L20 Length Contraction

Total Page：16

File Type：pdf, Size：1020Kb

Science One Physics Lesson 20 Length Contraction Relativity of Simultaneity Recap and Preview Last class • Α constant speed of light in all frames means time and distance stop making sense. • Most people would be deterred, but Einstein was like “No, our notion of space and time is broken.” This class • A clickertastic adventure through time and space • Length contraction • Relativity of Simultaneity Time Dilation 2 Muons Created in Upper atmosphere Frisch-Smith Experiment (1963) Experimental Evidence Experimental Evidence Length Contraction Length Contraction Twin Paradox One resolu*on is that in the frame of the ship the distance between the planets is contracted, so the journey takes less *me on the spaceship. The Ladder Paradox You watch your friend, who is travelling at near the speed of light, carry a ladder into a garage. When they’re inside the garage, the doors close for an instant, so the ladder just ﬁts. The doors then open to let you friend out. What happens in your friend’s frame? B) In the frame of the train, observers see the light hit the front and the back of the train exactly at noon. In the frame of the track, shown above, what can we say about the time on clock at the front of the train when light hits the back of the train. A) The clock at the front reads 12:00. B) The clock at the front reads earlier than 12:00. C) The clock not he front reads later than 12:00. In the frame of the train, observers see the light hit the front and the back of the train exactly at noon. In the frame of the track, shown above, what can we say about the time on clock at the front of the train when light hits the back of the train. A) The clock at the front reads 12:00. B) The clock at the front reads earlier than 12:00. C) The clock not he front reads later than 12:00. In the second picture, the back clock reads noon, but the front clock reds earlier than noon, since the light hasn’t hit it yet. Spacetime Drawings Frame of train Spacetime Drawings Frame of track Relativity of Simultaneity The Ladder Paradox Barn Frame Ladder Frame Simultaneous events in the barn frame are not simultaneous in the ladder frame. Principle of Relativity.

Copy Link

Recommended publications

Einstein's Mistakes
Einstein’s Mistakes Einstein was the greatest genius of the Twentieth Century, but his discoveries were blighted with mistakes. The Human Failing of Genius. 1 PART 1 An evaluation of the man Here, Einstein grows up, his thinking evolves, and many quotations from him are listed. Albert Einstein (1879-1955) Einstein at 14 Einstein at 26 Einstein at 42 3 Albert Einstein (1879-1955) Einstein at age 61 (1940) 4 Albert Einstein (1879-1955) Born in Ulm, Swabian region of Southern Germany. From a Jewish merchant family. Had a sister Maja. Family rejected Jewish customs. Did not inherit any mathematical talent. Inherited stubbornness, Inherited a roguish sense of humor, An inclination to mysticism, And a habit of grüblen or protracted, agonizing “brooding” over whatever was on its mind. Leading to the thought experiment. 5 Portrait in 1947 – age 68, and his habit of agonizing brooding over whatever was on its mind. He was in Princeton, NJ, USA. 6 Einstein the mystic •“Everyone who is seriously involved in pursuit of science becomes convinced that a spirit is manifest in the laws of the universe, one that is vastly superior to that of man..” •“When I assess a theory, I ask myself, if I was God, would I have arranged the universe that way?” •His roguish sense of humor was always there. •When asked what will be his reactions to observational evidence against the bending of light predicted by his general theory of relativity, he said: •”Then I would feel sorry for the Good Lord. The theory is correct anyway.” 7 Einstein: Mathematics •More quotations from Einstein: •“How it is possible that mathematics, a product of human thought that is independent of experience, fits so excellently the objects of physical reality?” •Questions asked by many people and Einstein: •“Is God a mathematician?” •His conclusion: •“ The Lord is cunning, but not malicious.” 8 Einstein the Stubborn Mystic “What interests me is whether God had any choice in the creation of the world” Some broadcasters expunged the comment from the soundtrack because they thought it was blasphemous.
[Show full text]
1 Meaning and Resolution of the Ladder Paradox for Special
Meaning and Resolution of the Ladder Paradox for Special Relativity Theory Tsuneaki Takahashi Abstract Regarding to the Ladder Paradox, there are some misunderstanding and insufficient understanding of the special relativity theory. Accurate recognition of the theory would make clear the core mechanism of both the theory and the paradox. 1. Introduction While there are many explanations for the Ladder paradox, we may be able to summarize the essence of these as following. About mutually and relatively moving garage and ladder, garage sees contracted ladder based on the contraction effect of special relativity theory, also ladder sees contracted garage on same reason. Then there are the cases that one side of the two linefit in the garage. This looks like a contradiction. 2. View from s system We consider about following two systems s system( 2dimensions(푐푡, 푥)) and 푠′ system(2dimensions(푐t′, 푥′)). [1] Here both are moving relatively with velocity 푣. This situation can be shown as Minkowsky graph. (Fig.1) 푥 푥′ θ α 푐푡′ θ 푐푡 Fig. 1 On Fig.2, point A stays in 푠′ system. Its track is 푃푄̅̅̅̅. This is elapse of time in 푠′ system. Also point B stays in 푠′ system. Its track is 푅푆̅̅̅̅. This is elapse of time in 푠′ system. These points A, B are simultaneous for 푠′ system but not for 푠 system. Then regarding to these two tracks, simultaneous points for 푠 system are T, U, for example. On this situation, space distance 퐴퐵̅̅̅̅ for 푠′ system is recognized as space distance 푇푈̅̅̅̅ for 푠 system. 1 푥 푥′ Q A T P S U B 푐푡′ R 푐푡 Fig.
[Show full text]
Relativity -1
Relativity -1 Special Relativity After Newton and his mechanics, after Maxwell and his E&M, came three great revolutionary new theories of the 20th century. Albert Einstein was responsible for 2 and one-quarter of these theories. 1) Special Relativity, a theory of space and time (Einstein 1905) 2) General Relativity, a theory of gravity (Einstein, 1916) 3) Quantum Mechanics, a theory of the behavior of atoms (Planck, Einstein, Bohr, Heisenberg, Schrodinger, Born, Dirac, Pauli, …, 1900-1928) Comment about the word "theory": In science, the word "theory" means "a self-consistent model which is consistent with all known experimental facts and which makes specific predictions which can be tested by further experiment." This is a very different meaning than the common use of the word : In street talk, the word "theory" seems to mean "conjecture" or "some random notion", as in "it's just a theory". This is exactly the opposite of the meaning of the word in science: In science, a "theory" is the most complete, reliable form of knowledge (about the physical universe) that we possess. Special Relativity is based on 2 postulates (axioms) I. All the laws of physics are in the same in every inertial frame of reference. Inertial frame = one moving at constant velocity = one which is not accelerating, not rotating. II. (the weird one). The speed of light is the same for all observers regardless of the motion of the observer or the motion of the source of the light. Postulate I says that there is no way to determine the velocity of your inertial frame, except by comparing your motion to the motion of other bodies.
[Show full text]
© in This Web Service Cambridge University
Cambridge University Press 978-1-107-60217-5 - Revolutions in Twentieth-Century Physics David J. Griffiths Index More information Index B factory, 125 k,18 C, 124 n, 59, 100 G, 14, 15 p, 59, 100 K, 115 s, 120 K shell, 101 t, 124 L shell, 101 u, 101, 105, 120 Q, 118 S, 118 absolute rest, 53 T ,16 absolute zero, 27, 151 W, 128, 134 absorption spectrum, 75 Z, 101, 104, 128, 134 abundance, 157 , 5, 84, 116 accelerated expansion, 162 , 115, 163 acceleration, 6, 7, 10, 56 , 119, 140, 161 acceleration of gravity, 7, 15, 159 ,80 action-at-a-distance, 13, 92, 112 , 115 age of the Universe, 3, 150, 151 ϒ, 124 agnostic, 90, 93 α, 106, 131, 133 air resistance, 7 βC, β, 106 alkali metal, 101 η, 121 allowed energy, 76, 78, 87, 101 γ , 48, 51, 56, 58, 126 allowed orbit, 76, 77, 101 λ,30 allowed radius, 78 μ, 48, 113 alpha decay, 106, 108 ν, 59, 111 alpha particle, 100, 106 νμ, 114 ampere (C/s), 18 νe, 114 amplitude, 30 π, 113 Anderson, Carl, 88, 113 ψ, 123 annihilate, 126 ρc, 162 anticorrelation, 94 σ , 152 antimatter, 126, 156 τ, 123 antiparticle, ix, 87, 119, 120, 126, 130, 131 c, 32, 42, 69, 123 apparent brightness, 149 d, 120 area of a sphere, 152 e, 59, 76, 99, 100 Aristotle, 9 g, 7, 15, 27 Aspect, Alain, 93, 94 h,70 atom, 88, 99–101, 144, 155, 156 166 © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-1-107-60217-5 - Revolutions in Twentieth-Century Physics David J.
[Show full text]
The Special Theory of Relativity
The Special Theory of Relativity Chapter II 1. Relativistic Kinematics 2. Time dilation and space travel 3. Length contraction 4. Lorentz transformations 5. Paradoxes ? Simultaneity/Relativity If one observer sees the events as simultaneous, the other cannot, given that the speed of light is the same for each. Conclusions: Simultaneity is not an absolute concept Time is not an absolute concept It is relative How much time does it take for light to Time Dilation Travel up and down in the space ship? a) Observer in space ship: 2D ∆t = proper time 0 c b) Observer on Earth: speed c is the same apparent distance longer ν 2 = v∆t Light along diagonal: 2 D2 + 2 2 D2 + v2∆t 2 / 4 c = = ∆t ∆t 2D ∆t = c 1− v2 / c2 ∆t This shows that moving observers ∆t = 0 = γ∆t 2 2 0 must disagree on the passage of 1− v / c time. Clocks moving relative to an observer run more slowly as compared to clocks at rest relative to that observer Time Dilation Calculating the difference between clock “ticks,” we find that the interval in the moving frame is related to the interval in the clock’s rest frame: ∆t ∆t = 0 1− v2 / c2 ∆t0 is the proper time (in the co-moving frame) It is the shortest time an observer can measure 1 with γ = ∆t = γ∆t 1− v2 / c2 then 0 Applications: Lifetimes of muons in the Earth atmosphere Time dilation on atomic clocks in GPS (v=4 km/s; timing “error” 10-10 s) On Space Travel 100 light years ~ 1016 m If space ship travels at v=0.999 c then it takes ~100 years to travel.
[Show full text]
Varying Speed of Light in an Anisotropic Four-Dimensional Space J
VARYING SPEED OF LIGHT IN AN ANISOTROPIC FOUR-DIMENSIONAL SPACE J. C. Pérez Ramos (e-mail: [email protected]) −Simplified version of original paper in Spanish− ABSTRACT: We show how the theory of relativity disagrees with the isotropy of the expanding universe and with the experimental arguments in favour of the existence of a preferred frame. We postulate a new heuristic principle, the invariance of the radius of the universe, deriving new transformation equations. Then we develop the geometric scenario and we prove how the universe equals an anisotropic inhomogeneous hyperboloid in four-space. The new model quite naturally incorporates the expanding universe, solves the cosmological horizon problem, explains the asymmetrical time dilation effect (for example, in the twin paradox) and describes the Big Bang in an original way by reducing the radius of the hypersphere to zero. The speed of light acquires a new geometrical meaning that justifies a varying speed of light (VSL) theory and clarifies unsolved problems in physics as the Pioneer anomaly, cosmological puzzles, the dark energy and the Loschmidt paradox. 1. INTRODUCTION _______________________________________________________________________________________ “The most important result of our reflections is, however, that precisely the apparently simplest mechanical principles are of a very complicated character; that these principles are founded on uncompleted experiences, even on experiences that never can be fully completed; that practically, indeed, they are sufficiently secured, in view of the tolerable stability of our environment, to serve as the foundation of mathematical deduction; but that they can by ho means themselves be regarded as mathematically established truths, but only as principles that not only admit of constant control by experience but actually require it.” Ernst Mach [1] 1.1.
[Show full text]
Proposed Graduate Curriculum Changes
LECTURE NOTES ON ELECTRODYNAMICS PHY 841 – 2017 Scott Pratt Department of Physics and Astronomy Michigan State University These notes are for the one-semester graduate level electrodynamics course taught at Michi- gan State University. These notes are more terse than a text book, they do cover all the mate- rial used in PHY 841. They are NOT meant to serve as a replacement for a text. The course makes use of two textbooks: The Classical Theory of Fields by L.D. Landau and E.M. Lifshitz, and Classical Electrodynamics by J.D. Jackson. Anybody is welcome to use the notes to their heart’s content, though the text should be treated with the usual academic respect when it comes to copying material. If anyone is interested in the LATEX source ﬁles, they should con- tact me ([email protected]). Solutions to the end-of-chapter problems are also provided on the course web site (http://www.pa.msu.edu/courses/phy841). Please beware that this is a web manuscript, and is thus alive and subject to change at any time. PHY 841 CONTENTS Contents 1 Special Relativity Primer 4 1.1 γ Factors and Such .................................. 4 1.2 Lorentz Transformations ............................... 6 1.3 Invariants and the metric tensor gαβ ........................ 9 1.4 Four-Velocities and Momenta ............................ 9 1.5 Examples of Invariants ................................ 11 1.6 Tensors ........................................ 13 1.7 Homework Problems ................................ 14 2 Dynamics of Relativistic Point Particles 16 2.1 Lagrangian for a Free Relativistic Particle ...................... 16 2.2 Interaction of a Charged Particle with an External Electromagnetic Field ....
[Show full text]
Special and General Relativity and the Relativistic Ether As Observer Dependent by the Retardation Azzam Almosallami Zurich, Switzerland [email protected]
Special and General Relativity and the Relativistic Ether as observer dependent by the Retardation Azzam Almosallami Zurich, Switzerland [email protected] Abstract In this paper I’ll show how the relativistic effect in SRT must be observer dependent which is leading to field and retardation, and that is leading to the wave-particle duality and the uncertainty principle by the vacuum fluctuation. In this I propose a new transformation by translating the retardation according to the invariance by the entanglement which is leading to the relativistic ether from the point of view of the quantum vacuum which is leading to the wave-particle duality and the uncertainty principle by the vacuum fluctuation. According to my transformation, there two pictures for the moving train, and these two pictures are separate in space and time as a result of the retardation but they are entangled by the invariance of the energy momentum. That will lead also to explain the double slit experiment from the point of view of quantum theory. In my new transformation, I propose there is no space-time continuum, as in special relativity; it is only time, and space is invariant. That leads to the new transformation being vacuum energy dependent instead of relative velocity dependent as in Einstein’s interpretation of the Lorentz transformation equations of the theory of special relativity. Furthermore, the Lorentz factor in my transformation is equivalent to the refractive index in optics. That leads to the disappearance of all the paradoxes of the theory of special relativity: The Twin paradox, Ehrenfest paradox, the Ladder paradox, and Bell’s spaceship paradox.
[Show full text]
Section 5 Special Relativity
North Berwick High School Higher Physics Department of Physics Unit 1 Our Dynamic Universe Section 5 Special Relativity Section 5 Special Relativity Note Making Make a dictionary with the meanings of any new words. Special Relativity 1. What is meant by a frame of reference? 2. Write a short note on the history leading up to Einstein's theories (just include the main dates). The principles 1. State Einstein's starting principles. Time dilation 1. State what is meant by time dilation. 2. Copy the time dilation formula and take note of the Lorentz factor. 3. Copy the example. 4. Explain why we do not notice these events in everyday life. 5. Explain how muons are able to be detected at the surface of the Earth. Length contraction (also known as Lorentz contraction) 1. Copy the length contraction formula. Section 5 Special Relativity Contents Content Statements................................................. 1 Special Relativity........................................................ 2 2 + 2 = 3................................................................... 2 History..................................................................... 2 The principles.......................................................... 4 Time Dilation........................................................... 4 Why do we not notice these time differences in everyday life?.................................... 7 Length contraction................................................... 8 Ladder paradox........................................................ 9 Section 5:
[Show full text]
OUR DYNAMIC UNIVERSE Part 2
OUR DYNAMIC UNIVERSE part 2 J A Hargreaves Lockerbie Academy August 20152016 CONTENTS CHAPTER 6: GRAVITATION CONTENTS TABLE OF CONTENTS GRAVITATION .................................................................................................................................................... 4 Suggested Activities ................................................................................................................................... 4 Astronomical Data ............................................................................................................................................. 4 Gravitational Field Strength on other planets ................................................................................................... 5 Projectiles .......................................................................................................................................................... 5 Projectiles fired Vertically .......................................................................................................................... 5 Projectiles fired horizontally...................................................................................................................... 5 Projectiles at an angle ............................................................................................................................... 7 Task: Launch Velocity ................................................................................................................................ 8 Notes on Projectile
[Show full text]
Interpretational Scenarios of Special Relativity
Interpretational Scenarios of Special Relativity A MONOGRAPH ON SPECIAL RELATIVITY T HEORY COPYRIGHT© 2016 BERNARDO SOTOMAYOR VALDIVIA This monograph is an evolving document and is updated regularly. You may click on the following link to obtain its newest version, Scenarios of SR. Copyright© Bernardo Sotomayor Valdivia 2016 Revision published at ResearchGate, April 2016. Edition 1.0.1 Thank you for downloading Interpretational Scenarios of Special Relativity. You are welcome to share it with your friends or peers. This document may be reproduced, copied and distributed for non-commercial purposes, provided the document remains in its complete original content and form. The author is always grateful for constructive feedback through the network where you obtained this document. REVISION HISTORY Rev. Date Description Published at: 1.0.1 30/04/16 First upload ResearchGate, DOI: 10.13140/RG.2.1.3576.4084 1.0.1 30/04/16 First upload viXra 1.0.2 08/05/16 Correction of velocity addition equations ResearchGate, viXra ACKNOWLEDMENTS Date Description 08/05/16 Special thanks to Erkki J. Brändas, Uppsala University, for his revision and correction of the relativistic velocity addition equations in this monograph. INTRODUCTION This monograph was motivated by the following question posted by the author at the ResearchGate (RG) Website: In the context of Special Relativity (SR): is it time dilation, clock frequency increase, both of the above or none of the above? This question may seem overbeaten, but the evidence is that in spite of hundreds, perhaps thousands, of answers in RG posts related to this question, the controversy seems endless.
[Show full text]
Senior Math Circles March 11, 2020 Special Relativity III Relativity Of
Senior Math Circles March 11, 2020 Special Relativity III Relativity of Simultaneity Recall the process for a pair of observers to synchronize their clocks. Alice sends a light signal to Alice-prime who reflects it back to Alice. Alice can divide the transit time in half to establish that events P and P0 are simultaneous. Now suppose Bob and Bob-prime are moving at a speed v relative to Alice and Alice-prime such that B and B0 pass A and 0 A , respectively, at tA = 0. How would B and B0 synchronize their clocks? They could use the same procedure as A and A0 (but in their frame) to find events Q and Q0 which they deem to be simultaneous. But what would this look like to A and A0? Suppose 8 seconds elapse for Bob while waiting for the light pulse to return. He would note tB = 4 s as the time of event Q and instruct Bob-prime to do the same for event Q0 but observe what this implies: Events Q and Q0 are simultaneous for B and B0 but not simultaneous for A and A0. Specifically, A and A0 would say event Q happens before event Q0. 1 We call this the relativity of simultaneity. That is, whether or not an observer deems two events to be simultaneous depends on their frame of reference (i.e., the velocity). Question. What are the implications of relativity of simultaneity on how different observers will measure the distance between fixed points in space? Imagine the same experiment but with a line up of observers in the Bob frame.
[Show full text]