Spacetime physics taylor wheeler pdf

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Spacetime-Physics-2nd-Ed-Taylor-Wheelerpdf - Ebook download as PDF File .pdf) or read book online. Spacetime Physics by Taylor and Wheeler - Download as PDF File .pdf), Text File .txt) or read online. First Edition First Twenty Pages. American Journal of Physics 61, (); · Edwin F. Taylor, John A. Wheeler, and Jeffrey M. Bowen. more PDF · CHORUS.

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Spacetime Physics Introduction To Special Relativity [ Taylor Wheeler] PDF. The BookReader requires JavaScript to be enabled. Please check that your browser. Full text of "Spacetime Physics Introduction To Special Relativity [ Taylor Wheeler ] PDF". See other formats. fmmmm VM W THE AUTHORS John Archibald. Full text available for download (63MB, pdf format) Citation: Taylor, Edwin F., and John Archibald Wheeler. Spacetime Physics: Introduction to Special Relativity.

In the following, assume that the light just grazes the surface of Sun in passing. Thus the spaceship serves as a reference frame relative to which the passenger does not experience any acceleration. The ball has the same morion as ic did before. Neither, Einstein tells us. Think of constructing a frame by assembling meter sticks into a cubical latticework similar to the jungle gym seen on playgrounds Figure

Chapter 1: The exercises for chapter 1 take pages Chapter 2: This first edition spans a total of pages give or take the covers and preface. This edition seems to lack all the subjectively annoying features that seem to plague according to some reviewer on Amazon the second edition. There are no black crows as far as I can tell. All in all I am delighted to have it in my library.

So, again thanks for the guidance. QuantumCurt Education Advisor. I'm doing a bit of self-studying out of this book over my winter break. Could anyone point me toward a solutions manual for it? All of the odd numbered exercises have answers in the back, but I'd like to have the even answers as well just to verify that I'm working the problems correctly.

I've done a fair amount of searching and I've come up empty. Could anyone point me in the right direction? The 1st ed has only pages while the 2nd ed has ! Apr 18, I see now that SredniVashtar posted some comments earlier about the differences between the two editions.

I have to admit though, after seeing the general preference on these forums for the 1st edition, I was surprised to discover that the 2nd edition has so much additional content putting aside that the 1st ed has solutions. Want to reply to this thread? Taylor and John Archibald Wheeler" You must log in or register to reply here. Related Threads for: Spacetime Physics by Edwin F. Taylor and John Archibald Wheeler P.

Spacetime Physics by Taylor and Wheeler

Spacetime Physics by J. Wheeler and E. Plastic Photon. Greg Bernhardt. Poll Fundamentals of Aerodynamics by John D. But the enclosure in which we ride — falling near Earth or plunging through Earth — cannot be too large or fall for too long a rime without some unavoidable relative changes in motion being detected between particles in the enclosure. Because widely separated particles within a large enclosed space are differently affected by the nonuniform gravitational field of Earth, to use the Newtonian way of speaking.

For example, two particles released side by side are both attracted toward the center of Earth, so they move closer together as measured inside a falling long narrow horizontal railway coach Figure , center. This has nothing to do with "gravitational attrac- tion" between the particles, which is entirely negligible. As another example, think of two particles released far apart vertically but direcdy above one another in a long narrow vertical falling railway coach Figure , right.

This rime their gravitational accelerations toward Earth are in the same direction. Three vehicles in free fall near Earth t small space capsule f Einstein's old-fa- shioned railway coach in free fall in a horizontal orientation t and another railway coach in vertical orientation. However, the particle nearer Earth is more strongly attracted to Earth and slowly leaves the other behind: Even a small room fails to qualify as free-float when we sample it over a long enough time.

In the 42 minutes it takes our small room to fall through the tunnel from North Pole to South Pole, we notice relative motion between test particles released initially from rest at opposite sides of the room. Now, we want the laws of motion to look simple in our floating room. Therefore we want to eliminate all relative accelerations produced by external causes. We eliminate the problem by choosing a room that is sufficiently small.

Smaller room? Smaller relative accelerations of objects at different points in the room! Let someone have instruments for detection of relative accelerations with any given degree of sensitivity. No matter how fine that sensitivity, the room can always be made so small that these perturbing relative accelerations are too small to be detectable.

Within these limits of sensitivity our room is a free-float frame. Here, however, we often use the name free-float frame, which we find more descriptive. These are all names for the same thing. Wonder of wonders! This test can be carried out entirely within the free-float frame. The observer need not look out of the room or refer to any measurements made external to the room.

Before we certify a reference frame to be inertial, we require observers in that frame to demonstrate that every free particle maintains its initial state of motion or rest.

Free-float frame is local Free-float inertial frame formally defined When is the room, the spaceship, or any other vehicle small enough to he called a local free-float frame? Or when is the relative acceleration of two free particles placed at opposite ends of the vehicle too slight to he detected? For example, drop the old-fashioned meter-long railway coach in a horizontal orientation from rest at a height of 3 1 5 meters onto the surface of Earth Figure , center.


Time from release to impact equals 8 seconds, or million meters of light-travel time. At the same instant you drop the coach, release tiny ball bearings from rest — and in midair — at opposite ends of the coach.

In a free-float frame near Earth, particles separated vertically in- crease their separation with time; particles separated horizontally decrease their separation with time Figure More generally, a thin spattering of free-float test mosses, spherical in pattern, gradually becomes egg-shaped, with the long axis vertical.

Test masses nearer Earth, more strongly attracted than the average, move downward to form the lower bulge. Similarly, test masses farther from Earth, less strongfy attracted than the average, lag be- hind to form the upper bulge. By like action Moon, acting on the waters of Earth — floating free in space — would draw them out into an egg-shaped pattern if there were water everywhere, water of uniform depth.

There isn't. The narrow Straits of Gi- braltar almost cut off the Mediterranean from the open ocean, and almost kill all tides in it. Therefore it is no wonder that Galileo Galilei, although a great pioneer in the study of gravity, did not take the tides as seriously as the more widely traveled Johannes Kepler, an expert on the motion of Moon and the planets. Of Kepler, Galileo even said, "More than other people he was a person of independent genius.

But mariners in northern waters face destruction unless they track the tides. For good reason they remember that Moon reaches its summit overhead an average Their own bitter experience tells them that, of the two high tides a day — two because there are two protections on an egg — each also comes about 50 minutes later than it did the day before. Geography makes Mediterranean tides minuscule. Geography also makes tides in the Gulf of Maine and Bay of Fundy the highest in the world.

How come? Build a big power- producing dam in the upper reaches of the Bay of Fundy? Shorten the length of the bathtub? Decrease the slosh time from 13 hours to exact resonance with Moon? Then get one-foot higher tides along the Maine coast! Want to see the highest tides in the Bay of Fundy?

Then choose your visit according to these rules: At nearby Leaf Basin, a unique value of 16,6 meters 54,5 feet was recorded in Why do they move toward one another?

Not because of the gravitational attraction between the bail bearings; this is far too minute to bring about any '"coming together. As another example, drop the same antique railway coach from rest in a vertical orientation, with the lower end of the coach initially meters from the surface of Earth Figure , right. Again release tiny ball bearings from rest at opposite ends of the coach.

In this case, during the time of fall, the ball bearings move apart by a distance of 2 millimeters because of the greater gravitational acceleration of the one nearer Earth, as Newton would pur it. This b twice the change that occurs for horizontal separation.

In either of these examples let the measuring equipment in use in the coach be just short of the sensitivity required to detect thb relative motion of the ball bearings. Then, with a limited time of observation of 8 seconds, the railway coach — or, to use the earlier example, the freely falling room — serves as a free-float frame.

When the sensitivity of measuring equipment is increased, the railway coach may no longer serve as a local free-float frame unless we make additional changes. Either shorten the meter domain in which observations are made, or decrease the time given to the observations. Or better, cut down some appropriate combination of space and time dimensions of the region under observation.

Or as a final alternative, shoot the whole apparatus by rocket up to a region of space where one cannot detea locally the "differential gravitational acceleration" between one side of the coach and another — to use Newton's way of speaking. In another way of speaking, relative accelerations of particles in different parts of the coach must be too small to perceive.

Only when these relative accelerations are too small to detea do we have a reference frame with respea to which laws of motion are simple.

That's why ""local" is a tricky word! Hold on! You just finished saying that the idea of local gravity is unnecessary. Yet here you use the " differential gravitational acceleration" to account for relative accelera- tions of test particles and ocean tides near Earth , Is local gravity necessary or not?

Near Earth, two explanations of projectile paths or ocean flow give essentially the same numerical results, Newton says there is a force of gravity, to be treared like any other force in analyzing motion. Einstein says gravity differs from all other forces: Get rid of gravity Locally by climbing into a free-float frame. Near the surface of Earth both explanations accurately predia relative accelerations of falling panicles toward or away from one another and morions of the tides.

In thb chaprer we use the more familiar Newtonian analysis to predict relative accelerations. Thb justifies Einstein's insbtence on getting rid of gravity locally using free-floar frames.

All that remains of gravity b the relative accelerations of nearby particles — tidal accelerations, 2. The long narrow railway coach in Figure probes spacetime for a limited stretch of time and in one or another single direction in space.

It can be oriented north -south or east -west or 2. Whatever its orientation, relative acceleration of the tiny ball bearings released at the two ends can be measured. For all three directions — and for all intermediate directions — let it be found by calculation that the relative drift of two test particles equals half the minimum detectable amount or less. Then throughout a cube of space 20 meters on an edge and for a lapse of time of 8 seconds million meters of light-travel time , test particles moving every which way depart from straight-line motion by undetectable amounts.

Why pay so much attention to the small relative accelerations described above? Why not from the beginning consider as reference frames only spaceships very far from Earth, far from our Sun, and far from any other gravitating body?

At these distances we need not worry at all about any relative acceleration due to a nonuniform gravitational field, and a free-float frame can be huge without worrying about relative accelerations of particles at the extremities of the frame.

Why not study special relativity in these remote regions of space? Most of our experiments are carried out near Earth and almost all in our part of the solar system. Near Earth or Sun we cannot eliminate relative accelerations of test particles due to nonuniformity of gravitational fields. So we need to know how large a region of spacetime our experiment can occupy and still follow the simple laws that apply in free-float frames.

For some experiments local free-float frames are not adequate. For example, a comet sweeps in from remote distances, swings close to Sun, and returns to deep space. Consider only the head of the comet, not its million-kilometer-long tail. Particles traveling near the comet during all those years move closer together or farther apart due to tidal forces from Sun assuming we can neglect effects of the gravitational field of the comet itself.

These relative forces are called tidal, because similar differential forces from Sun and Moon act on the ocean on opposite sides of Earth to cause tides Box 2- 1.

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A frame large enough to include these particles is not free-float. So reduce spatial size until relative motion of encompassed particles is undetectable during that time. The resulting frame is very much smaller than the head of the comet!

You cannot analyze the motion of a comet in a frame smaller than the comet. So instead think of a larger free-float frame that surrounds the comet for a limited time during its orbit, so that the comet passes through a series of such frames. Or think of a whole collection of free-float frames plunging radially toward Sun, through which the comet passes in sequence.

In either case, motion of the comet over a small portion of its trajectory can be analyzed rigorously with respect to one of these local free-float frames using special relativity. However, questions about the entire trajectory cannot be answered using only one free-float frame; for this we require a series of frames. General relativity — the theory of gravitation — tells how to describe and predict orbits that traverse a string of adjacent free-float frames. Only general relativity can describe motion in unlimited regions of spacetime.

Please stop beating around the bush!

Can't you be more specific? Why do these definitions depend on whether or not we are able to perceive the tiny motion of some test particle? My eyesight gets worse. Or I take my glasses off. Surely science is more exact, more objective than that! An astronaut in an orbiting space station releases a pencil that Boats at rest In front of her; do you want to track its position to 1 -millimeter accuracy for 2 hours?

Each case places different demands on the inertial frame from which the observations are made. Specific figures imply specific requirements for inertial frames, requirements that must be verified by test particles.

The astronaut takes off her glasses; then she can determine the position of the pencil with only 3 -millimeter accuracy. Suddenly — yes! It must have so little mass that, within some specified accuracy, its presence does not affect the motion of other nearby particles. In terms of Newtonian mechanics, gravitational attraction of the rest particle for other particles musr be negligible within the accuracy specified.

As an example, consider a particle of mass 1 0 kilograms. At least one of these test particles, initially at rest, would not remain at rest within the falling room. That is, the room would not be a free-float frame according to definition. How sure are we that particles in the same location but of different substances all fall toward Earth with equal acceleration? John Philoponus of Alexandria argued, in A.

It follows that a particle made of any material can be used as a test particle to determine whether a given reference frame is free-float. A frame that is free-float for a test particle of one kind is free-float for test particles of ail kinds. An event is specified not only by a place but also by a time of happening. Some examples of events ate emission of a particle or a flash of light from, say, an explosion , reflection or absorption of a particle or light flash, a collision.

How can we determine the place and time at which an event occurs in a given free- float frame? Think of constructing a frame by assembling meter sticks into a cubical latticework similar to the jungle gym seen on playgrounds Figure At every intersection of this latticework fix a dock. These clocks are identical. They can be constructed in any manner, but their readings are in meters of light-travel time Section 1,4.

How are the clocks to be set? We want them all to read the "same rime" as one another for observers in this frame. When one dock reads midnight That is, we want the docks to be synchronized in this frame. How are the several docks in the lattice to be synchronized? As follows: Pick one dock in the lattice as the standard and call it the reference clack.

Latticework of meter sticks and clocks. At this instant let it send out a flash of light that spreads out as a spherical wave in all directions. Call the flash emission the reference event and the spreading spherical wave the reference flash. When the reference flash gets to a slave clock 5 meters away, we want that clock to read 5 meters of light-travel time. Because it takes light 5 meters of light-travel time to travel the 5 meters of distance from reference clock to slave clock.

So an assistant sets the slave clock to 5 meters of time long before the experiment begins, holds it at 5 meters, and releases it only when the reference flash arrives. The assistant has zero reaction time or the slave clock is set ahead an additional time equal to the reaction time. When assistants at all slave clocks in the lattice follow this prearranged procedure each setting his slave clock to a time in meters equal to his own distance from the reference clock and starting it when the reference light flash arrives , the lattice clocks are said to be synchronized.

This is an awkward way to synchronize lattice clocks with one another. Is there some simpler and more conventional way to carry out this synchronization? There are other possible ways to synchronize clocks. For example, an extra portable clock could be set to the reference clock at the origin and carried around the lattice in order to set the rest of the clocks. However, this procedure involves a moving clock. We saw in Chapter 1 that the time between two events is not necessarily the same as recorded by clocks in relative motion.

The portable clock will not even agree with the reference clock when it is brought back next to it! This idea is explored more fully in Section 4. However, when we use a moving clock traveling at a speed that is a very small fraction of light speed, its reading is only slightly different from that of clocks fixed in the lattice. In this case the second method of synchronization gives a result nearly equal to the first — and standard — method.

Moreover, the error can be made as small as desired by carrying the portable clock around sufficiently slowly. Locate event with latticework Use the latticework of synchronized clocks to determine location and time at which any given event occurs.

The space position of the event is taken to be the location of the clock nearest the event. The location of this clock is measured along three lattice directions from the reference clock: The time of the event is taken to be the time recorded on the same lattice clock nearest the event.

The spacetime location of an event then consists of four numbers, three numbers that specify the space position of the clock nearest the event and one number that specifies the time the event occurs as recorded by that clock.

The clocks, when installed by a foresighted experimenter, will be recording clocks. Each clock is able to detect the occurrence of an event collision, passage of light-flash or particle. Each reads into its memory the nature of the event, the time of the event, and the location of the clock.

The memory of all clocks can then be read and analyzed, perhaps by automatic equipment. Why a latticework built of rods that are 1 meter long? What is special about 1 meter? Why not a lattice separation of meters between recording clocks? Or 1 millimeter? When a clock in the 1 -meter lattice records an event, we will not know whether the event so recorded is 0. The location of the event will be uncertain to some substantial fraction of a meter. The time of the event will also be uncertain with some appreciable fraction of a meter of light- travel time, because it may take that long for a light signal from the event to reach the nearest clock.

However, this accuracy of a meter or less is quite 2. It is extravagantly good for measure- ments on planetary orbits — for a planet it would even be reasonable to increase the lattice spacing from 1 meter to hundreds of meters.

Neither 1 00 meters nor 1 meter is a lattice spacing suitable for studying the tracks of particles in a high-energy accelerator. There a centimeter or a millimeter would be more appropriate. The location and time of an event can be determined to whatever accuracy is desired by constructing a latticework with sufficiently small spacing. Where is this observer? At one place, or all over the place? So it is best to think of the observer as a person who goes around reading out the memories of all recording clocks under his control.

We intentionally limit the observer's report on events to a summary of data collected from clocks. We do not permit the observer to report on widely separated events that he himself views by eye. The reason: It can take a long time for light from a distant event to reach the observer's eye. Even the order in which events are seen by eye may be wrong: We see these two events in the 1 wrong order" compared with observations recorded by our far-flung latticework of recording clocks.

For this reason, we limit the observer to collecting and reporting data from the recording docks. The wise observer pays attention only to clock records. Even so, light speed still places limits on how soon he can analyze events after they occur.

Suppose that events in a given experiment arc widely separated from one another in interstellar space, where a single free-float frame can cover a large region of spacetime. Let remote events be recorded instantly on local docks and transmitted by radio to the observer's central control room. This information transfer cannot take place faster than the speed of light — the same speed at which radio waves travel.

Information on dispersed events is available for analysis at a central location only after light -speed transmission. This information will be full and accurate and in no need of correction — but it will be late.

Thus all analysis of events must take place after — sometimes long after! The same difficulty occurs, in prindple, for a free-float frame of any size. Nature puts an unbreakable speed limit on signals. This limit has profound consequences for decision making and control. A space probe descends onto Triton, a moon of the planet Neptune. This probe must carry equipment to detect its distance from Triton's surface and use this information to regulate rocket thrust on the spot, without help from Earth.

Earth is never less than light-minutes away from Neptune, a round-trip radio-signal time of minutes — more than eight hours. Therefore the probe would crash long before probe- to-surface distance data could be sent to Earth and commands for rocket thrust returned. This rime delay of information transmission does not prevent a detailed retrospective analysis on Earth of the probe's descent onto Triton — -but this analysis cannot take place unril at least minutes Observer defined Observer limited to clock readings Speed limit; c It's the law!

Interstellar Command Center receives word by radio that a meteor has just whizzed past an out- post situated light-seconds distant a fifth of Earth-Sun distance. The radio signal moves with tight speed from outpost to Command Center, covering the light-seconds of distance in seconds of time. During this seconds the meteor also travels toward Command Center. The meteor moves at one quarter light speed, so in seconds it covers one quarter of light-se- conds, or 25 light-seconds of distance.

Center at one quarter light speed. Assume radio signals travel with light speed. How long do Com- mand Center personnel have to take evasive ac- tion? The meteor takes an additional seconds of time to move each additional 25 light-seconds of distance. So it covers the remaining 75 light-se- conds of distance in an additional time of seconds.

In brief, after receiving the radio warning, Command Center personnel have a relaxed seconds — or five minutes — to stroll to their me- teor-proof shelter. Could we gather last-minute information, make a decision, and send back control instructions? Nature rules out micromanagement of the far-away Sample Problem How can the path of the particle be described in terms of numbers? By recording locations of these events along the path.

Distances between locations of successive events and time lapse between them reveal the partide speed — speed being space separation divided by rime taken to traverse this separation. The conventional unit of speed is meters per second. However, when rime is Speed in meters per meter measured in meters of light-travel rime, speed is expressed in meters of distance covered per meter of time. A flash of light moves one meter of distance in one meter of light-travel time: In contrast, a partide loping along at half light speed moves one half meter of distance per meter of time; its speed equals one half in units of meter per meter.

More generally, partide speed in meters per meter is the ratio of its speed to light speed: Some authors use the lowercase Greek letter beta: Let stand for velocity in conventional units such as meters per second and c stand for light speed in the same conventional units. IF records show a that — within some specified accuracy — a test particle moves consecutively past clocks that lie in a straight line, b that test-particle speed calculated from the same records is constant — again, within some specified accuracy — and, c that the same results are true for as many test-particle paths as the most industrious observer cares to trace throughout the given region of space and dme, THEN the lattice constitutes a free-float inertial frame throughout that region of spacetime.

Test for free-float frame Particle speed as a fraction of light speed is certainly an unconventional unit of measure , What advantages does it have that justify the work needed to become familiar with it? The big advantage is that it is a measure of speed independent of units of space and time. Suppose that a particle moves with respect to Earth at half light speed.

Then it travels — with respect to Earth — one half meter of distance in one meter of light travel time. It travels one half light-year of distance in a period of one year. It travels one half light-second of distance in a time of one second, one half light- minute in one minute. Fundamentally, v is unit-free. Let two reference frames be two different lattice works of meter sticks and docks, one moving uniformly relative to the other, and in such a way that one row of clocks in each frame coincides along the direction of relative motion of the two frames Figure Call one of these frames laboratory frame and the other — moving to the right relative to the laboratory frame — rocket frame.

The rocker is unpowered and coasts along with constant velocity relative to the laboratory. Let rocket and laboratory latticeworks be overlapping in the sense that a region of spacetime exists common to both frames.

Test particles move through this common region of spacetime. From motion of these test particles as recorded by his own docks, the laboratory observer verifies that his frame is free-float inertial. From motion of the same test particles as recorded by her own docks, the rocket observer verifies that her frame is also free-float inertial. Now we can describe the morion of any particle with respect to the laboratory frame. The same particles and— if they collide — the same collisions may be mea- sured and described with respect to the free-float rocket frame as well.

A second ago the two taf networks were intermeshtd. Different frames lead to different descriptions pendent of any free-float frames in which they are observed, recorded, and described. Every track that is straight as plotted with respect to one reference frame is straight also with respect to the other frame, because both are free- float frames. However, the direction of this path differs from labora- tory to rocket frame, except in the special case in which the particle moves along the line of relative motion of two frames.

How many different free- float rocket frames can there be in a given region of spacetime? An unlimited number! Any un powered rocket moving through that region in any direction is an acceptable free-float frame from which to make observations. There is nothing unique abou t any of these frames as long as each of them is free-float. All free-float inertial frames are equivalent arenas in which to carry out physics experiment.

The firecracker explodes. Does this even t — the explosion — take place in the rocket frame or in the laboratory frame? A second firecracker , originally at rest in the laboratory frame, explodes , Does this second event occur in the laboratory frame or in the rocket frame? Events are primary, the essential stuff of Nature. Reference frames are secondary, devised by humans for locating and comparing events.

A given event occurs in both frames — and in all possible frames moving in all possible directions and with all possible constant relative speeds through the region of spacetime in which the event occurs. The appararus that " causes" the event may be at rest in one free-float frame; another apparatus that "causes" a second event may be at rest in a second free-float frame in motion relative to the first. No matter. Each event has its own unique existence.

Neither is "owned" by any frame at all. A spark jumps l millimeter from the antenna of Mary 's passing spaceship to a pen in the pocket of John who lounges in the laboratory doorway Section 1,2. The spark jump — in w hich frame does this event occur? It b not the property of Mary, not the property of John— not the property of any other observer in the vicinity, no matter what his or her state of motion. The spark -jump event provides data for every observer.

Drive a steel surveying stake into the ground to mark the comer of a plot of land. Is this a "Daytime stake" or a "Nighttime stake"? It is just a stake, marking a location in space, the arena of surveying. Similarly an event is neither a "laboratory event" nor a "rocket event. Laboratory frame or rocket frame: There is no way to tell! Someone switches the nameplates while we sleep. When we wake up, there is no way to decide which is which. This realization leads to Einstein s Principle of Relativity and proof of the invariance of the interval, as described in Chapter 3.

Where does that frame of reference sit? Where do the east-west, north-south, up-down lines run? We might as well ask where on the flat landscape in the state of Iowa we see the lines that mark the boundaries of the townships. A concrete marker, to be sure, may show itself as a corner marker at a place where a north-south line meets an east-west line. Apart from such on-the-spot evidence, those lines are largely invisible.

Nevertheless, they serve their purpose: They define boundaries, settle lawsuits, and fix taxes. Likewise imaginary for the most part are the clock and rod paraphernalia of the idealized inertial reference frame. Work of the imagination though they are, they provide the conceptual framework for everything that goes on in the world of particles and radiation, of masses and motions, of annihilations and creations, of fissions and fusions in every context where tidal effects of gravity are negligible.


Our ability to define a free-float frame depends on the fact that a test particle made of any material whatsoever experiences the same acceleration in a given gravita- tional field Section 2. How- ever, in such a frame, free test particles typically accelerate toward or away from one another because of the nonuniform field of the gravitating body Section 2.

This limits — in both space and time — the size of a free-float frame, the domain in which the laws of motion are simple. The frame will continue to qualify as free-float and special relativity will continue to apply, provided we reduce the spatial extent, or the time duration of our experiment, or both, until these relative, or tidal, motions of test particles cannot be detected in our circumscribed region of spacetime.

General relativity the theory of gravitation removes this limitation Chapter 9. So there are three central characteristics of a free-float frame. All three characteristics appear in a fuller version of the quotation by Albert Einstein that began this chapter: At that moment there came to me the happiest thought of my life.

That is, if the observer releases any objects, they remain in a state of rest or uniform motion relative to him, respectively, independent of their unique chemical and physical nature. Einstein is referring to the year Italics represent material underlined in the original.

Photocopy of the original provided by Professor Holton. Present translation made with the assistance of Peter von Jagow. Information on Nova Scotia tides in Box Relative acceleration of different materials, Section Roll, R. Krotkov, and R. Clifford Will, Was Einstein Right? Think of the elevator after it leaves the cannon and is moving freely in the gravitational field of Earth.

Neglect air resistance, a While the elevator is still on the way up, the person inside jumps from the "floor" of the elevator. Will the person 1 fall back to the "floor" of the elevator? If so, what? Will your answers to part a be different in this case? Fasten a weight- measuring bathroom scale under your feet and bounce up and down on a trampoline while reading the scale. During what part of each jump will the scale have zero reading?

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Ne- glecting air resistance, what is the longest part of the cycle during which you might consider yourself to be in a free-float frame?

You wish to synchronize your dock with the one at the origin. Describe in detail and with numbers how to proceed. Engelsberg does not approve of our method of synchronizing docks by light flashes Section 2. Is he right? He uses a third clock, identical in construction with the first two, that travels with constant velocity between them.

As his moving clock passes Big Ben, it is set to read the same time as Big Ben. When the moving clock passes Little Ben, that outpost clock is set to read the same time as the traveling clock. Evaluate this lack of synchronism in milliseconds when the traveling clock that Mr. Typically these laboratories are not in free fall! Nevertheless, under many circumstances laboratories fixed to the surface of Earth can satisfy the conditions required to be called free-float frames.

An example: For what length of laboratory time is this particle in transit through the spark chamber? How far will a separate test particle, released from rest, fall in this time? How long will it take the test particle to fall this distance from rest? How far does the fast elementary particle of part a move in that time? Therefore how long can an earthbound spark chamber be and still be considered free-float for this sensitivity of detection?

Schematic diagram of two ball bearings falling onto Earth's surface. Not to scale. Demonstrate that when released from rest relative to Earth the particles move closer to- gether by 1 millimeter as they fall meters, using the following method of similar triangles or some other method.

Each particle falls from rest toward the center of Earth, as indicated by arrows in the figure. Solve the problem using the ratio of sides of similar triangles ahc and a' b' c. These triangles are upside down with respect to each other. However, they are similar be- cause their respective sides are parallel: Sides ac and a' c' are parallel to each other, as are sides be and b' c f and sides ab and a b'. Windows Version tested on Windows Macintosh Version requires Powermac.

The student workbook "Demystifying Quantum Mechanics" contains background and activities for student use of the software above. Files are in Adobe Acrobat format, and require the free Adobe Acrobat reader software. Demystifying Quantum Mechanics Student Workbook. Taylor, All Rights Reserved eftaylor mit. Halfman, M. McVicar, W. Martin, Edwin F. Taylor and Jerrold R.

Zacharias, Occasional Paper No. A light-hearted, avuncular look at difficulties of academic change and tactics for change compiled by educational innovators of the s and s, long before Physics Education Research became a discipline of its own.