Physical Science: Special and General Relativity PDF

PHYSICAL SCIENCE QUARTER 4 – WEEK7 Special Theory of Relativity and General Theory of Relativity BEVERLY L. GARCIA Subject Teacher MOST ESSENTIAL LEARNING COMPETENCIES 1. Explain the consequences of the postulates of Special Relativ...

PHYSICAL SCIENCE QUARTER 4 – WEEK7 Special Theory of Relativity and General Theory of Relativity BEVERLY L. GARCIA Subject Teacher MOST ESSENTIAL LEARNING COMPETENCIES 1. Explain the consequences of the postulates of Special Relativity (e.g., relativity of simultaneity, time dilation, length contraction, mass-energy equivalence, and cosmic speed limit) (S11/12PS-IVi-69) 2. Explain the consequences of the postulates of General Relativity (e.g., correct predictions of shifts in the orbit of Mercury, gravitational bending of light, and black holes) (S11/12PS-IVi-70) Special and General Theory of Relativity The Theories In 1865, James Clerk Maxwell theorized that electromagnetic field moves through space at a fixed speed. He wrote set of four equations that describe all the laws of electricity and magnetism. Upon evaluating Maxwell’s equation for the speed of light, c is equal to 2.99792458✕10​8 m/s. This showed that the speed of electromagnetic waves is universal. The Theories The Special Theory of Relativity was coined and developed by Albert Einstein in 1905 as an answer to the long-debated conflict between James Clerk Maxwell’s Theory of Electromagnetism and Isaac Newton’s Three Laws of Motion.  Newtonian Mechanics Newtonian mechanics is grounded on the use of Newton’s three laws of motion. The mechanics explains that space (distance), time, and mass, are absolute. This means that the distance between two objects and the time that passes between two events does not depend on the environment where the object is in. Furthermore, according to Newton’s second law, objects in the environment moves in a straight line; hence, the change of location from one environment to another environment must register a straight line to other straight lines. Moreover, it is said that no matter where you are or how fast you are moving, there will be no changes in space or time. In all places, a kilometer is a kilometer and a minute is a minute. And you can travel as fast as you want, with adequate acceleration. Maxwell’s Electromagnetic Theory of Light James Clerk Maxwell had predicted that the electric field, magnetic field, and light are different representations of the same phenomena or event. He further predicted that visible lights are electromagnetic waves that move in a manner like ripples in the water when a stone is dropped. According to Maxwell, light as a wave have both electrical and magnetic components and that it moves at a constant speed of 186,000 miles per second. It means that the speed of light is the same for everything and for all observers The CONFLICT There is only one conflict between the two theories: according to Maxwell, light in a vacuum moves at 186,000 miles per second. And it does not change for all observers and situation. However, according to Newtonian physics, all speeds are relative – meaning speed depend on the observers, viewpoint and situation. Resolution: Einstein and the Special Theory of Relativity In 1905, Albert Einstein published his observation about the differing ideas of the two theories through the special theory of relativity. His theory is based on the observations of events from different viewpoints. He stressed that while Newtonian physics is true, Maxwell’s theory is also correct. He resolved the opposing ideas by establishing the two foundations of the special theory of relativity. Resolution: Einstein and the Special Theory of Relativity The first principle in Einstein theory is the consistent law principle. It states that all motions are relative to the selected reference frame or viewpoint. It means that the motion of an object is based on the observers’ viewpoint. First Principle: Consistent Law Example A teenage boy is standing inside a train that is passing equally between two oak trees. Because the train is moving, he saw that a lightning struck the tree on his left first then the tree on the right. Another boy, who is standing at a train platform, also saw the same event. Only, in his viewpoint, the lightning struck both trees at the same time. Resolution: Einstein and the Special Theory of Relativity The second principle in Einstein’s theory deals with the speed of light. This is the constancy of speed. He established that light moves in a speed of 186,000 miles per second and is the same for all observers’ viewpoint. Second Principle: Constancy of Speed Example An astronaut that is moving towards the source of light will think that light is moving at 186,000 miles per second. Hence, an astronaut that is not moving towards the source of light will think that light is moving at 186,000 miles per second. In short, regardless of the rate movement of the source of light and the rate movement of the astronauts, the speed of light will remain the same Einstein and the Special Theory of Relativity These two postulates clarify that if two events happen at different places, it is not always likely to say which of the two events happens first or that they occur at the same time. Einstein and the Special Theory of Relativity These two postulates clarify that if two events happen at different places, it is not always likely to say which of the two events happens first or that they occur at the same time. The Special Theory of Relativity Space “contracts” and the time “dilates” as a consequence of relativity. The amount of length contraction and time dilation is given by the Lorentz factor, named after Hendrik Lorentz who had been exploring transformation equations. Hendrik Lorentz Time Dilation A person who is initially stationary tends to observe a slower “clock” than a person travelling at a speed of light. It is only significant when one of the objects involved travel at relativistic speed, or speed near the speed of light. This observation is referred as time dilation. A classic example of time dilation is the twin paradox. Time Dilation Twin paradox Time Dilation Time dilation has been established to be equal to where Δ​t is the relative time or the time observed in the other reference frame, Δ​t0 is the proper time of the time in observer’s own frame of reference, v is the velocity of two frames, and c is the speed of light. The denominator is equivalent to the Lorentz factor. Suppose the traveller travelled the space at 95% the speed of light. How much time did his twin observed on Earth if upon returning, the traveller measured the journey time to be 10 years based on his clock? Suppose the traveller travelled the space at 95% the speed of light. How much time did his twin observed on Earth if upon returning, the traveller measured the journey time to be 10 years based on his clock? Step 1: Identify what is required to find in the problem. You are asked to calculate for relative time (​Δ​t) observed by the traveller’s twin on Earth. Suppose the traveller travelled the space at 95% the speed of light. How much time did his twin observed on Earth if upon returning, the traveller measured the journey time to be 10 years based on his clock? Step 2: Identify the given in the problem. The proper time and the speed of the traveller as measured by the percentage of the speed of light are given. Suppose the traveller travelled the space at 95% the speed of light. How much time did his twin observed on Earth if upon returning, the traveller measured the journey time to be 10 years based on his clock? Step 3: Write the working equation. Suppose the traveller travelled the space at 95% the speed of light. How much time did his twin observed on Earth if upon returning, the traveller measured the journey time to be 10 years based on his clock? Step 4: Substitute the given values. Suppose the traveller travelled the space at 95% the speed of light. How much time did his twin observed on Earth if upon returning, the traveller measured the journey time to be 10 years based on his clock? Step 5: Find the answer. The twin left on Earth aged 32 years, compared to the traveller that aged only 10 years. Length Contraction The length of an object seems to contract when travelling at relativistic speeds, according to equation: where L is the relative length or the length measured by another observer, L0 is the proper length or the length measured by the observer on the original reference frame, v is the relative velocity of the two frames; and c is the speed of light. A rocket is observed by a person on Earth. What is the length of the rocket as observed by the astronaut inside it if the observer on Earth sees that the rocket is 5.5 m long and it zooms in a speed of 95% that of the speed of light? A rocket is observed by a person on Earth. What is the length of the rocket as observed by the astronaut inside it if the observer on Earth sees that the rocket is 5.5 m long and it zooms in a speed of 95% that of the speed of light? Step 1: Identify what is required to find in the problem. You are asked to calculate for proper length (L) of the rocket as observed by the astronaut inside it. A rocket is observed by a person on Earth. What is the length of the rocket as observed by the astronaut inside it if the observer on Earth sees that the rocket is 5.5 m long and it zooms in a speed of 95% that of the speed of light? Step 2: Identify the given in the problem. The relative length and the speed of the traveller as measured by the percentage of the speed of light are given. A rocket is observed by a person on Earth. What is the length of the rocket as observed by the astronaut inside it if the observer on Earth sees that the rocket is 5.5 m long and it zooms in a speed of 95% that of the speed of light? Step 3: Write the working equation. A rocket is observed by a person on Earth. What is the length of the rocket as observed by the astronaut inside it if the observer on Earth sees that the rocket is 5.5 m long and it zooms in a speed of 95% that of the speed of light? Step 4: Substitute the given values. A rocket is observed by a person on Earth. What is the length of the rocket as observed by the astronaut inside it if the observer on Earth sees that the rocket is 5.5 m long and it zooms in a speed of 95% that of the speed of light? Step 5: Find the answer. This suggests that even though the rocket ship is 17.6 m, it appears to be “contracted” and smaller for an observer seeing it at relativistic speeds. The General Theory of Relativity It is the extension of the special relativity. It includes the effects of accelerating objects and their mass on space-time. It explains the concept of gravity. The General Theory of Relativity It is based on two postulates: The principle of equivalence states that the effects of gravity and the effects of acceleration are the same. Gravity is not a force but a consequence of the curvature of space-time, caused by the uneven distribution of mass/energy. The General Theory of Relativity General relativity also states that light can be bent by massive objects such as a star (e.g., Sun). Gravitational bending of light The General Theory of Relativity In 1919, Arthur Eddington confirmed Einstein’s prediction that light is bent by gravity. During a solar eclipse, light from distant stars that passed very near the sun can be observed. Eddington observed that the stars shifted position, consistent with Einstein’s prediction. The General Theory of Relativity It also predicted the existence of bodies massive enough to pull light and keep it from escaping. Black holes are formed when supermassive stars collapse upon itself, forming a body with a very strong gravitational pull. Image of a black hole at the center of galaxy M87  In 1905, Einstein published his theory of special relativity 1 to explain how motions can be compared in different inertial frames. The principle of relativity states that the physical laws have 2 the same mathematical form for all frames of reference moving at a constant velocity with respect to each other. The speed of light in a vacuum is independent of the 3 motion of its source and observer.  The consequences of the special theory of relativity 4 include time dilation and length contraction. The general theory of relativity is the extension of the 5 special relativity. It includes the effects of accelerating objects and their mass on space-time. The principle of equivalence states that the effects of 6 gravity and the effects of acceleration are the same.  Gravity is not a force but a consequence of the curvature 7 of space-time, caused by the uneven distribution of mass/energy. Identify the term or terms described in each item below. 1. He is a great scientist who pioneered relativity and modern physics. 2. It is the principle which states that all physical laws are correct in all frames of reference. 3. It is the theory of relativity that applies only to objects that move in uniform motion. 4. It is the factor that is incorporated in calculating time dilation and length contraction. 5. It is the value of the speed of light in vacuum expressed in m/s.