# Albert Einstein Nobel Lecture

## The lecture was given to participants of the Nordic Assembly of Naturalists at Gothenburg* 11th July 1923

## The fundamental concepts and issues in theories of relativity

If we look at the part in the relativity theory, which could in the present be considered as genuine scientific research, we will notice two factors that are of great importance to the theory. The entire development of the theory is based on whether there exists a physically preferential state of motions in Nature (physical relativity issue). Additionally, distinctions and concepts are only valid only if observable facts are able to be attributable to them without confusion (stipulation that distinctions and concepts must have a significance). This proposition, which is related to epistemology proves to be fundamentally important. Both of these aspects are evident when they are applied to a particular situation, e.g. to classical mechanics.

First, we can see that at every point that is filled with matter, there is a preferred state of motion, which is the case of the material at the time that is being considered. Our issue is the question of whether physically preferential states of motion exist with the context of large areas. From the standpoint of classical mechanics, the answer is yes that the most physically desirable states of motion from the standpoint of mechanics are those inertial frames. This claim, as with the foundation of the entire field of mechanics in the way it is commonly was described prior to that theory of relativity, is far from meeting the “stipulation of meaning”. Motion is only understood as the movement of objects. In the field of mechanics, motion related to the coordinate system is implied when only motion is mentioned. However, this interpretation doesn’t meet” stipulation of meaning “stipulation of meaning” if the coordinate system is viewed as being purely imaginary.

## Vision

If we shift our focus to the physics of experiments, we will find that it is always represented by the form of a “practically rigid” body. In addition, it is believed that rigid bodies can be placed in a resting position relative to each other in common with bodies in Euclidian geometry. As we imagine the rigid measuring body something that can be perceived and experienced, it is believed that the “system of coordinates” concept and the notion of the motion of matter with respect to it is a valid concept in terms of the “stipulation of meaning”. However, Euclidian geometry, in this definition is modified to meet the demands of the science that is”the “stipulation of meaning”. The issue of whether Euclidean geometry is valid has become important physically; its validity is recognized in the classical physics, and later in the theory of relativity that is specialized.

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In classical mechanics, the inertial frame and the time are best defined through a proper definition of the law of Inertia. There is a way to define the duration of time and assign an inertial frame state to the coordinate system (inertial frame) so that, with reference to it materials that are not subject to force, they undergo no acceleration, and it is believed that the time is measurable without dispute through identical clocks (systems that run on a regular basis) in any condition of motion. There is an infinite amount of inertial frames that are in a uniform translational motion with respect to one another which means that there is an infinity of physically preferential types of states. It is an absolute time, i.e.independent of the choice of the inertial frame. It’s defined by more factors than is strictly necessary, but it is implied by the concept of mechanics – this shouldn’t cause contradictions with the experience. It is worth noting that the main weakness of this explanation from the perspective of the definition of meaning in the absence of an experimental test to determine the determination of whether a point in a material is not force-free; consequently, the notion of an inertial frame is still a bit ambiguous. This omission results in an overall theory on relativity. We will not be discussing it for now.

The idea of the “rigid body” (and the concept of the clock) has a significant bearing on the prior examination of the fundamentals of mechanics, a concept that has a reason to challenge. The rigid body can only be about what it appears to be in Nature but not in the desired precision; this idea is not in any way a perfect fit for that “stipulation of meaning”. It is also unlogical to base all considerations of physical science on the solid or rigid body, and then reconstruct it atomically by the use of fundamental physical laws, which were determined through the use of measurement by a rigid body. I’m mentioning these flaws of methodology because, in the same way, they are also a part of the theory of relativity that is in the schematic exposition I am promoting in this article. It is certainly more logical, to begin with, the entire set of laws and employ to the “stipulation of meaning” to the whole, i.e. to place the clear relation to the experience world in the last place, rather than merely implementing the condition in a weak format for an artificially isolated component, such as the space-time measurement. However, we aren’t enough proficient in our understanding of the basic laws of Nature to be able to apply this superior method without getting out of our understanding. After our review, we’ll see with the most current research there is a plan, in the spirit of Levi-Civita Weyl as well as Eddington to adopt this more logically pure method.

It is clear from the previous the meaning of “preferred states of motion”. They are favored in the context of Nature’s law of Nature. The state of motion is preferred when, in relation to the formulating of laws of Nature the coordinate systems that are inside them are distinguished in the sense that, in relation to them, the laws take on a shape that is favored by their simplicity. According to classical mechanics, the states of motion in the inertial frames are preferred physical. Classical mechanics allows the making of a distinction between (absolutely) accelerations and motions that are not accelerated. It further states that velocities possess only a limited exist (dependent on the choice for the frame) however, accelerations and rotations are absolute (independent of the choice for the frame). This situation is reflected in the following way in the classical mechanics “velocity relativity” exists, however, it is not “acceleration relativity”. After these first considerations, we can proceed onto the subject of our considerations, the theory of relativity, explaining its evolution up to now by defining its principles.

The special theory of relativity is an adaption of physical concepts to electrodynamics based on Maxwell-Lorentz. From earlier physics, it makes as a presumption the Euclidian geometry is applicable to the laws that govern the position of rigid bodies as well as the inertial frame, and the laws of inertia. A postulate on the equivalence between inertial frames in the formulation that governs the nature of Nature is thought to be true for the entire field of the field of physics (special the relativity rule). In Maxwell-Lorentz electrodynamics, it is the idea of invariance in the speed of light in the absence of space (light principles).

In order to reconcile the relativity concept and the light principle the idea of an absolute clock (agreeing with all the inertial frames) exists, needed to be discarded. This means that the notion that can be arbitrarily moved, and appropriately placed identical clocks function in a way so that the times displayed by two clocks, that are in agreement. A time-specific value is given to every inertial frame. The state of motion and the date that the inertial frame is are determined according to the definition of meaning according to the principle of light that should be applied to it. It is assumed that the existence of the frame so identified and the legitimacy for the inertial law regards to it are taken as a given. The time of every inertial frame is recorded by the same clocks which are stationary in relation to the frame.

The principles of transformation that govern time and space coordinates for transitioning from one frame inertial to another, or the Lorentz transformations, as they are referred to can be confirmed through these definitions, and the theories concealed behind assumptions that claim they’re not subject to of contradiction. Their primary physical importance lies in the effects of the movement relative to the inertial frame upon the form of solid bodies (Lorentz contraction) as well as on the speed of clocks. In accordance with the special relativity rule, the laws of Nature are covariant to Lorentz transformations. The theory, therefore, provides a definition for the general law of Nature. It is primarily responsible for an alteration to the Newtonian Point Motion Law, in where the velocity of light within a vacuum can be regarded as the limit velocity. it results in the realization that mass and energy are similar in nature.

The theory of special relativity has led to substantial technological advances. It brought together electrodynamics and mechanics. It decreased the number of logically distinct hypotheses concerning electrodynamics. It also emphasized the need for a clearer understanding of the basic concepts in the epistemological sense. It unified the principle of momentum and energy and established a similar nature of energy and mass. However, it wasn’t entirely satisfying – apart from the quantum issues, which theories have not been able to solve. Like classical mechanics, the theory of special relativity favours certain kinds of motion, specifically the inertial frames, over any other state of motion. It was more difficult to live with than the preferential treatment of only one state of motion in the theories of light that relies on an ether that is stationary because it was a plausible reason behind this choice, i.e. it was the Light ether. A theory that at the beginning is an absence of any motion state would be more logical. Additionally, the above-mentioned ambiguity regarding the meaning of an inertial frame as well as regarding the formulating of the law of Inertia raises questions that have a significant impact due to the empirical theory for the equality of inertial mass and the heavy mass given the subsequent consideration.

Consider K represents an inertial frame that is not surrounded by any gravitational field K is a set of coordinates that are accelerated uniformly in relation to K. The behaviour of the material points in relation to K is similar to the case if K was an inertial frame of which a homogeneous gravitational force exists. Based on the well-known nature of gravitational fields the definition of an inertial frame proves to be inadequate. It is evident that any frame is equal to all other frames to formulate Nature’s law. Nature and therefore there aren’t physical states of motion that are preferred with respect to areas of infinite expansion (general the relativity concept).

The implementation of this concept necessitates an even more profound modification of the geometric-kinematical principles than the special relativity theory. In the Lorentz contraction, an extension of the former is the result that for an inertial frame K that is arbitrarily moved in relation to a (gravity field-free) Inertial Frame K and the rules of Euclidian geometry that govern the location of rigid (at still) K’) bodies do not apply. This means that it is the case that Cartesian systems of coordinates disappear as regards the definition of its meaning. Similar reasoning is applicable to time. With regard to K” the time cannot be meaningfully determined by the signification of identical clocks that are at rest in relation K’. K’, or even by the law that governs the transmission of light. In generalizing, we come to the conclusion that the gravitational field and the measurement are simply two different manifestations of the identical physical field.

The formal definition of this field is through the following analysis. For each infinitesimal area of an undefined gravitational field, the local coordinates frame can be described for an arbitrary state of motion in which is relative to the local frame, no gravitational field is present (local inertial frame). In the context of this inertial frame, it is possible to consider the findings of the theory of special relativity as a valid first approximation to this infinitely small area. There are infinite numbers of these local inertial frames at each time point in space and they are connected with Lorentz transformations. They are distinguished by the fact that they preserve their “distance” ds of two infinity-wide point events as defined by the following equation:

that distances can be determined through the use of clocks or scales. For instance, x Z, t, and x represent coordinates as well as time determined by reference to an inertial frame local to the location.

To represent space-time regions with an infinite extent, coordinates of arbitrary points that are four dimensions are needed that serve no other function beyond providing an unambiguous definition of space-time points using four numbers, the numbers x1,x2, x3, and x4, taking into account the continuous nature of this four-dimensional manifold (Gaussian coordinates). The mathematical definition that is the basis of the general relativity principle states also that the equation systems that express universal laws in Nature are identical for any of these coordinate systems. Because the differentials in coordinates for the frame local to the frame can be expressed linearly in the differentials dx from the Gaussian systems of coordinates when this system is employed to calculate the distance ds between two events, an expression in the form of

The result is. The gu v that are continuous functions of the variable xv determine the metric within the four-dimensional manifold, where it is defined by ds as an (absolute) parameter that is measurable through the use of clocks as well as rigid scales. The parameters gu v but also explain using the Gaussian system of coordinates the gravitational field, which has been previously proven to be the same as the physical basis of the metric. The argument for the validity of the particular theories of relativity for the finite region can be described by the fact that when the coordinate system is selected correctly the guv values for finite regions are independent of xv.

According to the general theory of relativity, the law of motion at a point in the gravitational field of pure gravity is expressed as the Geodetic Line. In reality, the geodetic line is the most straightforward mathematically that is the case in the particular instance of constant gu transforms into rectilinear. This is why we are faced with the application of Galileo’s inertia law to the General Theory of Relativity.

In mathematical terms, the search for the field equations equates to finding the simplest dependent differential equations, to which gravitational fields gu v may be affected. According to the definition, these equations must not have higher derivatives of gu v relation to xv than the second and only linearly that is, which reveals the equations to be an appropriate transfer to that Poisson field equation from the Newtonian theory of gravity to the general theory of relativity.

The reasons mentioned lead to the concept of gravity, which gives Newtonian theory. Newtonian theory as a first approximation. further, it provides an explanation for the movement of the perihelion of Mercury and that of the light reflected from the sun and the shift in spectrum lines in line with the observations (As in the case of shifting in red, relationship with the experience isn’t fully confirmed, but it is).

In order to complete the foundations of the theory generalissimo of relativity the electromagnetic field needs to be introduced into the theory which is, in our current belief, is the element that we construct the fundamental structure of matter. It is believed that the Maxwellian field equations can easily be integrated into the general theories of relativity. It is a clear acceptance if it is believed that the equations are free of differential quotients of gu more than the initial and that they are in the usual Maxwellian formula they apply to an inertial frame local to. It is also feasible to enhance the equations of gravitational fields with electromagnetic terms in the manner defined by the Maxwellian equations to contain the gravitational influence of electromagnetic fields.

The field equations haven’t been able to provide a theory of the universe. To include the field-generating effect of ponderable mass in this theory, the concept of matter needed to be (as in classical physical physics) been introduced to the theories using the form of a phenomenological, approximate representation.

That is the complete effect that the concept of a relative. I will now turn to the issues that are connected to the evolution I have observed. In the past, Newton realized the fact that inertia’s law was not satisfactory in a situation that is not yet addressed in this explanation, namely that it does not provide a reason for the particular physical location of the motion states within the frames of inertial motion compared to the different states. It is the cause of the visible material objects accountable for the gravitational behaviour of a particular point. It, however, doesn’t provide any material explanation for the inertial behaviour of the material point, however, it proposes the reason for it (absolute spatial ether, or the inertial). This is not inadmissible logically however it is not satisfactory. Because of this, E. Mach demanded a modification to the inertia law, in the sense that inertia is to be understood as the resistance to the acceleration of bodies to one another, instead of “space”. This interpretation is in accordance with the notion that bodies with acceleration have unconcordant acceleration similarly to the other body (acceleration inducement).

This interpretation is more feasible in light of general relativity that does away with the difference between gravitational and inertial effects. This is essentially saying that, besides the arbitrariness of the ability to select directions, the field is completely determined by the facts. Mach’s stipulation is supported in general relativity due to the fact that acceleration-induced induction according to gravitational field equations actually exists however it is of such a small magnitude that detection with mechanical methods is out of the question.

Mach’s stipulation could be taken into account within the theory general of relativity thinking of the universe in terms of spatial dimensions as self-contained and finite. This theory also allows one to think that the average density of matter throughout the universe is finite, and in a space-time infinite (quasi-Euclidian) world, it would disappear. It is, however, impossible to be denied that in order for Mach’s proposition to be satisfied with the manner described above, the term “cosmological problem” that has no base should be introduced into the field equations. This means that it is not in any way influenced by other equations. Therefore, this answer to”cosmological “cosmological problem” will not be entirely satisfying for the moment.

Another problem that currently is the topic of intense attention is the relationship that exists between gravitational fields as well as the electromagnetic field. The mind that is striving for the unification of the theory can’t be content that two fields exist that, in their own nature, are completely separate. A mathematically coherent field theory is desired in which the gravitational and the electromagnetic field are seen as distinct parts or aspects of the same field, with the field equations, if they are possible, do not comprise the logically mutually distinct summands.

The gravitational theory, which is viewed as a mathematical formalism i.e. Riemannian geometry, ought to be reformulated so that it incorporates the laws of the electromagnetic field. Unfortunately, we are not able to base our reasoning on the empirical evidence when we are determining from the theory of gravitation (equality of inertial and heavy mass) However, we are confined to the criteria of mathematical simplicity, which is not completely free of arbitrariness. The current attempt that is most likely to succeed is based on the theories from LeviCivita Weyl as well as Eddington that seeks to replace Riemannian geometric geometry with a broader theory called an affine correlation.

The most fundamental principle that is the basis of Riemannian geometry is that it assigns to two infinitely adjacent points the “distance” ds, the square of which is a homogeneous, second-order function of the differentials of coordinates. From this, (apart from certain limitations of the real world) Euclidian geometry is valid in any infinitely small area. Therefore, to each Line component (or vector) at a particular point P, there is an equal lines component (or vector) for any infinitesimally near location (P’) (affine correlation). Riemannian metrics are used to determine an affinity correlation. In contrast, if the affine relationship (law of infinitesimal displacement) is mathematically determined there is usually there is no Riemannian measurement is available that it can be calculated.

The most significant notion that is a part of Riemannian geometries “space curvature”, upon where the gravity equations are on, is based solely upon”affine correlation. “affine correlation”. If one is presented in a continuum without first derived through a metric, it is a broadening of Riemannian geometry, but it retains the most significant related parameters. In order to find the simplest differential equations that can be solved with an affine correlation, there is reason to believe that a generalization to the gravitation equations can be found that incorporates electromagnetic laws. field. The hope has actually been realized although I am not sure if the mathematical connection that was created can be considered as an improvement in physical science so long as it doesn’t produce any additional physical connection. Particularly, a field theory could, to my eyes, be considered satisfactory if it allows the basic electrical structures in a way that they can be described as solutions that are free of singularities.

Furthermore, it must not be overlooked that a theory that deals with the fundamental electrochemical structures cannot be dissociated from the quantum theory questions. As of now, the relativity theory has been ineffective when it comes to this important physical issue at present. If the structure of these general equations one time, as a result of the solution of the quantum problem undergo a radical change or even an entire modification in the parameters using which we describe the fundamental process, the principle of relativity is not going to be abandoned and the principles that were previously drawn from it will at the very least maintain their value as laws that limit.

Albert Einstein – Nobel Lecture. NobelPrize.org. Nobel Media AB 2020. Tue. 20 Oct 2020.