Metric of Universe The Causes of Red Shift.

Transcription

1 Metri of Universe The Causes of Red Shift. ELKIN IGOR. Annotation Poinare and Einstein supposed that it is pratially impossible to determine one-way speed of light, that s why speed of light in different ways may differ. They also supposed that till there is no the eperiment whih would depend on the value of one-way speed of light, it is possible to onsider that all one-way speeds of light are equal to two-way speed of light. It is offered the eplanation of the eperiment onneted with Red shift with the aid of one-way speed of light, therefore it is shown the dependene on magnitude of one-way speed of light. Mehanis is set up based on the unidiretional speeds of light. For eample, the eperiment of Mihelson-Morley is eplained with the aid of this mehanis. The ause of the ineption of Fitzgerald ontration is eplained. Key-words. One-way speed of light, two-way speed of light, Red shift, the Fitzgerald ontration, the metri of the universe. Part one. The Red Shift. Introdution. For the beginning we d most like to remind, how Einstein ame to the idea of the inalterability of the speed of light in any diretion. The seret is in the aepted lok synhronization, whih as it was onsidered makes undetetable differene of the one-way speeds of light. Inasmuh as the synhronization onverts to the moving from some point (with time on the lok 0 ) of the synhronized light signal and with transmission of this signal into another synhronized point by the setting in this point of time on the lok. Time on the lok in this another point is fied equal to the half of the time of signal transmission of the way to this another point (from starting point) and by the way of the getting bak returned signal into the initial point. That s why it isn t important with what one-way speed the light-signal moved on either side, just middle speed is important. The proedure of length measurement, set up on the basis of this lok synhronization, made possible a lot of eperiments, where different one-way speeds of light are possible and we may trae them to the analogial eperiments with two-way speeds of light. Einstein suggested that if eperiments lead to the two-way speeds

2 of light and there is no dependene on the one-way speeds of light, there is no sense to onsider them. That time a postulate was taken whih tells that all one-way speeds of light are equal and they are equal to two-way speed of light. Let s try to reeive with the aid of different one-way speeds of light ( to observer and from observer ) generally known eperimental fat, preisely: emission spetrum omes shifted into the red side from the distant galay, and as this galay is on the longer distane, as the shift beomes bigger. P 1. The Re d Shift Real Cause. Let s onsider our galay and some distant galay. We take it that two-way speeds of light are unhangeable everywhere, it means that emission in these two galaies in relation of two-way speed of light is unhangeable and it has one wavelength, we mark it as: L. It is really so, beause a metre is mensurated with two-way speed of light. That s why as this speed of light will be hanged, a metre will be also hanged and it ll be impossible to fi this hange. Now we onsider that the light that omes to our diretion from the side of distant galay at speeds of < where is two-way speed of light. Differene in time of arrival of fore and bak wave front L t =, but as it is known on the Earth we oneive this time as oming by light-signal some way with two-way speed of light. Or else at short distanes one-way speeds of light less differ from the two-way speeds of light than at long distanes. That s why, we on the Earth, onsider that the wave-length of the light-signal is l = t = L( ). In other words wave-length was inreased. Correspondingly the frequeny was dereased and we reeived The Red Shift. The data of these researhes may help estimate one-way speed in the distane of one megaparse. By estimate of osmologists, it s nearly: = 70km/se Now we ll mark k = Than we ll find the orrelations on the way h: We should mention that these formulas are taken for the estimation of one-way speeds of light, more proimate formulas we may use after numerial alulations of metris this is in item part. h h h T1 =, T = at this ase mid-speed on the way h is: = = T T or 1 k = = 1 k 1 k (1) Or

3 70 (1 k) = = (1 ) Or roughly: k = 1 0, 0005 We haven t reeived yet the dependene of shift on the distane. It is deduted a bit more ompliated. Let s think bak that lok synhronization initiated by Poinare and then transformed by Einstein uses two-way speed of light as synhronizing signal. Though Einstein wrote that it is possible to use any signal, but the speed should be fied and measured by some way. That s why at any ase lok setting in total omes into synhronization by the light signal with two-way speed. The dependene of wave-length of inoming signal on the one-way speed of light, reeived so elementary, put in doubt that one-way speeds of light an t influene on the result of any eperiment and it is possible at any ase to put in twoway speed of light. As far as this hypothesis may be aompanied by serious mistakes and loss of real auses of events is also possible, - that is observed in Physis. As far as the setting of synhronism in two points is fied, so: Synhronization: let s onsider that with light signal output (or analogial to it signal) zero is set and with oming of light signal zero is also set in the orrespondent point for the given proess. The moving in some onrete diretion is onsidered as the given proess. At this ase there is a neessity to onsider all the proesses separately from eah other. This synhronization hanges the onept of simultaneity, and also type of time oordinate. And if the time oordinate is hanged the type of interval is also hanged, and type of metri tensor is hanged too. It may mean that spae metris is also hanged. We ll try to investigate this question. Item. New Time Coordinate. Metris of the Universe. We onsider it in the ontet of new synhronization. If we mark material point at the beginning of the oordinates M, and the other arbitrary point - 0 M, time oordinate of the point 1 M - 1 t would depend on the diretion of M 1 the signal by this way: 1) ) t t R = t - in the ase of sending of the signal from M1 M0 R = t - in the ase of sending of the signal M1 M0 M to 0 M. 1 M to 1 M. 0 Where and are orrespondingly the speeds of light in the onrete side (we ll mark it), oordinate of the point M. 0 t is the time M 0 I ll eplain a bit: it s understandable that in 1) from the usual onsideration of time at the point overoming with light the distane between the points is just taken off. M 1 time for It is analogially in ), just in this ase usual for us time is at the point M 0 is taken with minus, as far as in the ase of slower synhronizing signal than light we reeive information about the objet from more distant past.

4 R and R Eulidean distane (length) between the onsidered points, in units of speeds and respetively. R is the length, in units of two-way speed of light. For simpliity we ll mark t = M 1 q, t = q. Then: M 0 1) q ) q R = q moving from zero. R = q moving to zero. Let s now onsider moving to zero. Let s admit there is a dependene of one-way speed of light on X-oordinate. We ll searh for the dependene like this: = f = f( ) () X-oordinate is defined in two-way speed of light, oordinate is defined in two-way speed of light for approimating. For Minkowski spae in two-way speeds of light the net interval is known: ds = dt d (3) d d d = d = ( ) = d = (4) f In terms of q = q for event spae (whih is orresponded to Minkowski spae) letter q means time at the observing point, in other words t, so, it means that in the oordinates of one-way speed of light time: 1 t = q = q or f f 1 d dt = d dq (5) f f substitute in (3) formulae (4) and (5). And we onsider just spae part of interval: 1 d f d ds = ( ) (1 ) ( ) f f f 1 ( f ) ( ds d )[( = f f ] (6) f f (fator out and produt of differene of squares)

5 We ll seek the solution using the method of Oam's razor. It s understandable that the most simple type of interval is at this ase: f ' = A = onst, I ll remark, that then formula: f = A B, where B = onst Can be easily taken in the form of a bit hanged Hubble s law, whih is easily eplained for the ase of different one-way speeds of light. This law works in ase that: H A = and B= 1, where H Hubble onstant. In other words one-way speed of light is dereased when the distane is inreased. Or f = 1 H Square brakets in formula of interval will be simplified by this way: H H H [( f f] = =( ) The interval will ontain just spae omponents, in other words it will be metris of spae on this diretion. dr H ( )( d ) H = ( ) H 4 [1 ( )] (7) It is understandable that the Pythagorean theorem doesn t work, in other words one-sided metris in unilateral oordinates is non-eulidean. This metris is of the form of spae whih is desribed by Lobahevskian geometry. Formula (1) proves that, one-way speeds of light are onneted with two-way speed of light asymmetrially. That s why metris will be different on the diretion from the observer and to the observer. The non-eulideanism of metris eplains the hanges of one-way speed of light. As far as metre in the spae with non-eulidean, metris isn t invariant. In other words, subpaths of light signal whih are equal for the spae with non-eulidean metris will be of different length, beause length is Eulidean metri. And light, of ourse, when moving may use just the harateristis of the spae (in non-eulidean metri), but not foolish theories of the sientifi men, who require fied speed of light in the metris of another's spae. Part. The Causes of the Contration in the Diretion of Motion. Item.1 Mihelson-Morley Eperiment. In the result of getting new lok synhronization and researhing of different one-way speeds of light to the observer and from the observer spae metris of Universe was reeived. Formulae are elementary and after simplifiation they easily transfer into short and understandable ones. That s why their original long and boring states shouldn t distrat. I ll reollet shortly: The following formulae were reeived:

6 f ( ) d dt = d dq f f (8) d d d = d = = f (9) Where - one-way speed of light to the observer, = f = f( ) - the dependene of one-way speed of light on -oordinate. -oordinate is defined in two-way speed of light, oordinate is defined in one-way speed of light for approimating, q means time at the point of observer, q - means time at the observed point. Formula of interval: ds = dt d (10) If we put (8), (9) in (10), we ll reeive interval in one-way speeds: 1 f 1 f ds = dq ( ) d dq ( ) ( )[( ) ] d f f f f f f Or d 1 f f ds = dq [ (1 ( )] ( d ) ( )[( ) f f ] (11) 4 dq f f f With regard: f H = 1 ( ) (1) H d H ds = dq ( ) ( ) dq H [1 ( )] [1 ( )] ( d ) ( ( )) 1 H 4 (13) This long formula just proves that for long distanes spae metris is Lobahevsky metris. It s not diffiult to hek that for the speed of light to the observer we ll reeive analogial formula (just spae oordinate will be and it is defined with the speed of light for moving off).

7 We larified with reession of galaies in the first artile. (referene in the beginning). It s understandable that only the magnitude of one-way speed of light impats on the red shift. And there is no universal red shift. Now Mihelson-Morley eperiment and physial meaning of the length ontration in the diretion of motion are interesting. In fat STR doesn t give physial auses and physial meaning of this ontration and it is not understandable what for fields (and spae) should redue their length. We an eplain it even with the aid of the magnitude from other ISO as far as the proedure of the length determination by Einstein wouldn t afford it. The interval beomes easier in short distanes: d ds = dq a d (14) ( ) *( )*( ) dq Where H a = In this ase, the spae part of the interval will give us spae metris (for the simpliity we ll use instead of - ): dr = ard or a - is sale number, it s understandable, that further it an be ounted as equal to unity element. dr = d (15) This formula shows what metris should be aounted in short distanes. Ordinary sale number takes into aount numbers of dimensions. The formula itself means that metris, in other words, the distane between two points is equal to numbers of unit elements of equal open intervals of oordinates or just the same the unit of measurement of oordinate of one-way speed of light. Under ondition, that one point is at the beginning of the oordinates with the oordinate, and the other point has the - oordinate. Of ourse, we ll not follow verbal proof (all the subpaths of light signal in oordinates, measured by light are desribed in thousands of works) and we ll write at one formula with light lok? Moving from the observer with a speed. Coordinate is measured with the orresponding speed of light, in this ase, we ll take into aount formula (8) for eah interval (lok length L): t1 = Ut1 L It is understandable, that all the meanings are taken in absolute magnitude. or L t1 =, by analogy with motion into another diretion: ( V)

8 t L = ( V), total time of the motion of the signal: L ( U) t = t1 t = ( U) ( U) (16) Now by analogy we ll onsider known formula with ross olloating of light lok. L = ( t ) ( Ut ) 3 3 So, we reeive total time: L t = t3 = ( U) (17) We an see, that total time formula (16) and formula (17) differs by multiplier: ( U) N = ( U) (18) We an begin to lie as in STR, that this is a feature of spae and it is redued by unknown ways, and L is redued with it too, or we may analyze what the time part of the interval an give us, beause we onsider time in motion. It is understandable that interval (14) in short distanes as for osmologial measures, and at steady speed moving of the mirror (moving of ISO) time part of the interval will be: of the dq = dq ( U ), what gives (for approimating): dq = dq ( U ) (19) It s understandable that the same time interval with the speed of light for deleting gives: dq = dq ( U ) (0) It s also lear that the motion of light signal and ISO are taken to onsideration in eah ase that s why for the eperiment with light lok (or the same one with the eperiment of Mihelson-Morley), the neessary for us intervals will look like: dq1 = dq ( U ) dq = dq ( U ) (1) dq = dq 1 ( U) () And formula, desribing time of absolute signal transmission, will be (I shan t desribe it, beause it is easy for understanding): ( U) U dqsum = dq = dq ( U) U (3)

9 So, it appears that there is the inreasing of the unit of time in the diretion of the motion in the moving ISO. And if there is hange like that and there is the definition of metre, onneted with the unit of time. It is obtained that metre in moving ISO also inreases in orresponded number of times, that s why our light lok obtains less of these metres (and the arm in Mihelson Morley eperiment respetively). So: U L = L U (4) That s why if in the formula (16) instead of L we ll write L'and put the meaning by formula (4), multiplier n will be left: n = U U (5) The value of transmission time with light signal over the way in fore-and-aft and ross diretion differ on this multiplier. And this multiplier is eplained with the differene of time metris in fore-and-aft and ross diretion. In other words without ontrive, ausative «spae ontration» we an easily eplain the differene of transmission time with light-signal of fore-and-aft and ross diretion. And short eplanation: In ISO moving at speed U relatively stationary observer, we an observe anisotropy of timing metris in the diretion of moving. Beause stationary observer is going to observe in moving ISO. And only in Einstein variant of the ourse of events loation of observer doesn t matter, in our variant we should take into aount this loation. Anisotropy of metri units ours due to anisotropy, timing metris in this ISO in the ontet of stationary observer (beause metre is observed by the speed of light and time. These both fators lean the differene in transmission time with the signal fore-and-aft and ross diretion in light lok (and orrespondingly in Mihelson Morley eperiment). Item.. Correlation of one-way and two-way speed of light. I get bak to the question of the formula for the middle speed of light. It is important beause in ase of determination the measurement of the way of light signals with the aid of two-way speed of light there is some delimitation below the measurements of the one-way speeds. This delimitation ontains the formula: p = As far as the delimitation is below in the measurement of one-way speed of light it ouldn t be the arbitrary relation of wave-length (due to the given theory) in the emissions of distant and lose galaies. But these very orrelations are observed. Pratially we should arise from the eamination of the middle speed and we should estimate the distanes in one-way speeds as it was doing for Mihelson Morley eperiment: S = = dt S = = dt Net,

10 S S = = S S (6) - this formula has no delimitations below for the one-way speeds of light and the orrelations of wave-length is not fied. Consequently there are no disrepanies of the eperiment and theoretial hypothesis now. Deember Igor Elkin.