DOCSLIB.ORG

A Tale of Two Twins

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read 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. In consist in imagining that two twins (i.e. two persons with exactly the same age) have different history. One of the twins leaves the earth with velocity near the light velocity, travels toward a star and comes back to earth. In the meantime the other twin remains on earth. When the traveler twin arrives on earth, it appears that he/she is younger that the twin on earth. This thought experience was proposed by Langevin in 1911, more that hundred years ago. His provocative intention was to show that the new relativistic kinematics can have very surprising results and that the new concepts of space and time are different from the usual ones. I do not know if Langevin was aware of the success of the experiment he proposed. Today the normal place of the twin paradox problem is only in textbooks since solutions of the problem are well established either in the frame of Special Relativity or that of General Relativity. However from the time of its first appearance (1911) until now, articles (see for example H.Lichtenegger and L.Iorio (2011)) were and are regularly published on this subject. In general these articles intend to present new and original solutions or merely repeat what was already published. This continuity in publishing such articles is really puzzling. What is the reason to publish more and more papers on this theoretical subject? Rindler (2001) wrote: "Reams of literature were written on it unnecessarily for more than six decades. At its root apparently lay a deep psychological barrier to accepting time dilatation is real. From a modern point of view, it is difficult to understand the earlier fascination with this problem or even to recognize it as a problem." p.67). Following Grøn (2006) (who wrote himself a paper on the subject) more than three hundred articles were published on the twin paradox! The situation is really complex and one can ask why people proposed so many solutions? Furthermore, why the solutions are so complicated, even in textbooks? One has the feeling that a too simple solution will destroy the mystery of the twin paradox. This problem was also at the center of harsh controversies among physicists about Relativity and its place as a science. All this shows that this phenomenon (the paradox itself and all its manifestations) might have roots in the unconscious mind of human beings. 2 I thought that it was worth to investigate this strange situation and try to understand this fascination. The paper is divided in two parts. In the first, I describe with more details the history of the "paradox" and its solutions. It appears that there are some errors in many articles and this why I recall some results in Special Relativity. This will help in understanding the solution proposed in this paper that I shall call the simplest solution. First I analyze the Langevin article and then I define precisely the problem. In fact, it is possible to see that there are two versions of this experiment and the distinction is not done in the majority of the articles. I begin the second part in discuting some of the proposed solutions, mentioning the controversies and trying to understand the issue of these disputes. I present also some speculations which can help to decipher what are the possible psychological mechanisms behind the phenomenon: why this obsession? Why too many complicated solutions? Why the controversies? Clearly I am not able to prove the assertions relatively to the phenomenon but I hope that they will suggestive enough to help understanding it. One can already note that Langevin did not write about a paradox or twins as we shall see below. The first mention of the twins in the context of the paradox is probably due to Weyl in his book Space-Time-Matter published in 1922. At the page 187 he writes: " Suppose we have two twin-brothers who take leave one another at a world-point A, and suppose one remains at home (that is, permanently at rest in an allowable reference-space), whilst the other sets out on voyages, during which he moves with velocities (relative to "home") that approximate to that of light. When the wanderer returns home in later years he will appear appreciably younger than the one who stayed at home." It seems that during a long time the name "twin paradox" was forgotten and people used only "clock paradox" as it is possible to see from the books and articles published before 1955: books of Tolman (1934) and of Møller (1952), article of Hill (1947) and that of Milne and Whitrow (1949). In all these texts, only appear the words "clock paradox". Some authors relate the problem to Einstein in his famous paper of 1905 (Einstein (1905)). It concerns two clocks, one at rest and the second making a closed path. It is a slightly different problem and I shall discuss it later. 3 Part one: two twins with two or three clocks I 1. Some results in Special Relativity The relativistic kinematics concerns systems which move relatively one to another with constant velocity (in absolute value and in direction). For the time these systems never stop, move indefinitely and are called inertial systems. Later I shall discuss what happens if one system will stop. Inside a system, an event is defined as: "something that happens in a place defined by its Cartesian coordinates and by a time given by clocks". It is possible to imagine that in each place of the system there is a clock such it is possible in all places to know the time. All the clocks are at rest and it possible to synchronize them all together. 1.1 Lorentz transformation Now consider two reference systems S and S' such that the axis xyz of S are parallel to those of S' x'y'z'. In S the time is measured as t and in S' as t'. The two system move relatively each to other with velocity V parallel to x and x'. S' moves relatively to S with velocity V and S move relatively to S' with velocity – V. If an event takes place in S at (x,y,z,t) what are the values of (x'y'z't') of this event measured by an observer in S'? The answer is given by the Lorentz transformation. Supposing that an event can happen only along the x and x' axis, the Lorentz transformation can be written as x' = γ(x – Vt) (1) t' = γ (t – Vx/c2) (2) where c is the light velocity, γ = (1− β2)-0.5 and β = V/c . In (1) and (2) it is implied that in the two systems S and S', there is coincidence of their origin O and O' (such that x = x' = 0) when the clocks in S and S' indicate the same time taken equal to 0. It is also possible to take choice of x and x' different from zero, for t = t' and a constant must be added to the right side of (1). Form (1) and (2), one can obtain the value of x and t corresponding to an event (x', t') taking place in S' x = γ(x' + Vt') (3) 4 t = γ(t' + Vx'/c2) (4) 1.2 Applications of the Lorentz transformation Now one applies the Lorentz transformation to the following cases. First, one considers a process compound of two events in the frame S'. One event is the beginning of the process and takes place in S' at (x' = 0, t' = 0), and the a second (which is the end of the process) takes place at (x' = 0, t' = τ1) i.e. at the same place. The total time of this process is τ1 in S'. What is the time τ2 of the process measured in S? From (3) and (4), one gets for the end of the process, x = γVτ1 and τ2 = γτ1. In other terms, the time measured in S is larger than that measured in S' since γ >1.
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 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]
  • 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]
  • Length Contraction the Proper Length of an Object Is Longest in the Reference Frame in Which It Is at Rest
    Newton’s Principia in 1687. Galilean Relativity Velocities add: V= U +V' V’= 25m/s V = 45m/s U = 20 m/s What if instead of a ball, it is a light wave? Do velocities add according to Galilean Relativity? Clocks slow down and rulers shrink in order to keep the speed of light the same for all observers! Time is Relative! Space is Relative! Only the SPEED OF LIGHT is Absolute! A Problem with Electrodynamics The force on a moving charge depends on the Frame. Charge Rest Frame Wire Rest Frame (moving with charge) (moving with wire) F = 0 FqvB= sinθ Einstein realized this inconsistency and could have chosen either: •Keep Maxwell's Laws of Electromagnetism, and abandon Galileo's Spacetime •or, keep Galileo's Space-time, and abandon the Maxwell Laws. On the Electrodynamics of Moving Bodies 1905 EinsteinEinstein’’ss PrinciplePrinciple ofof RelativityRelativity • Maxwell’s equations are true in all inertial reference frames. • Maxwell’s equations predict that electromagnetic waves, including light, travel at speed c = 3.00 × 108 m/s =300,000km/s = 300m/µs . • Therefore, light travels at speed c in all inertial reference frames. Every experiment has found that light travels at 3.00 × 108 m/s in every inertial reference frame, regardless of how the reference frames are moving with respect to each other. Special Theory: Inertial Frames: Frames do not accelerate relative to eachother; Flat Spacetime – No Gravity They are moving on inertia alone. General Theory: Noninertial Frames: Frames accelerate: Curved Spacetime, Gravity & acceleration. Albert Einstein 1916 The General Theory of Relativity Postulates of Special Relativity 1905 cxmsms==3.0 108 / 300 / μ 1.
    [Show full text]
  • The Pole Vaulter and the Barn Picture a Pole Vaulter Running Towards a Long Barn (With Doors at Each End) at Maximum Speed
    Special Relativity Dr. Kevin Kelly Saturday Morning Physics October 5th, 2019 Rewind back to the 1890s ▸ Let’s take a minute and think about what we (they) knew about the world in the late 1800s. Rewind back to the 1890s ▸ Let’s take a minute and think about what we (they) knew about the world in the late 1800s. ▸ Newton (1687): Gravity governs the motion of bodies on earth as well as in space. Newton’s Principia also gave us his famous “three laws” for motion of objects. Rewind back to the 1890s ▸ Let’s take a minute and think about what we (they) knew about the world in the late 1800s. ▸ Newton (1687): Gravity governs the motion of bodies on earth as well as in space. Newton’s Principia also gave us his famous “three laws” for motion of objects. ▸ Thermodynamics (1700s/1800s): contributions of many physicists. Determined how heat transfer works, led to the development of engines, etc. Rewind back to the 1890s ▸ Let’s take a minute and think about what we (they) knew about the world in the late 1800s. ▸ Newton (1687): Gravity governs the motion of bodies on earth as well as in space. Newton’s Principia also gave us his famous “three laws” for motion of objects. ▸ Thermodynamics (1700s/1800s): contributions of many physicists. Determined how heat transfer works, led to the development of engines, etc. ▸ Electricity & Magnetism (1700s/1800s): a collection of newly-discovered laws were determined to be related, brought together as “Maxwell’s Equations” In terms of describing what we see around us, and how we interact with the world, we have a pretty good handle on everything! This is a VERY famous quote, often attributed to Lord Kelvin (one of the titans of Thermodynamics).
    [Show full text]
  • Galileo and Einstein Time Dilation Length Contraction Two Coordinate Systems X’Y’Z’ Displaced by X = Xî
    Relativity Galileo and Einstein Time dilation Length contraction Two coordinate systems x’y’z’ displaced by X = Xî z z’ X (x,y,z) y y’ x x’ Two coordinate systems x’y’z’ displaced by X = Xî z z’ X (x’,y’,z’) y y’ x x’ x’ = x–X y’ = y z’ = z Two coordinate systems x’y’z’ moving at constant velocity V =V î z z’ u = (ux’,uy’,zz’) (x’,y’,z’) Vt y a = (ax’,ay’,az’) x a = a u = u – V x’ = x – Vt x’ x x’ x Galilean a = a u = u y’ = y y’ y y’ y Transformation az’ = az uz’ = uz z’ = z In General z’ x’y’z’ moving at constant velocity V Vt z u’ = (ux’,uy’,zz’) (x’,y’,z’) = r’ y a’ = (ax’,ay’,az’) x Galilean a ‘ = a u’ = u – V r’ = r – Vt Transformation Galilean Relativity If one coordinate system moves with respect to another then accelerations are the same in both Forces and their effects on acceleration do not change if you change to another frame of reference which is moving at constant velocity with respect to the first. All inertial frames of reference are equivalent “Galilean principle of relativity” Newton’s laws are valid all masses, forces and accelerations are the same. Fly in the ointment Theory of light and radio waves doesn’t obey Galilean Relativity light and radio signals are waves in what medium? aether! (universal jello) What’s the speed of the earth through it? Michelson Interferometer Both arms have same medium same wavelength, same distance Half silvered mirror constructive interference & screen is bright Michelson Interferometer different medium different wavelength Half silvered mirror may get destructive interference Michelson Morley Vearth Experiment light speed = c If earth is flying through the aether Time for this arm L the time it takes light to t = 2L 1 c travel one arm may be different from the other one.
    [Show full text]