1) Einstein's Gedanken experiment involves lightning flashes striking the ends of a railway line simultaneously according to an observer in the middle. However, an observer on a passing train would see the flash at the front of the train first due to the train's motion.
2) Looking at it from the perspective of both observers, the train observer would deduce that the flashes were not simultaneous, while the stationary observer would still deduce simultaneity.
3) This demonstrates that two events simultaneous in one frame of reference may not be simultaneous in another, meaning time itself is behaving differently in the different frames.
This document discusses computational modeling of the structures of biological macromolecules like proteins docking together. It focuses on using the geometry of molecular surfaces and conformal mappings between surfaces to predict docked configurations. Circle packing is proposed as a method to construct approximate conformal mappings between molecular surfaces by triangulating one surface, constructing a circle packing with the same triangulation on a sphere, and finding conformal transformations between the surfaces and standard metrics on spheres.
The document discusses the development of quantum electrodynamics (QED) from its origins in Dirac's 1927 paper on the quantum theory of radiation. It provides an overview of the key topics covered in the subsequent chapters, including particles and fields, quantization of the electromagnetic field, Feynman diagrams, and renormalization in QED. The goal is to show how electrons and photons interact using quantum field theory by representing particles as excitations of underlying fields and developing perturbative techniques to calculate processes like scattering and radiation.
This document discusses Einstein's theory of special relativity and its implications. It begins by describing Galilean relativity and frames of reference. It then discusses Michelson-Morley's famous experiment which found that the speed of light is constant regardless of the motion of the observer, contradicting the theory of the luminiferous aether. This led Einstein to postulate that the laws of physics are the same in all inertial frames and that the speed of light in a vacuum is constant. The document explores the implications of these postulates through various thought experiments, showing that simultaneity is relative, time dilates and lengths contract for moving observers. It concludes by discussing some implications of special relativity like mass-energy equivalence and the twins paradox
Relativity theory project & albert einstenSeergio Garcia
Albert Einstein was a German-born theoretical physicist who developed the theory of relativity, one of the pillars of modern physics. He was born in 1879 in Germany and died in 1955 in the United States. He is best known for his mass-energy equivalence formula E=mc2, which has been called the world's most famous equation. He developed the special theory of relativity, which describes the laws of motion at high speeds and led to his famous equation, and the general theory of relativity, which describes gravity as a geometric property of space and time.
Relativity theory project & albert einstenSeergio Garcia
Albert Einstein was a German-born theoretical physicist who developed the theory of relativity, one of the pillars of modern physics. He was born in 1879 in Germany and died in 1955 in the United States. He is best known for his mass-energy equivalence formula E=mc2, which has been called the world's most famous equation. The document provides background on Einstein's life and work, and summarizes his theories of special relativity, which describes physics at high speeds, and general relativity, which proposes that gravity results from the curvature of spacetime.
Based on Einstein’s equation matter and anti-matter annihilate into photonic radiation energy. Photons have unique characteristics since they are massless and they travel at the speed of light in all the inertial reference frames. No other
particle shares these unique characteristics. We claim that this unique behavior is due to the fact that photons do not apply gravitational effects on space-time, meaning,although photons will be forced to move in a curved line if space-time is curved they will not curve space time by themselves or apply gravity forces and time dilation .
In order to prove our claims we suggest a thought experiment that leads to a blue shift paradox which happens after annihilating 2 symmetrical in size and mass, matter and
anti- matter (A&B) in the center of a hollow particles spherical shell . The only way to explain this paradox is to conclude that anti-matter imposes anti–gravity and therefore matter and anti-matter together impose zero gravity. Furthermore, this
proves that the photonic energy from the annihilation phase has also zero gravity effect on space-time.
This document discusses computational modeling of the structures of biological macromolecules like proteins docking together. It focuses on using the geometry of molecular surfaces and conformal mappings between surfaces to predict docked configurations. Circle packing is proposed as a method to construct approximate conformal mappings between molecular surfaces by triangulating one surface, constructing a circle packing with the same triangulation on a sphere, and finding conformal transformations between the surfaces and standard metrics on spheres.
The document discusses the development of quantum electrodynamics (QED) from its origins in Dirac's 1927 paper on the quantum theory of radiation. It provides an overview of the key topics covered in the subsequent chapters, including particles and fields, quantization of the electromagnetic field, Feynman diagrams, and renormalization in QED. The goal is to show how electrons and photons interact using quantum field theory by representing particles as excitations of underlying fields and developing perturbative techniques to calculate processes like scattering and radiation.
This document discusses Einstein's theory of special relativity and its implications. It begins by describing Galilean relativity and frames of reference. It then discusses Michelson-Morley's famous experiment which found that the speed of light is constant regardless of the motion of the observer, contradicting the theory of the luminiferous aether. This led Einstein to postulate that the laws of physics are the same in all inertial frames and that the speed of light in a vacuum is constant. The document explores the implications of these postulates through various thought experiments, showing that simultaneity is relative, time dilates and lengths contract for moving observers. It concludes by discussing some implications of special relativity like mass-energy equivalence and the twins paradox
Relativity theory project & albert einstenSeergio Garcia
Albert Einstein was a German-born theoretical physicist who developed the theory of relativity, one of the pillars of modern physics. He was born in 1879 in Germany and died in 1955 in the United States. He is best known for his mass-energy equivalence formula E=mc2, which has been called the world's most famous equation. He developed the special theory of relativity, which describes the laws of motion at high speeds and led to his famous equation, and the general theory of relativity, which describes gravity as a geometric property of space and time.
Relativity theory project & albert einstenSeergio Garcia
Albert Einstein was a German-born theoretical physicist who developed the theory of relativity, one of the pillars of modern physics. He was born in 1879 in Germany and died in 1955 in the United States. He is best known for his mass-energy equivalence formula E=mc2, which has been called the world's most famous equation. The document provides background on Einstein's life and work, and summarizes his theories of special relativity, which describes physics at high speeds, and general relativity, which proposes that gravity results from the curvature of spacetime.
Based on Einstein’s equation matter and anti-matter annihilate into photonic radiation energy. Photons have unique characteristics since they are massless and they travel at the speed of light in all the inertial reference frames. No other
particle shares these unique characteristics. We claim that this unique behavior is due to the fact that photons do not apply gravitational effects on space-time, meaning,although photons will be forced to move in a curved line if space-time is curved they will not curve space time by themselves or apply gravity forces and time dilation .
In order to prove our claims we suggest a thought experiment that leads to a blue shift paradox which happens after annihilating 2 symmetrical in size and mass, matter and
anti- matter (A&B) in the center of a hollow particles spherical shell . The only way to explain this paradox is to conclude that anti-matter imposes anti–gravity and therefore matter and anti-matter together impose zero gravity. Furthermore, this
proves that the photonic energy from the annihilation phase has also zero gravity effect on space-time.
1) Albert Einstein developed the theory of relativity, which describes the laws of physics for both non-accelerating and accelerating frames of reference.
2) The theory of special relativity, published in 1905, describes motion at constant velocity while general relativity, published in 1915, describes accelerated frames and gravity.
3) One of the most famous equations in physics, E=mc2, comes from the theory of relativity and shows that mass and energy are equivalent and interconvertible.
Nature is quirky. Whenever things don't quite match up, She changes them so they will. The results often seem to be bizarre and nonsensical, but the more you study it you realize how profoundly wise Nature is. It all started with a thought experiment that Einstein said he came up with at around the age of 16. The young Einstein wondered what would happen if he chased a light beam and caught up with it. This essay describes two of the most important discoveries in science: The Special Theory of Relativity and the General Theory of Relativity. Both of these discoveries were made by a single man, Albert Einstein, over a period of one decade (1905 – 1915). This essay is directed at an audience of amateur scientists like myself. I will approach these two theories on the basis of their underlying principles, deriving as much as possible using basic geometry and a bit of elementary calculus. I will not go into the depth needed to become a “relativist.” Mastery of general relativity would require a good working knowledge of tensors, which is beyond the scope of this essay. Nevertheless, I think amateur scientists like myself will get something useful out of it.
1) Einstein's theory of special relativity resolved contradictions between Galilean relativity and the constant speed of light by postulating that the laws of physics are the same in all inertial frames and that the speed of light has the same value in all frames.
2) Time dilation occurs such that moving clocks are observed to tick slower than stationary clocks. This effect increases as the relative velocity approaches the speed of light.
3) The twin paradox is resolved by recognizing that only one twin experiences accelerations during a round trip, so their frame of reference is not inertial for the entire journey.
1. Special relativity describes the laws of physics in different inertial reference frames where the speed of light in a vacuum is constant. It includes time dilation and length contraction effects at relativistic speeds.
2. General relativity describes gravity as a consequence of the curvature of spacetime caused by the uneven distribution of mass/energy. It predicts phenomena like gravitational time dilation, gravitational lensing, and the bending of light by massive objects.
3. Both theories have been validated experimentally through observations of subatomic particles, GPS satellites, and images of distant galaxies. They form the basis of modern physics.
This document discusses Einstein's principle of relativity of simultaneity and his thought experiment involving synchronized clocks. It explains that according to Einstein, events that are simultaneous in one frame are not necessarily simultaneous in another frame. However, Einstein's statements caused confusion because he referred to clocks showing identical displays, rather than the fact that clocks in different frames run at different rates. The document then describes Einstein's thought experiment involving identical clocks A and B at rest and clocks α and β on a moving train, and how clocks A and B were synchronized using light signals.
The study of motion of the object is an important section of the physics. The motion of a body is can be measured as absolute motion and relative motion. Practically any motion is measured is relative only, because one or the other way all the bodies are in motion. In this case we as observer can not measure the exact speed of the an object, because measured quantity of motion of other object is vary with the magnitude and direction of our motion. This can be studied with mathematical proof in this chapter. The Inertial frame and non inertial frame of reference, Special theory of relativity is covered here.
This document provides a summary of the key developments in the history of quantum mechanics:
- Max Planck proposed quantizing light energy in 1900 to explain blackbody radiation.
- Albert Einstein showed that light behaves as both waves and particles in 1905.
- Niels Bohr applied quantization to explain hydrogen atom spectra in 1913.
- Louis de Broglie proposed that all particles exhibit wave-particle duality in 1924.
- Werner Heisenberg formulated matrix mechanics in 1925.
- Erwin Schrodinger developed wave mechanics and the Schrodinger equation in 1926.
- Max Born correctly interpreted the Schrodinger wavefunction as a probability amplitude in 1926.
The document summarizes the Michelson-Morley experiment, which attempted to detect the motion of Earth through the hypothesized luminiferous ether but found no evidence of such motion. It describes the experimental setup, calculations of expected results assuming an ether, and the actual null results. It then explains how Einstein's theory of special relativity, including postulates that the speed of light is constant and physics is the same in all inertial frames, provides the proper explanation for why no ether drag was detected.
B.tech sem i engineering physics u iii chapter 1-the special theory of relati...Rai University
This document provides an overview of Einstein's Special Theory of Relativity. It begins by defining frames of reference and discussing the Michelson-Morley experiment, which found that the speed of light is constant regardless of the observer's motion. It then outlines Einstein's two postulates of special relativity: 1) the laws of physics are the same in all inertial frames; and 2) the speed of light in a vacuum is the same for all observers, regardless of their motion. The document concludes by deriving the Lorentz transformations, which describe how space and time are related for observers in different inertial frames of reference according to special relativity.
Absolute truth is conceptualized with reference to meaning and procedure, within the limits of self-containment, which is a characteristic feature that is shared commonly between the universe, humans, and the institutions that they establish in society; and the human intellect is presented as being endowed with the capacity to appreciate it, given the appropriate environment
Einstein published two theories of relativity - Special Relativity, which described how space and time are relative based on the observer's frame of reference and that the speed of light is constant, and General Relativity, which explained that gravity results from the curvature of spacetime caused by massive objects. Some key effects are time dilation, length contraction, and the bending of light near massive bodies like the sun.
B.Tech sem I Engineering Physics U-III Chapter 1-THE SPECIAL THEORY OF RELATI...Abhi Hirpara
The document discusses Einstein's theory of special relativity. It provides background on Einstein's two postulates: 1) the laws of physics are the same in all inertial frames of reference, and 2) the speed of light in a vacuum is the same for all observers regardless of their motion. It describes how these postulates led Einstein to develop the Lorentz transformations, which show that time and space are relative between different frames of reference moving at a constant velocity with respect to each other.
Albert Einstein (1879-1955) developed the theories of special and general relativity. Special relativity, published in 1905, established that the laws of physics are the same in all inertial frames of reference and that the speed of light in a vacuum is constant. General relativity, published in 1915, introduced gravitation as a result of the curvature of spacetime caused by the uneven distribution of mass and energy. One of Einstein's most famous equations is E=mc2, which shows that mass and energy are equivalent and interconvertible.
The document discusses Einstein's theory of special and general relativity. It explains that special relativity applies to inertial reference frames with constant velocity, while general relativity describes how mass warps spacetime and affects motion. An example is given of how the laws of motion are the same on an airplane moving at constant velocity as on the ground. The document then discusses how general relativity explains Mercury's shifting orbit due to the sun's gravitational field warping spacetime.
03) la nuova fisica. newton, einstein, la fisica quantisticaRiccardoGaluca
This document provides an overview of the transition from classical Newtonian physics to modern physics through Einstein's theories of relativity and the development of quantum mechanics. It discusses how Newton's view of absolute space and time and deterministic universe was overturned by Einstein's theory of special relativity in 1905. This challenged the concepts of absolute simultaneity and showed that time is relative depending on the observer's frame of reference. The document then discusses how Einstein further developed his general theory of relativity in 1915, replacing the concept of gravitational force with that of spacetime being curved by mass and energy. This marked a transition to a new era of physics beyond the limits of Newtonian mechanics.
1) Einstein published his special theory of relativity in 1905, in which he dismissed the idea of absolute motion and established the principle of relativity - that the laws of physics are the same in all inertial frames of reference.
2) According to Einstein, the speed of light is constant for all observers regardless of their motion, which led to the conclusion that moving objects experience time dilation and length contraction.
3) Einstein developed transformation equations and proposed that time should be considered the fourth dimension, establishing the concept of spacetime and explaining why the speed of light remains constant for all observers.
This document discusses reference frames and summarizes key findings from the Michelson-Morley experiment. It provides definitions for inertial and non-inertial reference frames. The Michelson-Morley experiment aimed to detect the motion of Earth through the luminiferous ether but found no evidence of ether drift. This led to developments in relativity. Lorentz transformations were derived based on relativity postulates and reduce to Galilean transformations for low speeds. Galilean transformations violate relativity while Lorentz transformations form its foundation.
This document provides an overview of Einstein's special and general theories of relativity. It begins by explaining how special relativity resolved the conflict between Newtonian mechanics and Maxwell’s electromagnetic theory by establishing that the speed of light is constant in all reference frames. It then describes the key postulates of special relativity, including that the laws of physics are the same in all inertial frames and that the speed of light in a vacuum is independent of the motion of the light source. This leads to effects like time dilation and length contraction. The document also provides an introduction to general relativity and how it addresses accelerated motion and gravity through the equivalence of mass and energy.
1) The document discusses three cases involving two people, A and B, moving pencils and observing each other.
2) In the first case, with both A and B stationary, the author finds a paradox arises from the fact that light has a finite speed.
3) In the second case, with A moving at constant velocity relative to B, the author again finds a contradiction arises from applying Lorentz transformations.
4) The third case considers A accelerating relative to B, to explore if a contradiction again arises.
This document provides a brief introduction and history of quantum mechanics. It discusses how quantum mechanics developed from Planck's hypothesis of quantized energy in 1900 to Schrodinger formulating the wave equation in 1926. The key developments include Einstein explaining the photoelectric effect in 1905, de Broglie proposing that particles are associated with waves in 1924, and Born correctly interpreting Schrodinger's wave as a probability amplitude in 1926.
This document contains a biology passage and 43 multiple choice questions about the passage content. The questions cover topics like DNA base percentages, population graphs of predator-prey relationships, cell structures, aquatic ecosystem oxygen levels, food webs, mercury levels in fish, laboratory processes, human transport systems, and information about a new bird flu virus. For each question, the correct multiple choice answer is provided, along with short explanations for some answers.
This document contains an astronomy homework assignment with multiple choice questions about the phases of the Moon and the scale of planetary orbits. It includes diagrams of the Moon at different positions in its orbit around Earth and asks the student to rank the Moon's appearance in terms of the illuminated area visible from Earth. The homework aims to test the student's understanding of the relative positions of Earth, the Sun and Moon and how this determines what lunar phase we see from Earth.
1) Albert Einstein developed the theory of relativity, which describes the laws of physics for both non-accelerating and accelerating frames of reference.
2) The theory of special relativity, published in 1905, describes motion at constant velocity while general relativity, published in 1915, describes accelerated frames and gravity.
3) One of the most famous equations in physics, E=mc2, comes from the theory of relativity and shows that mass and energy are equivalent and interconvertible.
Nature is quirky. Whenever things don't quite match up, She changes them so they will. The results often seem to be bizarre and nonsensical, but the more you study it you realize how profoundly wise Nature is. It all started with a thought experiment that Einstein said he came up with at around the age of 16. The young Einstein wondered what would happen if he chased a light beam and caught up with it. This essay describes two of the most important discoveries in science: The Special Theory of Relativity and the General Theory of Relativity. Both of these discoveries were made by a single man, Albert Einstein, over a period of one decade (1905 – 1915). This essay is directed at an audience of amateur scientists like myself. I will approach these two theories on the basis of their underlying principles, deriving as much as possible using basic geometry and a bit of elementary calculus. I will not go into the depth needed to become a “relativist.” Mastery of general relativity would require a good working knowledge of tensors, which is beyond the scope of this essay. Nevertheless, I think amateur scientists like myself will get something useful out of it.
1) Einstein's theory of special relativity resolved contradictions between Galilean relativity and the constant speed of light by postulating that the laws of physics are the same in all inertial frames and that the speed of light has the same value in all frames.
2) Time dilation occurs such that moving clocks are observed to tick slower than stationary clocks. This effect increases as the relative velocity approaches the speed of light.
3) The twin paradox is resolved by recognizing that only one twin experiences accelerations during a round trip, so their frame of reference is not inertial for the entire journey.
1. Special relativity describes the laws of physics in different inertial reference frames where the speed of light in a vacuum is constant. It includes time dilation and length contraction effects at relativistic speeds.
2. General relativity describes gravity as a consequence of the curvature of spacetime caused by the uneven distribution of mass/energy. It predicts phenomena like gravitational time dilation, gravitational lensing, and the bending of light by massive objects.
3. Both theories have been validated experimentally through observations of subatomic particles, GPS satellites, and images of distant galaxies. They form the basis of modern physics.
This document discusses Einstein's principle of relativity of simultaneity and his thought experiment involving synchronized clocks. It explains that according to Einstein, events that are simultaneous in one frame are not necessarily simultaneous in another frame. However, Einstein's statements caused confusion because he referred to clocks showing identical displays, rather than the fact that clocks in different frames run at different rates. The document then describes Einstein's thought experiment involving identical clocks A and B at rest and clocks α and β on a moving train, and how clocks A and B were synchronized using light signals.
The study of motion of the object is an important section of the physics. The motion of a body is can be measured as absolute motion and relative motion. Practically any motion is measured is relative only, because one or the other way all the bodies are in motion. In this case we as observer can not measure the exact speed of the an object, because measured quantity of motion of other object is vary with the magnitude and direction of our motion. This can be studied with mathematical proof in this chapter. The Inertial frame and non inertial frame of reference, Special theory of relativity is covered here.
This document provides a summary of the key developments in the history of quantum mechanics:
- Max Planck proposed quantizing light energy in 1900 to explain blackbody radiation.
- Albert Einstein showed that light behaves as both waves and particles in 1905.
- Niels Bohr applied quantization to explain hydrogen atom spectra in 1913.
- Louis de Broglie proposed that all particles exhibit wave-particle duality in 1924.
- Werner Heisenberg formulated matrix mechanics in 1925.
- Erwin Schrodinger developed wave mechanics and the Schrodinger equation in 1926.
- Max Born correctly interpreted the Schrodinger wavefunction as a probability amplitude in 1926.
The document summarizes the Michelson-Morley experiment, which attempted to detect the motion of Earth through the hypothesized luminiferous ether but found no evidence of such motion. It describes the experimental setup, calculations of expected results assuming an ether, and the actual null results. It then explains how Einstein's theory of special relativity, including postulates that the speed of light is constant and physics is the same in all inertial frames, provides the proper explanation for why no ether drag was detected.
B.tech sem i engineering physics u iii chapter 1-the special theory of relati...Rai University
This document provides an overview of Einstein's Special Theory of Relativity. It begins by defining frames of reference and discussing the Michelson-Morley experiment, which found that the speed of light is constant regardless of the observer's motion. It then outlines Einstein's two postulates of special relativity: 1) the laws of physics are the same in all inertial frames; and 2) the speed of light in a vacuum is the same for all observers, regardless of their motion. The document concludes by deriving the Lorentz transformations, which describe how space and time are related for observers in different inertial frames of reference according to special relativity.
Absolute truth is conceptualized with reference to meaning and procedure, within the limits of self-containment, which is a characteristic feature that is shared commonly between the universe, humans, and the institutions that they establish in society; and the human intellect is presented as being endowed with the capacity to appreciate it, given the appropriate environment
Einstein published two theories of relativity - Special Relativity, which described how space and time are relative based on the observer's frame of reference and that the speed of light is constant, and General Relativity, which explained that gravity results from the curvature of spacetime caused by massive objects. Some key effects are time dilation, length contraction, and the bending of light near massive bodies like the sun.
B.Tech sem I Engineering Physics U-III Chapter 1-THE SPECIAL THEORY OF RELATI...Abhi Hirpara
The document discusses Einstein's theory of special relativity. It provides background on Einstein's two postulates: 1) the laws of physics are the same in all inertial frames of reference, and 2) the speed of light in a vacuum is the same for all observers regardless of their motion. It describes how these postulates led Einstein to develop the Lorentz transformations, which show that time and space are relative between different frames of reference moving at a constant velocity with respect to each other.
Albert Einstein (1879-1955) developed the theories of special and general relativity. Special relativity, published in 1905, established that the laws of physics are the same in all inertial frames of reference and that the speed of light in a vacuum is constant. General relativity, published in 1915, introduced gravitation as a result of the curvature of spacetime caused by the uneven distribution of mass and energy. One of Einstein's most famous equations is E=mc2, which shows that mass and energy are equivalent and interconvertible.
The document discusses Einstein's theory of special and general relativity. It explains that special relativity applies to inertial reference frames with constant velocity, while general relativity describes how mass warps spacetime and affects motion. An example is given of how the laws of motion are the same on an airplane moving at constant velocity as on the ground. The document then discusses how general relativity explains Mercury's shifting orbit due to the sun's gravitational field warping spacetime.
03) la nuova fisica. newton, einstein, la fisica quantisticaRiccardoGaluca
This document provides an overview of the transition from classical Newtonian physics to modern physics through Einstein's theories of relativity and the development of quantum mechanics. It discusses how Newton's view of absolute space and time and deterministic universe was overturned by Einstein's theory of special relativity in 1905. This challenged the concepts of absolute simultaneity and showed that time is relative depending on the observer's frame of reference. The document then discusses how Einstein further developed his general theory of relativity in 1915, replacing the concept of gravitational force with that of spacetime being curved by mass and energy. This marked a transition to a new era of physics beyond the limits of Newtonian mechanics.
1) Einstein published his special theory of relativity in 1905, in which he dismissed the idea of absolute motion and established the principle of relativity - that the laws of physics are the same in all inertial frames of reference.
2) According to Einstein, the speed of light is constant for all observers regardless of their motion, which led to the conclusion that moving objects experience time dilation and length contraction.
3) Einstein developed transformation equations and proposed that time should be considered the fourth dimension, establishing the concept of spacetime and explaining why the speed of light remains constant for all observers.
This document discusses reference frames and summarizes key findings from the Michelson-Morley experiment. It provides definitions for inertial and non-inertial reference frames. The Michelson-Morley experiment aimed to detect the motion of Earth through the luminiferous ether but found no evidence of ether drift. This led to developments in relativity. Lorentz transformations were derived based on relativity postulates and reduce to Galilean transformations for low speeds. Galilean transformations violate relativity while Lorentz transformations form its foundation.
This document provides an overview of Einstein's special and general theories of relativity. It begins by explaining how special relativity resolved the conflict between Newtonian mechanics and Maxwell’s electromagnetic theory by establishing that the speed of light is constant in all reference frames. It then describes the key postulates of special relativity, including that the laws of physics are the same in all inertial frames and that the speed of light in a vacuum is independent of the motion of the light source. This leads to effects like time dilation and length contraction. The document also provides an introduction to general relativity and how it addresses accelerated motion and gravity through the equivalence of mass and energy.
1) The document discusses three cases involving two people, A and B, moving pencils and observing each other.
2) In the first case, with both A and B stationary, the author finds a paradox arises from the fact that light has a finite speed.
3) In the second case, with A moving at constant velocity relative to B, the author again finds a contradiction arises from applying Lorentz transformations.
4) The third case considers A accelerating relative to B, to explore if a contradiction again arises.
This document provides a brief introduction and history of quantum mechanics. It discusses how quantum mechanics developed from Planck's hypothesis of quantized energy in 1900 to Schrodinger formulating the wave equation in 1926. The key developments include Einstein explaining the photoelectric effect in 1905, de Broglie proposing that particles are associated with waves in 1924, and Born correctly interpreting Schrodinger's wave as a probability amplitude in 1926.
This document contains a biology passage and 43 multiple choice questions about the passage content. The questions cover topics like DNA base percentages, population graphs of predator-prey relationships, cell structures, aquatic ecosystem oxygen levels, food webs, mercury levels in fish, laboratory processes, human transport systems, and information about a new bird flu virus. For each question, the correct multiple choice answer is provided, along with short explanations for some answers.
This document contains an astronomy homework assignment with multiple choice questions about the phases of the Moon and the scale of planetary orbits. It includes diagrams of the Moon at different positions in its orbit around Earth and asks the student to rank the Moon's appearance in terms of the illuminated area visible from Earth. The homework aims to test the student's understanding of the relative positions of Earth, the Sun and Moon and how this determines what lunar phase we see from Earth.
1) The document describes a ranking task that orders major events in the history of the universe from longest ago to most recent. It then provides context about the "cosmic calendar" that compresses the 14 billion year history of the universe into a single calendar year.
2) On the cosmic calendar, the Big Bang occurred at the start of the year on January 1st, approximately 14 billion years ago.
3) Earth formed in early September on the calendar, around 4.5 billion years ago.
The document discusses the moon's orbit around Earth and how it became synchronous. Originally, the moon rotated faster than it revolved around Earth, so different sides were visible from Earth over time. However, now the moon's rotation is synchronized exactly with its orbital period, so the same face always points towards Earth. We can only see the far side of the moon from photographs taken by spacecraft that have traveled to the other side.
This document provides an overview of celestial motions as seen from Earth. It defines key celestial concepts like the celestial sphere, zenith, horizon, and celestial poles. It describes how the apparent motions of celestial objects differ depending on an observer's latitude on Earth. The Sun's annual path against the background stars is called the ecliptic. The document aims to explain how humans developed an understanding of Earth's place in the universe by observing celestial motions.
This document does not contain any text to summarize. It appears to contain only repeated images without any context or explanation. The document consists solely of images without any accompanying text or context to understand the purpose or meaning of the images.
- Ancient astronomers initially constructed a model that placed Earth at the center of the universe, with all other objects orbiting around it. This was known as the geocentric model.
- Over time, as better instruments allowed for more detailed observations, this model could no longer explain all the observed facts about planetary motion.
- A new heliocentric model, placing the Sun at the center, was proposed and eventually accepted because it fit the experimental evidence better. This shows how scientific models evolve as new evidence is obtained through observation.
This document provides an overview of astronomy and the scientific method. It discusses:
1) Astronomy as the study of objects beyond Earth and how they interact, with the goal of organizing our understanding of the universe's history.
2) The scientific method as a process of making observations, developing hypotheses, and testing them through experiments or further observations. Hypotheses must be falsifiable to be scientific.
3) Scientific laws as consistent rules that describe natural phenomena, allowing our understanding to be applied universally throughout the universe. Laws are subject to revision with new evidence.
5Page43 how to classify stars parkslope heard from Annie.pdfDr Robert Craig PhD
This document discusses the spectral classification of stars. It explains that the advent of the spectroscope in the 1800s allowed astronomers to classify stars according to their spectral similarities. Originally there were 26 classes, but now there are 7 major classes - O, B, A, F, G, K, M - representing decreasing temperatures from 30,000 K to 3,000 K. Three problems are presented: 1) sorting 5 stellar spectra by closest match to standard spectra, 2) noting how spectral lines change with temperature, and 3) identifying which spectral types are missing from the sample.
This lab involves graphing the motion of people moving between positions. Students will record the time it takes a teacher or classmate to reach cones spaced 20 meters apart on a 100-meter track. They will create a position vs. time graph and calculate average velocities for each track segment. Students will then record each other performing different motions (walking, jogging, etc.) between the same positions and create their own position vs. time graphs to analyze and compare.
The document is a worksheet containing problems involving calculating average rates of change of functions over given intervals and finding equations of secant lines between two given points on functions. It includes 13 problems - the first 8 involve average rates of change, the next 4 involve secant lines, and the final problem is a critical thinking question about using two photos as evidence of speeding.
Johannes Kepler was a German mathematician and astronomer in the late 16th and early 17th centuries. He is most famous for discovering the three laws of planetary motion, which describe how planets move around the sun in elliptical orbits. Kepler also made important contributions to optics, geometry, and astronomy through his calculations of astronomical tables and discoveries in other areas of mathematics and science. He is considered a key figure in the scientific revolution.
Galileo Galilei's observations of Venus, Jupiter, and the Moon provided strong evidence supporting Copernicus' heliocentric model of the solar system. Galileo observed phases of Venus similar to Earth's Moon, proving that Venus orbits the Sun. He also discovered four moons orbiting Jupiter, showing that other celestial bodies can orbit something other than Earth.
This document provides an overview of topics to be covered in an astronomy course, including instructions and study questions. It discusses the celestial sphere model used by ancient Greeks to visualize the night sky, and how the apparent motions of celestial objects are caused by the rotation of Earth on its axis. Key points covered include the north and south celestial poles, celestial equator, constellations, and how the view of the night sky depends on the observer's latitude on Earth.
- Galileo Galilei was the first to use the telescope astronomically in 1609, observing sunspots on the Sun and features on the Moon like seas. His observations of Jupiter's moons provided evidence that bodies can orbit something other than Earth. His observations of Venus' phases provided evidence that Venus orbits the Sun.
- Kepler developed his three laws of planetary motion based on Brahe's astronomical measurements. His laws improved the Copernican model by showing planets orbit in ellipses rather than perfect circles.
This document provides materials for a lesson on how latitude affects the seasonal path of the sun. It includes an overview, objectives, preparation needed, and a procedure for an activity using hemisphere models. Students will study the sun's path above the Arctic Circle and compare it to locations at 42°N and the equator. They will explain how latitude impacts the duration of sunlight throughout the year. The activity aims to help students understand concepts like celestial motions, seasons, and how the sun's path varies with latitude.
How to Fix the Import Error in the Odoo 17Celine George
An import error occurs when a program fails to import a module or library, disrupting its execution. In languages like Python, this issue arises when the specified module cannot be found or accessed, hindering the program's functionality. Resolving import errors is crucial for maintaining smooth software operation and uninterrupted development processes.
How to Make a Field Mandatory in Odoo 17Celine George
In Odoo, making a field required can be done through both Python code and XML views. When you set the required attribute to True in Python code, it makes the field required across all views where it's used. Conversely, when you set the required attribute in XML views, it makes the field required only in the context of that particular view.
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Walmart Business+ and Spark Good for Nonprofits.pdfTechSoup
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Answers about how you can do more with Walmart!"
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...Dr. Vinod Kumar Kanvaria
Exploiting Artificial Intelligence for Empowering Researchers and Faculty,
International FDP on Fundamentals of Research in Social Sciences
at Integral University, Lucknow, 06.06.2024
By Dr. Vinod Kumar Kanvaria
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...PECB
Denis is a dynamic and results-driven Chief Information Officer (CIO) with a distinguished career spanning information systems analysis and technical project management. With a proven track record of spearheading the design and delivery of cutting-edge Information Management solutions, he has consistently elevated business operations, streamlined reporting functions, and maximized process efficiency.
Certified as an ISO/IEC 27001: Information Security Management Systems (ISMS) Lead Implementer, Data Protection Officer, and Cyber Risks Analyst, Denis brings a heightened focus on data security, privacy, and cyber resilience to every endeavor.
His expertise extends across a diverse spectrum of reporting, database, and web development applications, underpinned by an exceptional grasp of data storage and virtualization technologies. His proficiency in application testing, database administration, and data cleansing ensures seamless execution of complex projects.
What sets Denis apart is his comprehensive understanding of Business and Systems Analysis technologies, honed through involvement in all phases of the Software Development Lifecycle (SDLC). From meticulous requirements gathering to precise analysis, innovative design, rigorous development, thorough testing, and successful implementation, he has consistently delivered exceptional results.
Throughout his career, he has taken on multifaceted roles, from leading technical project management teams to owning solutions that drive operational excellence. His conscientious and proactive approach is unwavering, whether he is working independently or collaboratively within a team. His ability to connect with colleagues on a personal level underscores his commitment to fostering a harmonious and productive workplace environment.
Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
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বাংলাদেশের অর্থনৈতিক সমীক্ষা ২০২৪ [Bangladesh Economic Review 2024 Bangla.pdf] কম্পিউটার , ট্যাব ও স্মার্ট ফোন ভার্সন সহ সম্পূর্ণ বাংলা ই-বুক বা pdf বই " সুচিপত্র ...বুকমার্ক মেনু 🔖 ও হাইপার লিংক মেনু 📝👆 যুক্ত ..
আমাদের সবার জন্য খুব খুব গুরুত্বপূর্ণ একটি বই ..বিসিএস, ব্যাংক, ইউনিভার্সিটি ভর্তি ও যে কোন প্রতিযোগিতা মূলক পরীক্ষার জন্য এর খুব ইম্পরট্যান্ট একটি বিষয় ...তাছাড়া বাংলাদেশের সাম্প্রতিক যে কোন ডাটা বা তথ্য এই বইতে পাবেন ...
তাই একজন নাগরিক হিসাবে এই তথ্য গুলো আপনার জানা প্রয়োজন ...।
বিসিএস ও ব্যাংক এর লিখিত পরীক্ষা ...+এছাড়া মাধ্যমিক ও উচ্চমাধ্যমিকের স্টুডেন্টদের জন্য অনেক কাজে আসবে ...
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Odoo 17 CRM allows us to track why we lose sales opportunities with "Lost Reasons." This helps analyze our sales process and identify areas for improvement. Here's how to configure lost reasons in Odoo 17 CRM
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Odoo provides an option for creating a module by using a single line command. By using this command the user can make a whole structure of a module. It is very easy for a beginner to make a module. There is no need to make each file manually. This slide will show how to create a module using the scaffold method.
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Einsteins traingedanken
1. VCE Physics
Einstein’s Train and other ‘Gedanken’ experiments
In his book Relativity: The Special and the General Theory Einstein uses a ‘thought experiment’ involving
lightning flashes striking a railway line at two different places, A and B, simultaneously to illustrate the difficulty of
defining this concept. Since his use of this ‘Gedanken’ (German for thought experiment) many ‘popular’
explanations of relativity have copied him. However, not all of these popular accounts are consistent with Einstein’s
– or each other. Much of the confusion centres around the ‘look-back time’ issue and so it is important to be clear
about this. We illustrate this with Einstein’s original Gedanken experiment and then some other versions.
How do we know if two events are simultaneous? Einstein says we must agree on a method of determining
simultaneity before we can talk of two events being simultaneous. Suppose we carefully measured the distance AB
along a railway embankment and then placed a suitably equipped observer M at the mid point of AB. If that observer
sees flashes at A and B at the same time then we can say that they must have been simultaneous – because the light
would have taken the same time to travel from both A and B to M. However, note that observer M, let’s call him
Mike, saw the flashes a little after they actually occurred in his frame. We can call that time the ‘look-back time’. It
is simply equal to d/c where c is the speed of light and d the distance from M to A or B. Also notice that when we say
that the observer ‘sees the flashes’ we are referring to the time at which the light actually entered the observer’s eyes,
not the time at which the flashes actually occurred.
Einstein’s Train
Now imagine that a (very fast) train is travelling along the track
in the direction from A toward B and it so happens that the lightning
flashes at A and B hit the ends of the train. The question is: “Do the
flashes hit the train simultaneously?” As far as our observer Mike is
concerned, as he saw the flashes together the answer must be “yes”. If
the flashes hit the ends of the train, the ends must have been at A and
B at the moments of the flashes. But what of an observer N, Nina,
inside the train, let us say at the mid point of the train?
The same definition of simultaneity applies in the train’s frame of
reference. If the observer sees two flashes which have travelled equal
distances at the same time they must have been simultaneous in that
frame of reference.
So, do observers in the train also see the two lightning strokes A
and B as simultaneous? Imagine that Nina happens to be opposite
Mike, that is, also half way between A and B at the moment the
flashes occurred (as determined in the embankment frame). See
diagram M1. This is NOT the time at which Mike and Nina see the
flashes. They see them a little after this moment when the light reaches
them – we need to take into account the ‘look-back time’, that is, the
time taken for light to travel from the flashes to the observer.
For Mike to see the events as simultaneous, the light must have
come from A and B and met at his position. Remember that Mike is at
rest relative to the embankment. Nina in the train, however, is racing
away from A and towards B and so will see the flash from B first
(diagram M2) because it will have less distance to travel. Note that we
could not take a photo and see what is represented in the diagrams!
(The camera only ‘sees’ the light when it enters the lens.) They must
be seen as ‘reconstructions’ of what must have been. Diagram M3
shows the moment that Mike sees both flashes and diagram M4 shows
the moment a little later again when Nina sees the flash from A.
Another thing to contemplate is that there really is no need for a
train. The train is simply a physical object to help us think about a
different reference frame. In reality it could be a car or a spaceship –
or simply a hypothetical observer travelling through space.
There is also another small problem – everything we have said so
far would be true if A and B were bells that struck just as the ends of
the train went by and we were talking about the speed of sound! Mike
2. VCE Physics: Einstein’s Train and other ‘Gedanken’ experiments Page 2
would hear the bells simultaneously and Nina would hear bell B first. However, Nina would realise that she was
travelling through the air and so would be able to calculate that in fact the bells struck at the same time.
Likewise, in the case of the light flashes, Nina saw the flash from B first, but will be able to figure out, given
that she knows the various distances and speeds involved, that the flashes at A and B would have actually occurred at
the same time. So where is the need for Einstein’s relativity?
Those Einstein postulates!
Notice that in the previous paragraphs both Mike and Nina assumed that Nina was moving. In other words, they
were both looking at the situation from the same frame of reference – Mike’s frame, the railway embankment. But
what happens if they look at the situation from the frame of reference of the train – Nina’s frame? Einstein’s first
postulate says that all inertial frames of reference are equivalent – there is no ‘preferred’ frame. So we can equally
look at the situation from Nina’s point of view, that is, that she is at rest and Mike is whizzing along beside the track.
This is where the difference between the situation with light and with sound enters. If we were talking about
bells at A and B, Nina would take into account that the sound travels through air at a fixed speed relative to the air.
She would have to add the velocity of the air to that of the sound to obtain the velocity of sound relative to her train.
Relativity makes life simpler! There is no medium in which the
light is travelling and the speed of light is always 3×10 m/s no matter8
what. That is Einstein’s second postulate – the speed of light is the
same for all observers.
Let’s assume that Mike and Nina are intelligent physicists who
are aware of Einstein’s two postulates. Nina will still, of course, see
the flashes in the same order – flash B before flash A. Likewise,
although Mike is now moving (toward A) he must still see the two
flashes together. The fact that we are looking from a different frame
can not change what the two people actually see. It is their deductions
about when the flashes occurred that will differ!
In order to deduce when the flashes actually occurred, the two
observers can use their knowledge of physics and their measurements
of the times and distances involved to calculate the actual times of the
flashes. We will not do that, but we can use another set of simple
diagrams like that used above. Remember that we are taking into
account the look-back times and deducing what must have been
happening before the observers actually see the light flashes!
We know that Nina is at rest this time and saw flash B first.
Because they occurred at equal distances from her (the ends of the
train) she deduces that B must indeed have occurred first (diagram
N1). Remember, and this is the big difference between light and other
waves, that she knows that light is still travelling at c, the same speed
for both flashes, as in the previous example.
A little while later (diagram N2) Nina actually sees the flash from
B, and deduces (from what she sees later) that flash A must have
occurred. Shortly after that (diagram N3) the flashes were in the same
place at the same time and this is when Mike saw them. A little while
later again (diagram N4) Nina sees the flash from A.
This is what is remarkable about relativity. What, from one
frame of reference (the ground) were deduced to be two simultaneous
flashes were not simultaneous in another (the train)! Remember that
this is not just a case of who ‘sees’ what first. Mike would also
deduce that flash B must have occurred first given that he knows that
he is the one in motion. He saw them at the same time at a place closer
to A than B and so deduces that B must have occurred earlier as it has
had further to travel.
Also remember that this is not simply a case of some difference in
‘look-back time’, a delay due to the distance light has to travel. It is a
fundamental difference in describing a situation from two different
frames of reference and is a consequence of the second postulate. The
3. VCE Physics: Einstein’s Train and other ‘Gedanken’ experiments Page 3
only conclusion can be that it is time itself that is acting differently in the two frames.
Whether the observers ‘see’ the flashes separately or simultaneously depends on their position in the train or
along the embankment. If they are indeed in the centre (of their own frame of reference) they will see the flashes in
the correct sequence – as Mike does in the first case (simultaneously) and Nina does in the second (B then A). If they
were in different positions along the track or the train they may see one or the other flash first, but would deduce that
the flashes must have occurred in the same sequence as above.
To repeat, the important conclusion we reach is that what was simultaneous in one frame was not simultaneous
in the other! Remember that this is not a case of what various observers saw first, it was a case of what they deduced
actually happened. If two events which were simultaneous in one frame were not simultaneous in another what does
that mean? The answer must be that time is behaving differently in the two frames. This is the point of these
‘Gedanken’ experiments – they help us to get our minds around what is really a very weird concept.
Line diagrams
The diagram on the left below is a different way of describing the same situation as we had above (diagrams M1
to M4). The slopes of the various lines indicate the speeds. In this diagram Mike is at rest – we are looking at the
situation from his frame. Nina is moving toward B as shown by the slope of her line. The slope of the light lines
represents the speed of light, c. (Note that the slopes are not ‘equal’ to the speeds, the diagrams are not the usual x-t
graph.) The order of events can be seen from the ‘star circles’: Nina sees flash B, Mike sees both flashes, Nina sees
flash A.
In the right hand diagram we see the situation from Nina’s frame of reference. According to her Mike is moving
toward A. She knows that the flashes occurred at the ends of the train, that is, at equal distances from her position in
the centre of the train. Given that she saw flash B first, she deduces that it must have occurred before flash A (as
shown by the fact that it is higher in the diagram). Notice that the order of the events is still the same as in the first
diagram.
It is worth pointing out that while these types of diagrams can be used to sort out the general sequence of events
as seen from different frames of reference, they take no account of length contraction and time dilation and so can not
be used in a quantitative sense.
4. VCE Physics: Einstein’s Train and other ‘Gedanken’ experiments Page 4
In the situation we have discussed so far, our two observers saw the flashes at different times and places. There
were three ‘events’: Mike seeing both flashes, Nina seeing flash B and Nina seeing flash A. Let us now consider a
different scenario. Imagine that instead of the flashes actually occurring at the moment Nina is opposite Mike, the
flashes arrive at Mike and Nina at that moment. In other words, Mike saw the flashes at the same moment as Nina
passed him. Because Nina passing and the flashes arriving was at the same moment and place these were all one
‘event’. As Nina was present at this ‘event’, she must have seen the flashes at the same moment. If this was the case,
what will the two observers say about the simultaneity (or not) of the flashes at A and B this time?
As far as observer Mike is concerned this case is similar to the last. He is at rest relative to the embankment and
half way between A and B. He must conclude that the flashes were simultaneous. But what of observer Nina in the
train?
The situation for Mike and Nina is shown in the two diagrams below. The left diagram shows us Mike’s point
of view and the right, the situation from Nina’s frame of reference.
In fact, we find that the situation is much the same as before. As Mike is still mid-way between A and B he says
the flashes were simultaneous. Nina will agree with Mike (when they talk about it later) as far as his frame is
concerned, but will say that in her frame flash B must have occurred first. There is a simple reason for this. The only
difference between this and the previous case is that Nina was further toward A when the actual flashes occurred –
as shown by the top line in the diagrams above. Compare the two diagrams on this page with those on the previous
page and you will see that the only real difference is that Nina started further to the left (from M’s point of view) or
Mike started further to the right (from N’s point of view). This could have either been because N was not in the
centre of the train, or because the ends of the train were not at A and B when the lightning flashes occurred.
So far, our trains have experienced mysterious simultaneous (or not) lightning flashes at either end. You may
think that’s a little far fetched. Remember, however, that these are ‘gedanken’ experiments - we can think as far as
we like (no fetching involved). The more prosaic amongst us might prefer the next example – we have a simple light
bulb in the middle of the carriage that can be switched on whenever we like. Mind you, our train is still going rather
fast!
5. VCE Physics: Einstein’s Train and other ‘Gedanken’ experiments Page 5
A different train
A different version of the train Gedanken has the flashing light
in the centre. Just as the train passes an external observer (C) the
light flashes. As can be seen in these diagrams (right) the light
from the flash takes a little while to reach the observers at either
end of the train. However, because of the motion of the train, the
light reaches A (at the left hand end) before it reaches B.
Remember that observer C will have to take into account the look-
back time for the light to reach her from the points where it reflects
off A and B, but she will deduce that the light was seen by A first.
So in the frame of a stationary observer outside the train, A
will see the flash before B does. But what about the observers
inside the train? What do they say from their frame of reference?
This is a very simple situation. The observers in the train are
equal distances from the light and so must see the flash at the same
time (diagrams below). The speed of light, as always, is the same
for both of them and the distances are equal.
A and B see observer C speeding by in the other direction. If
they were to calculate how observer C saw the flash they would be
able to work out that she must have been opposite the light when it
flashed and so would have seen a single flash as she passed the
light – just as observer C would have said.
Notice that while there was only the one event of C seeing the
flash, there were two different events for A and B seeing the
flashes (light arriving at A and light arriving at B). C saw the flash
as she passed the light. The seeing and the passing occurred at the
same time and same place (same event) and so there can be no
different versions of that. However, the two different events of A
and B seeing the flashes are separated in space and time and so, as
we have seen, may be perceived differently by different observers.
Indeed while any observers inside the train will conclude that the
flashes reached the ends of the train at the same time (in the train
frame) any observers outside will decide that the flash reached the
left hand end first (in the ground frame). Again, the only
explanation is that time itself behaves differently in different frames of reference.
It was by analysing situations like these that Einstein
discovered his famous time dilation and length contraction
equations. It is worth noting that, while it makes no difference to
our qualitative descriptions, all the moving trains we have been
discussing should be ‘length contracted’ due to their speed.
Indeed, we can use further ‘thought experiments’ to see that the
length of a fast moving train (or any object) must be contracted in
the direction of its motion.