3- phases supply rail 94, ensures phase integrity of the extracted energy. How the load distributes across the individual extractor windings 90, 91, 93 and 86, 87, 93 changes energy distribution. i

[83] The total free energy F_t

F_p is the sum of the series connected generator windings nF_s and of the parallel connected generator windings

The total free energy assumes a changing current which enables 1 to 1 symmetry calculations and is applicable to both direct and alternating source currents. This assumes the total energy in generator windings energized by a direct current has the maximum range 0 < l_i,1 < I_s where /_s is the source current.

Fig.6 Fig.7 Fig.9

[84] Fig.6 Fig.7 Fig.9 detail minimal TTSBEEGS systems where the generator windings are interconnected either in series or in parallel with a direct current source and where the current is directed by a governor. Fig.9 details a mixed system interconnected both in series and in parallel and connected to a direct current source that is directed by a governor. 94, 110, 111 are current sources. 96, 97, 103, 104 and 112 to 118 are primary SC generator windings.

100, 108, 126, 127 are power functions that use the power generated. 98, 99, 105, 106 and

119 to 124 are secondary copper windings. 130 is also secondary copper windings, however its role is to act as a current source. The systems are grounded as detailed by 95, 102, and 128 and they have governors detailed by 101, 109, 129. The function of the governor is to divert and dissipate current and then redirect the current to reenergize the generator windings in a periodic fashion thus making the current variable. 125 is the phase supply rail.

Fig-8

[85] Fig.8 is a cylindrical bar magnet with SC wire wound around the axial length of the magnet such that the SC wire is in contact with the long sides of the magnet and so that the polls of the magnet labelled with N for the north pole and S for the south pole are the two sides that don’t come into contact with SC wire assuming the geometry of the cylinder bar magnet has 3 sides and two edges. The arrows show the predicted direction of flow of the induced constant SC current produced from the phonon transport of the potential difference that develops due to the phase shift between the electrons of C’pair ground state harmonic oscillators so as to minimize the forced exerted on the electrons by the magnetic field.

Graphs List

Fig.10

[86] Fig.10 graphs current in amps verse the phase angle ratio.

Fig· 11

[87] Fig.11 graphs power in mega joules per second verses the magnetic field density in Tesla at different temperatures defined by the legend on the right side of the figure.

Fig.12

[88] Fig.12 graphs the partial energy gap verses the phase angle for type II superconductors.

Fig.13

[89] Fig.13 graphs the partial energy gap verses the phase angle for type I superconductors.

Fig.14

[90] Fig.14 graphs the magnetisation verses the magnetic field density of type I superconductors.

Fig.15

[91] Fig.15 graphs the magnetisation verses the magnetic field density of type II superconductors.

Technical Field

[92] This invention relates to the configuration an operation of superconducting and non superconducting electrical components for the generation of TTSB (Time Translation Symmetry Breaking) electrical energy.

Technical Problem

[93] The technical body considers energy conservation beyond reproach; TTSB energy is considered impossible since essentially the energy is free requiring only instantiation and material cost. The technical misunderstanding of TTSB is a complex matter and must be rigorously addressed. Solutions to Problem

[94] The problem is addressed in four parts; 1^st Clarification of conserved energy foundation and TTSB; 2^nd demonstrate natural systems violate energy conservation; 3^rd prove the TTSB property of a Superconductors; 4^th define buildable TTSBEEGS. Axioms address technical problem 1; the binary system of brown dwarfs and the energy density of an expanding universe address technical problem 2; The theoretical investigation of superconductivity address technical problem 3; All of the diagrams from Fig.l to Fig.9 and the supporting text address technical problem 4.

Advantageous Effects of Invention

[95] The use of superconductors to generate TTSB energy enables weather-independent reliable clean energy that can be situated anywhere; energy that will power a future where mankind can mitigate the effects of climate change and service the worlds growing energy demand. It will also enable mankind to readdress fundamental assumptions about the nature of our universe.

Citation List

[96] Ref.l F. Wilczek, Phys. Rev. Lett. 109, 160401 (2012)

[97] Ref.2 F. Wilczek, Phys. Rev. Lett. 109, 160402 (2012)

[98] Ref.3. Bruno, arXiv: 1211.4124vl (2012)

[99] Ref.4 Z Eker et al, arXiv:1501.06585vl (2015)

[100] Ref.5 Marcello Carla, Am. J. Phys. Vol. 81, No. 7 (2013)

[101] Ref.6 Tongcang Li et al, Phys. Rev. Lett. 109, 163001 (2012)

[102] Ref.7 P. Bruno, arXiv: 1210.4792vl (2012)

[103] Ref.8 Tongcang Li et al, arXiv: 1212.6959 (2013)

[104] Ref.9 Ryusuke Nakasaki et al, Continuous Improvements in Performance and Quality of 2G HTS Wires Produced by IBAD-MOCVD for Coils Applications, Superpower Inc, Furukawa Electric Co Ltd, International Conference on Magnet Technology, Seoul, Korea, 24 October 2015

[105] Ref 10 Drew W Hazelton, Recent Developments in 2G HTS Coil Technology, Superpower Inc, Applied Superconductivity Conference Washington, DC August 1-6, 2010 [106] Ref.l 1 Yifei Zhang et al, Progress in production and performance of second generation (2G) HTS wire for practical applications, IEEE 2013 International Conference on Applied Superconductivity and Electromagnetic Devices, Superpower Inc. is a subsidiary of Furukawa Electric Co. Ltd. Beijing, China, October 25-27, 2013

[107] Ref.12 McLyman, Colonel Wm. T, High reliability of magnetic devices: design and fabrication,. Dekker Marcel, New York, 2002

[108] Ref.13 Yue Wang et al, Phys. Rev. B 83, 054509 (2011).

[109] Ref.14 Rajveer Jha et al, Revisiting heat capacity of bulk polycrystalline YBa₂Cu₃O_7-δ National Physics Laboratory (CSIR), New Delhi-110012, India.

[110] Ref.15 Ryusuke Nakasaki et al, lMOr2A-03++Superpower-Inc+ASC-2016+Final, Progress of 2G HTS Wire Development at Superpower, Superpower Inc., Furukawa Electric Co., Ltd, Denver USA, 2016

Theoretical Investigations

[111] Emmy Noether is recognized for her theoretical contributions showing how all conservation laws result from symmetries i.e. energy conservation is the physical correspondence of time translation symmetry. However some of the academic papers in the Citation List have misunderstood the limited application of Noether theorem with respect to TTSB Time Translation Symmetry Breaking and it is therefore necessary to clarify the foundational physics defining TTSB. A set of free energy axioms will be stated and proven so that the inconsistencies are easily identified and made consistent with Noether’s Theorem and TTSB.

[112] Axiom 1 : ΔP_ε(t₀ + Δt) > 0, A system that breaks time translation symmetry creates real positive energy; energy destruction 0 < Pt < P_ct is addressed by Axiom 5 since the inequality implies a limit when all the energy is destroyed Pt = 0. Let the total energy be

Pt = (P_ε + P_c)t where P_c is the total conserved power, R_ε is the total non-conserved power and time t = (t₀ + At) where t₀ is the initial time used to define positive energy at t₀ and At is time translation.

thus a system that generates real non conserved positive energy violates energy conservation, therefore ΔP_εΔt > 0 ■

[114] In Ref.1 and Ref.2 Wilczek implied the existence of a middle ground where a time crystal may violate TTS Time Translation Symmetry without violating perpetual motion of the 3^rd kind or 1st kind. Axiom 1 proves no middle ground exists and perpetual motion of the 1^st kind is created when TTS is broken, which is also contrary to Bruno’s understanding Ref. 3, Ref.7.

[115] Axiom 2: ΔF = ΔP_εt By time translation, the change in the total free energy of Pt₀ equals the change in the total created non-conserved energy.

[116] then the total free energy at the initial time t₀ is

by time translation symmetry a change in the total free energy is equal to the change in the total created non-conserved energy ΔF = ΔP_εt, thus there is no hidden free energy·

[117] Axiom 3: C = 0 the cost of generating positive free energy is always zero.

[118] Proof: Let ΔF, F ∈ R > 0 where F is the total free energy ΔF is the change to the free energy and let C be the costs to produce the total free energy. Assume free energy costs is

[119] Axiom 4: The principle of energy conservation

applies to a TTSBEEGS only in the limits.

[120]

supposes a state that violates TTS persists while the free energy condition 0 < ΔF = P_ut < P_εt is true; proof will be given in two parts; 1^st) proof the limit exists and 2^nd) evaluate the limit. is trivially verified by direct evaluation of

the total energy P

[121] Constructing a generalised free energy function

where the function P_u depends on n controlled parameters and therefore the function is well behaved. The function F(P_U) represents the energy that can potentially exit the boundary isolating a TTSBEEGS and P_εt is the maximum potential free energy limit of the isolated system. Accounting for the total energy due to selecting any 1 of n parameters to reach the limit,

[122] Proof: part 1 the limit exists; let e, d, t₀, P_c, R_ε E M > 0; P_u, At E M > 0 t = t₀ + At given limp _®p (R_e + P_c)t — P_ut = P_ct then if the limit exists 35 > 0 ne > 0 such that

[123] Par

P_ct «® (

[124] Axiom A system that breaks TTS can destroy real positive energy.

[125] Proof: Δ The total energy in this TTSB System is Pt = (P_c — P_ε)t where P_c is

the total conserved power, P_ε is the TTSB power over time translation t = (t₀ + Δt). Let

[126] Axiom 5 also implies

_{£ c} 0 thus the system is conserved in the limit ■ ■ However the definition may be ambiguous since it is a contradiction to destroy conserved energy. For clarity, the definition is Newtonian conserved energy is destroyed due to TTS violations.

[127] The misapplication of energy conservation to TTSB and specifically QTC Quantum Time Crystals led to the widely adopted misconception known as the “No Go Proof’, the result of Buno’s correspondence Ref.3. Bruno’s paper is a reply to Wilczek’s paper Ref.l in which Wilczek proposed a theoretical coulomb charged particle with attractive particle to particle interactions. However, the following classical proposal, somewhat analogous to Wilczek’s proposal, demonstrates energy isn’t conserved. Furthermore in an expanding universe energy is destroyed and Bruno’s solution Ref.7 is a contradiction as it also violates energy conservation. [128] Consider a ring of real distinguishable particles acting under the influence of gravity; particles sufficiently large in number and biased so as to form a binary system of brown dwarfs with equal mass; it shall be shown that such a system violates perpetual momentum of the 1^st and 3^rd kind and spontaneously generates conserved angular momentum.

[129] According to Stefan Boltzmann law each dwarf star will radiate power P = σ∈A ΔT⁴ into the surroundings where ΔT⁴ = T⁴ — T_b is the surface temperature difference of the dwarf star T_s from the background T_{b .} Under the force of gravity the system develops perpetual motion of the 3^rd kind as they orbit a common centre of mass at r/2 where the stars do work on each other at all orbital trajectory points except perihelion and aphelion. The system also develops conserved angular momentum L_t = mωr² and if an instability is introduce so that in the limit the separation r → 0, a single body is formed; the equivalent of Bruno’s standing wave Ref.3. Assuming the single body doesn’t become a main sequence star, then the solution also radiates power P = σ∈A ΔT⁴ into the universe and has the same angular momentum L_{1 ,}

[130] The accelerating expansion of the universe, where the Friedmann-Lemaitre-Robertson- Walker metric is parameterised with zero curvature, has lead to the generally accepted fact that the cosmos will undergo a thermodynamic heat death.

[131] Consider the following simplified model defining the visible universe’s energy density given the total energy U₀ at t₀ and where r = CΔt defines the radius in terms of

At which is the time from the big bang until today and C the speed of light. In this simple model, the universe expands with t³ and the energy density decreases to zero in the limit; lim_r →_∞ E(r) = 0. The argument can be made more definite by the restriction lim_r →_r E(r ) = ph where h is some finite radius given p\ 0 < p < 1 where p is the density per unit time scalar and h is Plank’s constant.

[132] Consider the final rest state

which is an eternal conserved state. By Noether theorem, all extrapolations from this final state to all preceding states must conserve the final state. However Therefore today’s energetic

expanding universe violates TTS on the cosmic time scale.

[133] Tongcang Li et al Ref.6 proposed a more reasonable model for a time crystal, a model that is experimentally testable. Bruno Ref.7 also challenged this model but Tongcang Li et al Ref.8 successfully rebutted Bruno in a manner consistent with the axioms. Also, Bruno’s solution is a thermodynamic sink that violates TTS in the limit since pinning potentials are destroyed.

[134] Bruno’s argument gives

[135] Proof: let

Evaluating the limits in the order

posed by Bruno reveals a thermodynamic sink when N = ¥ for all pinning potentials v > 0 since

[136] The widespread misunderstanding of Noether Theorem, TTS and TTSB assumes that energy conservation can never be broken. However, energy conservation has limited application to systems that break TTS physics, and the misunderstanding has made it difficult to progress TTSBEEGS. The axiomatic proofs clarify TTSB physics and establish general theoretical conditions governing the application of energy conservation to TTSB systems.

Theoretical Investigation of Superconductivity

[137] It is also necessary to address the claim by Wilczek and Tongcang li et al Ref. 1, Ref.6 that a SC (Super-Conducting) ring doesn’t violate TTS. Specifically, Wilczek claimed “if the current is constant then nothing changes in time so time-translation symmetry is not broken...” and Tongcang li et al claimed “the wave functions are homogeneous and no time translation symmetry is broken”. However, their conclusion is inconsistent with Faradays Law.

[138] Consider the following naive derivation of Df due to a solenoid of windings with the cross section area A_w made from N turns of SC wire with the cross section area A_s and threaded with a changing SC current density By Faraday’s law the changing

magnetic flux due to windings threaded with the changing SC current density ΔJ_S is £ =

[139] Given the definition / = nev_d , the change in the SC current density over the change in n. By Newton’s law F = eE = m_sa thus Faraday’s law is restated n where n_s is the charge carrier density, e is the charge of the SC charge

carriers, v_d is the average drift velocity of the SC charge carriers, E is the electric field, L is the inductance, m_s is the mass of the SC charge carriers and

[140] Assume the SC windings are connected to a current source for the time t₀ where at that moment At = t₀ — 0 a simple SC ring is formed, threaded with the SC current density J₀ generating a constant magnetic field density B ; then the total change in the magnetic flux is

[141] Using the convention if current flows through a coil in the t

direction then the magnetic field is in the k direction, the north pole is in - k direction, then / x E = B. Since the current and velocity are in the same direction, let

since = 1 and if / varies over the time Therefore

are two non-zero solutions

consistent with Faraday’s law in the limited sense that if t < t_Q then B > 0 and if t = t₀ then B = 0. However, a persists in SC rings threaded with current. The math also suggests that the force acting on a (Cooper pair)

C’pair harmonic oscillator has zero net charge yet it drives a persistent current? μ is a dimensionless scalar.

[142] The London brothers postulated that the SC state is a macroscopic quantum wave function and determined the SC charge carrier density distribution concentrates at the surface of the superconductor according to the London penetration depth l = and the London

curl of the current is approximately

[143] The London curl of a constant current density offers no insight into why there is a persistent magnetic field. However E correlates with Faradays law except when / = / ₀ yet the cross product

shows the net charge of a C’pair is always zero, so how can a magnetic moment be preserved in SC rings? Furthermore, the London penetration depth suggests topological dependent conduction; regardless, only 50% of the potential energy of a C’pair contributes to conduction in the real space of the SC planes.

[144] Assuming the coulomb potential of a C’pair is then the total energy of a C’pair is

,2

E_T = K + U =

— assumes completely confined waves. Setting the centripetal force of an elementary charge carrier e equal to the coulomb force gives F_c = F_ε →

thus only half of the potential energy is available as kinetic energy. In type 1 superconductors, the Coulomb potential assumes 2e = q. However, type 2 superconductors are less obvious.

[145] Due to quantization, its boson nature and a here proposed restriction on SC charge carrier mobility, the C’pair has no energy gradient. A change in the current dependent energy over time must depend on developing a phase difference in the C’pair wave functions. The energy gap is approximated by A_E(Q) =

see Fig.13; in the limit the SC state is destroyed:

the displacement to the 1^st energy state above the ground state. D_E(Q) is supported experimentally by the diamagnetic graph of type 1 superconductors, see Fig.14.

[146] The power gradient of type 2 superconductors, see Fig.12, confirms that the energy gap is mapped by which is predicted by the energy

density curve due to the magnetisation of type II superconductors see Fig.15. The vortex glass region between the two critical magnetic field densities B₁ and B₂ suggests a barrier shields half of the C’pair Coulomb interactions. A possible shielding model is A

such that due to the

intermolecular forces such that h, h are effective length scales given the fields E_b B_{j .}

[147] Eiji _j^ is an intractable problem, however functionals are used to compute the average intermolecular forces and estimate the Fermi energy. The Fermi energy can be manipulated to improve the SC potential; however modelling superconductivity is greatly simplified by assuming the phase space remains independent of doping and the Fermi energy.

[148] The heat capacity of a superconductor at the low temperature-limit supports the hypothesis that SC charge carriers have restricted access to electron graduation implying confinement rather than free electron flow. As the temperature decreases, the SC induction potential increases. Confinement also suggests individual SC charge carriers change electric potential proportional to the energy transfer of charge particles under constant acceleration, i.e. locality is conserved if the SC charge carriers recoil at the maximum amplitude thus forming antinodes. This implies that the phonons have a causal link in the propagation of SC charge. It implies SC charge carriers experience constant acceleration due to the phonons’ motive of minimizing the phase difference. In simplified sinusoidal terms, phonons restrict the transverse degree of freedom i.e. the phonons drain and store the energy of all SC charge carriers with a velocity opposing the restriction and impart the stored energy to the charge carriers with a velocity that cooperates with the restriction.

[149] This leads to the confinement hypothesis; “locally confined SC charge carriers transition to excited electron flow due to increase perturbation causing a jump from the ground state into a higher energy state, thus SC charge carries are driven normal.” The confinement hypothesis is indirectly experimentally verified by the low temperature limit heat capacity experiments of simple D-wave superconductors Fig.13, Fig.14. Phonons are prerequisite to the charge mobility and confined long-range coherency of the C’pair harmonic oscillators.

Dimensionless parameters F_u di are used to track a charge carrier’s perturbation from the ground state equilibrium.

[150] A classical approach is taken to model the SC state as confined elementary charge carriers of C’pair harmonic oscillators, in terms of a macroscopic wave distribution. Let

define sub-quantum-unit vector scales in terms of a fractional energy gap D_s =

where

be the phonon force that confines a C’pair harmonic oscillator and d_a defines the unitary perturbation from equilibrium with initial amplitude d_i = 0. Let ±d be the maximum displacement where 2d is the displacement needed to promote the C’pair electrons. By Hooke’s law the maximum force due to phonons is

, the fractional gap implies

D_E.

[151] Let a one dimensional lattice chain of N_ε elementary charge carriers form a SC ring with a circumference L_c, with uniquely indexed partitions and where the

number of C’pairs is J standing waves of length l = 2 I_f confine the

elementary charge carriers to the centre of each partition I_f as a ground state harmonic oscillator with initial perturbed amplitude d_j = 0. Let the perturbing of the harmonic oscillator parameterized by d be maximised at ( then the

maximum phonon force The harmonic oscillator projects onto the z axes vi however due to electron

promotion

where k₀: {0,1} e k₀ is the SC order parameter; assuming the phase of a C’pair is strongly correlated with a maximum difference of thus the phase limit of type 2

superconductor is quantised.

[152] Let I_l = 2 I_f, then the total of JV_S confined SC charge carriers are each uniquely identified

carrier identity is functionally differentiated with respect to its left neighbour except the datum n₀: hus SC macroscopic identity function

1 since the cardinality of L_c is always odd.

[153] Given d_h the perturbed ground state of a ring of N _S C’pairs threaded with a SC current has an energy that depends o

Note: A Gaussian sum over any given range must be adjusted to sum over a ring of n elements. To avoid double counting one of its elements, the datum 0 is counted s a finite ring closed under +,X and a finite field. By construction is a bijection that

maps particle confinement to the energy distribution. The energy distribution D is defined by

[155] is a wave

distributed over 4 quadrants; to define the energy of a SC ring before electron promotion [156] Thus Y(Z^, D) is consistent with the London macroscopic quantum wave in the aggregated sum of JV_S uniquely identified localized harmonic oscillating SC charge carriers mapped as a sinusoidal distribution via the aggregated sum over the product of the change in electron perturbation and the change in phonon force. The theoretical model is applicable to type 2 superconductors and it is expected to map to type 1 superconductors by modifying the limit ϋih_q®7G/4 F(dz ) since d{d{) maps to the perturbed displacement of the C’pair harmonic oscillator while the limit preserves quantisation.

Proof Superconducting Rings Break Time Translation Symmetry

[157] The energy transfer of the wave propagates via the phonons with speed

and relates to the harmonic oscillation speed and the period of a

harmonic oscillator is define the power

equal to the multiplicative inverses of the confinement boundaries of a C’pair recovers Faraday’s law. Thus the derivation of proves consistency with Faraday’s law and

lends convincing support for both the confinement hypothesis and the argument that a SC rings break TTS. An explicit proof that a SC simple ring threaded with a current of confined SC charge carriers breaks TTS follows. [158]

simple ring threaded with a constant current of confined SC charge carriers. By Faradays law, a changing flux is needed to generate a persistent n’t violated then

is a contradiction persistent B field produced by a SC ring threaded with a constant cu

Preamble To Claims

[159] It was necessary to seek guidance from at least three test cases to clarify how to construct claims for this patent which has moved the prior state of the art from a foundation that incorrectly considered the art of this patent impossible.

[160] This patent necessarily addresses inconsistencies and fallacies in the prior state of the art that out of ignorance, may have been used to object to TTSBEEGS which take for granted the clarified foundations of TTSB physics essential to proving TTSBEEGS are viable. By Unilever PLC v Chefaro Proprietaries Ltd (1994) RPC 567 at 580, there is scope to identify the essential inventive concept which necessarily includes clarifications of TTSB physics, which redefines the state of the art in a manner consistent with the clarifications outlined in this patent and not as an overall generalisation.

[161] It is understood that claims are written with purposive construction as defined by Catnic Components Ltd and another v Hill and smith Ltd (1982) RPC 183 at 243 and also by Kirin- Amgen Inc v Hoechst Marion Roussel Ltd (2005) RPC 9 at para 34. The purpose of some of the claims is to broadly establish precedence to consider the new scope of the art and the proofs that establish the validity thereof, and which challenges the prior state of the art interpretation of energy conservation as defined by Emmy Noether in 1918 and also challenges the claim that superconductors don’t violate TTS. The basis of the challenges are proven and defined within this document and are therefore essential to the acceptance of TTSBEEGS

Claims

Claims

[Claim 1] The law of energy conservation applies to conserved energy systems only and cannot be applied accurately and correctly to TTSB (Time Translation Symmetry Breaking) energy systems.

[Claim 2] The axioms in the section titled Theoretical Investigations are a general framework defining the limited application of energy conservation.

[Claim 3] The law of energy conservation is violated by natural systems of which both the twin dwarf stars system and our expanding universe defined within the section titled Theoretical Investigations are examples of natural systems that violate the law of energy conservation.

[Claim 4] is a general solution for an ideal TTSBEEGS that

enables the design and analysis of real TTSBEEGS.

[Claim 5] By the confinement hypothesis, a SC (Superconducting) ring threaded with a constant current is consistent with Faraday’s law and therefore violates time translation symmetry.

[Claim 6] Phonon transport of the potential difference of perturbed ground state SC Cooper pair harmonic oscillators gives rise to the persistent current threaded within a SC ring.

[Claim 7] The energizing of the SC generator windings constructed from windings of SC wire generates useful TTSB electrical energy since the cost of generating the energy is 0.

[Claim 8] The TTSB electrical energy generated by SC generator windings can be extracted for use by inductively coupling secondary windings.

[Claim 9] Generator transformers are constructed by combining SC generator windings and either normal conducting or SC secondary windings so that they are inductively coupled.

[Claim 10] TTSBEEGS are constructed by interconnecting numerous generator transformers so that the SC generator windings form a SC closed circuit and therefore the secondary windings violate number symmetry.

[Claim 11] TTSBEEGS can have an in series interconnection of numerous SC generator transformers with at least one alternating current source as represented by Fig.1 and Fig.2.

[Claim 12] TTSBEEGS can have an in parallel interconnection of numerous SC generator transformers energized by at least one alternating current source as represented by Fig.3 and Fig.4.

[Claim 13] TTSBEEGS can have a combination of an in series and an in parallel interconnection of numerous SC generator transformers energized by at least one alternating current source as represented by Fig.5.

[Claim 14] That SC windings wound around the axial length of a cylindrical bar magnet with an axially aligned magnetic field and as detailed by Fig.8 will generate a constant current within the SC windings via phonon transport.

[Claim 15] TTSBEEGS constructed as a SC circuit of numerous interconnected generator transformers either in series, in parallel or a combination in series and in parallel can be energized by a direct constant current source and produce useful and usable TTSB energy only if the secondary winding are SC windings.

[Claim 16] Fig.1, Fig.2, Fig.3, Fig.4, and Fig.5 are also representations of Claim 15

[Claim 17] TTSBEEGS constructed as a SC circuit of numerous interconnected generator transformers either in series, in parallel or a combination of in series and in parallel interconnections, can be connected to a direct constant current source and produce useful and usable TTSB energy that is extractable by inductively coupling normal conducting secondary windings when a governor is used to regulate the constant current to make it variable so as to induce current in the secondary windings.

[Claim 18] Fig.6, Fig.7 and Fig.9 are a representations of Claim 17.

[Claim 19] The design of real TTSBEEGS is not limited only to the circuit diagrams illustrated by Fig.1 to Fig.9.

[Claim 20] That alterations to real TTSBEEGS may include alterations to the number of transformers, variations to the interconnections, variations to the number of source currents and the arrangement, and changes to the choice of materials use to construct the windings.