Special and general theory of relativity pdf

As long as it is moving imiformly, the occupant of the carriage is not sensible of its motion, and it is for this reason that he can with- out reluctance interpret the facts of the case as indicating that the carriage is at rest, but the embankment m motion. Moreover, according to the special principle of relativity, this inter- pretation is quite justified also from a physical point of view. The retarded mo- tion is manifested in the mechanical behaviour of bodies relative to the person in the railway carriage.

The mechanical behaviour is different from that of the case previously considered, and for this reason it would appear to be impossible that the same mechanical laws hold relatively to the non-imiformly moving carriage, as hold with reference to the carriage when at rest or in uni- form motion.

At all events it is clear that the GaMleian law does not hold with respect to the non-imiformly moving carriage. Because of this, we feel compelled at the present jimcture to grant a kind of absolute physical reality to non-uniform motion, in opposition to the general principle of relativity. But in what follows we shall soon see that this conclusion cannot be maintained. As a result of the more careful study of electromagnetic phenomena, we have come to regard action at a distance as a process impossible without the intervention of some intermediary medium.

If, for instance, a magnet attracts a piece of iron, we cannot be content to regard this as meaning that the magnet acts directly on the iron through the intermediate empty space, but we are constrained to imagine — after the manner of Faraday — that the magnet always calls into being something physically real in the space it, aroimd that something being what we call a "magnetic field.

We shall only mention that with its aid electromagnetic phenomena can be theoret- ically represented much more satisfactorily than it, without and this appHes particularly to the transmission of electromagnetic waves. The effects of gravitation also are regarded in an analogous manner. The action of the earth on the stone takes place indirectly. The earth produces in its sur- roundings gravitational field, which acts on the a stone and produces its motion of fall.

As we know from experience, the intensity of the action on body diminishes according to quite definite a a law, as we proceed farther and farther away from the earth.

From our point of view this means: The law governing the properties of the gravita- tional field in space must be perfectly definite a one, in order correctly to represent the diminution of gravitational action with the distance from operative bodies. It something like this: The is body e. Bodies which are moving under the sole influence of a gravitational field receive an acceleration, which does not in the least depend either on the material or on the physical state of the body.

This law, which holds most accurately, can be expressed in a different form in the Hght of the following consideration. By a suitable choice of units we can thus make this ratio equal to unity.

We then have the following law: The gravitational mass of a body is equal to its inertial mass. It is true that this important law had hitherto been recorded in mechanics, but it had not been interpreted. A satisfactory interpretation can be obtained only if we recognise the following fact: The same quality of a body manifests itself ac- cording to circumstances as "inertia" or as "weight" lit.

In the following section we shall show to what extent this is actually the case, and how this question is con- nected with the general postiilate of relativity. It is then possible to choose a Galileian reference-body for this part of space world , relative to which points at rest remain at rest and points in motion continue permanently in imiform rectilinear motion. As reference-body let us imagine a spacious chest resembling a room with an observer inside who is equipped with apparatus.

Gravitation nat- urally does not exist for this observer. He must fasten himself with strings to the floor, otherwise the sHghtest impact against the floor will cause him to rise slowly towards the ceiling of the room.

In course of time their velocity will reach unheard-of values — provided that we are viewing all this from another reference-body which is not being pulled with a rope. But how does the man in the chest regard the process? The acceleration of the chest will be transmitted to him by the reaction of the floor of the chest. He is then standing in the chest in exactly the same way as anyone stands in a room of a house on our earth. If he release a body which he previously had in his hand, the acceleration of the chest wUl no longer be transmitted to this body, and for this reason the body will approach the floor of the chest with an accelerated relative motion.

The observer wiU further convince himself that the acceleration of the body towards the floor of the chest is always of the same magnittide, whatever kind of body he may happen to use for the experiment. Rel3dng on his knowledge of the gravitational field as it was discussed in the preceding section , the man in the chest will thus come to the con- clusion that he and the chest are in a gravitational field which is constant with regard to time. Just then, however, he discovers the hook in the middle of the Ud of the chest and the rope which it, is attached to and he consequently comes to the conclusion that the chest suspended at rest is in the gravitational field.

Ought we to smUe at the man and say that he errs in his conclusion? Even though being accelerated with is it respect to the "Galileian space" first considered, we can nevertheless regard the chest as being at rest. We have thus good grounds for extending the principle of rdativity to include bodies of reference which are accelerated with respect to each other, and as result we have gained a a powerful argimaent for generahsed postulate a of relativity.

We must note carefully that the possiblility of this mode of interpretation rests on the fundamen- tal property of the gravitational field of giving all bodies the same acceleration, or, what comes to the same thing, on the law of the equaUty of inertial and gravitational mass. The result of this wiU be to stretch the rope so that it will hang "vertically" downwards. If we ask for an opinion of the cause of tension in the rope, the man in the chest will say: "The suspended body experiences a downward force in the gravitational field, and this is neutrahsed by the tension of the rope; what determines the magnitude of the ten- sion of the rope is the gravitational mass of the suspended body.

The tension of the rope is just large enough to effect the acceleration of the body. That which determines the magnitude of the tension of the rope is the inertial mass of the body. Thus we have obtained a physical interpretation of this law. In point of fact, the systematic piu-suit of the general idea of relativity has supplied the laws satisfied by the gravitational field. Before pro- ceeding farther, however, I must warn the reader against a misconception suggested by tijese con- siderations.

A gravitational field exists for the man in the chest, despite the fact that there was no such field for the co-ordinate system first chosen. Now we might easily suppose that the existence of a gravitational field is always only an apparent one. We might also think that, regardless of the kind of gravitational field which may be present, we could always choose another reference-body such that no gravitational field exists with reference to it.

This is by no means true for aU gravitational fields, but only for those It is, of quite special form. We can now appreciate why that argument is not convincing, which we brought forward against the general principle of relativity at the end of Section XVIII. But he is compelled by nobody to refer this jerk to a "real" acceleration retardation of the carriage.

He might also interpret his experience thus: "My body of reference the carriage remains permanently at rest. With reference to it, however, there exists during the period of application of the brakes gravitational field a which directed forwards and which variable is is with respect to time. Under the influence of this field, the embankment together with the earth moves non-uniformly in such manner that their a original velocity in the backwards direction is continuously reduced.

We have also repeatedly emphasised that this fundamental law can only be vahd for bodies of reference K which possess certain unique states of motion, and which are in imiform translational motion relative to each other. Relative to other reference-bodies K the law is not valid. Both in classical mechanics and in the special theory of relativity we there- fore differentiate between reference-bodies K relative to which the recognised "laws of nature" can be said to hold, and reference-bodies K relative to which these laws do not hold.

But no person whose mode of thought is logical can rest satisfied with this condition of things. What is the reason for this preference? In order to show clearly what mean I I by this question, shall make use of a comparison.

I am standing in front of a gas range. Stand- ing alongside of each other on the range are two pans so much alike that one may be mistaken for the other. Both are half full of water. I am surprised at this, even if I have never seen either a gas range or a pan before. But if I now, notice a luminous something of bluish colour under the first pan but not under the other, I cease to be astonished, even if I have never before seen a gas flame. For I can only say that this bluish something will cause the emission of the steam, or at least possibly it may do so.

If, however, I notice the bluish something in neither case, and if I observe that the one continuously emits steam whilst the other does not, then I shall remain astonished and dissatisfied until I have discovered some circumstance to which I can attribute the different behaviour of the two pans. But E. Mach recognised it most clearly of all, and because of this objection he claimed that mechanics must be placed on a new basis.

It can only be got rid of by means of physics which conformable to the general is a principle of relativity, since the equations of such a theory hold for every body of reference, whatever may be its state of motion. The objection of importance more especially when the state 1 is of motion of the reference-body of such nature that does not it is a require any external agency for its maintenance, e.

Let us suppose, for instance, that we know the space-time "course" for any natural process whatsoever, as regards the manner in which it takes place in the GaHleian domain relative to a GaUleian body of reference K.

But since a gravitational field exists with respect to this new body of reference K', our consideration also teaches us how the gravitational field in- fluences the process studied. This acceleration or curvature corresponds to the influence on the moving body of the gravitational field prevailing relatively to K'. It is known that a gravita- tional field influences the movement of bodies in this way, so that our consideration supplies us with nothing essentially new.

However, we obtain a new result of fundamental importance when we carry out the analogous consideration for a ray of light. With respect to the Galileian reference-body K, such a ray of Hght is transmitted rectilinearly with the velocity c.

It can easily be shown that the path of the same ray of light is no longer a straight line when we consider it with reference to the accelerated chest reference-body i? From this we con- clude, that, in general, rays of light are propagated curvilinearly in gravitational fields. In two re- spects this result is of great importance. In the first place, it can be compared with the reality. Although a detailed examination of the question shows that the curvature of light rays required by the general theory of relativity is only exceedingly small for the gravitational fields at our disposal in practice, its estimated magni- tude for light rays passing the sun at grazing incidence is nevertheless seconds of arc.

This ought to manifest itself in the following way. At such times, these stars ought to appear to be displaced outwards from the sun by an amount indicated above, as compared with their apparent position in the sky when the sun is situated at another part of the heavens. The examination of the correctness or otherwise of this deduction is a problem of the greatest im- portance, the early solution of which is to be expected of astronomers.

Now we might think that as a consequence of this, the special theory of relativity and with it the whole theory of relativity would be laid in the dust. But in reality this is not the ' By means of the star photographs of two expeditions equipped by a Joint Committee of the Royal and Royal Astronomical Societies, the existence of the deflection of light demanded by theory was con- firmed during the solar eclipse of 29th May, Appendix III.

Since it has often been contended by oppo- nents of the theory of relativity that the special theory of relativity is overthrown by the general theory of relativity, it is perhaps advisable to make the facts of the case clearer by means of an appropriate comparison.

Before the development of electrodynamics the laws of electrostatics were looked upon as the laws of electricity. At the present time we know that electric fields can be derived correctly from elec- trostatic considerations only for the case, which is never strictly realised, in which the electrical masses are quite at rest relatively to each other, and to the co-ordinate system.

Should we be justified in saying that for this reason electro- statics is overthrown by the field-equations of Maxwell in electrodynamics? Not in the least. Electrostatics is contained in electrodynamics as a limiting case; the laws of the latter lead directly to those of the former for the case in which the fields are invariable with regard to time.

In the example of the transmission of light just dealt with, we have seen that the general theory of relativity enables us to derive theoretically the influence of a gravitational field on the course of natural processes, the laws of which are already known when a gravitational field is absent.

But the most attractive problem, to the solution of which the general theory of relativity supplies the key, concerns the investigation of the laws satisfied by the gravitational field itself. Let us consider this for a moment. We are acquainted with space-time domains which behave approximately in a "Galileian" fashion imder suitable choice of reference-body, i.

If we now refer such a domain to a reference-body K' possessing any kind of motion, then relative to K' there exists a gravitational field which is variable with respect to space and time. Accord- ing to the general theory of relativity, the general law of the gravitational field must be satisfied for all gravitational fields obtainable in this way. Even though by no means all gravitational fields ' This follows from a generalisation of the discussion in Sec- tion XX.

We require to extend our ideas of the space-time continuum still farther. As a consequence, Iam guilty of a certain slovenliness of treatment, which, as we know from the special theory of relativity, is far from beiug unim- portant and pardonable.

It is now high time that we remedy this defect; but I would mention at the outset, that this matter lays no smaU claims on the patience and on the power of abstraction of the reader. We start off again from quite special cases, which we have frequently used before. Let us consider a space-time domain in which no gravi- tational field exists relative to a reference-body K whose state of motion has been suitably chosen. K is then a Galileian reference-body as regards the domain considered, and the results of the special theory of relativity hold relative to K.

In order to fix our ideas, we shall imagine K' to be in the form of a plane circular disc, which rotates uniformly in its own plane about its centre. But the observer on the disc may regard his disc as a reference-body which is "at rest"; on the basis of the general principle of relativity he is justified in doing this. The force acting on himself, and in fact on aU other bodies which are at rest relative to the disc, he regards as the effect of a gravitational field.

Nevertheless, the space-distribution of this gravi- tational field is of a kind that would not be possible on Newton's theory of gravitation. In doing so, it is his intention to arrive at exact definitions for the signification of time- and space-data with reference to the circular disc K', these definitions being based on his observations. What wiU be his experience in this enterprise?

To start with, he places one of two identically constructed clocks at the centre of the circular disc, and the other on the edge of the disc, so that they are at rest relative to it.

We now ask our- selves whether both clocks go at the same rate from the standpoint of the non-rotating Galileian reference-body K. As judged from this body, the clock at the centre of the disc has no velocity, whereas the clock at the edge of the disc is in motion relative to iT in consequence of the rota- tion.

According to a result obtained in Section XII, it followsthat the latter clock goes at a rate permanently slower than that of the clock at the centre of the circular disc, i. It is obvious that the same effect would be noted by an observer whom we will imagine sitting alongside his clock at the centre of the circular disc.

Thus on our circular disc, or, to make the case more general, in every gravitational field, a clock wiU go more quickly or less quickly, according to the position in which the clock is situated at rest.

A similar difficulty presents itself when we attempt to apply our earlier definition of simultaneity in such a case, but I do not wish to go any farther into this question.

Moreover, at this stage the definition of the space co-ordinates also presents xmsurmoimtable difficulties. If the observer applies his standard measuring-rod a rod which is short as compared with the radius of the disc tangentiaUy to the edge of the disc, then, as judged from the Galileian system, the length of this rod wiU be less than i, since, according to Section XII, moving bodies suffer a shortening in the direction of the motion.

On the other hand, the measuring-rod wiU not experience a shortening in length, as judged from K, if it is applied to the disc in the direction of the radius. This proves that the propositions of Euclidean geometry cannot hold exactly on the rotating disc, nor in general in a gravitational field, at least if we attribute the length I to the rod in all positions and in every orientation. Hence the idea of a straight line also loses its meaning.

We are therefore not in a position to define exactly the co-ordinates X, y, z relative to the disc by means of the method used in discussing the special theory, and as long as the co-ordinates and times of events have not been defined we cannot assign an exact meaning to the natural laws in which these occur. Thus all our previous conclusions based on general relativity would appear to be caUed in question. In reality we must make a subtle detour in order to be able to apply the postulate of general relativity exactly.

I shall prepare the reader for this in the following paragraphs. We if is express this property of the surface by describing the latter as a continuum. Let us now imagine that large number of a little rods of equal length have been made, their lengths being smaU compared with the dimensions of the marble slab.

When say they are of equal I length, mean that one can be laid on any other I without the ends overlapping. We next lay four of these Uttle rods on the marble slab so that they constitute quadrilateral figure square , the a a diagonals of which are equally long. To this square we add similar ones, each of which has one rod in common with the first.

We proceed in like manner with each of these squares untU finally the whole marble slab is laid out with squares. The arrangement is such, that each side of a square belongs to two squares and each comer to four squares. It is a veritable wonder that we can carry out this business without getting into the greatest We only need to think of the fol- difficulties.

If at any moment three squares meet at a comer, then two sides of the fourth square are already laid, and as a consequence, the ar- rangement of the remaining two sides of the square is already completely determined. But I am now no longer able to adjust the quadrilateral so that its diagonals may be equal.

If they are equal of their own accord, then this is an especial favour of the marble slab and of the little rods about which I can only be thankfully surprised. We must needs experience many such surprises if the construction is to be successful. If everything has really gone smoothly, then I say that the points of the marble slab constitute a Euclidean continuiun with respect to the little rod, which has been used as a "distance" line- interval.

I only need state how many rods I must pass over when, starting from the origin, I proceed towards the "right" and then "upwards," in order to arrive at the comer of the square under consideration. These two numbers are then the "Cartesian co-ordmates" of this comer with reference to the "Cartesian co- ordinate system" which is determined by the arrangement of Uttle rods.

By making use of the following modification of this abstract experiment, we recognise that there must also be cases in which the experiment would be unsuccessf;il. We shall suppose that the rods "expand" by an amoimt proportional to the increase of temperature. We heat the central part of the marble slab, but not the periphery, in which case two of our Uttle rods can still be brought into coincidence at every position on the table. But our construction of squares must necessarily come into disorder diuiug the heating, because the Uttle rods on the central region of the table expand, whereas those on the outer part do not.

With reference to our Uttle rods — defined as imit lengths — the marble slab is no longer a EucUdean continuum, and we are also no longer in the position of defining Cartesian co-ordinates directly with their aid, since the above constmc- tion can no longer be carried out. The method of Cartesian co-ordinates must then be discarded, and replaced by another which does not assume the vaUdity of Euclidean geometry for rigid bodies. If we are given a surface e. Gauss undertook the task of treating this two-dimensional geometry from first principles, without making use of the fact that the surface belongs to a Euclidean continuum of three dimensions.

If we im- agine constructions to be made with rigid rods in similar the surface to that above with the marble slab , we should find that different laws hold for these from those resulting on the basis of Euclidean plane geometry. The surface is not a Euclidean continuum with respect to the rods, and we cannot define Cartesian co-ordinates in the surface.

Gauss indicated the principles according to which we can treat the geometrical relationships in the surface, and thus pointed out the way to the method of Riemann of treating multi- dimensional, non-Euclidean continua. Thus it is that mathemati- cians long ago solved the formal problems to which we are led by the general postulate of relativity.

We imagine a system of arbitrary ciurves see Fig. These we designate as M-curves, and we indicate each of them by means of a number. Thus a perfectly definite value of u belongs to every point on the surface of the marble slab.

These satisfy the same conditions as the «-curves, they are provided with numbers in a correspond- ing manner, and they may hkewise be of arbitrary shape.

It follows that a value of u and a value of belong to every point on the surface of the V table. We call these two numbers the co-or- dinates of the surface of the table Gaussian co-ordinates. In similar manner we may indicate the distance a and P', as measured P line-interval between with little rod, by means of the very small a number ds. Under these conditions, the w-curves and j;-curves are straight Hnes in the sense of EucHdean geom- etry, and they are perpendicular to each other.

Here the Gaussian co-ordinates are simply Car- tesian ones. It is clear that Gauss co-ordinates are nothing more than an association of two sets of numbers with the points of the surface con- sidered, of such a nature that mmierical values diEEering very sHghtly from each other are asso- ciated with neighbouring points "in space.

But the Gaussian method can be applied also to a continuum of three, four or more dimensions. If, for instance, a continuum of four dimensions be supposed available, we may represent it in the following way. With every point of the continuum we associatearbitrarily four numbers, Xi, 0C2, Xz, Xi, which are known as "co-ordinates. Only when the continuimi is a Euchdean one is it possible to associate the co-ordinates Xi.

In this case relations hold in the foiir-dimensional continuimi which are analogous to those holding in our three-dimensional measurements. It is only possible when sufficiently small regions of the continuum xmder consideration may be regarded as Euclidean continua. For example, this obviously holds in the case of the marble slab of the table and local variation of temperature. The temperature is practically constant for a small part of the slab, and thus the geometrical behaviour of the rods is almost as it ought to be according to the ndes of Euchdean geometry.

Hence the imperfections of the construction of squares in the previous section do not show them- selves clearly imtil this construction is extended over a considerable portion of the surface of the table. To every point of a continuum are assigned as many numbers Gaussian co-ordi- nates as the continuum has dimensions.

This is done in such a way, that only one meaning can be attached to the assignment, and that niunbers Gaussian co-ordinates which differ by an in- definitely small amount are assigned to adjacent points. The Gaussian co-ordinate system is a logical generaUsation of the Cartesian co-ordinate system. It is also apphcable to non-Euchdean continua, but only when, with respect to the defined "size" or "distance," smaU parts of the continuiun under consideration behave more nearly like a Euclidean system, the smaller the part of the continuum under our notice.

In accordance with the special theory of relativity, certain co-ordinate systems are given preference for the description of the four-dimensional, space-time continuimi. We called these "Galileian co-ordinate systems. For the transition from one Galileian sjrstem to another, which is moving imiformly with reference to the first, the equations of the Lorentz trans- formation are vaUd. Minkowski foimd that the Lorentz transforma- tions satisfy the following simple conditions.

Let us consider two neighbouring events, the relative position of which in the four-dimensional continuum is given with respect to a GaUleian reference-body K by the space co-ordinate dif- ferences dx, dy, dz and the time-difference dt. With to a second Galileian system we reference shall suppose that the corresponding differences for these two events are dx', dy', dz', dt'.

Then these magnitudes always fulfil the condition. Appendices and We call the magnitude ds the "distance" apart of the two events or four-dimensional points. This was possible on the basis of the law of the constancy of the ve- locity of Hght. But according to Section XXI, the general theory of relativity cannot retain this law. On the contrary, we arrived at the result that according to this latter theory the velocity of light must always depend on the co- ordinates when a gravitational field is pres- ent.

In cormection with a specific illustration in Section XXIII, we found that the presence of a gravitational field invahdates the definition of the co-ordinates and the time, which led us to our objective in the special theory of relativity. Just as it was there impossible to construct a Cartesian co-ordinate system from equal rods, so here it is impossible to build up a system reference-body from rigid bodies and clocks, which shall be of such a nature that measuring-rods and clocks, arranged rigidly with respect to one another, shall indicate posi- tion and time directly.

We refer the four-dimensional space-time continuum in an arbitrary manner to Gauss co-ordinates. This arrangement does not even need to be of such a kind that we must regard Xi, X2, Xs, as "space" co-ordinates and Xi as a "time" co-ordinate. More careful consideration shows, however, that this anxiety- is imfoimded. Let us consider, for instance, a material point with any kind of motion.

Thus its permanent existence must be char- acterised by an infinitely large nimiber of such systems of values, the co-ordinate values of which are so close together as to give continuity; corresponding to the material point, we thus have a uni-dimensional line in the four-dimensional continuima. In the same way, any such lines in oiur continuum correspond to many points in motion.

The only statements having regard to these points which can claim a physical existence are in reality the statements about their en- counters. When we were describing the motion of a material ppint relative to a body of reference, we stated nothing more than the encoxmters of this point with particular points of the reference-body. We can also determine the correspondiag values of the time by the observation of encounters of the body with clocks, in conjunction with the observation of the encounter of the hands of clocks with particular points on the dials.

It is just the same in the case of space-measurements by means of measuring-rods, as a Uttle considera- tion will show. I The following statements hold generally: Every physical description resolves itself into a number of statements, each of which refers to the space- time coincidence of two events A and B.

Thus in reality, the description of the time-space continuum by means of Gauss co-ordinates completely replaces the description with the aid of a body of reference, without suffering from the defects of the latter mode of description; it is not tied down to the Euclidean character of the continuum which has to be represented. The form there used, "All bodies of reference K, K', etc. The Gauss co-ordinate system has to take the place of the body of reference.

The following statement corresponds to the fundamental idea of the general principle of relativity: "All Gaus- sian co-ordinate systems are essentially equivalent for the formulation of the general laws of nature.

According to the special theory of relativity, the equations which express the general laws of nature pass over into equations of the same form when, by making use of the Lorentz transformation, we replace the space-time variables X, y, z, t, of a Galileian reference-body K by the x', y', z', space-time variables t', of new reference- a body K'. According to the general theory of relativity, on the other hand, by appUcation of arbitrary substitutions of the Gauss variables Xi, Xi, Xz, Xi, the equations must pass over into equations of the same form; for every transfor- mation not only the Lorentz transformation corresponds to the transition of one Gauss co-ordi- nate system into another.

If we desire to adhere to our "old-time" three- dimensional view of things, then we can char- acterise the development which being imder- is gone by the fundamental idea of the general theory of relativity as follows: The special theory of relativity has reference to Galileian domains, i. In this connection Galileian reference-body a serves as body of reference, i.

A gravitational field of a special kind is then present with respect to these bodies cf. In gravitational fields there are no such things as rigid bodies with Euclidean properties; thus the fictitious rigid body of reference is of no avail in the general theory of relativity.

The motion of clocks is also influenced by gravitational fields, and in such a way that a physical definition of time which is made directly with the aid of clocks has by no means the same degree of plausibility as in the special theory of relativity.

For this reason non-rigid reference-bodies are used which are as a whole not only moving in any way whatsoever, but which also suffer alterations in form ad lib.

Clocks, for which the law of motion is of any kind, however irregular, serve for the definition of time. We have to imagine each of these clocks fixed at a point on the non-rigid reference-body. These clocks satisfy only the one condition, that the "readings" which are observed simultaneously on adjacent clocks in space differ from each other by an indefinitely small amoimt.

Every point on the moUusk is treated as a space-point, and every material point which is at rest relatively to it as at rest, so long as the mollusk is considered as reference-body. We start off from a consideration of a Gahleian domain, i. The behaviour of measuring-rods and clocks with reference to K is known from the special theory of relativity, likewise the behaviour of "isolated" material points; the latter move uniformly and in straight lines.

Then with respect to K' there is a, gravitational field G of a particular kind. We learn the behaviour of measuring-rods and clocks and also of freely-moving material points with reference to K' simply by mathematical trans- formation.

Hereupon we introduce a hypothesis: that the influence of the gravitational field on measuring-rods, clocks and freely-moving material points continues to take place according to the same laws, even in the case when the prevailing gravitational field is not derivable from the GaUleian special case, simply by means of a transformation of co-ordinates.

The next step is to investigate the space-time behaviour of the gravitational field G, which was derived from the GaHleian special case simply by transformation of the co-ordinates. This be- haviour is formulated in a law, which is always valid, no matter how the reference-body mollusk used in the description may be chosen. Too many unreal explanations of this experiment have been published. Einstein also clearly confirmed the crucial importance of the constancy of the speed of light in all the frames of reference.

This formulation does not point directly that the speed of light is the same in all the frames of reference. But the use of the Lorentz transformations demonstrates that Einstein adopted and applied in the special theory of relativity the wrong statement that the speed of light is constant in all the inertial frames of reference.

That is why the invariance of the speed of light is indeed with primary importance for the veracity of the theory of relativity. With this, the principle of the constancy of the velocity of light, which forms one of the two foundation pillars on which the theory is based, would be refuted. The Logic of the Reality According to the above illustrated thought experiment, it is clear that the observer is located in the stationary frame of reference. In this frame of reference, the units of time and length are defined and accepted to be constant.

There is another claim which is a basis of a very widespread paradox. It is that the units of time and length are really changing in the moving frame of reference. This claim does not correspond to the elementary logic, because in case of two inertial frames moving uniformly and rectilinearly - it cannot be determined which of them actually moves.

Therefore, if the units of time and length really are changing in the moving frame of reference, it cannot be determined in which of the two frames this change actually happens. However, it can be only a source of interesting, but unreal fantastic stories without scientific meaning. The electromagnetic field exists on the gravitational field.

In fact, the wavelength and frequency of the electromagnetic radiation are its spatial- and time- characteristics respectively. It lays among the elementary particles of matter, among all the planets, stars and galaxies.

All these levels are mutually interconnected, depending on each other, and changing in perfect, but not discovered yet synchrony. That is the reason why it is impossible to register any kind of variation in the speed of light, due to the motion of the Earth together with the surrounded time-spatial domain around the Sun. At an entrance toward the increasing intensity of the gravitational field of the time-spatial domain surrounded the Earth, the photons are losing energy, which is absorbing and accumulating by the gravitational field.

This experiment proves that the speed of light decreases, when the electromagnetic signals pass through a stronger gravitational field. This difference of the speed of light corresponds to the linear speed of the Earth at this latitude [see subsection 4. It means that the speed of light is not the same in all frames of reference. The Uncertainty in the Macro-World The characteristics of the electromagnetic field are changing together with the change of the gravitational field intensity; the properties of the atoms are also changing; all the units and constants are changing… all the physical reality is changing in synchrony in still undiscovered way.

We can receive information from the Universe only by means of the electromagnetic radiation. The electromagnetic signals travel to the Earth during uncertain period of changing time, cover uncertain distance of warped space at uncertain speed. Thus, the values of all the local physical constants will be measured the same too, because the units of time and length will exactly differ in correspondence to the intensity of the gravitational field in these time-spatial domains.

As a result, all the local physical units and physical constants will vary in synchrony, and we will not be able to register whatever change. This is because the electromagnetic radiation is a vibration, which occurs at the quantum level and does not depend on the speed of the body to which the atom belongs the atom which emits or absorbs the photons. Paragraph 3 The measured velocity of the electromagnetic radiation in areas with equal gravitational field intensity is not the same for all the reference systems.

Mathematically, in areas with equal gravitational intensity, the relationship between the readings in the different reference systems is expressed through Galilean transformations - it is a subject of Newtonian mechanics.

The speed of the electromagnetic radiation in vacuum changes when passes through the areas with different intensity of the gravitational field. In more details, the speed of the electromagnetic radiation increases in areas with weaker gravitational field and decreases in areas with stronger gravitational field.

This fact is actually proved by Shapiro time-delay effect. Paragraph 2 The properties of atoms photon emission and absorption are different in areas with different intensity of the gravitational field.

This is so, because the electromagnetic field exists on the gravitational field. The logical consequence is not only the fact that the characteristics of electromagnetic radiation frequency, wavelength, speed change when the photons are passing through the areas with different intensity of the gravitational field, but also the properties of atoms change in areas with different intensity of the gravitational field.

These statements give a genuine explanation of the results of all the experiments related to the measurement of the speed of light. Using GPS, Kelly [12] show that a light signal takes The transmitter, the receiver and the propagation path the path of light are located in a time-spatial domain with equal intensity of the gravitational field on the surface of the Earth.

The distance on the ground surface between station A and station B is equal to D. According to [see subsection 3. The light source, collimator, beam-splitter, light pencils and 4 mirrors of the interferometer Fig. Description of the experiment: A monochromatic light beam is split and the two beams are designed to follow the same path but in opposite directions around a polygonal mirror course.

The two recombined beams are then focused on a photographic plate, permitting measurement of fringe shifts with a high accuracy, as was described by Sagnac [2]. The observed effect is that the displacement of the interference fringes is changing with the change of the velocity of the disk rotation.

This property of space experimentally characterizes the luminiferous aether. The plane of the disk represents the x,y plane and the origin of the DCI coordinate frame is the center of the disk. Examination of the Sagnac's experiment in the frame of reference related to the space itself — in the so named DCI frame of reference: According to [subsection 3. However, all the apparatuses mounted on the spinning disc are rotating moving in the stationary DCI frame of reference.

The two light beams travel in opposite directions. Therefore, in this frame of reference, the pathlengths, which the two light beams actually cover in the space, are different. Thus, the pathlength of one of the light beams is shortening and the pathlength of the light beam which travels in the direction of the disk rotation is extending.

As a result of the change of the pathlengths of the two light beams due to the different velocities of the disk rotation - different phases between the two beams are created. Examination of the Sagnac's experiment in the frame of reference related to the rotating disk: In this frame of reference, the mirrors, light source and photographic plate are stationary and the pathlengths of the beams the distances among the mirrors are not changing when the disk is rotating.

Therefore, the conclusion for this frame of reference is that the displacement of the interference fringes is due to the change of the speed of the two light beams, which in turn is dependent on the velocity of the disk rotation. For that purpose, we can examine a simple ring interferometer a single fiber-optic coil mounted on the rotating disk. The two light beams are travelling in opposite directions in the same fiber optic circle. Each point of the optical circuit moves during the rotation at a linear speed equal to R.

After subtraction: , where In this way it is clear that the derivation of the equation commonly seen in the analyses of rotation, is in accordance with the above mentioned thesis about the behavior of the electromagnetic radiation Nowadays, the result of this experiment has very significant implications and applications in the practice.

Actually, it is irrefutable evidence about the invalidity of the special theory of relativity… That is why it is understanding that these evidences do not match with the opinion of the orthodox part of the physical society… 4. For James Clerk Maxwell and other scientists of the time, the answer was that the light traveled in a hypothetical medium called luminiferous ether.

Albert Michelson designed experimental apparatus later known as a Michelson interferometer and made his first experiment in , in order to determine the change of the speed of light due to the motion of the Earth through the stationary luminiferous ether. However, the expected shifts of the interference fringes were not observed.

Well, except for the portions of the book that used mundane objects such as a train, an embankment, Times Square or a clock to Download relativity the special and general theory or read online here in PDF or EPUB. Please click button to get relativity the special and general theory book now. The Special and the General Theory. In , at the age of 26, Albert Einstein proposed his special theory of relativity.