Understanding the Relativistic Effects of Special Relativity

Introduction The following presentation is a thought experiment designed to provide an understanding of the relativistic assumption that the speed of light is a constant and an understanding of the resulting three basic effects of Special Relativity. When we talk about fast speeds we mean near the speed of light. These are speeds that we are not accustomed to experiencing. It also provides an understanding of how the effects follow from the assumption. However, the many derivatives of the three relativistic effects, such as energy is mass times the speed of light squared, are beyond the scope of our introductory presentation. Theory by Dr. Michael Steib PowerPoint by Kenan Doyle Branam

Relativistic Assumption Special Relativity assumes that the speed of a light beam is the same with respect to us as with a frame of reference speeding past us. (For the speed of light there is no addition of velocities.) Theory by Dr. Michael Steib PowerPoint by Kenan Doyle Branam

Constancy of the Speed of Light We will see that this constancy of the speed of light implies that we need to include the three basic relativistic effects to assure the visuals we provide represents reality. We also tacitly assume the intuitive Principle of Relativity which states that within a uniformly moving frame of reference, the frame of reference can be considered as standing still. In other words, within a frame of reference in uniform motion, the laws of physics hold the same as if the frame of reference were standing still. Theory by Dr. Michael Steib PowerPoint by Kenan Doyle Branam

Three Relativistic Effects These three effects are at the very core of how space and time exist in our universe and force us to relate one moment of our time with several different moments of time in any frame of reference speeding past us. They also challenge our intuition. • The Three Relativistic Effects: • Shrinkage of Distance • Change in Synchronization • Time Slowdown • The effects are from our point of view as we see a frame of reference speeding past us near the speed of light. They are “with respect to us” as the observer. (Continued) Theory by Dr. Michael Steib PowerPoint by Kenan Doyle Branam

If an object is speeding with uniform velocity past us, we will experience it’s dimension in direction of it’s motion as shorter than if it were stationary with us. Effects 1 – Shrinkage of Distance However, this change in length happens only in the direction in which the object is moving. Theory by Dr. Michael Steib PowerPoint by Kenan Doyle Branam

The time at the front of a speeding frame of reference is behind the time at the rear of the frame of reference (as seen by us at each one moment in our own time). Effects 2 – Change in Synchronization If two events occur simultaneously in their frame of reference and they are uniformly speeding past us, one ahead of the other in space and in the direction of their uniform motion, then we will experience it as being behind the other in time. From our perspective, it is ahead in space but behind in time. Theory by Dr. Michael Steib PowerPoint by Kenan Doyle Branam

We will experience the rate of a clock moving past us with uniform velocity as less than the rate of a clock that is stationary with us. Effects 1 – Time Slowdown Theory by Dr. Michael Steib PowerPoint by Kenan Doyle Branam

The Experiment The experiment is based on the standard Michelson Morely idea of having two light beams traveling perpendicular to each other starting at the same point and reflecting back to return to this same common point. • Our thought experiment happens on a platform moving past us at a uniform speed near the speed of light. One beam travels perpendicular to the motion of this platform and one travels the direction of platform’s motion. • Beam 1(red) goes from E to F and back. • Beam 2 (green) goes from E to G and back. • The beams leave E at the same time and return to E at the same time with respect to the platform. Theory by Dr. Michael Steib PowerPoint by Kenan Doyle Branam

Speed of Light • In this view, the platform is depicted as moving from left to right and the beam paths have changed shape accordingly. Also, the platform width in the direction of this motion has shrunk. • For the experiment to make sense from our perspective, the two beam’s trajectories must have certain properties. The beams leave E at the same time and return to E at the same time. Theory by Dr. Michael Steib PowerPoint by Kenan Doyle Branam

The Two Observers • This illustration will show the light beam paths on the left, as seen by us, and on the right, as seen by the observer on the platform. • The circles represent clocks which will show the progression time through the experiment. The clock on the left displays our time. The clocks on the right displays the platform observer’s time. • The rectangle, on the left, and the square, on the right, depict the same platform as experienced by us and by the observer on the platform. • It is important that the experiment makes sense to both observers. Theory by Dr. Michael Steib PowerPoint by Kenan Doyle Branam

Change in Synchronization • The relativistic effect, Change of Synchronization, shows why and how the experience of the observer on the platform is represented across an amount of platform time rather than at one single platform moment. We picture the experience of the observer on the platform at one single time in our time (not a single moment across the platform) as we see the platform speed by. • This explanation shows why the representation of the experience of the observer on the platform cannot be both "at one single moment" by our time and "at one single moment" by platform time. • This is a prime example of how Special Relativity encourages us to think differently about space and time and to use phrases like "space-time continuum.“ These "slices" of platform time each correspond to the one moment in our time and are labeled t1, t2, t3, and t4. • This explanation will help us understand seeing the different clocks related to the different platform times. • The next 14 views show the experiment as it proceeds. Theory by Dr. Michael Steib PowerPoint by Kenan Doyle Branam

View 1 • The red and green dots represent the beginning of the light beam paths. • For each picture, what is depicted on each side is determined by the position that Beam 1 (red) has achieved in its progression. In this way, the pictures show each perspective with clocks that are to coincide with the particular position of Beam 1 (red). • The relativistic Effect, Change of Synchronization, makes it too complicated to have the pictures directly show the two perspectives "at the same time" rather than having the progression of Beam 1 be the common feature between the two sides of the picture. Theory by Dr. Michael Steib PowerPoint by Kenan Doyle Branam

View 2 • Reminder: The observer on the platform experiences several "slices" of time on the platform that correspond to the one single time that we are at. • In the visual on the right, the "slices" across time are labeled t1, t2, t3, and t4. These all correspond to one single moment of our time. Theory by Dr. Michael Steib PowerPoint by Kenan Doyle Branam

View 3 Theory by Dr. Michael Steib PowerPoint by Kenan Doyle Branam

Half Way – Effects – Shrinkage of Distance Beam 1 (red) has reached F, half of the distance of the round trips in half the amount of the trips' time. • The actual distance traveled by Beam 1 and by Beam 2 with respect to us, up till now, is the same. They are traveling the same speed of light in the same amount of time, half the trip time. • This picture shows that the relativistic effect of shrinking the distance from E to G is logically needed here for Beam 2 to have enough headway to be a bit more than half way (Half the trip time is used up!) to G. This is needed in order for Beam 2 to meet Beam 1 back at E exactly using up the second half of the trip time. That is exactly when Beam 1 (red) will arrive back at E. (Relativistic Effect 1, shrinkage of Distance) • Note that if the shrinkage were enough to get Beam 2 "all the way" to G, then Beam 2 would get back to E before Beam 1. For the experiment to make sense, the shrinkage needs to be just right to get the two beams back to E at the same time using exactly the second half of the trip time. Theory by Dr. Michael Steib PowerPoint by Kenan Doyle Branam

Half Way - Relativistic Effects • Change in Synchronization • With respect to the observer on the platform, Beam 1 reaches F (event at F) at the same platform time as when Beam 2 reaches G (event at G). In this way, the platform observer experiences these events at F and at G synchronized, not having the event at G behind the event at F, as we experience them, unsynchronized. Theory by Dr. Michael Steib PowerPoint by Kenan Doyle Branam

View 13 - Beam 2 Reaches G • Now we experience the clock at G on the platform as saying the same time when Beam 2 reaches G as the clock at F on the platform said when Beam 1 reached F, a while back in our time. This is in line with the two events being simultaneous with respect to the platform time. • (relativistic effect 2, Change in Synchronization) Theory by Dr. Michael Steib PowerPoint by Kenan Doyle Branam

View 14, End • Both beams are back at E. • We logically need the slow down of platform time so that less time has passed with respect to the platform, just the right amount of time for the round trips (with their shorter distance) to be made with respect to the platform. • (relativistic effect 3, Time Slowdown) • Relativistic Effects are beyond our intuitive • The three relativistic effects are hard to accept for us. However, we saw that they allowed the experiment to happen for both observers, us and the observer on the platform, not an easy task as we honor the constancy of the speed of light. Theory by Dr. Michael Steib PowerPoint by Kenan Doyle Branam

Confidence Builders • Looking into the matter further would reveal ways to compliment and build our confidence in what we saw, Special Relativity and its three basic relativistic effects in action. • The math works out. • Empirical evidence supports it. • There is a four dimensional coordinate axis that yields the relativistic effects. • Special Relativity is not the only place where our intuition is challenged . • Also see several supporting web links. Theory by Dr. Michael Steib PowerPoint by Kenan Doyle Branam

The Math • The math works out just right. When all three basic relativistic effects are considered and the quantities are put into equations, then it turns out that each of two frames of reference with fast motion between them can consider the other to have the relativistic effects without contradictions. This supports the Principle of Relativity. • It is a surprising and strong support that there are no mathematical contradictions. Theory by Dr. Michael Steib PowerPoint by Kenan Doyle Branam

Empirical Evidence • When sophisticated equipment is used in physical experiments and measurements, results support Special Relativity. Both the constancy of the speed of light and the relativistic effects are detected as well as derivatives related to matter, mass and energy. In other words, empirical evidence supports Special Relativity and all of its ramifications. • For instance, measurements show that no matter how fast a star is moving away or toward an astronomer measuring the speed of its light beam, the astronomer always obtains a value of exactly 299,792,458 meters per second for its speed. Even if the star is moving near the speed of light itself! The strangeness of this result does not end here, for this single fact, when taken to its logical consequences, implies yet another strange set of outcomes; the color of light from a star going away from us gets redder; going toward us it gets bluer! • The clock of a passerby runs slower than our own. The passerby's meter stick is shorter than ours. His mass increases the faster he goes by us! Even the more well-known result, the icon of relativity, that the energy contained in an object with mass m is equal to its mass times the speed of light squared. An enormous amount of energy. Relativity is all about one weird result, the constancy of the speed of light, leading toward these others. Theory by Dr. Michael Steib PowerPoint by Kenan Doyle Branam

Coordinate System • A coordinate axis can be set up so that the effects of a rotation of axis on the projections to the coordinate axis is a meaningful representation of Special Relativity. This can be set up to parallel the relativistic effects related to constant motion. Here the projections to the coordinates represent the distances and amounts of time between events. The events are represented as points in the coordinate system. • The results from this coordinate system representation with rotations of axis representing relativistic effects and the results from the logic that derives the relativistic effects match up exactly. This helps to visually show in a convenient four dimensional geometry (three for space and one for time) how space and time are interconnected. Theory by Dr. Michael Steib PowerPoint by Kenan Doyle Branam

Other Challenges to Intuition • Special Relativity is not alone in showing us that our intuition fails us if we venture out of our limited realm of the universe. Quantum Mechanics also does this in the area of very small particles rather than the very fast speeds of Special Relativity's domain. • While Special Relativity dispels our idea that distances, synchronization of events and amounts of time are definite absolutes, Quantum Mechanics dispels our idea that things have a definite position and definite velocity. This encourages us to question our limited intuition more and question the counterintuitive results of Special Relativity less. • Next: Web References Theory by Dr. Michael Steib PowerPoint by Kenan Doyle Branam

Credits Dr. Michael Lee Steib, PhD. is responsible for the concept and theory of this presentation. Kenan Doyle Branam created the PowerPoint and graphic presentation. The presentation is an entry the Pirelli Relativity Challenge, September 15, 2005. A PowerPoint and PowerPoint converted to an HTML Accessibility site are available for download at : http://www.branam.com/makingsense/emc2/ Pencil drawing byKenan Doyle Branam (1969) Theory by Dr. Michael Steib PowerPoint by Kenan Doyle Branam

Web References 1, 2 • http://www2.slac.stanford.edu/vvc/theory/relativity.html • http://casa.colorado.edu/~ajsh/sr/sr.shtml • http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Special_relativity.html • http://science.howstuffworks.com/relativity.html • http://en.wikipedia.org/wiki/Special_relativity/ • http://theory.uwinnipeg.ca/mod_tech/node133.html • http://www.geocities.com/zcphysicsms/sr.htm • http://www.bartleby.com/173/ • http://members.tripod.com/conduit9SR/ • http://astro.physics.sc.edu/selfpacedunits/Unit56.html • http://www.phys.vt.edu/~takeuchi/relativity/notes/ • http://www.motionmountain.net/C-2-CLSC.pdf • http://math.ucr.edu/home/baez/physics/Relativity/SR/velocity.html • http://www.physics.mq.edu.au/~jcresser/Phys378/LectureNotes/SpecialRelativityNotes.pdf • http://atschool.eduweb.co.uk/rmext04/92andwed/pf_quant.html • http://web.wt.net/~cbenton/relativity.htm • http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html • http://scienceworld.wolfram.com/physics/SpecialRelativity.html • http://musr.physics.ubc.ca/~jess/hr/skept/STR/STR.html Theory by Dr. Michael Steib PowerPoint by Kenan Doyle Branam

Web References 1, 2 • http://www.einsteinyear.org/facts/special_relativity/fact_view • http://www.rfjvanlinden171.freeler.nl/ • http://www.tat.physik.uni-tuebingen.de/~weiskopf/sr/ • http://spoirier.lautre.net/en/relativity.htm • http://gregegan.customer.netspace.net.au/FOUNDATIONS/01/found01.html • http://www.ncsu.edu/felder-public/kenny/papers/relativity.html • http://www.btinternet.com/~j.doyle/SR/sr2.htm • http://www.btinternet.com/~j.doyle/SR/sr1.htm • http://www.upscale.utoronto.ca/GeneralInterest/Harrison/SpecRel/SpecRel.html • http://www.glenbrook.k12.il.us/gbssci/phys/Class/relativity/reltoc.html • http://koshun.cool.ne.jp/physics/b/b_es1.pdf • http://www.geocities.com/autotheist/Physics/sr.htm • http://www.mtnmath.com/whatth/node50.html • http://www.adamauton.com/warp/ • http://www.ux1.eiu.edu/~cfadd/1160/Ch27SpRl/ApLrntz.html • http://casa.colorado.edu/~ajsh/sr/postulate.html • http://instruct1.cit.cornell.edu/courses/astro101/lec21.htm • http://nobelprize.org/physics/educational/relativity/ • http://sol.sci.uop.edu/~jfalward/relativity/relativity.html • http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/conrel.html Theory by Dr. Michael Steib PowerPoint by Kenan Doyle Branam

Understanding the Relativistic Effects of Special Relativity

Understanding the Relativistic Effects of Special Relativity

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Introduction to introduction to introduction to … Optimization

INTRODUCTION/ INTRODUCTION

Introduction

INTRODUCTION

Introduction

Introduction