Einstein’s 1905 Paper on Relativity

 

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Reference: Disturbance Theory

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Einstein’s theory of relativity works for cosmological dimensions, but not when it comes to atomic dimensions. Einstein was critical of the quantum mechanics having no coherent theory, while he could not come up with a physical theory to explain quantum effects. This bothered him for the rest of his life.

An examination of Einstein’s postulates follows that led to his original paper on relativity. This 1905 paper of Einstein is available at the following link.

On the Electrodynamics of Moving Bodies

Parts of this paper are quoted below that show Einstein’s non-mathematical reasoning. Einstein’s statements are in black italics. My understanding follows in bold color italics.

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Basic Postulates

It is known that Maxwell’s electrodynamics—as usually understood at the present time—when applied to moving bodies, leads to asymmetries which do not appear to be inherent in the phenomena. Take, for example, the reciprocal electrodynamic action of a magnet and a conductor. The observable phenomenon here depends only on the relative motion of the conductor and the magnet, whereas the customary view draws a sharp distinction between the two cases in which either the one or the other of these bodies is in motion. For if the magnet is in motion and the conductor at rest, there arises in the neighbourhood of the magnet an electric field with a certain definite energy, producing a current at the places where parts of the conductor are situated. But if the magnet is stationary and the conductor in motion, no electric field arises in the neighbourhood of the magnet. In the conductor, however, we find an electromotive force, to which in itself there is no corresponding energy, but which gives rise—assuming equality of relative motion in the two cases discussed—to electric currents of the same path and intensity as those produced by the electric forces in the former case.

This introductory paragraph from the paper mentions asymmetry observed in the relative motion between a magnet and a conductor. This asymmetry occurs in the customary view, which uses the lab as its frame of reference. This results in different interpretation of the same phenomenon.

This “asymmetry” disappears when we use the magnetic lines of force, which are attached to the magnet, as the frame of reference. The conductor moves relative to these lines of force the same way in either case producing the same result. So, the problem has to do with how the frame of reference is selected.

Examples of this sort, together with the unsuccessful attempts to discover any motion of the earth relatively to the “light medium,” suggest that the phenomena of electrodynamics as well as of mechanics possess no properties corresponding to the idea of absolute rest. They suggest rather that, as has already been shown to the first order of small quantities, the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good. We will raise this conjecture (the purport of which will hereafter be called the “Principle of Relativity”) to the status of a postulate, and also introduce another postulate, which is only apparently irreconcilable with the former, namely, that light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body. These two postulates suffice for the attainment of a simple and consistent theory of the electrodynamics of moving bodies based on Maxwell’s theory for stationary bodies. The introduction of a “luminiferous ether” will prove to be superfluous inasmuch as the view here to be developed will not require an “absolutely stationary space” provided with special properties, nor assign a velocity-vector to a point of the empty space in which electromagnetic processes take place.

The Michelson-Morley’s experiment was very precise but it failed to discover any motion of earth relative to the light medium. That was because the inertia of light is imperceptibly small compared to the inertia of earth. But light does have inertia that causes its velocity to be finite (see the paper on The Problem of Inertia.)

Einstein suggests that there is no such thing as absolute rest. The fact is that motion reduces with increase in inertia. Only a body with infinite inertia shall come close to absolute rest.

Einstein postulates, “… the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good.” Equations of mechanics hold good for frames of reference in which velocities correspond to the inertia of matter. They are many such frames for a range of inertia. The only value of inertia that would relate to all of them would be the reference value of zero inertia.

Einstein postulates light to provide such a reference point. This works for material frames of reference because inertia of light is imperceptibly small in comparison. However, it is questionable if Einstein’s postulate would work for particles of inertia in the atomic range, because inertia of light cannot be ignored in that range.

Einstein also postulates, “… light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body.” The velocity of light is constant because it is determined by an inertia that is constant in the relatively small range of the frequencies of visible light. This inertia is not influenced by the inertia of emitting material body. Therefore, the velocity of light is independent of the state of motion of the emitting body.

The “luminiferous ether” was assumed to be a material-like medium of light waves. The inertial frame with the above two postulates then replaces the idea of “luminiferous ether”.

The theory to be developed is based—like all electrodynamics—on the kinematics of the rigid body, since the assertions of any such theory have to do with the relationships between rigid bodies (systems of co-ordinates), clocks, and electromagnetic processes. Insufficient consideration of this circumstance lies at the root of the difficulties which the electrodynamics of moving bodies at present encounters.

Rigidity of body corresponds to the material level of inertia. The systems of co-ordinates for space-time are designed with that rigidity in mind. So they apply to material bodies. It is questionable that these rigid space-time coordinates would apply to electromagnetic processes that have a level of inertia many orders of magnitude less than the inertia of matter.

Einstein’s theory of relativity is based on the dichotomy of “inertia – no inertia”.

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I. KINEMATICAL PART

§ 1. Definition of Simultaneity

Let us take a system of co-ordinates in which the equations of Newtonian mechanics hold good. In order to render our presentation more precise and to distinguish this system of co-ordinates verbally from others which will be introduced hereafter, we call it the “stationary system.” 

If a material point is at rest relatively to this system of co-ordinates, its position can be defined relatively thereto by the employment of rigid standards of measurement and the methods of Euclidean geometry, and can be expressed in Cartesian co-ordinates.

Einstein defines a “stationary system” in which the equations of Newtonian mechanics hold good. The space-time coordinates of this system have the rigid characteristics of the inertia applied to matter.

If we wish to describe the motion of a material point, we give the values of its co-ordinates as functions of the time. Now we must bear carefully in mind that a mathematical description of this kind has no physical meaning unless we are quite clear as to what we understand by “time.” We have to take into account that all our judgments in which time plays a part are always judgments of simultaneous events. If, for instance, I say, “That train arrives here at 7 o’clock,” I mean something like this: “The pointing of the small hand of my watch to 7 and the arrival of the train are simultaneous events”.

To describe the motion of a material point we give the values of its coordinates as functions of “time”. To represent this motion mathematically, we must define “time” with the understanding of simultaneity of events.

It might appear possible to overcome all the difficulties attending the definition of “time” by substituting “the position of the small hand of my watch” for “time.” And in fact such a definition is satisfactory when we are concerned with defining a time exclusively for the place where the watch is located; but it is no longer satisfactory when we have to connect in time series of events occurring at different places, or—what comes to the same thing—to evaluate the times of events occurring at places remote from the watch.

The judgment of simultaneous events is possible only at the location of the event. Additional considerations are required to define simultaneity of events at different locations.

We might, of course, content ourselves with time values determined by an observer stationed together with the watch at the origin of the co-ordinates, and co-ordinating the corresponding positions of the hands with light signals, given out by every event to be timed, and reaching him through empty space. But this co-ordination has the disadvantage that it is not independent of the standpoint of the observer with the watch or clock, as we know from experience. We arrive at a much more practical determination along the following line of thought.

The “time-value” comes from the position of the hand of the watch that is moving at a constant rate. The position of hands of watches at two different locations would have to be coordinated to achieve simultaneity. The communication between the two locations can be made through light signals.

If at the point A of space there is a clock, an observer at A can determine the time values of events in the immediate proximity of A by finding the positions of the hands which are simultaneous with these events. If there is at the point B of space another clock in all respects resembling the one at A, it is possible for an observer at B to determine the time values of events in the immediate neighbourhood of B. But it is not possible without further assumption to compare, in respect of time, an event at A with an event at B. We have so far defined only an “A time” and a “B time.” We have not defined a common “time” for A and B, for the latter cannot be defined at all unless we establish by definition that the “time” required by light to travel from A to B equals the “time” it requires to travel from B to A. Let a ray of light start at the “A time” tA from A towards B, let it at the “B time” tB. be reflected at B in the direction of A, and arrive again at A at the “A time” t’A.

In accordance with definition the two clocks synchronize if tB – tA = t’A – tB.

Simultaneity of clocks between two locations requires that light takes the same “time” of travel between the two locations in either direction.

We assume that this definition of synchronism is free from contradictions, and possible for any number of points; and that the following relations are universally valid:—

  1. If the clock at B synchronizes with the clock at A, the clock at A synchronizes with the clock at B.
  2. If the clock at A synchronizes with the clock at B and also with the clock at C, the clocks at B and C also synchronize with each other.

Thus with the help of certain imaginary physical experiments we have settled what is to be understood by synchronous stationary clocks located at different places, and have evidently obtained a definition of “simultaneous,” or “synchronous,” and of “time.” The “time” of an event is that which is given simultaneously with the event by a stationary clock located at the place of the event, this clock being synchronous, and indeed synchronous for all time determinations, with a specified stationary clock.

In agreement with experience we further assume the quantity 2AB/( t’A – tA) = c to be a universal constant—the velocity of light in empty space.

Einstein is assuming that light provides the fastest means of coordination to ascertain simultaneity of mechanical events. This is probably the case when mechanical systems are used for detection.

But for reasonable synchronization of clocks only a synchronization of tempo is needed. The rest is taken care of by the knowledge of distance between the two locations and the speed of light.

It is essential to have time defined by means of stationary clocks in the stationary system, and the time now defined being appropriate to the stationary system we call it “the time of the stationary system.”

The above concept of “time” may be understood in the following two ways:

  1. We take the velocity of light as our reference point. This velocity is so large that compared to it the differences in velocities of material objects are negligible. This allows us a constant rate of change (tempo) with which to measure the motion of material bodies.

  2. We take the inertia of light as our reference point. It is so small that we can treat it as the “zero” for the range of inertia for material bodies. This allows us a basis from which to measure the inertia, and therefore, the motion of all material bodies.

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§ 2. On the Relativity of Lengths and Times

[Please refer this section in the original paper. I am only writing my comments on the contents of this section here.]

The theory of relativity stipulates that the laws by which the states of physical systems undergo change are not affected by translatory motion of frames of reference. This stipulation applies to material systems only, and not to rest of the physical systems covered in The Spectrum of Substance.

The theory of relativity stipulates the velocity of light ‘c’ to be a universal constant. This is true only for the range of frequencies that describe visible light. It is not certain that ‘c’ would apply to the whole range of frequencies on The Spectrum of Substance because ‘c’ represents the “drift velocity” that varies with inertia of the substance.

In this section Einstein develops his mathematical model to determine the relationship between two systems of coordinates that are moving at a uniform velocity relative to each other. In both coordinate systems the velocity of light ‘c’ is assumed to be the same. Einstein did not know that this relationship was already calculated by Lorentz earlier.

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§ 3. Theory of the Transformation of Co-ordinates and Times from a Stationary System to another System in Uniform Motion of Translation Relatively to the Former

[Please refer this section in the original paper. I am only writing my comments on the contents of this section here.]

This section is purely mathematical. It derives the relationship between two co-ordinate systems that are moving uniformly relative to each other when the principle of relativity is applied. According to this principle, the velocity of light is constant in both stationary and moving frames of reference.

The mathematical stipulations are as follows:

  • Both “stationary” and “moving” frames of references are rigid like matter. They are homogenous throughout. In other words, the units of space and time maintain the same characteristics throughout.

  • The moving frame moves at a uniform velocity in the same direction.

  • Simultaneity of clocks at the two ends of a distance requires that light takes the same “time” of travel between the two locations in either direction.

  • The velocity of the moving frame is negligibly small compared to the speed of light.

Einstein then comes up with the same relationship that Lorentz had come up earlier.

Lorentz Boost

Lorentz used the following assumptions:

  • The speed of light is the same in all inertial systems.

  • The gamma “fudge” factor is the same for all inertial systems.

  • The above assumptions are good for a “v/c ratio” of 1/10,000 or less. This is the ratio of the velocity of earth to the velocity of light.

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§ 4. Physical Meaning of the Equations Obtained in Respect to Moving Rigid Bodies and Moving Clocks

[Please refer this section in the original paper. I am only writing my comments on the contents of this section here.]

The equations obtained above predict that length and time shrink with motion. But it is not stated how a velocity is introduced to the moving frame. In reality, velocity can be introduced only through acceleration, which then increases the inertia of the system. This is similar to the observation that wavelength and period of an electromagnetic wave shrink with frequency with resulting increase in inertia.

Force must be applied to generate acceleration or a frequency gradient. The application of force raises the inertia of the system to a new level. Thus, Einstein’s exercise with the “principle of relativity” indirectly supports a continuum of inertia. This continuum has been presented as The Spectrum of Substance. Here substance is primarily represented as an electromagnetic field. With decreasing inertia, substance regresses back to emptiness. With increasing inertia, substance advances towards matter.

Einstein’s own interpretations of the relativity of time have raised many interesting speculations, such as, “time travel”. But such interpretations assume that the principle of relativity works without limitation. This is not so. The workability of the principle of relativity is limited to the upper band of matter in The Spectrum of Substance, where the drift velocities are very low compared to the velocity of light, and any influence on length and time is infinitesimal.

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§ 5. The Composition of Velocities

[Please refer this section in the original paper. I am only writing my comments on the contents of this section here.]

Einstein’s theory assumes that inertia of light is zero, because only then can light be treated the same in all inertial frames of reference. In other word, Einstein’s theory implicitly assumes the velocity of light to be infinite.

In reality, light has a very small amount of inertia as evidenced by a very large, but finite, velocity (see The Problem of Inertia). This inertia may be ignored because Einstein’s frames of reference are limited to matter, but we cannot ignore the implicit assumption of “infinite velocity” for light when dealing with composition of velocities.

Therefore, the following conclusions of Einstein are correct only when ‘c’ is infinite.

  1. “It follows from this equation that from a composition of two velocities which are less than c, there always results a velocity less than c.”

  2. “It follows, further, that the velocity of light c cannot be altered by composition with a velocity less than that of light.”

These conclusions are incorrect when ‘c’ is given a finite value. Thus, we see that math can be fallible when the assumptions are ignored.

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II. ELECTRODYNAMICAL PART

§ 6. Transformation of the Maxwell-Hertz Equations for Empty Space. On the Nature of the Electromotive Forces Occurring in a Magnetic Field During Motion

[Please refer this section in the original paper. I am only writing my comments on the contents of this section here.]

Einstein uses his theory to modify the explanation of forces that are acting on an electric charge, which is moving in a magnetic field. This helps explain the asymmetry observed in the relative motion between a magnet and a conductor mentioned at the beginning of this paper.

We need to reexamine this explanation in the light of the understanding that “empty space” is essentially an electromagnetic field (see The Problem of “Empty Space”).

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§ 7. Theory of Doppler’s Principle and of Aberration

[Please refer this section in the original paper. I am only writing my comments on the contents of this section here.]

From the mathematics in this section Einstein concludes that to an observer approaching a source of light with the velocity c, this source of light must appear of infinite intensity.

In this case the conclusion might be correct because the applicable assumption that inertia of light is negligible compared to the inertia of the source of light is valid.

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§ 8. Transformation of the Energy of Light Rays. Theory of the Pressure of Radiation Exerted on Perfect Reflectors

[Please refer this section in the original paper. I am only writing my comments on the contents of this section here.]

Einstein concludes, “It is remarkable that the energy and the frequency of a light complex vary with the state of motion of the observer in accordance with the same law.”

That means we have a relationship between frequencies of a substance, which represent inertia in some way, and its ‘drift velocity’. See The Problem of Inertia. It may be possible to work out these relationships mathematically.

The weakness of Einstein’s theory is that it assumes the inertia of light to be zero. Once this is corrected, we may be able to achieve some groundbreaking result.

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§ 9. Transformation of the Maxwell-Hertz Equations when Convection-Currents are Taken into Account

[Please refer this section in the original paper. I am only writing my comments on the contents of this section here.]

We don’t really know the exact nature of charge. It could result from the misalignment of frequency gradients in the electromagnetic field, but this needs to be researched further.

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§ 10. Dynamics of the Slowly Accelerated Electron

[Please refer this section in the original paper. I am only writing my comments on the contents of this section here.]

It is not certain if Newton’s laws of force can apply to an electron, which is a particle just forming out of electromagnetic field. The nature of electron appears to be more like a whirlpool in an electromagnetic field. It’s inertia is not comparable to the inertia of a material point.

Einstein’s analysis of the motion of electron is, therefore, inconclusive.

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