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Thread: General question on relativity

  1. #1 General question on relativity 
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    I'm confused sometimes about how relativity works. As an object approaches the speed of light, it's concept of time slows down, right? So, how does this relate with the Lorentz contraction?

    Suppose we have a space ship traveling at 3/4 C. If my math is right, its perception of time is approximately 2/3 what it normally would be.

    Quote Originally Posted by Vaedrah
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    So, if they're headed to Alpha Centari about 5 light years away, they would perceive the trip to take about 4.4444 years. (From our perspective, we'd see it as taking 6.6666 years) Wouldn't that mean that they perceived the star to be coming toward them at a speed faster than C? Or does the Lorentz contraction take effect to make the distance seem shorter, so everything balances out?


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    G'day from the land of ozzzzzzzz

    People alway get confused with Actual time unable to be changed.

    And

    Relative time.

    Because of this confusion we have evolved Time travel and what ever and made it fit fantasy movies with black holes and worm holes .


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  4. #3 Re: General question on relativity 
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    Quote Originally Posted by kojax
    I'm confused sometimes about how relativity works. As an object approaches the speed of light, it's concept of time slows down, right?
    Wrong. It does nothing to its concept of time. Time dilation is something you measure as happening to an object with a relative motion to yourself. You measure time for it as moving more slowly. Nothing happens to "your" time. Rule of thumb: "Relativistic effect always occur to the other guy".

    So, how does this relate with the Lorentz contraction?

    Suppose we have a space ship traveling at 3/4 C. If my math is right, its perception of time is approximately 2/3 what it normally would be.

    Quote Originally Posted by Vaedrah
    P


    So, if they're headed to Alpha Centari about 5 light years away, they would perceive the trip to take about 4.44 years. (From our perspective, we'd see it as taking 6.6 years) Wouldn't that mean that they perceived the star to be coming toward them at a speed faster than C? Or does the Lorentz contraction take effect to make the distance seem shorter, so everything balances out?
    We see the passengers age more slowly due to time dilation, so they only age 4.4444 years in the 6.6666 years we experience. We also see their ship shrink to 2/3 of its length due to length contraction.

    From their perspective they see no change in their time, but because the Earth and Alpha Centauri have a relative motion with respect to them, they see the distance between the two as length contracted to 3.3 light yrs. And it takes 4.44 yrs to cross 3.3 light yrs at 0.75c

    Of course this brings up the issue as to what they see as happening to us aging wise. and the answer is that they see us as aging more slowly, and we age only 2.9 years during the trip. The resolution of this apparent paradox lie in the Relativity of Simultaneity. (A concept that I think should be taught before time dilation, as doing so would reduce a lot of headaches later.)

    In a nutshell, it means that events that are deemed simultaneous by one observer will not be deemed as simultaneous by an observer with a relative motion to the first.

    Let's use the trip to Alpha Centauri as an example. Let's assume that there are clocks both on Earth and at Alpha Centauri and that they read the same time according to us on the Earth.

    From our perspective when the spaceship leaves Earth both clocks read zero and both clocks read 6.66 yrs when the Ship arrives at Alpha Centauri.

    From the Ship's perspective the two clocks do not read the same. The Earth clock reads Zero when the ship leaves, but the Alpha Centauri clock reads 3.76 years. The AC clock ages 2.9 years during the trip and reads 6.66 yrs when the ship reaches AC.
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  5. #4  
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    So basically, with light, when you learn about something actually is when it happened (relativistically).

    So supposing there's a stationary observer located exactly between the Sun and Alpha Centauri that has a calendar in sync with ours. So it's 2.5 light years from us.

    If the ship leaves on January 1st 2009 from our perspective, the observer perceives it as having waited until June 1st 2011 (or thereabouts) to leave. (Because it finds out 2.5 years later) and sees it arrive 0.833 years after that. (Because the ship has traveled for 3.333 years total by our count)

    And.... now I'm confused again.
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  6. #5  
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    Let's give the stationary observer some more detail here: A space station is set up half way between Earth and Alpha Centari. The Earth is constantly updating the space station as to what's going on using radio waves. The space station, therefore, always hears about things 2.5 years after they happen, but the crew knows this, and has accordingly set their calendar 2.5 years back from the dates given in the radio broadcast.

    If one day the crew hears that a spaceship capable of traveling at .75 C has left Earth headed their way. (Some how it managed to accelerate very quickly without killing the crew, or it has no crew) They'd see the ship arrive .833 years after first hearing that it left. If they had a really good telescope, they might even physically see it traverse the entire distance in that amount of time. (Of course, the light would be somewhat blue shifted)

    So, if they're looking through their super telescope, and listening to the radio at the same time, then on the first day they see the space ship they hear the radio announcer say: "Today, on January 1, 2009 we just launched this really fast space ship.")

    On the day they see the space ship speed past them, they hear the radio announcer say: "Today, on August 10, 2009 the New York Mets beat the Cardinals 3-2 in an amazing upset...... " (etc)
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    G'day

    Janus said

    We see the passengers age more slowly due to time dilation, so they only age 4.4444 years in the 6.6666 years we experience. We also see their ship shrink to 2/3 of its length due to length contraction.
    In actual time they do not age faster or slower.

    In relative time they do. This is because of the time taken for light to travel and allow us to communicate.

    In reality if you could communicated by a faster medium as instant you would notice the same time. But because we are limited by the speed of light, so things become relative.

    Some say communication by gravity is instant. Right or wrong?

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  8. #7  
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    Quote Originally Posted by kojax
    So basically, with light, when you learn about something actually is when it happened (relativistically).

    So supposing there's a stationary observer located exactly between the Sun and Alpha Centauri that has a calendar in sync with ours. So it's 2.5 light years from us.

    If the ship leaves on January 1st 2009 from our perspective, the observer perceives it as having waited until June 1st 2011 (or thereabouts) to leave. (Because it finds out 2.5 years later) and sees it arrive 0.833 years after that. (Because the ship has traveled for 3.333 years total by our count)

    And.... now I'm confused again.
    No, the disagreement in the simultaneity is not due to a difference in signal delay. It is what is left over after you've accounted for that.

    With your observer halfway to Alpha Centauri, imagine another observer traveling from Earth to Alpha Centauri passing him. At the instant they pass each other, they both receive a signal from Earth and Alpha C. The Observer stationary to both will determine that the signals originated at Earth and Alpha C at the same time. The traveling Observer will determine that the signal from Alpha C was sent first and then the One from Earth.
    They both receive the both signals at the same time, but disagree as to the timing of when they were sent.
    "Men are apt to mistake the strength of their feelings for the strength of their argument.
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  9. #8  
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    Why would they disagree? Suppose there's another space station located on Alpha Centauri. So we've got the Earth, The Middle Station, and the Alpha Centauri Station, all three approximately stationary relative to each other.


    The Middle Station and the Alpha Centauri Station both synchronize their calendars to Earth time, accounting for the difference in distance, by listening to a continual radio broadcast from Earth. IE. people on the middle station know that, when the radio says it's January 1, 2008, it's really July 1, 2011. People on the Alpha Centauri Station know that when the radio says it's January 1, 2008, it's really January 1, 2013.

    Now, suppose the Alpha Centauri Station also has a continual radio broadcast going, which announces the date every day. (The date the announcer believes to be the real time)

    If the people on the space ship are listening to both stations on the day they pass the Middle Station, they'll hear the announcer from Earth say that the date is August 10, 2008. And the Announcer from AC will say the same thing: August 10, 2008.

    Of course, if the middle station had a radio broadcast running, their announcer would say that it's March 1, 2012.
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    Time dilation is always fascinating. I remember the early physics derivation for



    based on a moving observer shining a light on a reflecting mirror and then receiving the light some time later based on the distance to the mirror and the time traveled at some velocity . The two time "frames of reference" for a stationary mirror based observer and the moving observers allows a simple right angle triangle to be drawn a,d surprise, surprise, Pythagoras comes up with Einstein's time dilation formula!

    It is interesting that constant velocity is used in this derivation but the "twin paradox" results from this. The "paradox" is not that one twin ages less than the other but that both age less that each other.

    For example, twin A leaves twin B and speeds off close to c. Twin B should age less than twin A. However, from twin B's perspective, twin A races away instead - so twin A should age less than twin B. Surely there is no "preferred" or "absolute" frame of reference to use.

    So, the constant velocity derivation suggests twin A ages less than twin B but also twin B ages less than twin A. Both, therefore, age less than each other.

    To correct this, Einstein needed to include "acceleration" into time dilation estimates. Twin B knows of acceleration from a force. Twin A has no force. (but could be presented with an equivalent force in an elevator etc). So there is an asymmetry - but how can a formula derived from constant velocity between frames of references still derive the familiar time dilation formula?

    Time dilation is certainly fascinating. Maybe we need the good Dr Who to visit the forum and shed some trans dimensional light?
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  11. #10  
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    Quote Originally Posted by kojax
    Why would they disagree? Suppose there's another space station located on Alpha Centauri. So we've got the Earth, The Middle Station, and the Alpha Centauri Station, all three approximately stationary relative to each other.


    The Middle Station and the Alpha Centauri Station both synchronize their calendars to Earth time, accounting for the difference in distance, by listening to a continual radio broadcast from Earth. IE. people on the middle station know that, when the radio says it's January 1, 2008, it's really July 1, 2011. People on the Alpha Centauri Station know that when the radio says it's January 1, 2008, it's really January 1, 2013.

    Now, suppose the Alpha Centauri Station also has a continual radio broadcast going, which announces the date every day. (The date the announcer believes to be the real time)

    If the people on the space ship are listening to both stations on the day they pass the Middle Station, they'll hear the announcer from Earth say that the date is August 10, 2008. And the Announcer from AC will say the same thing: August 10, 2008.

    Of course, if the middle station had a radio broadcast running, their announcer would say that it's March 1, 2012.
    Here's the thing, the station because the station receives both signals at the same time and that it is an equal distance from Earth and Alpha C, and that the speed of light is a constant, it knows that the signals left the transmitters at the same time. (when its own clock read August 10, 2008.)

    For the Spaceship it is different. It also knows that it was an equal distance from Alpha C and Earth when it received the signals and that it received the signals at the same time. He also knows that the speed of light is a constant.

    At this point I'm going to clear something up. When we say that the speed of light is a constant we mean that everyone measures it as have the same value relative to themselves.. So for the spaceship the both signals approach him at c.

    Since there is a relative motion between the ship and the other three, the Ship, in order to be next to the station when it receives the signal, has to have been closer to Earth when the signals were sent. And since it was not an equal distance from Alpha C and Earth when the signals were transmitted, the signal had to have been transmitted at different times in order for the ship to receive them at the same time. The signal from Alpha C has to be sent first, and then some time later the Signal form Earth, so that the two signals and the ship will meet at the station (even though both carry the same time stamp).

    Thus while the station says that August 10, 2008 occurs at the same instant for both Earth and Alpha C, The ship says that August 10, 2008 occurs at Alpha C before it does on Earth.
    "Men are apt to mistake the strength of their feelings for the strength of their argument.
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  12. #11  
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    Quote Originally Posted by Janus
    At this point I'm going to clear something up. When we say that the speed of light is a constant we mean that everyone measures it as have the same value relative to themselves.. So for the spaceship the both signals approach him at c.
    This is probably the part that I really have the hardest time understanding. So, the ship doesn't see itself moving at 3/4 C and the radio broadcast from Earth moving at 1/4 C relative to it. As far as its concerned, the radio broadcast from Earth is moving at full C relative to the ship?

    And the broadcast from AC, rather than moving at 7/4 C relative to the ship, is perceived as moving at just plain C as well?

    How does it perceive the red shifting effects? Is the signal from Earth red shifted, and the signal from AC blue shifted?

    Since there is a relative motion between the ship and the other three, the Ship, in order to be next to the station when it receives the signal, has to have been closer to Earth when the signals were sent. And since it was not an equal distance from Alpha C and Earth when the signals were transmitted, the signal had to have been transmitted at different times in order for the ship to receive them at the same time. The signal from Alpha C has to be sent first, and then some time later the Signal form Earth, so that the two signals and the ship will meet at the station (even though both carry the same time stamp).

    Thus while the station says that August 10, 2008 occurs at the same instant for both Earth and Alpha C, The ship says that August 10, 2008 occurs at Alpha C before it does on Earth.
    I worry to try and add any more objects to this analogy, but I almost want to start investigating how multiple ships moving in the same direction from a distance apart , and sending radio signals, would perceive time.

    Of course, it would be better if I stay focused on the current problem until I understand it.
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  13. #12  
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    Quote Originally Posted by kojax
    Quote Originally Posted by Janus
    At this point I'm going to clear something up. When we say that the speed of light is a constant we mean that everyone measures it as have the same value relative to themselves.. So for the spaceship the both signals approach him at c.
    This is probably the part that I really have the hardest time understanding. So, the ship doesn't see itself moving at 3/4 C and the radio broadcast from Earth moving at 1/4 C relative to it. As far as its concerned, the radio broadcast from Earth is moving at full C relative to the ship?
    Yes

    And the broadcast from AC, rather than moving at 7/4 C relative to the ship, is perceived as moving at just plain C as well?
    Yes

    How does it perceive the red shifting effects? Is the signal from Earth red shifted, and the signal from AC blue shifted?
    Yes in both cases[quote]

    Here's ananimation that demostrates how this works.

    It shows a lightsource with a relative motion with respect to two "observers"

    Note how as each part of the light wave is emitted, it expands as a circular wave front from the point it was emitted. Since the source is moving towards the blue dot, each successive part of the wave is emitted a little closer to that dot, causing the wave fronts to follow more closely behind each other, decreasing the wavelength and causing a blue shift as seen by this observer. In the other direction, each wave front is emitted a little further away from the red dot than the one before, stretching out the wavelength causing a red-shift.

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  14. #13  
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    Quote Originally Posted by kojax


    Of course, it would be better if I stay focused on the current problem until I understand it.
    Maybe this will help.

    This is similar situation with a train embankment.

    The first animation shows events as they transpire according to an observer standing beside the tracks. He is equidistant from the origin points of two light flashes. (the expanding circles). Just as the flashes reach him, an observer riding a car on the tracks passes him and he sees the flashes also.



    Here's the same events according to the observer riding the car.



    Both the embankment observer and the car observer see the flashes at the same time, but the flashes originate at different times.
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    Janus, in common language, you rock
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    The simplest way to observe the Doppler effect is to stand on a pedestrian overpass over a motorway.

    You will see as white the lights of the cars that move towards you. Those moving away will appear red. If any car has broken down and is immobilized with the warning blinkers on, you will see those blinkers as orange.

    Hope this helps,
    Leszek.
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    The problem I see with trying to ask ourselves when a radio wave is perceived as being emitted is that there's no way for the observer to assign a time to the moment of emission. Or is there?

    I'm assuming that, as the space ship passes the Middle Station, its crew still hears the announcers on both radio stations (Earth and AC) quote the same date. At least that part of its perception of time would be the same as Earth's, wouldn't it?

    Also: as far as the redshift/blue shift effects of the two radio stations (Earth and AC), after the crew adjusted the ship's listening frequencies so they could hear both radio stations, would the announcer on the Earth station appear to be talking really slow, and the announcer on the AC station appear to be talking really fast?
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  18. #17  
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    Quote Originally Posted by kojax
    The problem I see with trying to ask ourselves when a radio wave is perceived as being emitted is that there's no way for the observer to assign a time to the moment of emission. Or is there?
    Sure there is. You know when you received the signal, and in the case of the space ship you know when you left Earth and the relative speed between you and the Earth, and you know the speed at which the signal traveled (c). It is quite a simple matter to figure out when the signal was sent.

    I'm assuming that, as the space ship passes the Middle Station, its crew still hears the announcers on both radio stations (Earth and AC) quote the same date. At least that part of its perception of time would be the same as Earth's, wouldn't it?
    This really has nothing to do with the ship's perception of time, it just tells them what date the calendars on each planet read according to the occupants when they were sent.

    Also: as far as the redshift/blue shift effects of the two radio stations (Earth and AC), after the crew adjusted the ship's listening frequencies so they could hear both radio stations, would the announcer on the Earth station appear to be talking really slow, and the announcer on the AC station appear to be talking really fast?
    Yes.
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    Ok, so now I'm wondering: Suppose the ship has two radio receivers about a mile or so apart (it's a very big ship), one toward the front of the ship, and one toward the back of the ship. These receivers have synchronized clocks, and they mark the time at which they received each signal.

    Would the time between the moment the rear receiver picks up the signal from Earth, and the moment the front receiver picks up the signal from earth be the same length as the time between the moment the front receiver picks up the signal from Alpha Centauri, and the moment the rear receiver picks up the signal form Alpha Centauri?

    Let's assume they are very precise clocks.
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  20. #19  
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    Quote Originally Posted by kojax
    Ok, so now I'm wondering: Suppose the ship has two radio receivers about a mile or so apart (it's a very big ship), one toward the front of the ship, and one toward the back of the ship. These receivers have synchronized clocks, and they mark the time at which they received each signal.

    Would the time between the moment the rear receiver picks up the signal from Earth, and the moment the front receiver picks up the signal from earth be the same length as the time between the moment the front receiver picks up the signal from Alpha Centauri, and the moment the rear receiver picks up the signal form Alpha Centauri?

    Let's assume they are very precise clocks.
    The time recorded by the clocks for each interval will be the same. IOW, if the front clock reads 0 when the signal from Alpha C reaches it, the rear clock will read 5.38 milliseconds when the signal reaches its. For the Earth signal, the rear clock will read zero and the front clock will read 5.38 ms.

    So, from the ship the signal from Alpha C travels from front to back in the same time as the signal from Earth travels from back to front.

    However, from Earth, Alpha C or the Station the signal from Alpha C will take less time to travel from front to back than the Earth signal takes to travel from back to front. The ship clock readings upon detection of the signals will remain the same as seen from the ship.
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    I get the impression, however, that this is, based on the impossibility of ever synchronizing the clocks well enough so that they're telling the same exact time from the Earth's perspective.

    I mean so that, if both clocks sent signals exactly when they read 10:00 AM (and zero seconds, 0 milliseconds, 0 microseconds, 0 picoseconds) the receiver on Earth would receive the one signal 5.38 milliseconds before the other. (Because the operator receiving the signal knows one clock is physically a mile further out, and should therefore have its signal arrive a5.38 milliseconds later if their times are exactly synchronized in a non-relativistic sense of synchronization)

    If instead, the clocks are set so that their signals reach Earth at exactly the same time, then it would make sense to perceive the signal from AC crossing between the clocks at the same speed as the signal from Earth crosses between them. Basically, the signal from Earth has a head start because the first clock is not really in sync with the other clock in a non-relativistic sense, but rather the first clock is 5.38 milliseconds ahead.


    Does this lead to a possible revision for the Michealson-Morley's experiment? Maybe we can detect the Earth's absolute motion after all, just by using properly synchronized clocks.

    Or... I guess not. All we can tell is how fast something is moving relative to another inertial frame this way. All these continual radio waves do is allow the Earth to communicate what it sees happening. I guess it doesn't change what the spaceship sees happening.
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    Quote Originally Posted by kojax
    I get the impression, however, that this is, based on the impossibility of ever synchronizing the clocks well enough so that they're telling the same exact time from the Earth's perspective.

    I mean so that, if both clocks sent signals exactly when they read 10:00 AM (and zero seconds, 0 milliseconds, 0 microseconds, 0 picoseconds) the receiver on Earth would receive the one signal 5.38 milliseconds before the other. (Because the operator receiving the signal knows one clock is physically a mile further out, and should therefore have its signal arrive a5.38 milliseconds later if their times are exactly synchronized in a non-relativistic sense of synchronization)
    The Earth actually receives the signals 8.3 ms apart. Here's why:

    1. According to Earth's clocks, the clock closest to the Earth sends out its signal 2.69ms before the further clock does. Assuming the signals are sent at the same time according to the rocket. (Relativity of Simultaneity)

    2. During this 2.69ms, the further end will recede from the Earth at 3/4c an additional distance of 2.02 light milliseconds.

    3. The distance between the clocks is length contracted to 2/3 of a mile by Earth measurement and it takes the signal an additional 3.58 milliseconds to cross this distance.

    Total time 8.3 ms between reception of the signals.
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    I think I'm starting to understand the concept (kind of).


    If the clocks on the ship synchronize to each other. Say the front clock sends a signal with its current time to the rear clock. It arrives in 4/7 the normal time (from Earth's perspective), because of the added velocities of 3/4 C + C.

    Suppose the ship hasn't reached the middle station yet, but is still like 2 months away.

    The two clocks send their signals, the Middle Station reads the times as being 11/7 * 5.38 ms apart.

    If it were the other way around, the rear clock sends a signal to the front clock, and then they broadcast their times, the front clock would be 4 * 5.38 ms ahead, and the Middle Station would read the it as being 3 * 5.38 ms faster than the rear clock.

    ........ and in the midst of it all.......

    I think I'm starting to see how it is that all of these values add up from the perspective of the crew to give the appearance of the times being properly in sync, minus whatever artificial adjustments they might be trying to make in order to synchronize with Earth.
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    I am a hopeless case when it comes to relativity, but I thought I could add a question to this thread that deals with the Doppler effect and light. With sound, the actual waves spread out or close towards each other depending on the situation. With light though, the frequency is not dependent on the distance between particles. So, where does the energy go that is lost to red shifting?
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    Quote Originally Posted by Cold Fusion
    I am a hopeless case when it comes to relativity, but I thought I could add a question to this thread that deals with the Doppler effect and light. With sound, the actual waves spread out or close towards each other depending on the situation. With light though, the frequency is not dependent on the distance between particles. So, where does the energy go that is lost to red shifting?
    What particles are you talking about? If you mean photons, they are not particles in the classical sense. They are wave packets that exhibit some particle like properties. A photon is simply the smallest division of energy you can have for a certain wavelength. And with light it is the actual wavelength of the photon which is stretched out. And with photons, longer wavelengths equal lower energy.
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    The heated mind resents the chill touch & relentless scrutiny of logic"-W.E. Gladstone


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  26. #25  
    Time Lord
    Join Date
    Mar 2007
    Posts
    8,035
    I suppose what he's asking is, when a light beam bounces off of an object moving away from the emitter, and returns with a lower frequency, where does the energy go?

    Does the object moving away from the emitter gain a very small amount of momentum? Does the returning beam of light gain a small amount of amplitude to make up for the decrease in frequency? It's basically a conservation of energy question. I don't know the answer. That's why I'm just rephrasing it in case somebody else does.
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