by Manoj Agravat. Also available as: PDF, LaTeX. ... derives the Special relativity equation based on time correction. Vc/c based in ... Lorentz contraction states there is a symmetry transformation as evidenced in for time and velocity. Einstein ...
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Time dilation by Manoj Agravat Also available as: PDF, LaTeX. You may: edit definition, delete, view history.
1 Time Dilation The new method for time correction from the author is based on measuring variables already described in De Broglie’s waves, lambda based momentum (Agravat 2012 SJP), and photoelectric effect. The method involves time correction or time dilation from the simple harmonic oscillator. First the author derives the Special relativity equation based on time correction. Vc/c based in “Time Correction Energy and Momentum” also produced a value in magnitude or power of slower by 4.67E5 (Carroll, 2011) while others say faster than speed of light by 105. The formula includes Ec or energy correction (Agravat 2012) and the new time correction (Agravat 2012 SJP) method for neutrinos.
1.1 Introduction Dilation and Similarity is relevant to acceleration. The short distant method (Valdimir Kalitivianski) for integrating distance is relevant today because there are important needs to observe why distance matters. 2V0= v and 5V0 =V are observations setting people off then what they know. As predicted by Einstein there were different relations of distance and velocity. The effect of distance is not linear with velocity. The rate law mechanics do work but require some help with mathematics. For higher distance in dilation may mean there were less velocity which is a principle similar to acceleration. The physics measures do show that time dilation is possible and that not all velocity is linear. More distance is like the less velocity. The inverse nature of time and velocity is proof which shows the rates. More momentum can be from less velocity. More velocity can lead to less momentum. Time correction is a new approach that explains a fourth dimension parameter value of time that is now capable of being involved in special relativity calculations of energy and momentum (Agravat 2012 SJP) and is provided in this paper. Momentum calculation now includes the author’s time correction or wavelength based method as well as relativistic momentum, and Newton’s linear momentum. Time correction and newer methods for calculation of time exist that includes probability algorithms (Agravat 2011, Agravat 2012, Agravat 2012 SJP). The author is now suggesting new methods for the time based calculations of time dilation from angular momentum, energy, as well as acceleration and time formulations based on time correction and describe the similarities. A new time dilation formulation formula shows time calculation to behave differently from time correction. Special relativity (Einstein, 1905) is also derived based on the time correction method (Agravat 2012 SJP); however Newton’s linear momentum formula is required. A new derivation of complex equations related to the rate times time equation is demonstrated for angular quantum mechanics and energy of new Psi wave function. Lorentz contraction states there is a symmetry transformation as evidenced in for time and velocity. Einstein states likewise there was no absolute time or space in accordance with Newton. Based on the authors time and energy correction method while not violating the “three body mass problem” of Poincaire`. Time is proportional to the square root of c or speed of light, hence or speed of light is equivalent to time squared t 2 ≈c based on the relationship derived above. Else based on the ‘Ec ‘and ‘ tc‘ or energy correction and time correction time is also proportional to square root of energy over P, momentum also assuming independence (Agravat 2012).
1.2 Time symmetry Time when proportional to speed of light is behaving as a wave in a dual pattern. Time is symmetric with respect to speed of light for negative and positive scales for time values as based on the Opera experiment at CERN for neutrinos that are dark matter particles. Also, Time with respect to energy and momentum is demonstrating a band pattern for light where red hues are darker for lower speeds and lower time values for blue. The red is in the minus 1 phase, while blue is in the +1 phase with respect to sine of speed of neutrinos. In contrast the double slit experiment shows that visible light may have both particle and wave nature that are dark and light bands prove the existence of waves that is in comparison. The transform and derivation involve different methods of Energy and momentum calculations such as: special relativity, Lambda based momentum, energy correction, time correction, angular energy and momentum. The Plot in splines for energy vs. momentum or momentum vs. energy produces something that looks like a ‘particle in a box.’ The dot for the first observation that is different from linear momentum of Newton. The difference is that the second state has a 2π transform for time and velocity. The first level is the dot, while the second produces the box. Angular energy by uncertainty for based on times observed from time corrected for times including 2pi transformation. P1 and E1 in the time correction problem of the Opera experiment 2011 can have 0, 0 coordinates for particle in box.
1.3 Derivation of Proper Time Property In reference to proper time (wikipedia), or the change in time with reference to two events as a measured by a clock, as in CERN, OPERA 2011, the below
relationship is derived to explain the relationship between change of time, angular energy, and angular time. The new methods for time correction, energy, and momentum. A right triangle relationship based on the estimate of a right triangle proof (Agravat, 2012), the author proceed to estimate a new parameter of angular (of a circle) velocity in terms of time based on quantum mechanics terms. The author believes that because of negative parameters potential or complex numbers for time (Agravat , 2012), the four coordinate vector system in special relativity space time may have ranges that include negative values of time or complex numbers that result in symmetric relationship around an axis. Time dilation and velocity in terms of time plots shows symmetry is around 0 and halfway is with respect to radius on another axis, while the measure is in velocity. Instead of the x,y,z, plane with time, the author incorporates the new lambda method for wavelength (Agravat,2012).
1.4 Results The t ω is 65.35 seconds for maximal velocity of neutrinos. The slower or 2π time correction is t ω of 10.40 s. The maximal velocity of neutrinos is 299,778 km/s and slower one is 47710 km/s.The Pᵺ is 3.02E36 kgkm/s and 1.29E38 kgkm/s from energy conservation.The Pᵻ is 8.97E51 kg km/s and 2.22 E48 kgkm/s. The P(Cl) is 8.18E44 kg km/s and 1.30 E44 kg km/s. The Eᵺ is 2.46E40 J and 6.23E42 J.The Pᵺ is 6.59E41 kg km/s and 1.70E42 kg km/s. The time correction are 0.0153 s and 0.096 seconds for time correction. − − − hc λ t≈ ⎷
(1)
h λ
(2)
t≈√v
t
t
≈v
(3)
≈d
(4)
2
3
c tω≈ (πab)
(5)
2
(6)
t ω ≈√v
2πr Vc ≈
(7)
tc
−− − m V ω ≈ = 2\pir ∗ √
(8)
E
πv P ω ≈4m ∗
(9)
t
2m(\piAB) Pλ≈
(10)
2
Rc t c
m0v
P \rel ≈
− −−−−−− √1 − (
v c
)
P c ≈Energy c ∗ T
(11)
2
(12)
3 c
1.5 Mass effects The question of Mass effect in time dilation is examined next. The principles once looked at are about singularity. Condition one is if mv 2 can be approaching 0 or from infinite of mass. The Condition two is if energy correction goes to zero from infinite time. The next condition number three is about the principle of least action. One method to observe is through Schwartzchild radius. An equilibrium reaction is possible. Independence is a possibility. I. 2 mD 1 2 4 2 2 2 4 2 2 2 2 2 2 mD /t mD II. mD /t < D > mD III. mD /t D IV. mDt c ∗ mDt c ∗ D D V. VI. ( mD ) 1 c c c t t mD
c
c
tc
VII. mD/t 2c
∗ mD
3
D
Mass 1/ ∗ mD V≈
D T
1 hence mv
≈
2
/t
T mD
2
VIII. F 1/mD IX. 1 m 2 D 2 /t 2c X. (mD/t c )
XIV. IfM ∗ mD 2 /t 2c c 2
1
XV. M 2
t
2 c
/D
2
2
1
XI. P 2
XVI. Mass
1
XII. M ∗
mD t
tc D
2
2
1
XIII.
c
which shows the inverse relation of momentum from momentum and mass effects.
1.6 Discussion Time difference can also be calculated by parameters: 1) vc ; 2)vᵺ 3)v; 4)t observed. Time is calculated to be .016. Time that is approximately that calculated by the author (‘Time Correction energy and Momentum ’) of 0.0153 s. A new measure of P/P2π in tables shows values of: 1)9.95 (from ratio of
Pᵺ and V 1.57 E44/9.88E44 (kgkm/s ) ; 2) Pᵻ .0.158 ( ratio of Vc 4.55E42/1.79E40); 3) 6.29 (ratio of P(rel) 8.18E44/1.30E44) ; and 4) Pᵻ 0.02 (ratio of t obs and two pi correction ) ; and 5) Pc 0.004 (ratio of tc 9.30E44/2.17E41) or Pc a ratio of 247 from time omega a ratio of ( 6.83E33/ 2.75E35 kg km/s) . The reverse proportion of P(rel) may seem like time correction relevant tot 2π like lower velocity over maximal velocity and inverse relation. This ratio or Prel to Pᵻ compared of P relativity gives 0.0179 for the faster speed but 0.00007 for the slower speed a far greater difference of momentum for slower speed. Pᵻ follows time correction but for maximal velocity over minimal or 2π. According to quantum terms and its relationship to time correction, time is the square root of velocity. This relationship demonstrates that his ratio is also proportional to: 1)time is about 2.506 seconds for ratio of V c to V c2π . The ratio of time omega 65.35 : 10.40 is 6.28 also. 65.35 squared will give a speed of 4270.6 km/s two times similar to Bohr Velocity for 4XD for time dilation based on distance. Only the lambda for momentum method supports that the possiility of the clock at lower length will have higher speeds for Pᵻ vs Tᵺ(s) showing less distance for more time and more momentum for less time a point similar to time dilation and distance. Time dilation expects more speed and less distance while less speed with more distance. The energy equations for relativity may be better off if modeled after the elliptical nature of the orbit of the earth rather than the circumference of a circle. Dark matter and energy is far more common yet needs to be better understood. The distance relation to time is a cube root of distance which is like the defined 2V0=V and 5V0=V of the short distance method by Vladimir Kalitivianski. Time cubed and distance can be related. The infrared catastrophe can be relevant to the Bosons problems, time dilation of 60 degrees and symmetry of triangles are occurring.30, 60, and 90 degree are where methods of uncertainty may occur based on time. Alternate I and Alternate II methods do occur in time also where disambiguation happened. Ordinary perturbations may occur with De Broglie waves since omega approaches 0 which is not small compared to unity. Time of angular conservation is showing larger magnitude of differences. The unity does not follow low rest mass assumption when dilation of time occurs. Low photon energies can converge with the duality of light and particles based on total energy (Effective Field Theory) to conserve photons energy. In addition, time correction displays a right triangle. The right triangle estimate method can be used to estimate the parameter of the third leg, potentially distance or distance squared because the relationship of rate times time equals in distance. According to Photoelectric effect and Planck’s equation, and the new angular momentum based on time correction can be utilized to depict speed as based on earth. This approach involves quantum terms and formulas of new derivations from angular time corrections. Time correction calculation shows a pattern where the trend approaches 0 with ‘tc’. Plus the time dilation product formulation demonstrates symmetry as well as an additive effect for cosine of speed or velocity (Y) for the OPERA experiment involving neutrinos.
1.7 Conclusion:A Small Note on Time Dilation and S.H.O The simple harmonic oscillator may be modified to work with time correction.The γ will be 1 from the slow or negative speed of 6.57 E6 km/s enough to do shocks with time dilation of EinsteinLorentz. The t ω is still 9.54 E6 seconds. This may feed the Power law tail [4].The small gravitons may occur then. The Vω
is 6.57 E6 km/s. The an issue of
D 2 =(
T ω x2 Vω
)
2
TxD 2
as alternate I and
(TxD)
2
(2)
as alternate II may occur to find the distance D with V ω . D 1 =
T ω x2 Vω
and
.Polarization of the graviton is done at 45 degrees [3,6] on the (x,y) axes.The time dilation method here can be meant for the Method (5) in
'Small Gravitons' for time parameters with simple harmonic oscillator (S.H.O.). D 1 =RxT is −6.57E − 6x9.54E − 6= − 6.26E − 11km ; D 2 =RxT is 2.34E − 14x2.09E − 29=4.89E − 43km . The faster speed of 6.57 E6 km/s (S.H.O) in negative results in 6.26 E11 km. The slower speed of 2.34 E 14 km/s gives a distance of 4.89 E43 km. The faster speed has more distance though negative from the rate law. The slower speed has less absolute value distance. The slopes are for
D1 R
=T
of 9.52 E6 s and the
D2 R
=T
of 2.08 E29 s. However the simple harmonic oscillator is described with a different
outcome. Cos(2pi ∗ 9.54E − 6)=1 is and Cos(2pi ∗ 2.09E − 29)=1. Hence, the distance is compared to be the same but not for the simple harmonic oscillator. The negative speed has negative distance hence less than the positive distance which is greater by sign but not by absolute. The relation of D1
D2
2
1
distance and time dilation is shown by the question of 90 degrees. D works with the S.H.O. model. D works with the ordinary but indiscreet inference of velocity from energy and energy correction. tω
ΔT (S.H.O.) =
√( 1 − (
Sin
−1
(
D1
) + Cos
−1
(
D2
Sin
−1
(
D2 D1
Vω c
D1
)
2
(13) )
)>90
0
(14)
0
(15)
D2
) + Cos
−1
(
D2
)>90
D1
; C ∗ t i `=V 2 ∗ t i ` + V 3 ∗ t i ` ; and C ∗ t i ``=V 2 ∗ t i `` + V 3 ∗ t i i`` Speed multiplied to time dilation will yield more momentum. When this scenario speed of time dilation and time difference may look similar. It is comparable to Minkowski diagram. Part of the diagram is possibly is due to nonsubstation of speed and light. This relation of proper time is from Minkowski or Einstein where the accelerating clock has less time than stationary clock from the Doppler Effect or twin paradox. Time Dilation by Manoj Agravat. References: [1] Manoj Agravat MPH "Time Correction, Energy and Momentum "Science Journal of Physics, Volume 2012, Article ID sjp111, 13 Pages, 2012. doi: 10.7237/sjp/111. [2] Vladimir Kalitvianski. On integrating out shortdistance physics.10242014. http://arxiv.org/pdf/1409.8326v5.pdf [3] Clara Moskowitz “Largest Molecules yet Behave like Waves in Quantum DoubleSlit Experiment”. (March 25, 2012) http://www.livescience.com/19268quantumdoubleslitexperimentlargestmolecules.html [4] Agravat, Manoj (2011). “Formulas Calculating Risk Estimates and Testing for Effect Modification and Confounding”. http://www.lexjansen.com/pharmasug/2011/sp/pharmasug2011sp03.pdf [5] Agravat, Manoj. (2012). “Effect Modification, Confounding, Hazard Ratio, Distribution Analysis, and Probability of Nonnormal Data for head Neck Caner”. Global SAS Forum 2012. http://support.sas.com/resources/papers/proceedings12/3152012.pdf [6] Carroll, Sean. ‘Faster than Light Neutrinos” (2011). http://blogs.discovermagazine.com/cosmicvariance/2011/09/23/fasterthanlightneutrinos/#more 7481 C ∗ t i =V 2 ∗ t i + V 3 ∗ t i
[7] Carroll, Sean. “Cosmic Invariance and You” (2012). http://blogs.discovermagazine.com/cosmicvariance/2005/10/25/lorentzinvarianceand you/#.UPK39Cd6CqY [8] Proper Time http://en.wikipedia.org/wiki/Proper_time [9] Special Relativity http://www.fourmilab.ch/etexts/einstein/specrel/www/ [10] Agravat, Manoj. Time correction. http://speedydeletion.wikia.com/wiki/Time_correction [11] Agravat, Manoj. Effective Field Theory. http://sciencewise.info/definitions/Effective_field_theory_by_Manoj_Agravat [12] Agravat, Manoj. Baryon Number. sciencewise.info http://sciencewise.info/definitions/Baryon_number_by_Manoj_Agravat [13] Agravat, Manoj. A small note on Time Dilation Proof. Science 2.0. 3/16/2014. https://www.researchgate.net/publication/294730561_A_Small_Note_on_Time_Dilation_Proof [14] Time Dilation https://en.wikipedia.org/wiki/Time_dilation Alternative definitions: by Manoj Agravat
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