DOCSLIB.ORG

1. RELATIVISTIC KINEMATICS 1.1. Einstein's Postulates

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
1. RELATIVISTIC KINEMATICS 1.1. Einstein's Postulates 1. RELATIVISTIC KINEMATICS The one truth of which the human mind can be certain – indeed, this is the meaning of consciousness itself – is the recognition of its own existence. That we may be secure in this truth is assured us by Descartes’ famous axiom even if everything else, including Descartes, is a figment of our imagination. Nothing else can be proved. Our most fundamental belief, then, is that the universe exists around us, consisting of three spatial dimensions and time, and that while we can move about in the three spatial dimensions, time flows inexorably onward, everywhere the same. Newton himself said it: “…absolute, true, and mathematical time, of itself, and from its own nature, flows equably and without relation to anything external.” But he was wrong. The theory of relativity shows us that time and space do not have the meaning we thought they had. In the words of Weyl, “…we are to discard our belief in the objective meaning of simultaneity; it was the great achievement of Einstein in the field of the theory of knowledge that he banished this dogma from our minds, and this is what leads us to rank his name with that of Copernicus” (italics his). But the discovery of relativity by Einstein in 1905 was not a bolt from the blue. People had been concerned about the nature of space and time for at least hundreds of years before that, becoming more and more disturbed by the inconsistencies in our understanding of the physical world toward the end of the 19th century. Nevertheless, even after the true nature of space and time became clear, the theory of relativity so contradicted our most fundamental belief that it was rejected for years. Einstein himself never received the Nobel Prize for this work that was, in the words of Bertrand Russell, “probably the greatest synthetic achievement of the human intellect up to the present time.” Some sixteen years afterward he was reluctantly awarded the Nobel Prize for a lesser work because the greatest physicist of the century, known to more people than the President of the United States, could not be completely ignored. Yet, the truth Einstein taught us displayed once again nature’s tendency to assume the most beautiful, symmetric form, in spite of our objections. And while the truth is a merger of space and time that prevents us from ordering events absolutely in time, it does not result in chaos, but preserves those features that we cannot logically be denied. The principle of causality is never violated, and as each of us progresses through this four-dimensional space-time, our individual perception of time as moving always forward is not contradicted. 1.1. Einstein’s Postulates Einstein's solution to the dilemma of the velocity of light was as beautiful as it was radical. He chose the most symmetric form for nature, stating that all inertial reference frames are equivalent. He embodied this concept in his two postulates of special relativity, which state: 1. The laws of nature are identical in all inertial frames of reference. That is, if we transform the mathematical equations of physics from one inertial reference frame to another they remain in the same form. 2. The speed of light c is the same to all observers at rest in inertial frames of reference. A more general statement of this principle might be that the influence of one particle is 1 not felt instantaneously by another. Instead, the influence propagates at some (maximum) velocity c . These two postulates can be summed up in a single postulate that states that there is no experiment that can be done to distinguish the absolute velocity of any coordinate system. Einstein’s postulates appear beautifully simple and symmetric. In fact they are deceptively simple, since within them lie profound consequences and more than a few startling paradoxes. Fundamental to all the paradoxes is the fact that simultaneity is no longer an objective reality, as Weyl points out, but rather a subjective one that depends on the observer. A simple example, shown in Figure 1, illustrates this. Consider the following "gedanken experiment" (thought experiment; Einstein loved gedanken experiments): Figure 1 On the moon, Buffy and Bubba, representating the lunar colonies Alpha and Beta, are having a green-cheese eating contest. When the winner is declared, the news is radioed to the folks back home in Alpha and Beta, which are equidistant from the site of the contest. Each colony receives the news, which travels at the speed of light, at exactly the same time. Right? Of course. But Hilda and Wolfgang, who are passing the moon in their space ship on their way back to earth after a vacation, watch the events on the moon and come to a different conclusion. Since, as they view it, the moon is moving to the left, the news reaches Beta, which is moving toward the contest, before it reaches Alpha. Right? Of course. Who is right? Well, they both are. There is no absolute meaning to the concept of simultaneity. In fact, let’s check in with Edgar and Eloise, who are in a space ship going the opposite direction from Wolfie and Hildie, just starting their vacation. As viewed by E and E, the moon is going the opposite direction and the news reaches Alpha before it reaches Beta. We can’t even get agreement on which of two events (the news arriving at Alpha and at Beta) occurred first. In fact, there is really no absolute meaning to simultaneity. Time just doesn’t work that way, although the effects are usually so small that you never noticed it. You may (you should!) wonder what has happened to cause and effect. For example, if event A causes event B, what happens if someone else observes events A and B to occur in the reverse order. This is similar to the logical difficulty that occurs when people travel back in 2 time. Can Dr. No travel back in time and kill his mother so that he himself is never born? Well, of course not, regardless of whether you liked “Back to the Future” or not. In fact, the theory of relativity does not violate causality. Two events can be reordered in time by other observers only if the events happen so far apart in distance and so close together in time that neither light nor anything else (which must travel slower than light) can get from the first event to the second. Therefore, event A cannot have any influence on (or cause) event B, and the principle of causality is not violated. Clearly, the two events called “news reaching Alpha” and “news reaching Beta” are too far apart in distance to be connected by a single light pulse. It takes two light pulses to reach the two events, so it is OK that they can be reordered in time by different observers. One of these two events can never cause or influence the other. 1.2. Time dilation Let’s do another gedanken experiment. This time we put a simple (in concept, at least) clock on the space ship with Wolfie and Hildie. The clock sends a short laser pulse up to a mirror, and when it strikes the mirror and returns the clock ticks once and sends out the next pulse. If the distance to the mirror is L , the round-trip distance traveled by the laser pulse is dL= 2 . If c is the (universal) velocity of light, the clock ticks once in the time Δ=tdc/2/ = Lc. But what do Buffy and Bubba, standing on the moon, think of this? Figure 2 As they see it, the light makes a triangular trip up and down as the laser and the mirror move to the right at the velocity v . The total distance the light travels in one tick is found from Pythagoras' theorem: dLvt'2222= ()2 +Δ ' (1.1) But light travels at the velocity c , so the time for the clock to tick once is Δ=tdc''/. The moving clock goes too slow (that is, it is observed by Buffy and Bubba to take too long to tick) by the factor Δt ' = γ (1.2) Δt where 3 1 γ = (1.3) 1− β 2 β = vc/ (1.4) are the relativistic parameters. But this isn’t just a case of a clock going too slow. The clock is just fine. In fact, everything on the moving space ship is going too slow. Wolfie and Hildie’s hearts beat too slowly, and they are aging too slowly, at least according to Buffy and Bubba. Wolfie and Hildie don’t see anything wrong. There is no experiment they can do to detect their motion, after all. Should Bubba and Buffy be jealous that Wolfie and Hildie are getting old slower? Not at all; Wolfie and Hilda are not enjoying the extra time. Their thoughts, their days, everything is going slower for them. They don’t experience any extra time. In fact, when you think of it, Wolfie and Hildie see a clock belonging to Buffy and Bubba going too slow compared with their clock. After all, they see themselves as stationary and Buffy and Bubba moving past them on a (very large) space ship. So they see Buffy and Bubba getting old slower than they are. Each one sees the other’s clock as moving slower than their own! This is known as time dilation; time on a moving space ship is observed to be stretched out. Once again, this is not a problem caused by bad clocks.
Load more

Recommended publications
  • Relativity with a Preferred Frame. Astrophysical and Cosmological Implications Monday, 21 August 2017 15:30 (30 Minutes)
    6th International Conference on New Frontiers in Physics (ICNFP2017) Contribution ID: 1095 Type: Talk Relativity with a preferred frame. Astrophysical and cosmological implications Monday, 21 August 2017 15:30 (30 minutes) The present analysis is motivated by the fact that, although the local Lorentz invariance is one of thecorner- stones of modern physics, cosmologically a preferred system of reference does exist. Modern cosmological models are based on the assumption that there exists a typical (privileged) Lorentz frame, in which the universe appear isotropic to “typical” freely falling observers. The discovery of the cosmic microwave background provided a stronger support to that assumption (it is tacitly assumed that the privileged frame, in which the universe appears isotropic, coincides with the CMB frame). The view, that there exists a preferred frame of reference, seems to unambiguously lead to the abolishmentof the basic principles of the special relativity theory: the principle of relativity and the principle of universality of the speed of light. Correspondingly, the modern versions of experimental tests of special relativity and the “test theories” of special relativity reject those principles and presume that a preferred inertial reference frame, identified with the CMB frame, is the only frame in which the two-way speed of light (the average speed from source to observer and back) is isotropic while it is anisotropic in relatively moving frames. In the present study, the existence of a preferred frame is incorporated into the framework of the special relativity, based on the relativity principle and universality of the (two-way) speed of light, at the expense of the freedom in assigning the one-way speeds of light that exists in special relativity.
    [Show full text]
  • Frames of Reference
    Galilean Relativity 1 m/s 3 m/s Q. What is the women velocity? A. With respect to whom? Frames of Reference: A frame of reference is a set of coordinates (for example x, y & z axes) with respect to whom any physical quantity can be determined. Inertial Frames of Reference: - The inertia of a body is the resistance of changing its state of motion. - Uniformly moving reference frames (e.g. those considered at 'rest' or moving with constant velocity in a straight line) are called inertial reference frames. - Special relativity deals only with physics viewed from inertial reference frames. - If we can neglect the effect of the earth’s rotations, a frame of reference fixed in the earth is an inertial reference frame. Galilean Coordinate Transformations: For simplicity: - Let coordinates in both references equal at (t = 0 ). - Use Cartesian coordinate systems. t1 = t2 = 0 t1 = t2 At ( t1 = t2 ) Galilean Coordinate Transformations are: x2= x 1 − vt 1 x1= x 2+ vt 2 or y2= y 1 y1= y 2 z2= z 1 z1= z 2 Recall v is constant, differentiation of above equations gives Galilean velocity Transformations: dx dx dx dx 2 =1 − v 1 =2 − v dt 2 dt 1 dt 1 dt 2 dy dy dy dy 2 = 1 1 = 2 dt dt dt dt 2 1 1 2 dz dz dz dz 2 = 1 1 = 2 and dt2 dt 1 dt 1 dt 2 or v x1= v x 2 + v v x2 =v x1 − v and Similarly, Galilean acceleration Transformations: a2= a 1 Physics before Relativity Classical physics was developed between about 1650 and 1900 based on: * Idealized mechanical models that can be subjected to mathematical analysis and tested against observation.
    [Show full text]
  • 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 9Hb: Special Relativity & Thermal/Statistical Physics
    PHYSICS 9HB: SPECIAL RELATIVITY & THERMAL/STATISTICAL PHYSICS Tom Weideman University of California, Davis UCD: Physics 9HB – Special Relativity and Thermal/Statistical Physics This text is disseminated via the Open Education Resource (OER) LibreTexts Project (https://LibreTexts.org) and like the hundreds of other texts available within this powerful platform, it freely available for reading, printing and "consuming." Most, but not all, pages in the library have licenses that may allow individuals to make changes, save, and print this book. Carefully consult the applicable license(s) before pursuing such effects. Instructors can adopt existing LibreTexts texts or Remix them to quickly build course-specific resources to meet the needs of their students. Unlike traditional textbooks, LibreTexts’ web based origins allow powerful integration of advanced features and new technologies to support learning. The LibreTexts mission is to unite students, faculty and scholars in a cooperative effort to develop an easy-to-use online platform for the construction, customization, and dissemination of OER content to reduce the burdens of unreasonable textbook costs to our students and society. The LibreTexts project is a multi-institutional collaborative venture to develop the next generation of open-access texts to improve postsecondary education at all levels of higher learning by developing an Open Access Resource environment. The project currently consists of 13 independently operating and interconnected libraries that are constantly being optimized by students, faculty, and outside experts to supplant conventional paper-based books. These free textbook alternatives are organized within a central environment that is both vertically (from advance to basic level) and horizontally (across different fields) integrated.
    [Show full text]
  • Two-Dimensional Rotational Kinematics Rigid Bodies
    Rigid Bodies A rigid body is an extended object in which the Two-Dimensional Rotational distance between any two points in the object is Kinematics constant in time. Springs or human bodies are non-rigid bodies. 8.01 W10D1 Rotation and Translation Recall: Translational Motion of of Rigid Body the Center of Mass Demonstration: Motion of a thrown baton • Total momentum of system of particles sys total pV= m cm • External force and acceleration of center of mass Translational motion: external force of gravity acts on center of mass sys totaldp totaldVcm total FAext==mm = cm Rotational Motion: object rotates about center of dt dt mass 1 Main Idea: Rotation of Rigid Two-Dimensional Rotation Body Torque produces angular acceleration about center of • Fixed axis rotation: mass Disc is rotating about axis τ total = I α passing through the cm cm cm center of the disc and is perpendicular to the I plane of the disc. cm is the moment of inertial about the center of mass • Plane of motion is fixed: α is the angular acceleration about center of mass cm For straight line motion, bicycle wheel rotates about fixed direction and center of mass is translating Rotational Kinematics Fixed Axis Rotation: Angular for Fixed Axis Rotation Velocity Angle variable θ A point like particle undergoing circular motion at a non-constant speed has SI unit: [rad] dθ ω ≡≡ω kkˆˆ (1)An angular velocity vector Angular velocity dt SI unit: −1 ⎣⎡rad⋅ s ⎦⎤ (2) an angular acceleration vector dθ Vector: ω ≡ Component dt dθ ω ≡ magnitude dt ω >+0, direction kˆ direction ω < 0, direction − kˆ 2 Fixed Axis Rotation: Angular Concept Question: Angular Acceleration Speed 2 ˆˆd θ Object A sits at the outer edge (rim) of a merry-go-round, and Angular acceleration: α ≡≡α kk2 object B sits halfway between the rim and the axis of rotation.
    [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]
  • 8. Special Relativity
    8. Special Relativity Although Newtonian mechanics gives an excellent description of Nature, it is not uni- versally valid. When we reach extreme conditions — the very small, the very heavy or the very fast — the Newtonian Universe that we’re used to needs replacing. You could say that Newtonian mechanics encapsulates our common sense view of the world. One of the major themes of twentieth century physics is that when you look away from our everyday world, common sense is not much use. One such extreme is when particles travel very fast. The theory that replaces New- tonian mechanics is due to Einstein. It is called special relativity. The effects of special relativity become apparent only when the speeds of particles become comparable to the speed of light in the vacuum. Universally denoted as c, the speed of light is c = 299792458 ms−1 This value of c is exact. In fact, it would be more precise to say that this is the definition of what we mean by a meter: it is the distance travelled by light in 1/299792458 seconds. For the purposes of this course, we’ll be quite happy with the approximation c 3 108 ms−1. ≈ × The first thing to say is that the speed of light is fast. Really fast. The speed of sound is around 300 ms−1; escape velocity from the Earth is around 104 ms−1; the orbital speed of our solar system in the Milky Way galaxy is around 105 ms−1. As we shall soon see, nothing travels faster than c.
    [Show full text]
  • The Experimental Verdict on Spacetime from Gravity Probe B
    The Experimental Verdict on Spacetime from Gravity Probe B James Overduin Abstract Concepts of space and time have been closely connected with matter since the time of the ancient Greeks. The history of these ideas is briefly reviewed, focusing on the debate between “absolute” and “relational” views of space and time and their influence on Einstein’s theory of general relativity, as formulated in the language of four-dimensional spacetime by Minkowski in 1908. After a brief detour through Minkowski’s modern-day legacy in higher dimensions, an overview is given of the current experimental status of general relativity. Gravity Probe B is the first test of this theory to focus on spin, and the first to produce direct and unambiguous detections of the geodetic effect (warped spacetime tugs on a spin- ning gyroscope) and the frame-dragging effect (the spinning earth pulls spacetime around with it). These effects have important implications for astrophysics, cosmol- ogy and the origin of inertia. Philosophically, they might also be viewed as tests of the propositions that spacetime acts on matter (geodetic effect) and that matter acts back on spacetime (frame-dragging effect). 1 Space and Time Before Minkowski The Stoic philosopher Zeno of Elea, author of Zeno’s paradoxes (c. 490-430 BCE), is said to have held that space and time were unreal since they could neither act nor be acted upon by matter [1]. This is perhaps the earliest version of the relational view of space and time, a view whose philosophical fortunes have waxed and waned with the centuries, but which has exercised enormous influence on physics.
    [Show full text]
  • APPARENT SIMULTANEITY Hanoch Ben-Yami
    APPARENT SIMULTANEITY Hanoch Ben-Yami ABSTRACT I develop Special Relativity with backward-light-cone simultaneity, which I call, for reasons made clear in the paper, ‘Apparent Simultaneity’. In the first section I show some advantages of this approach. I then develop the kinematics in the second section. In the third section I apply the approach to the Twins Paradox: I show how it removes the paradox, and I explain why the paradox was a result of an artificial symmetry introduced to the description of the process by Einstein’s simultaneity definition. In the fourth section I discuss some aspects of dynamics. I conclude, in a fifth section, with a discussion of the nature of light, according to which transmission of light energy is a form of action at a distance. 1 Considerations Supporting Backward-Light-Cone Simultaneity ..........................1 1.1 Temporal order...............................................................................................2 1.2 The meaning of coordinates...........................................................................3 1.3 Dependence of simultaneity on location and relative motion........................4 1.4 Appearance as Reality....................................................................................5 1.5 The Time Lag Argument ...............................................................................6 1.6 The speed of light as the greatest possible speed...........................................8 1.7 More on the Apparent Simultaneity approach ...............................................9
    [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]
  • Einstein's Boxes
    Einstein’s Boxes Travis Norsen∗ Marlboro College, Marlboro, Vermont 05344 (Dated: February 1, 2008) At the 1927 Solvay conference, Albert Einstein presented a thought experiment intended to demon- strate the incompleteness of the quantum mechanical description of reality. In the following years, the experiment was modified by Einstein, de Broglie, and several other commentators into a simple scenario involving the splitting in half of the wave function of a single particle in a box. This paper collects together several formulations of this thought experiment from the literature, analyzes and assesses it from the point of view of the Einstein-Bohr debates, the EPR dilemma, and Bell’s the- orem, and argues for “Einstein’s Boxes” taking its rightful place alongside similar but historically better known quantum mechanical thought experiments such as EPR and Schr¨odinger’s Cat. I. INTRODUCTION to Copenhagen such as Bohm’s non-local hidden variable theory. Because of its remarkable simplicity, the Einstein Boxes thought experiment also is well-suited as an intro- It is well known that several of quantum theory’s duction to these topics for students and other interested founders were dissatisfied with the theory as interpreted non-experts. by Niels Bohr and other members of the Copenhagen school. Before about 1928, for example, Louis de Broglie The paper is organized as follows. In Sec. II we intro- duce Einstein’s Boxes by quoting a detailed description advocated what is now called a hidden variable theory: a pilot-wave version of quantum mechanics in which parti- due to de Broglie. We compare it to the EPR argument and discuss how it fares in eluding Bohr’s rebuttal of cles follow continuous trajectories, guided by a quantum wave.1 David Bohm’s2 rediscovery and completion of the EPR.
    [Show full text]