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Thread: Time Dilation Thought Experiment

  1. #1 Time Dilation Thought Experiment 
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    I've come up with what I hope is a clear illustration of the rationale behind relativistic time.

    Here's my thought experiment: I procure a radio-clock transmitter, two radio receivers, and a space craft capable of traveling at half the speed of light. The radio-clock transmitter produces and transmits a tick sound once each second. I have a friend of mine board the space craft taking with him the radio-clock transmitter and a receiver. He accelerates his craft to 150,000 kilometers per second. As his craft speeds past a point close to where I'm at, he activates the radio-clock, and it transmits its first “tick,” a signal which both of our receivers get. Our receivers produce an audible sound like the tick of a clock. Since we are close, we hear this first tick at the same time. Let's call this time, t = 0.

    The second tick of the clock, unlike the first tick, is not simultaneous. On my friend's ship, the radio-clock produces and transmits its second tick one second after the first tick, and since his receiver is close to the radio-clock, he instantaneously receives and hears the second tick a second after after the first tick.

    My situation is different from my friend's. After one second, his craft has traveled 150,000 kilometers. (I'm using 300,000 kilometers per second for the speed of light which is also the speed of radio waves.) The second tick takes 1.5 seconds for me to receive and hear: one second for the radio-clock to produce and transmit the second tick plus one-half second for the radio signal to travel 150,000 kilometers.

    So far, since t = 0, my friend experiences one tick per second in his space craft, and I have received one tick per 1.5 seconds.

    The third tick, like the second, for my friend comes one second after the previous tick for a total of two seconds since t = 0. The time interval for me is two seconds for the transmitter to produce the third tick, plus another second for that signal to reach my radio receiver. (After two seconds his craft has traveled 150,000 kilometers per second X 2 seconds = 300,000 kilometers, and light would take one second to travel that distance.) From my perspective, when I hear the second tick three seconds have gone by since t = 0.

    A pattern is emerging. It takes my receiver 1.5 times more time to receive the ticks of the clock than my friend's receiver. From my point of view, the radio-clock on board my friend's space craft ticks more slowly for me than for my friend. If he continued on course at half the speed of light for ten years on board his craft, 15 years would go by here where I am.

    Conclusion: Time goes by more slowly for my friend moving at half the speed of light than for me.

    Jagella


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  3. #2 Re: Time Dilation Thought Experiment 
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    Quote Originally Posted by Jagella
    I've come up with what I hope is a clear illustration of the rationale behind relativistic time.

    Here's my thought experiment: I procure a radio-clock transmitter, two radio receivers, and a space craft capable of traveling at half the speed of light. The radio-clock transmitter produces and transmits a tick sound once each second. I have a friend of mine board the space craft taking with him the radio-clock transmitter and a receiver. He accelerates his craft to 150,000 kilometers per second. As his craft speeds past a point close to where I'm at, he activates the radio-clock, and it transmits its first “tick,” a signal which both of our receivers get. Our receivers produce an audible sound like the tick of a clock. Since we are close, we hear this first tick at the same time. Let's call this time, t = 0.

    The second tick of the clock, unlike the first tick, is not simultaneous. On my friend's ship, the radio-clock produces and transmits its second tick one second after the first tick, and since his receiver is close to the radio-clock, he instantaneously receives and hears the second tick a second after after the first tick.

    My situation is different from my friend's. After one second, his craft has traveled 150,000 kilometers. (I'm using 300,000 kilometers per hour for the speed of light.) The second tick takes 1.5 seconds for me to receive and hear: one second for the radio-clock to produce and transmit the second tick plus one-half second for the radio signal to travel 150,000 kilometers.

    So far, since t = 0, my friend experiences one tick per second in his space craft, and I have received one tick per 1.5 seconds.

    The third tick, like the second, for my friend comes one second after the previous tick for a total of two seconds since t = 0. The time interval for me is two seconds for the transmitter to produce the third tick, plus another second for that signal to reach my radio receiver. (After two seconds his craft has traveled 150,000 kilometers per second X 2 seconds = 300,000 kilometers, and light would take one second to travel that distance.) From my perspective, when I hear the second tick three seconds have gone by since t = 0.

    A pattern is emerging. It takes my receiver 1.5 times more time to receive the ticks of the clock than my friend's receiver. From my point of view, the radio-clock on board my friend's space craft ticks more slowly for me than for my friend. If he continued on course at half the speed of light for ten years on board his craft, 15 years would go by here where I am.

    Conclusion: Time goes by more slowly for my friend moving at half the speed of light than for me.

    Jagella
    Now reverse the situation and let your friend travel toward you. You reasoning will result in a different conclusion, time compression, but in special relativity that is not the case.

    What you are really explaining is the classic Doppler effect, which has nothing to do with relativistic time dilation.


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  4. #3 Re: Time Dilation Thought Experiment 
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    Quote Originally Posted by Jagella
    I've come up with what I hope is a clear illustration of the rationale behind relativistic time.

    {description of how light travel time delay causes a Doppler effect}

    Conclusion: Time goes by more slowly for my friend moving at half the speed of light than for me.

    Jagella
    Unfortunately, that is not the rationale behind relativistic time, that is simple Doppler effect.

    You should try it with your friend coming towards you, rather than moving away. If you do you should find the ticks then come closer together - a simple Doppler effect.

    Time-dilation doesn't work that way. Time dilation is what is left over after you account for these "time of light" effects, and it is a consequence of the constancy of c to all inertial frames, whatever their relative motions.

    See if you can revise your thought experiment (the setup is pretty good, although that synchronization of your "clocks" to t=0 when in motion is a little tricky, but nothing to worry about at this stage) but this time include relative motion and the constancy of c, and you should be able to find an illustration of relativistic time.

    EDIT: I notice DrRocket posted pretty much the same message, as I was composing this.
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  5. #4 Re: Time Dilation Thought Experiment 
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    Quote Originally Posted by SpeedFreek
    Unfortunately, that is not the rationale behind relativistic time, that is simple Doppler effect.

    You should try it with your friend coming towards you, rather than moving away. If you do you should find the ticks then come closer together - a simple Doppler effect.
    OK, if I try the same scenario with my friend's space craft approaching me at 150,000 km / sec, the ticks of his clock are on 0.5 seconds apart, which contradicts my previous conclusion. (The sound of paper crinkling and then a soft pop as that paper lands in a can)

    I was not aware that the Doppler Effect can apply to such a situation. Science is serendipitous, is it not? You look for one thing and find something else you weren't aware of.

    Quote Originally Posted by SpeedFreek
    See if you can revise your thought experiment (the setup is pretty good, although that synchronization of your "clocks" to t=0 when in motion is a little tricky, but nothing to worry about at this stage) but this time include relative motion and the constancy of c, and you should be able to find an illustration of relativistic time.
    Very well. Let's say that my friend positions his transmitter 300,000 kilometers directly above his receiver. At that distance, the radio signal will take one second to travel the vertical distance from the transmitter to the receiver. So my friend's clock ticks once per second.

    Now, let's say my friend is moving past me at 150,000 kilometers per second. My receiver is at the same height above a horizontal axis as my friend's receiver. At the instant he reaches my position, his transmitter emits a signal. Unlike my friend's receiver, due to the forward motion of his space craft the signal will need to travel a diagonal path to my receiver, the hypotenuse of a right triangle. Of course, this diagonal is longer than the vertical distance traveled by the radio signal, and I calculate it to be 355,410 kilometers. Assuming that time goes by at the same rate for me as my friend, the signal to my receiver would be moving at 355,410 kilometers per second.

    But wait—light's speed (and the signal's speed) is constant at 300,000 kilometers per second. The radio signal's speed can't be 355,410 kilometers per second.

    The solution to this paradox is to assume that the time it takes the radio signal to travel the diagonal distance of 355,410 kilometers is greater than the one second on board my friend's space craft. If I use 1.12 seconds for that time, then the speed of the signal traveling that diagonal is 355,410 km / 1.12 s = 300,000 km /s (approximately). Of course, the 1.12 seconds per tick of the clock from my perspective is longer than the 1 second per tick on my friend's space craft moving at one-half the speed of light.

    Conclusion: My friend's clock ticks more slowly for me than for him, so his time progresses more slowly than my time.

    Jagella
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  6. #5 Re: Time Dilation Thought Experiment 
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    Quote Originally Posted by Jagella
    Quote Originally Posted by SpeedFreek
    Unfortunately, that is not the rationale behind relativistic time, that is simple Doppler effect.

    You should try it with your friend coming towards you, rather than moving away. If you do you should find the ticks then come closer together - a simple Doppler effect.
    OK, if I try the same scenario with my friend's space craft approaching me at 150,000 km / sec, the ticks of his clock are on 0.5 seconds apart, which contradicts my previous conclusion. (The sound of paper crinkling and then a soft pop as that paper lands in a can)

    I was not aware that the Doppler Effect can apply to such a situation. Science is serendipitous, is it not? You look for one thing and find something else you weren't aware of.

    Quote Originally Posted by SpeedFreek
    See if you can revise your thought experiment (the setup is pretty good, although that synchronization of your "clocks" to t=0 when in motion is a little tricky, but nothing to worry about at this stage) but this time include relative motion and the constancy of c, and you should be able to find an illustration of relativistic time.
    Very well. Let's say that my friend positions his transmitter 300,000 kilometers directly above his receiver. At that distance, the radio signal will take one second to travel the vertical distance from the transmitter to the receiver. So my friend's clock ticks once per second.

    Now, let's say my friend is moving past me at 150,000 kilometers per second. My receiver is at the same height above a horizontal axis as my friend's receiver. At the instant he reaches my position, his transmitter emits a signal. Unlike my friend's receiver, due to the forward motion of his space craft the signal will need to travel a diagonal path to my receiver, the hypotenuse of a right triangle. Of course, this diagonal is longer than the vertical distance traveled by the radio signal, and I calculate it to be 355,410 kilometers. Assuming that time goes by at the same rate for me as my friend, the signal to my receiver would be moving at 355,410 kilometers per second.

    But wait—light's speed (and the signal's speed) is constant at 300,000 kilometers per second. The radio signal's speed can't be 355,410 kilometers per second.

    The solution to this paradox is to assume that the time it takes the radio signal to travel the diagonal distance of 355,410 kilometers is greater than the one second on board my friend's space craft. If I use 1.12 seconds for that time, then the speed of the signal traveling that diagonal is 355,410 km / 1.12 s = 300,000 km /s (approximately). Of course, the 1.12 seconds per tick of the clock from my perspective is longer than the 1 second per tick on my friend's space craft moving at one-half the speed of light.

    Conclusion: My friend's clock ticks more slowly for me than for him, so his time progresses more slowly than my time.

    Jagella
    This essentially the "light clock explanation of time dilation as shown in the following animation:



    Of course, if you riding along with the "moving" light clock, you would see your light pulse as moving straight up a down and the pulse of the other light clock as moving on a diagonal. As a result, you would determine that the other light clock ticks more slowly. Or put in terms of your example, your friend would say that it is your clock that is running slow.
    "Men are apt to mistake the strength of their feelings for the strength of their argument.
    The heated mind resents the chill touch & relentless scrutiny of logic"-W.E. Gladstone


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  7. #6  
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    Time doest not exists,theres only movement.

    Re-experiment the experiment.

    One guy have his voice accords, and his friend also has it own.
    They talk each other, and they hear each other at the same time.

    As they voices are object products that send waves through the air,
    his second friend get into a car and accelerate,
    as it moves the road(space) away from each other,
    the friends start stopping to hear each other.
    Even after they force it vocals to scream......

    Theres a distance point of communication where they can actually,
    hear each other at same second.
    What you have next must be packages to send it forward its limitations.

    The transmitter and a receiver that also has it limitations,
    but capable to send it,let say at forever movement(a continuous movement that does not stop).
    Or that it are much faster.

    There was no difference in time at any moment.
    Only measurement limitations.
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  8. #7 Re: Time Dilation Thought Experiment 
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    Quote Originally Posted by Jagella
    Conclusion: My friend's clock ticks more slowly for me than for him, so his time progresses more slowly than my time.Jagella
    Good, you have found the rationale behind time-dilation. But note, as Janus said, that if you put the transmitter above yourself rather than your friend, your moving friend will calculate that your signals are travelling diagonally - the situation has an inverse symmetry about it.
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  9. #8 Re: Time Dilation Thought Experiment 
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    Quote Originally Posted by Janus
    This essentially the "light clock explanation of time dilation as shown in the following animation...
    Thanks for the animation, but I was hoping that my rationale for time dilation was more original. I've seen the “light clock” illustrations, but I was hoping to do better with radio receivers and transmitters. Radio waves have the advantage of their not needing to be seen. If a light source was 150,000 kilometers away and visible, I think it would blind my friend on board the space craft. (I try to be realistic in most cases, but the 300,000 kilometer-high clock, I must admit, is not very realistic. It greatly simplified the calculations, though.)

    The animation is too fast, in my opinion. If I would design such an animation (and I have created animations in my graphic-design work), I'd make it run more slowly.

    Quote Originally Posted by Janus
    Of course, if you riding along with the "moving" light clock, you would see your light pulse as moving straight up a down and the pulse of the other light clock as moving on a diagonal. As a result, you would determine that the other light clock ticks more slowly. Or put in terms of your example, your friend would say that it is your clock that is running slow.
    Isn't that weird? My friend could just as easily think that I'm moving away from him at half the speed of light if he didn't know he was on board a space craft. So movement, like time, is relative to the observer.

    Many people can understand relativity, but what separates Einstein from the rest of us is that he understood it first. Originality is one of the hallmarks of true genius.

    Jagella
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  10. #9 Re: Time Dilation Thought Experiment 
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    Quote Originally Posted by SpeedFreek
    Quote Originally Posted by Jagella
    Conclusion: My friend's clock ticks more slowly for me than for him, so his time progresses more slowly than my time.Jagella
    Good, you have found the rationale behind time-dilation. But note, as Janus said, that if you put the transmitter above yourself rather than your friend, your moving friend will calculate that your signals are travelling diagonally - the situation has an inverse symmetry about it.
    Prior to Einstein's Theory of Relativity, I must wonder what philosophers would have thought of the statement: "To me, your time is slower than mine, and to you, my time is slower than yours." I'm guessing that they would have dismissed it as logically flawed. Fortunately, scientists make use of abduction. According to Scientific American: "The great insight of science is that is that the way to decide truth is not by pure deduction from assumptions but rather by experimenting on the physical world." (1). So in the same way that we know that heavy objects don't fall more quickly than lighter objects, we can also know that time varies based on the observer's "frame of reference."

    Jagella

    (1) Scientific American; "Thought Experiment: How Robots Reason; January 2011; p 76
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  11. #10 Re: Time Dilation Thought Experiment 
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    Quote Originally Posted by Jagella
    Quote Originally Posted by Janus
    This essentially the "light clock explanation of time dilation as shown in the following animation...
    Thanks for the animation, but I was hoping that my rationale for time dilation was more original. I've seen the “light clock” illustrations, but I was hoping to do better with radio receivers and transmitters. Radio waves have the advantage of their not needing to be seen. If a light source was 150,000 kilometers away and visible, I think it would blind my friend on board the space craft. (I try to be realistic in most cases, but the 300,000 kilometer-high clock, I must admit, is not very realistic. It greatly simplified the calculations, though.)
    Radio wave or visible light, it makes no difference. The light clock illustration isn't based on what is "seen"(what is actually seen would be different), but on the path taken, and that is the same whether you use radio waves or visible light.

    The animation is too fast, in my opinion. If I would design such an animation (and I have created animations in my graphic-design work), I'd make it run more slowly.
    How fast is it running for you? On my computer, it takes about 4 sec to run through.
    "Men are apt to mistake the strength of their feelings for the strength of their argument.
    The heated mind resents the chill touch & relentless scrutiny of logic"-W.E. Gladstone


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  12. #11  
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    Quote Originally Posted by WDHellS
    Time doest not exists,theres only movement.
    Exactly, I wish everyone would understand this simple concept. Time exists only in our mind but not in reality. "Time" it's just another convenient practical idea and convenient agreement (exactly like the concept that in math every "unity" is identical to another unity), but this is just in our mind, not in reality. Time is a measurement of movement and chemical change, is nothing more than a tool created by men to keep track of movements/changes, to describe the passing of events. Time is essentially nothing. You cannot add, subtract, slow, or speed up time.
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  13. #12  
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    Quote Originally Posted by Myuncle
    Quote Originally Posted by WDHellS
    Time doest not exists,theres only movement.
    Exactly, I wish everyone would understand this simple concept. Time exists only in our mind but not in reality.Time is essentially nothing. You cannot add, subtract, slow, or speed up time.
    I don't know enough about philosophy, and especially physics, to even attempt to understand and then go on to explain time. I do feel, however, that "time dilation" suggests time is something that exists and is not simply part of a conceptual framework, created by the human mind, so that we may make sense of what we consider to be our reality/surroundings.
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  14. #13  
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    The universe also thinks there is such a thing as time and it doesn't really care what you ( and some other members of this forum ) think.
    Time has a leading role in many physical processes and cannot be discounted as a figment of our collective imagination and solely as a result of movement.

    Consider the quantum mechanical observables energy and time. Because of their nature they must satisfy the Heisenberg Uncertainty Principle. Now consider virtual pair creation where 1022 MeV of energy spontaneously creates an electron/positron pair. Now, by the H U principle, these two particles MUST annihilate each other after a period of time such that the product of the change in energy and the change in time is always smaller than Planck'constant. This will happen even in a perfect vacuum and totally removed from any other influences and effects.
    So if as you say, the universe doesn't keep track of 'real' time, what motion or other real quantity is it using to judge the passage of this imaginary quantity we call time so that it knows when to anihilate the electron/positron pair ????
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  15. #14  
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    Is it true that there would be no relative time dilation between objects at different velocities, but that there would be a relative time dilation between objects experiencing different accelerations?

    And, if the above is true, is the relative time variance between different accelerations commensurate with the relative time variance between different gravitational fields?
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  16. #15  
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    According to special relativity you have relative speed time dilation where one observer on spaceship A, moving at a speed much lower than c, will 'see' the clock on another spaceship, B moving at speed close to c, running slower in accordance to the Lorentz transform.

    According to general relativity and the Equivalence Principle, accelerated motion and a gravitational field are equivalent, ie they both experience gravitational time dilation.
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