DOCSLIB.ORG

Unmatter Plasma, Relativistic Oblique-Length Contraction Factor, Neutrosophic Diagram and Neutrosophic Degree of Paradoxicity: Articles and Notes

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Unmatter Plasma, Relativistic Oblique-Length Contraction Factor, Neutrosophic Diagram and Neutrosophic Degree of Paradoxicity: Articles and Notes University of New Mexico UNM Digital Repository Faculty and Staff Publications Mathematics 2015 Unmatter Plasma, Relativistic Oblique-Length Contraction Factor, Neutrosophic Diagram and Neutrosophic Degree of Paradoxicity: Articles and Notes Florentin Smarandache University of New Mexico, [email protected] Follow this and additional works at: https://digitalrepository.unm.edu/math_fsp Part of the Cosmology, Relativity, and Gravity Commons, Dynamic Systems Commons, External Galaxies Commons, Mathematics Commons, Other Astrophysics and Astronomy Commons, Physical Processes Commons, Stars, Interstellar Medium and the Galaxy Commons, and the The Sun and the Solar System Commons Recommended Citation F. Smarandache (eds.) Unmatter Plasma, Relativistic Oblique-Length Contraction Factor, Neutrosophic Diagram and Neutrosophic Degree of Paradoxicity: Articles and Notes. Brussels: Pons Publishing, 2015. This Book is brought to you for free and open access by the Mathematics at UNM Digital Repository. It has been accepted for inclusion in Faculty and Staff Publications by an authorized administrator of UNM Digital Repository. For more information, please contact [email protected]. Unmatter Plasma and other articles and notes on physics Florentin Smarandache Unmatter Plasma, Relativistic Oblique-Length Contraction Factor, Neutrosophic Diagram and Neutrosophic Degree of Paradoxicity. Articles and Notes 1 Florentin Smarandache ISBN 978-1-59973-346-3 E-publishing: Georgiana Antonescu Pons asbl Bruxelles, Quai du Batelage, 5, Belgium © Pons&Florentin Smarandache, 2015 2 Unmatter Plasma and other articles and notes on physics Florentin Smarandache Unmatter Plasma, Relativistic Oblique-Length Contraction Factor, Neutrosophic Diagram and Neutrosophic Degree of Paradoxicity. Articles and Notes Pons Publishing Brussels, 2015 3 Florentin Smarandache Peer-Reviewers: Mumtaz Ali, Department of Mathematics, Quaid-i-Azam University, Islamabad, 44000, Pakistan Said Broumi, University of Hassan II Mohammedia, Hay El Baraka Ben M'sik, Casablanca B. P. 7951, Morocco Octavian Cira, Aurel Vlaicu University of Arad, Arad, Romania 4 Unmatter Plasma and other articles and notes on physics Contents Foreword ................................................................................. 11 ARTICLES 1. Unmatter Plasma discovered ............................................. 14 1.1. Introduction .................................................................. 14 1.2. Definition of Unmatter ................................................. 15 1.3. Definition of Unmatter Plasma ................................... 16 1.4. The Neutrosophic Triplets ........................................... 17 1.5. Verifications of Unmatter ............................................. 17 1.6. Verification of Unmatter Plasma ................................ 18 References ...................................................................... 18 2. Oblique-Length Contraction Factor in the Special Theory of Relativity ............................................................................ 20 2.1. Introduction ................................................................. 20 2.2. Length-Contraction Factor ......................................... 20 2.3. Time-Contraction Factor ............................................. 21 2.4. Oblique-Length Contraction Factor ........................... 22 2.5. Angle Distortion .......................................................... 25 References ...................................................................... 28 3. Relations between Distorted&Original Angles in STR ..... 29 3.1. Introduction ................................................................. 29 3.2. Tangential Relations between Distorted Acute Angles vs. Original Acute Angles of a Right Triangle ................... 30 5 Florentin Smarandache 3.3. Tangential Relations between Distorted Angles vs. Original Angles of a General Triangle ............................... 34 3.4. Other Relations between the Distorted Angles and the Original Angles .................................................................. 37 References ...................................................................... 38 4. n-Valued Refined Neutrosophic Logic and Its Applications to Physics ............................................................................... 40 4.1. Two-Valued Logic ........................................................ 40 4.1.1. The Two Symbol-Valued Logic ............................. 40 4.1.2. The Two Numerical-Valued Logic ........................ 41 4.2. Three-Valued Logic ..................................................... 41 4.2.1. The Three Symbol-Valued Logics ......................... 41 4.2.2. The Three Numerical-Valued Logic ..................... 42 4.3 Four-Valued Logic ........................................................ 43 4.3.1 The Four Symbol-Valued Logic ............................. 43 4.3.2 Four Numerical-Valued Neutrosophic Logic ....... 44 4.4. Five-Valued Logic ....................................................... 44 4.5. Seven-Valued Logic ..................................................... 45 4.6. n-Valued Logic ............................................................ 45 4.6.1. n-Symbol-Valued Refined Neutrosophic Logic ... 45 4.6.2. n-Numerical-Valued Refined Neutrosophic Logic ............................................................................... 45 4.7. n-Valued Neutrosophic Logic Connectors ................. 46 4.7.1. n-norm and n-conorm defined on combinations of t-norm and t-conorm ................................................. 46 4.7.2. n-norm and n-conorm based on priorities .......... 48 4.8. Particular Cases ........................................................... 49 6 Unmatter Plasma and other articles and notes on physics 4.9. Distinction between Neutrosophic Physics and Paradoxist Physics .............................................................. 49 4.9.1. Neutrosophic Physics ........................................... 50 4.9.2. Paradoxist Physics ................................................ 50 4.10. n-Valued Refined Neutrosophic Logic Applied to Physics ................................................................................ 50 4.10.1. Examples of paradoxist and neutrosophic entities ............................................................................. 51 4.11. Conclusion .................................................................. 52 References ...................................................................... 53 5. Neutrosophic Diagram and Classes of Neutrosophic Paradoxes or to the Outer-Limits of Science ........................ 55 5.1. Introduction to the neutrosophics .............................. 55 5.2. Applications of neutrosophics .................................... 58 5.3. Examples of neutrosophy in Arabic philosophy ......... 59 5.4. The Venn diagram ....................................................... 60 5.5. The neutrosophic diagram, as extension of the Venn diagram .............................................................................. 61 5.6. Classes of neutrosophic paradoxes ............................. 64 5.7. Neutrosophic operators .............................................. 65 5.8. Neutrosophic truth tables ........................................... 66 5.9. Neutrosophic operators and classes of neutrosophic paradoxes ........................................................................... 67 5.9.1. Complement/Negation ......................................... 67 5.9.2. Neuterization ........................................................ 68 5.9.3. Antonymization .................................................... 68 5.9.4. Intersection/Conjunction .................................... 68 7 Florentin Smarandache 5.9.5. Union / Weak Disjunction ................................... 69 5.9.6. Inclusion/Conditional .......................................... 69 5.9.7. Equality/Biconditional ......................................... 70 5.9.8. Combinations ....................................................... 72 5.9.9. Other logical connectors ...................................... 72 5.9.10. Substitutions ....................................................... 72 5.10. Some particular paradoxes ........................................ 72 5.10.1. Quantum semi-paradox ....................................... 72 5.10.2. Torture’s paradox ................................................ 73 5.10.3. Paradoxist psychological behavior ...................... 73 5.10.4. Law of Self-Equilibrium ...................................... 74 References ...................................................................... 74 REVIEWS&ABSTRACS 6. Unparticle, a Special Case of Unmatter ............................ 78 7. Connection Between Unparticle and Unmatter ............... 80 8. Neutrosophic Physics as A New Field of Research ........... 81 Acknowledgement ......................................................... 82 References ...................................................................... 83 9. Neutrosophic Degree of Paradoxicity of a Scientific Statement ............................................................................... 84 10. The Multispace with Its Multistructure as Unified Field Theory .................................................................................... 85 11. Multispace&Multistructure as a Theory of Everything .... 86 12. Five Paradoxes and a General Question on Time Traveling ...............................................................................
Load more

Recommended publications
  • The Special Theory of Relativity Lecture 16
    The Special Theory of Relativity Lecture 16 E = mc2 Albert Einstein Einstein’s Relativity • Galilean-Newtonian Relativity • The Ultimate Speed - The Speed of Light • Postulates of the Special Theory of Relativity • Simultaneity • Time Dilation and the Twin Paradox • Length Contraction • Train in the Tunnel paradox (or plane in the barn) • Relativistic Doppler Effect • Four-Dimensional Space-Time • Relativistic Momentum and Mass • E = mc2; Mass and Energy • Relativistic Addition of Velocities Recommended Reading: Conceptual Physics by Paul Hewitt A Brief History of Time by Steven Hawking Galilean-Newtonian Relativity The Relativity principle: The basic laws of physics are the same in all inertial reference frames. What’s a reference frame? What does “inertial” mean? Etc…….. Think of ways to tell if you are in Motion. -And hence understand what Einstein meant By inertial and non inertial reference frames How does it differ if you’re in a car or plane at different points in the journey • Accelerating ? • Slowing down ? • Going around a curve ? • Moving at a constant velocity ? Why? ConcepTest 26.1 Playing Ball on the Train You and your friend are playing catch 1) 3 mph eastward in a train moving at 60 mph in an eastward direction. Your friend is at 2) 3 mph westward the front of the car and throws you 3) 57 mph eastward the ball at 3 mph (according to him). 4) 57 mph westward What velocity does the ball have 5) 60 mph eastward when you catch it, according to you? ConcepTest 26.1 Playing Ball on the Train You and your friend are playing catch 1) 3 mph eastward in a train moving at 60 mph in an eastward direction.
    [Show full text]
  • 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]
  • Physics 200 Problem Set 7 Solution Quick Overview: Although Relativity Can Be a Little Bewildering, This Problem Set Uses Just A
    Physics 200 Problem Set 7 Solution Quick overview: Although relativity can be a little bewildering, this problem set uses just a few ideas over and over again, namely 1. Coordinates (x; t) in one frame are related to coordinates (x0; t0) in another frame by the Lorentz transformation formulas. 2. Similarly, space and time intervals (¢x; ¢t) in one frame are related to inter- vals (¢x0; ¢t0) in another frame by the same Lorentz transformation formu- las. Note that time dilation and length contraction are just special cases: it is time-dilation if ¢x = 0 and length contraction if ¢t = 0. 3. The spacetime interval (¢s)2 = (c¢t)2 ¡ (¢x)2 between two events is the same in every frame. 4. Energy and momentum are always conserved, and we can make e±cient use of this fact by writing them together in an energy-momentum vector P = (E=c; p) with the property P 2 = m2c2. In particular, if the mass is zero then P 2 = 0. 1. The earth and sun are 8.3 light-minutes apart. Ignore their relative motion for this problem and assume they live in a single inertial frame, the Earth-Sun frame. Events A and B occur at t = 0 on the earth and at 2 minutes on the sun respectively. Find the time di®erence between the events according to an observer moving at u = 0:8c from Earth to Sun. Repeat if observer is moving in the opposite direction at u = 0:8c. Answer: According to the formula for a Lorentz transformation, ³ u ´ 1 ¢tobserver = γ ¢tEarth-Sun ¡ ¢xEarth-Sun ; γ = p : c2 1 ¡ (u=c)2 Plugging in the numbers gives (notice that the c implicit in \light-minute" cancels the extra factor of c, which is why it's nice to measure distances in terms of the speed of light) 2 min ¡ 0:8(8:3 min) ¢tobserver = p = ¡7:7 min; 1 ¡ 0:82 which means that according to the observer, event B happened before event A! If we reverse the sign of u then 2 min + 0:8(8:3 min) ¢tobserver 2 = p = 14 min: 1 ¡ 0:82 2.
    [Show full text]
  • On Radar Time and the Twin ''Paradox''
    On radar time and the twin ‘‘paradox’’ Carl E. Dolbya) and Stephen F. Gullb) Astrophysics Group, Cavendish Laboratory, Madingley Road, Cambridge CB3 0HE, United Kingdom ͑Received 23 April 2001; accepted 13 June 2001͒ In this paper we apply the concept of radar time ͑popularized by Bondi in his work on k calculus͒ to the well-known relativistic twin ‘‘paradox.’’ Radar time is used to define hypersurfaces of simultaneity for a class of traveling twins, from the ‘‘immediate turn-around’’ case, through the ‘‘gradual turn-around’’ case, to the ‘‘uniformly accelerating’’ case. We show that this definition of simultaneity is independent of choice of coordinates, and assigns a unique time to any event ͑with which the traveling twin can send and receive signals͒, resolving some common misconceptions. © 2001 American Association of Physics Teachers. ͓DOI: 10.1119/1.1407254͔ INTRODUCTION time’’ ͑and related ‘‘radar distance’’͒ and emphasize that this definition applies not just to inertial observers, but to any It might seem reasonable to suppose that the twin paradox observer in any space–time. We then use radar time to derive has long been understood, and that no confusion remains the hypersurfaces of simultaneity for a class of traveling about it. Certainly there is no disagreement about the relative twins, from the ‘‘immediate turn-around’’ case, through the aging of the two twins, so there is no ‘‘paradox.’’ There is ‘‘gradual turn-around’’ case, to the ‘‘uniformly accelerating’’ also no confusion over ‘‘when events are seen’’ by the two case.
    [Show full text]
  • Relativity Contents.Pdf
    Contents 1 Kinematics, Part 1 1 1.1 Motivation . 2 1.1.1 Galilean transformations, Maxwell’s equations . 2 1.1.2 Michelson–Morley experiment . 5 1.2 The postulates . 10 1.3 The fundamental effects . 12 1.3.1 Loss of simultaneity . 12 1.3.2 Time dilation . 17 1.3.3 Length contraction . 23 1.3.4 A few other important topics . 28 1.4 Four instructive examples . 31 1.5 Velocity addition . 35 1.6 Summary . 43 1.7 Problems . 44 1.8 Exercises . 49 1.9 Solutions . 54 2 Kinematics, Part 2 71 2.1 Lorentz transformations . 71 2.1.1 First derivation . 72 2.1.2 Second derivation . 75 2.1.3 The fundamental effects . 78 2.2 Velocity addition . 79 2.2.1 Longitudinal velocity addition . 79 2.2.2 Transverse velocity addition . 80 2.3 The invariant interval . 82 2.4 Minkowski diagrams . 87 2.5 The Doppler effect . 92 2.5.1 Longitudinal Doppler effect . 92 2.5.2 Transverse Doppler effect . 94 2.6 Rapidity . 96 2.6.1 Definition . 96 2.6.2 Physical meaning . 98 2.7 Relativity without c ............................ 99 2.8 Summary . 102 2.9 Problems . 103 2.10 Exercises . 106 2.11 Solutions . 110 iii iv Contents 3 Dynamics 123 3.1 Energy and momentum . 123 3.1.1 Momentum . 124 3.1.2 Energy . 125 3.2 Transformations of E and p . 131 3.3 Collisions and decays . 134 3.4 Particle-physics units . 139 3.5 Force . 140 3.5.1 Force in one dimension .
    [Show full text]
  • A Tale of Two Twins
    A tale of two twins L.Benguigui Physics Department and Solid State Institute Technion-Israel Institute of Technology 32000 Haifa Israel Abstract The thought experiment (called the clock paradox or the twin paradox) proposed by Langevin in 1911 of two observers, one staying on earth and the other making a trip toward a Star with a velocity near the light velocity is very well known for its very surprising result. When the traveler comes back, he is younger than the stay on Earth. This astonishing situation deduced form the theory of Special Relativity sparked a huge amount of articles, discussions and controversies such that it remains a particular phenomenon probably unique in Physics. In this article we propose to study it. First, we lookedl for the simplest solutions when one can observe that the published solutions correspond in fact to two different versions of the experiment. It appears that the complete and simple solution of Møller is neglected for complicated methods with dubious validity. We propose to interpret this avalanche of works by the difficulty to accept the conclusions of the Special Relativity, in particular the difference in the times indicated by two clocks, one immobile and the second moving and finally stopping. We suggest also that the name "twin paradox" is maybe related to some subconscious idea concerning conflict between twins as it can be found in the Bible and in several mythologies. 1 Introduction The thought experiment in the theory of Relativity called the "twin paradox" or the "clock paradox" is very well known in physics and even by non-physicists.
    [Show full text]
  • A Short and Transparent Derivation of the Lorentz-Einstein Transformations
    A brief and transparent derivation of the Lorentz-Einstein transformations via thought experiments Bernhard Rothenstein1), Stefan Popescu 2) and George J. Spix 3) 1) Politehnica University of Timisoara, Physics Department, Timisoara, Romania 2) Siemens AG, Erlangen, Germany 3) BSEE Illinois Institute of Technology, USA Abstract. Starting with a thought experiment proposed by Kard10, which derives the formula that accounts for the relativistic effect of length contraction, we present a “two line” transparent derivation of the Lorentz-Einstein transformations for the space-time coordinates of the same event. Our derivation make uses of Einstein’s clock synchronization procedure. 1. Introduction Authors make a merit of the fact that they derive the basic formulas of special relativity without using the Lorentz-Einstein transformations (LET). Thought experiments play an important part in their derivations. Some of these approaches are devoted to the derivation of a given formula whereas others present a chain of derivations for the formulas of relativistic kinematics in a given succession. Two anthological papers1,2 present a “two line” derivation of the formula that accounts for the time dilation using as relativistic ingredients the invariant and finite light speed in free space c and the invariance of distances measured perpendicular to the direction of relative motion of the inertial reference frame from where the same “light clock” is observed. Many textbooks present a more elaborated derivation of the time dilation formula using a light clock that consists of two parallel mirrors located at a given distance apart from each other and a light signal that bounces between when observing it from two inertial reference frames in relative motion.3,4 The derivation of the time dilation formula is intimately related to the formula that accounts for the length contraction derived also without using the LET.
    [Show full text]
  • Massachusetts Institute of Technology Midterm
    Massachusetts Institute of Technology Physics Department Physics 8.20 IAP 2005 Special Relativity January 18, 2005 7:30–9:30 pm Midterm Instructions • This exam contains SIX problems – pace yourself accordingly! • You have two hours for this test. Papers will be picked up at 9:30 pm sharp. • The exam is scored on a basis of 100 points. • Please do ALL your work in the white booklets that have been passed out. There are extra booklets available if you need a second. • Please remember to put your name on the front of your exam booklet. • If you have any questions please feel free to ask the proctor(s). 1 2 Information Lorentz transformation (along the x­axis) and its inverse x� = γ(x − βct) x = γ(x� + βct�) y� = y y = y� z� = z z = z� ct� = γ(ct − βx) ct = γ(ct� + βx�) � where β = v/c, and γ = 1/ 1 − β2. Velocity addition (relative motion along the x­axis): � ux − v ux = 2 1 − uxv/c � uy uy = 2 γ(1 − uxv/c ) � uz uz = 2 γ(1 − uxv/c ) Doppler shift Longitudinal � 1 + β ν = ν 1 − β 0 Quadratic equation: ax2 + bx + c = 0 1 � � � x = −b ± b2 − 4ac 2a Binomial expansion: b(b − 1) (1 + a)b = 1 + ba + a 2 + . 2 3 Problem 1 [30 points] Short Answer (a) [4 points] State the postulates upon which Einstein based Special Relativity. (b) [5 points] Outline a derviation of the Lorentz transformation, describing each step in no more than one sentence and omitting all algebra. (c) [2 points] Define proper length and proper time.
    [Show full text]
  • Minkowski's Proper Time and the Status of the Clock Hypothesis
    Minkowski’s Proper Time and the Status of the Clock Hypothesis1 1 I am grateful to Stephen Lyle, Vesselin Petkov, and Graham Nerlich for their comments on the penultimate draft; any remaining infelicities or confusions are mine alone. Minkowski’s Proper Time and the Clock Hypothesis Discussion of Hermann Minkowski’s mathematical reformulation of Einstein’s Special Theory of Relativity as a four-dimensional theory usually centres on the ontology of spacetime as a whole, on whether his hypothesis of the absolute world is an original contribution showing that spacetime is the fundamental entity, or whether his whole reformulation is a mere mathematical compendium loquendi. I shall not be adding to that debate here. Instead what I wish to contend is that Minkowski’s most profound and original contribution in his classic paper of 100 years ago lies in his introduction or discovery of the notion of proper time.2 This, I argue, is a physical quantity that neither Einstein nor anyone else before him had anticipated, and whose significance and novelty, extending beyond the confines of the special theory, has become appreciated only gradually and incompletely. A sign of this is the persistence of several confusions surrounding the concept, especially in matters relating to acceleration. In this paper I attempt to untangle these confusions and clarify the importance of Minkowski’s profound contribution to the ontology of modern physics. I shall be looking at three such matters in this paper: 1. The conflation of proper time with the time co-ordinate as measured in a system’s own rest frame (proper frame), and the analogy with proper length.
    [Show full text]
  • Time Dilation and Length Contraction Shown in Three-Dimensional Space-Time Frames
    TIME DILATION AND LENGTH CONTRACTION SHOWN IN THREE-DIMENSIONAL SPACE-TIME FRAMES Tower Chen Division of Mathematical Sciences University of Guam e-mail:[email protected] Zeon Chen e-mail: zeon [email protected] (Received 9 December 2008; accepted 18 February 2009) Abstract In classical Newtonian physics, space and time are abso- lute quantities. Hence, space and time can be treated inde- pendently and discussed separately. With his theory of rel- ativity, Einstein proved that space and time are dependent and must not be treated separately. To maintain this in- terdependency and inseparability of space and time, a three- Concepts of Physics, Vol. VI, No. 2 (2009) 221 dimensional space-time frame, where time is embedded into a spatial coordinate system, has been conceptualized. Utiliz- ing this new type of frame, the concepts of time dilation and length contraction can easily be visualized with intuitive, ge- ometric graphs. The proposed three-dimensional space-time frame is an alternate mathematical frame that can be used to describe the motion of objects. It may also prove to be a use- ful tool in facilitating the understanding of Special Relativity and providing additional insights into space and time. 222 Concepts of Physics, Vol. VI, No. 2 (2009) TIME DILATION AND LENGTH CONTRACTION... 1 Introduction In classical Newtonian physics, the concepts of space and time are absolute. Space is composed of three orthogonal dimensions, and time is represented as a fourth dimension, perpendicular to each of the spatial axes. Both space and time are free to be discussed in- dependent of the other.
    [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]
  • Lecture 17 Relativity A2020 Prof. Tom Megeath What Are the Major Ideas
    4/1/10 Lecture 17 Relativity What are the major ideas of A2020 Prof. Tom Megeath special relativity? Einstein in 1921 (born 1879 - died 1955) Einstein’s Theories of Relativity Key Ideas of Special Relativity • Special Theory of Relativity (1905) • No material object can travel faster than light – Usual notions of space and time must be • If you observe something moving near light speed: revised for speeds approaching light speed (c) – Its time slows down – Its length contracts in direction of motion – E = mc2 – Its mass increases • Whether or not two events are simultaneous depends on • General Theory of Relativity (1915) your perspective – Expands the ideas of special theory to include a surprising new view of gravity 1 4/1/10 Inertial Reference Frames Galilean Relativity Imagine two spaceships passing. The astronaut on each spaceship thinks that he is stationary and that the other spaceship is moving. http://faraday.physics.utoronto.ca/PVB/Harrison/Flash/ Which one is right? Both. ClassMechanics/Relativity/Relativity.html Each one is an inertial reference frame. Any non-rotating reference frame is an inertial reference frame (space shuttle, space station). Each reference Speed limit sign posted on spacestation. frame is equally valid. How fast is that man moving? In contrast, you can tell if a The Solar System is orbiting our Galaxy at reference frame is rotating. 220 km/s. Do you feel this? Absolute Time Absolutes of Relativity 1. The laws of nature are the same for everyone In the Newtonian universe, time is absolute. Thus, for any two people, reference frames, planets, etc, 2.
    [Show full text]