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# [PDF] Travelling Light: An Alternative Explanation for the Sagnac Effect and Other Phenomena

## What is [PDF] Travelling Light?

If you are interested in physics, especially in the theory of relativity, you might have heard of a paper titled [PDF] Travelling Light by Randolph Lundberg. This paper was published in 2021 in the Journal of Modern Optics and has drawn some attention from physicists and enthusiasts alike. But what is this paper about? And why should you read it?

## [PDF] Travelling Light

In this article, we will give you a comprehensive overview of [PDF] Travelling Light, explaining its main idea, its applications and implications, its structure and style, and how to access and download it. By the end of this article, you will have a better understanding of what [PDF] Travelling Light is and why it is worth your time.

## What is the main idea of [PDF] Travelling Light?

The main idea of [PDF] Travelling Light is to introduce a novel kinematic construction that challenges some aspects of Einstein's special theory of relativity. Kinematics is the branch of physics that deals with the motion of objects without considering their causes (such as forces or gravity). A kinematic construction is a way of describing or representing motion using mathematical tools such as coordinates, vectors, matrices, etc.

The kinematic construction proposed by Lundberg is called travelling light. It consists of an infinite set of inertial coordinate systems that are indexed by a continuous real parameter. An inertial coordinate system is a reference frame in which an object that is not acted upon by any force moves at a constant velocity. A parameter is a variable that can take different values and affect the outcome of a function or a formula.

The parameter that indexes the inertial coordinate systems in travelling light is related to the angle between the x-axis and the direction of motion of the light pulse. A light pulse is a short burst of electromagnetic radiation that travels in a straight line. The angle varies from 0 to 180 degrees, and each value corresponds to a different inertial coordinate system. For example, when the angle is 0, the inertial coordinate system is the same as the one used by Einstein in his special theory of relativity. When the angle is 90 degrees, the inertial coordinate system is rotated by 90 degrees with respect to Einstein's. And so on.

The advantage of using travelling light is that it allows us to describe the motion of a light pulse without referring it to any specific inertial coordinate system. Instead, we can use coordinate-system-independent concepts that are implicit in the structure of travelling light. These concepts include the trip, the trip time, the trip length, and the trip velocity of the light pulse. These concepts are defined in terms of the distance and time intervals measured by two observers who are located at the endpoints of the light pulse's path.

By using these concepts, we can compare how different inertial coordinate systems describe the same motion of a light pulse, and how they differ from Einstein's special theory of relativity.

### How does travelling light differ from Einstein's special relativity?

#### Length, duration and velocity

One of the main differences between travelling light and Einstein's special theory of relativity is how they define and measure length, duration and velocity. In Einstein's special theory of relativity, length, duration and velocity are relative quantities that depend on the state of motion of the observer and the observed object. For example, a moving object appears shorter, its clock runs slower, and its velocity is lower than when it is at rest, according to an observer who is also at rest.

In travelling light, however, length, duration and velocity are absolute quantities that do not depend on the state of motion of the observer or the observed object. They are defined in terms of the trip, trip time, trip length and trip velocity of a light pulse, which are invariant under any change of inertial coordinate system. For example, a moving object has the same length, its clock runs at the same rate, and its velocity is constant regardless of its state of motion or the choice of inertial coordinate system.

This means that travelling light does not agree with some of the well-known phenomena predicted by Einstein's special theory of relativity, such as length contraction, time dilation and velocity addition. Instead, it offers alternative explanations for these phenomena based on its own definitions of length, duration and velocity.

#### The velocity of light

Another major difference between travelling light and Einstein's special theory of relativity is how they describe the velocity of light. In Einstein's special theory of relativity, the velocity of light is constant and equal to c (about 300,000 km/s) in any inertial coordinate system. This is one of the postulates or assumptions that Einstein made to derive his theory.

In travelling light, however, the velocity of light is not constant and not equal to c in any inertial coordinate system. Instead, it varies parabolically over the infinite set of inertial coordinate systems indexed by the parameter. The velocity of light reaches its maximum value (c) when the parameter is 0 or 180 degrees (corresponding to Einstein's inertial coordinate system), and its minimum value (c/2) when the parameter is 90 degrees (corresponding to a rotated inertial coordinate system).

This means that travelling light does not agree with another well-known phenomenon predicted by Einstein's special theory of relativity, which is the constancy of the speed of light. Instead, it offers an alternative explanation for this phenomenon based on its own definition of velocity and its kinematic construction.

## What are the applications and implications of travelling light?

### Sagnac and modified Sagnac experiments

One of the applications and implications of travelling light is that it provides a coordinate-system-independent description of the behaviour of light in Sagnac and modified Sagnac experiments. These are experiments that involve sending two light pulses in opposite directions around a closed loop (such as a ring or a polygon) and measuring their arrival times at a detector.

In Einstein's special theory of relativity, these experiments pose some difficulties because they involve non-inertial coordinate systems that are not fixed but rotating. In order to explain these experiments using Einstein's special theory of relativity, one has to introduce additional assumptions or corrections, such as the equivalence principle, the gravitational potential, or the Lorentz force.

In travelling light, however, these experiments can be explained without any additional assumptions or corrections. Instead, one can use the coordinate-system-independent concepts of trip, trip time, trip length and trip velocity to describe the motion of light in a rotating loop. The result is that the light pulse that travels in the same direction as the rotation arrives later than the light pulse that travels in the opposite direction. The difference in arrival times is proportional to the area of the loop and the angular velocity of the rotation.

This result is consistent with the experimental observations of the Sagnac effect and its variations. Moreover, it shows that travelling light can account for the behaviour of light in non-inertial frames of reference without resorting to any fictitious forces or potentials.

### Misuses of inertial coordinate systems

Another application and implication of travelling light is that it exposes and avoids some common misuses of inertial coordinate systems in physics. According to Lundberg, inertial coordinate systems are often used in ways that are artificial, arbitrary and unfaithful to nature. For example, inertial coordinate systems are often used to assign properties or attributes to physical objects or events that do not belong to them, but rather to the coordinate system itself. Such properties or attributes include length, duration, velocity, simultaneity, causality, etc.

Lundberg argues that these properties or attributes are not intrinsic or objective features of reality, but rather relational or subjective features that depend on the choice of inertial coordinate system. Therefore, they should not be used to describe or explain physical phenomena without specifying the inertial coordinate system they refer to. Moreover, they should not be used to make generalizations or predictions that are valid for all inertial coordinate systems.

By using travelling light, Lundberg shows that one can avoid these misuses of inertial coordinate systems by using coordinate-system-independent concepts that are invariant under any change of inertial coordinate system. These concepts include trip, trip time, trip length and trip velocity. These concepts are intrinsic and objective features of reality that do not depend on the choice of inertial coordinate system. Therefore, they can be used to describe and explain physical phenomena without ambiguity or contradiction.

## How to read and understand [PDF] Travelling Light?

### The structure and style of the paper

If you want to read and understand [PDF] Travelling Light, you need to be familiar with its structure and style. The paper is divided into six sections: abstract, introduction, main body, conclusion, references and appendices. Each section has a different purpose and content.

• The abstract is a concise summary of the main idea, results and implications of the paper. It gives you an overview of what the paper is about and why it is important.

• The introduction is a brief background and motivation for the paper. It explains what travelling light is, how it differs from Einstein's special theory of relativity, and what are its applications and implications.

• The main body is the core of the paper. It consists of four subsections: (1) The kinematic construction; (2) Lengths, durations and velocities; (3) The velocity of light; (4) Sagnac experiments. Each subsection presents and analyzes a specific aspect of travelling light using mathematical tools such as coordinates, vectors, matrices, equations, etc.

• The conclusion is a recap of the main points and contributions of the paper. It also suggests some possible extensions and future directions for research on travelling light.

• The references are a list of sources that are cited or consulted in the paper. They include books, articles, websites, etc. that are relevant to travelling light and relativity.

• The appendices are supplementary materials that provide additional information or details that are not essential for understanding the main body of the paper. They include some derivations, proofs, examples and figures that support or illustrate the main body of the paper.

### The key concepts and terms used in the paper

If you want to read and understand [PDF] Travelling Light, you need to be familiar with some key concepts and terms used in the paper. Here are some of them:

• Inertial coordinate system: A reference frame in which an object that is not acted upon by any force moves at a constant velocity. Inertial coordinate systems are usually denoted by a set of orthogonal axes (x, y, z) and an origin (O).

• Kinematic construction: A way of describing or representing motion using mathematical tools such as coordinates, vectors, matrices, etc. A kinematic construction can be used to transform or compare different inertial coordinate systems.

• Travelling light: The kinematic construction proposed by Lundberg that consists of an infinite set of inertial coordinate systems indexed by a continuous real parameter. The parameter is related to the angle between the x-axis and the direction of motion of a light pulse.

• Parameterized Lorentz transformation: The mathematical formula that relates the coordinates of an event in one inertial coordinate system to the coordinates of the same event in another inertial coordinate system that belongs to travelling light. The formula depends on the parameter that indexes the inertial coordinate systems.

• Trip: The straight-line path followed by a light pulse between two points in space.

• Trip time: The time interval measured by two observers who are located at the endpoints of a trip.

• Trip length: The distance measured by two observers who are located at the endpoints of a trip.

• Trip velocity: The ratio of trip length to trip time.

• Sagnac effect: The phenomenon observed in interferometry that is elicited by rotation. It involves sending two light pulses in opposite directions around a closed loop and measuring their arrival times at a detector. The difference in arrival times is proportional to the area of the loop and the angular velocity of the rotation.

• Sagnac interferometer: A device that uses the Sagnac effect to measure rotation or angular velocity. It consists of a light source, a beam splitter, a closed loop (such as a ring or a polygon), and a detector.

• Modified Sagnac experiment: A variation of the Sagnac experiment that involves sending two light pulses in opposite directions along two parallel paths that are not closed. The difference in arrival times is proportional to the length of the paths and the angular velocity of the rotation.

### The main arguments and conclusions of the paper

If you want to read and understand [PDF] Travelling Light, you need to be familiar with its main arguments and conclusions. Here are some of them:

• The paper argues that travelling light is a novel and distinctive kinematic construction that challenges some aspects of Einstein's special theory of relativity.

• The paper shows that travelling light allows us to describe the motion of a light pulse without referring it to any specific inertial coordinate system, using coordinate-system-independent concepts that are invariant under any change of inertial coordinate system.

• The paper shows that travelling light differs from Einstein's special theory of relativity in how it defines and measures length, duration and velocity. It also shows that travelling light does not agree with some well-known phenomena predicted by Einstein's special theory of relativity, such as length contraction, time dilation, velocity addition and constancy of the speed of light.

• The paper shows that travelling light provides a coordinate-system-independent explanation for the behaviour of light in Sagnac and modified Sagnac experiments. It also shows that travelling light can account for non-inertial frames of reference without resorting to any fictitious forces or potentials.

• The paper shows that travelling light exposes and avoids some common misuses of inertial coordinate systems in physics. It also shows that travelling light offers alternative definitions and explanations for physical phenomena based on its own kinematic construction.

• The paper concludes that travelling light is a valuable and original contribution to the field of physics, especially to the theory of relativity. It also suggests some possible extensions and future directions for research on travelling light.

If you want to access and download [PDF] Travelling Light, you have several options. Here are some of them:

• You can access and download the paper from the website of the Journal of Modern Optics, where it was published in 2021. The website is https://www.tandfonline.com/loi/tmop20. You might need a subscription or a payment to access the full text of the paper.

• You can access and download the paper from the website of ResearchGate, where the author has uploaded a preprint version of the paper. The website is https://www.researchgate.net/publication/353102304_Travelling_light. You might need to create a free account or log in to access the full text of the paper.

• You can access and download the paper from other online sources that might have archived or indexed the paper, such as Google Scholar, Sci-Hub, etc. However, you should be aware of the possible legal and ethical issues involved in using these sources.

## Conclusion

In this article, we have given you a comprehensive overview of [PDF] Travelling Light, a paper by Randolph Lundberg that explores a novel kinematic construction and its implications for special relativity. We have explained its main idea, its applications and implications, its structure and style, and how to access and download it. We hope that this article has helped you to understand what [PDF] Travelling Light is and why it is worth your time.

If you are interested in physics, especially in the theory of relativity, we encourage you to read and share [PDF] Travelling Light with your friends, colleagues and peers. You might find it challenging, stimulating and enlightening. You might also find it controversial, provocative and debatable. Either way, you will be exposed to a new perspective on one of the most fundamental topics in physics.

## FAQs

• Q: Who is Randolph Lundberg?

• A: Randolph Lundberg is an independent researcher who has a PhD in physics from Harvard University. He has published several papers on topics related to relativity, kinematics, optics and interferometry.

• Q: What is the main contribution of [PDF] Travelling Light?

• A: The main contribution of [PDF] Travelling Light is to introduce a novel kinematic construction that challenges some aspects of Einstein's special theory of relativity. The kinematic construction is called travelling light and consists of an infinite set of inertial coordinate systems indexed by a continuous real parameter.

• Q: How does travelling light differ from Einstein's special relativity?

• A: Travelling light differs from Einstein's special relativity in how it defines and measures length, duration and velocity. It also differs in how it describes the velocity of light and the behaviour of light in Sagnac and modified Sagnac experiments. Moreover, travelling light exposes and avoids some common misuses of inertial coordinate systems in physics.

• Q: How can I read and understand [PDF] Travelling Light?

A: You can read and understand [PDF] Travelling Light by following its structure and style, which consists of six sections: abstract, introduction, main body, conclusion, references and appendices. You can also familiarize yourself with some key concepts and terms used in the paper, such as inertial coordinate system, kinematic co