International Journal of Astronomy and Astrophysics, 2013, 3, 303-317 http://dx.doi.org/10.4236/ijaa.2013.33036 Published Online September 2013 (http://www.scirp.org/journal/ijaa) Cosmology Should Directly Use the Doppler’s Formula to Calculate the Red Shift of Ia Supernova —The Proofs That Metric Red Shift Is Inapplicable and Dark Energy Does Not Exist Xiaochun Mei, Ping Yu Institute of Innovative Physics, Fuzhou, China Email: [email protected], [email protected] Received March 28, 2013; revised April 29, 2013; accepted May 7, 2013 Copyright © 2013 Xiaochun Mei, Ping Yu. This is an open access article distributed under the Creative Commons Attribution Li- cense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. ABSTRACT The Doppler formula should be used directly to calculate red shift of Cosmology. The first is gravity, the second is the Doppler’s effect and the third is the Compton scattering. The red shift of cosmology is considered to be caused by the receding motions of celestial bodies, of which essence is the Doppler’s effect. However, the basic formula used to cal- culate the relationship between red shift and distance for Ia supernova in cosmology is zRtRt1 01 which is based on the R-W metric and related to the scalar factor Rt . This is different from the Doppler formula which is related to speed factor Rt . Because the R-W metric is only a mathematical structure of space, the metric red shift is not an independent law of physics, this inconsistence is not allowed in physics. It is proved strictly in this paper that the formula of metric red shift is only the result of the first order approximation. If higher order approximations are consid- ered, we can obtain a restrict condition Rt constant . It indicates that if the formula of metric red shift holds, it can only be suitable to describe the spatial uniform expansion, unsuitable for the practical universal process with accelera- tion. The further study reveals that the R-W metric violates the invariability principle of light’s speed in vacuum. The time delay caused by relative velocity between light’s source and observer is neglected. So the R-W metric violates the special relativity and is not suitable to be used as the basic space-time frame in cosmology. The formula used to calcu- late the relationship between red shift and distance of Ia supernova is wrong and subsequently the deduced results about dark energy and the accelerating universe are incredible. Cosmology should use directly the Doppler formula to calcu- late red shift. It is proved that based on the Doppler’s formula and by the method of numerical calculation, the relation of red shift and distance of Ia supernova can be explained well. The hypotheses of dark energy and the accelerating ex- pansion of the universe are completely unnecessary in cosmology. Keywords: Cosmology; Doppler Formula; R-W Metric; Hubble Law; Supernova; Dark Energy; Dark Material 1. Introduction gists declared that about 26% material in the universe was dark material and about 70% was dark energy. The As we known that there are mainly three mechanisms universe seems to do accelerating expansion [1,2]. leading to the red shift of spectrum. The first is gravity The red shift of cosmology is considered to be caused which relates to mass and gravity constant. The second is by the receding motions of celestial bodies, so its essence Doppler’s effect which relates to velocity. The third is is the Doppler’s effect related to speed. We should use the Compton scattering which is related to the energy Doppler’s formula to calculate the red shift. However, it transformation of photon. According to the Hubble law, is strange that the basic formula used to calculate the the spectrum red shift of extragalactic nebula was pro- portional to the distance between observer and luminous relation of red shift and distance of Ia supernova is com- celestial body. The red shift of cosmology is considered pletely different from the Doppler formula. The basic to be the Doppler’s effect. In 1998, cosmic observers formula used in cosmology is [3] found that the red shift of Ia supernova deviated from the v Rt linear relation of the Hubble law. By fitting the observa- z 1 1 0 (1) tion values with standard theory of cosmology, cosmolo- vRt01 Copyright © 2013 SciRes. IJAA 304 X. C. MEI, P. YU The formula is based on the R-W metric in which 1 2. Unavailability of Metric Red Shift is the frequency of emitted light at time t1 , 0 is the Formula frequency of received light at time t . The formula is 0 2.1. The Restriction Condition Rt Constant related to scalar factor Rt. But the Doppler’s formula for the Metric Red Shift Formula is related to speed factor Rt . It is proved in this paper that they can not be consistent. This inconsistence is not Standard cosmology uses the R-W metric to describe the allowed in physics. universal space-time with form It is proved strictly that Formula (1) is only the result ddsctRt2222 of first order approximation. When higher order ap- 2 (2) proximations are taken into account, the restriction con- dr 22 2 2 2 2 rrdsind dition Rt constan will be obtained. Therefore, For- 1r mula (1) is only suitable to describe the process of spatial Here Rt is scalar factor and is considered as uniform expansion; it’s unsuitable for the practical proc- the factor of spatial curvature. The co-moving coordinate ess of the universal expansion with acceleration. More is used in cosmology. The space is considered flat when strictly, if we do not consider approximation, both For- 0 . When (2) is used to describe the expansive uni- mula (1) and the restriction relations do not exist. That is verse, luminous celestial bodies are considered to be to say, we have no metric red shift actually. fixed on the coordinate r ,, which do not changed In fact, the W-R metric is only a mathematical struc- with time. Let’s repeat the process to obtain Formula (1) ture of space-time, rather than an independent law of based on the R-W metric. Suppose that light moves along physics. It is introduced to simplify the Einstein’s equa- the radius direction 0 with d0s , we get tion of gravity field to obtain the Friedmann equation of from (2) cosmology. It is not absolutely necessary to use the R-W ctdd r metric in cosmology. Using normal coordinates directly, (3) Rt 2 we can also establish the equation of cosmology based on 1r the Einstein’s equation of gravity field. In this case, there Light source is fixed at point r and r does not is no the metric red shift formula (1). In this sense, the change with time. But to light’s motion, r changes red shift of metric is not independent in physics. If it is with time. Suppose that photon’s coordinate is r1 at correct, it cannot be contradicted with the Doppler’s and moment t1 and photon arrives at the original point gravity red shifts. r0 0 at moment t0 . The integral of (3) is [3] The further analysis indicates that the R-W metric vio- t 0 0 ctdd r lates the invariability principle of light’s speed in vac- sin nr1 Rt 2 uum when it is used to describe the uniform motion of tr111 r (4) light’s source. The time contraction between observer sinrk1 1 and moving light’s source is also neglected when the rk1 0 R-W metric is use to describe the spatial expansion. So sinhrk 1 the R-W metric is not one of special relativity and is un- 1 suitable to be used as the basic space-time frame in cos- The negative sign indicates that light moves along the mology. Especially, it is not suitable to be used to de- direction to decrease r . Suppose that a light wave is scribe the high red shift of supernova in which the high emitted during the period of time from t1 to t11 speed expansion of the universe is involved. with period 1 c 1 . Observer receives the light during In summary, the formula used to calculate the relation the period of time from t0 to t00 with period of red shift and distance of Ia supernova in cosmology 00 c . According to the current understanding, be- has essential mistake. Therefore, dark energy and the cause t00 and t11 are decided by the same r1 , accelerating universe are incredible. The Doppler for- we have mula should be used directly to calculate red shift of tt00ddtt0 (5) Cosmology. It is proved by the method of numerical Rt Rt calculation that if the Doppler’s formula and the (revised) tt111 Newtonian formula of gravity are used, the high red shift Because 0 and 1 are small, according to present of Ia supernova can be explained well. We do not need the theory, we obtain from (5) hypothesis of dark energy and accelerating universe again. 0 1 (6) Let’s discuss the problem in the metric red shift for- Rt Rt mula. The inconsistence between the metric red shift and 01 the Doppler’s red shift will be discussed in appendix. Based on (6) and the definition of red shift, we obtain Copyright © 2013 SciRes. IJAA X. C. MEI, P. YU 305 (1). By considering (1) and the Friedmann equation of 3 Rt 0000 66 Rt Rt R t 4 cosmology, as described in Section 3, we can obtain (1).