jimc@haddock.UUCP (06/01/85)
I am very puzzled over something in Einstein's theory of time dilation, that is, that time passes more slowly for objects in motion then for objects at rest. Here is my understanding of th theory and how Einstein arrived at it. There has to be something wrong with my thinking somewhere, though this understanding is based on the book *The Universe and Dr. Einstein*, by Lincoln Barnett, a book which Einstein himself heartily praised. Einstein's theory about time dilation is based on the assumption that the speed of electromagnetic radiation is constant throughout the Universe, whether or not the object emitting the radiation is in motion. Here is an example which may clarify why Einstein arrived at this assumption: suppose an object that is travelling through space at a rate equal to 75 percent that of light and that it was emitting a light ray in the same direction it was travelling. For that light ray's speed to remain at C, the rate of time passage for the object must decrease proportionally. Yet, I find myself still asking this question: what about a light ray being emitted in the opposite direction? Can't it just as easily be said that time is speeding up for the object under these circumstances? I can't believe Einstein wouldn't have thought of this! Jim Campbell ...!ihnp4!ima!haddock!jimc
gwyn@brl-tgr.ARPA (Doug Gwyn <gwyn>) (06/03/85)
> I am very puzzled over something in Einstein's theory of time > dilation, that is, that time passes more slowly for objects in > motion then for objects at rest. Probably the reason that you are puzzled is that you are not stating the phenomena correctly. The time dilation effect is: The proper time of a (relatively) moving object appears to be advancing slower that that of the (stationary) observer, by an amount sqrt( 1 - (v / c)^2 ) where v is the apparent speed of the moving object and c is the speed of light. The only reason "c" is in the equation is to obtain natural units for space & time coordinates; the time dilation effect is not dependent on any communication by light, although such communication is often used in elementary texts to try to make the effect more intelligible. > I can't believe Einstein wouldn't have thought of this! Don't worry, Einstein knew what he was doing.
brooks@lll-crg.ARPA (Eugene D. Brooks III) (06/04/85)
> Einstein's theory about time dilation is based on the assumption > that the speed of electromagnetic radiation is constant > throughout the Universe, whether or not the object emitting the > radiation is in motion. Here is an example which may clarify why > Einstein arrived at this assumption: suppose an object that is > travelling through space at a rate equal to 75 percent that of > light and that it was emitting a light ray in the same direction > it was travelling. For that light ray's speed to remain at C, > the rate of time passage for the object must decrease > proportionally. This is easily understood using the contraption known as the light pulse clock. The device consists of a light bulb, that flashes in very short pulses, a light detector that causes the bulb to flash when it picks up light and a mirror placed any arbitrary distance from the bulb oriented to reflect light from the bulb to the detector that is sitting very close to the bulb. Each time the bulb flashes the light crosses to the mirror and back, hitting the detector to cause the bulb to flash again. You make the bulb flash once and the think doesn't quit until the battery runs out. The clock can be sitting still, moving parallel to the line connecting the bulb to the mirror, or moving perpendicular to the line connecting the bulb to the mirror. Or anywhere inbetween. If the clock is sitting still it pulses with a period given by the speed of light and the seperation between the mirror and bulb. This is the basic period of the clock. If the clock is moving perpendicular to the line connecting the bulb and the mirror with speed v/c you can easily work out the triangular trajectory that the light travels in the rest frame and the rate at which the clock fires as viewed in the rest frame. Its slower because the light travels farther in the rest frame. If the clock is moving parallel to the line connecting the bulb and the mirror with speed v/c you can again work out the firing rate of the clock in the rest frame. This time you will find that if fires at a different rate than above. This is accounted for in terms of a combination of the time dilation as in the case above with a forshortening of the distance separating the mirror and the bulb. If you have two such clocks and you augument them with counters to keep track of the time, synchronize them and them send one away at speed v/c and bring it back at speed v/c traveling to some distant place you will find that the "moving" clock has not "aged" as much and that the age difference does not depend on the orientation of the "moving" clock. Its all easily worked out with simple trig and algebra. Of course there is one of those flakey paradoxes here and you notice that I put "moving" in quotes in the paragraph above. All motion is relative and just how do the clocks keep straight on which one should "age" more slowly? The "moving" clock experiences something that the "non moving" clock does not and it involves Einsteins second theory. So what does that have to do with people in space ships you say!
brooks@lll-crg.ARPA (Eugene D. Brooks III) (06/04/85)
> The only reason "c" is in the equation is to obtain natural > units for space & time coordinates; the time dilation effect > is not dependent on any communication by light, although such > communication is often used in elementary texts to try to make > the effect more intelligible. The root from which all else was derived is the postulated constancy of the speed of light in any reference frame. Hence time dilatation as Einstein derived it, and the only way it has been derived to my knowledge please send references if I am wrong, is dependent on communication by light.
tino@hou2f.UUCP (A.TINO) (06/04/85)
>I am very puzzled over something in Einstein's theory of time >dilation, that is, that time passes more slowly for objects in >motion then for objects at rest. Here is my understanding of th >theory and how Einstein arrived at it. There has to be something >wrong with my thinking somewhere, though this understanding is >based on the book *The Universe and Dr. Einstein*, by Lincoln >Barnett, a book which Einstein himself heartily praised. >Einstein's theory about time dilation is based on the assumption >that the speed of electromagnetic radiation is constant >throughout the Universe, whether or not the object emitting the >radiation is in motion. Here is an example which may clarify why >Einstein arrived at this assumption: suppose an object that is >travelling through space at a rate equal to 75 percent that of >light and that it was emitting a light ray in the same direction >it was travelling. For that light ray's speed to remain at C, >the rate of time passage for the object must decrease >proportionally. >Yet, I find myself still asking this question: what about a light >ray being emitted in the opposite direction? Can't it just as easily >be said that time is speeding up for the object under these circumstances? >I can't believe Einstein wouldn't have thought of this! > Jim Campbell > ...!ihnp4!ima!haddock!jimc Perhaps the book was misleading... There's more to relativity than time dilation. To see how observers moving with respect to one another can measure the same speed for a given light beam requires an understanding of length contraction and the relativity of simultaneity as well as time dilation. The special theory of relativity (STR), which deals with observers that are in uniform relative motion, begins with two postulates: 1) the speed of light is the same for all observers, and 2) the laws of physics are the same for all observers. (The second postulate says that unless you look out the window you can't tell that you're moving. Furthermore, each observer has the perfect right to consider themselves to be at rest.) From these postulates Einstein deduced how space and time as measured by one observer's clocks and metersticks relate to space and time as measured by any other observer's clocks and metersticks. Let's rephrase your example. Consider two observers, A and B. A moves east as measured by B at a speed of .75 "c". As she moves east, A shines her flashlight eastward. From A's point of view, she is at rest and merely shining her flashlight. Whether she shines it east or west or north or south it is no surprise that she simply measures the speed of the beam to be "c". From B's point of view all he sees is someone flying by shining a flashlight. If we believe postulate #1 we are not surprised to find that, using his own clocks and metersticks, B measures the speed of light to be "c". So far so good. Of course the real "problem" is how can they both be right? Is there a way of using A's measurements to figure out what B will measure with his clocks? The answer is yes, that's what relativity is all about. When A measured the speed of the lightbeam she was finding the ratio of the distance the light traveled (as measured by her!) to the time the the light traveled (also as measured by her!). In order to deduce what B would measure as the speed of the lightbeam one has to figure out the distance the light traveled (according to B!) and the time it takes the light to travel that distance (again according to B!). If you correctly apply the relativistic transformations -- which incorporate contraction, dilation, and simultaneity -- you'll find that both A and B agree that they both, using their own measuring devices, measure the same speed for light -- "c". They better agree! -- Otherwise relativity would be inconsistent. Al Tino , Bell Labs at Holmdel