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Not Understanding Time Dilation.

  1. Aug 11, 2011 #1
    Hey there, guys. I’m kind of new to the whole physics thing, but I am starting on a quest to try and learn as much about how this universe works as I can. I am currently working on developing a good understanding of special and general relativity. I am not overly math-competent, so I have been sticking to the conceptual area of relativity as much as I possibly can. I have done quite a bit of studying on the subject, and I have most of the concepts at least “memorized.” I don’t necessarily “understand,” however, so don’t feel too shocked if I say a few things that make you scratch you heads.

    In trying to fully comprehend special relativity, the biggest road block I’ve hit is this: I don’t understand where the physical slowing of time for objects in relative motion comes into play in preserving the speed of light in all reference frames. This is what I am hoping you guys can answer for me.

    I have seen some examples. The most common one is the “light clock,” a clock where a beam of light bounces back and forth between two panels, and each period is one “tick” of the clock. To an observer who is stationary relative to the light clock, the light bounces back and forth between the panels along the shortest possible path. However, when the clock is put into near-light-speed-motion relative to the observer, the light has to travel a longer, diagonal path between the panels due to the fact that the clock itself has changed position. When in relative motion with its observer, the clock ticks more slowly. I understand this, and it makes perfect sense. However, what I am having trouble understanding is why it has to be that this applies to all things, and not just the light clock. In other words, I don’t understand why an hour glass takes longer than an hour to cycle through when viewed by an observer in relative motion, or why a person can take a high-speed journey for 100 years and come back only 50 years aged.

    I know I am wrong here, but it seems to me like relative simultaneity and length contraction would be enough to preserve the speed of light without any time dilation in addition. For example, a person is standing stationary with respect to two lightning rods, one that is 1,000,000 miles to his left, and another that is 1,000,000 miles to his right, and he sees two simultaneous lightning strikes. Meanwhile, I am whizzing past him in a rocket from left to right, traveling at near the speed of light. I fly into the wave of light coming from the lightning strike on the right, and the one from the left has to chase me down from behind. I see the lightning strike that I am flying towards before I see the lightning strike that I am flying away from. Both lightning strikes occurred the same distance from me, and advanced towards me at exactly speed c, and D=RT, so that means that the lightning strike that I was flying towards actually happened first, and the speed of light is preserved. I also understand that there is a length contraction in there, but I won’t go into the details of that. What I don’t see is where each observer viewing the other observer’s clock as running slowly comes into play here. It seems as though the speed of light is already preserved, and the laws of physics are the same in both reference frames, and it is mission accomplished. Where is my thinking off here?

    I’m hoping you guys can give me a mental picture of why time dilation has to be, so that I can truly understand this stuff. I understand that it might be impossible without getting mathematically involved, so feel free to just say so if it is.

    Thanks a bunch!
     
    Last edited: Aug 11, 2011
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  3. Aug 11, 2011 #2

    ghwellsjr

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    If you agree that the ruler that the traveler is carrying with him is length contracted along the direction of motion, then when he measures the speed of light using that ruler to measure the distance the light travels during some period of time, he will get the wrong answer unless his clock is also ticking at a slower rate.
     
  4. Aug 11, 2011 #3
    Thanks for the answer. I do have one question though. Suppose I am standing on the ground with a 10 light second ruler to my left. A space ship with an identical ruler hanging off the back of his ship then flies past me from left to right at near the speed of light, and at the precise time that he is alongside me, he fires a laser backwards. The laser beam has to travel at speed c relative to me and at speed c relative to him at the same time. Since he is moving relative to me, I see his 10 light second ruler as being scrunched, maybe only 5 light seconds, plus he is advancing away from the laser beam.

    10 seconds pass on my clock, and the laser beam is right at the end of my ruler. Meanwhile, the same beam of light is far beyond the end of the ruler that the space ship had been dragging behind him. Let’s say the light traveled 25 light seconds away from him by his measurements, in the same amount of time that it took to travel 10 light seconds away from me. This would mean that 25 seconds must have passed on his clock, and time for him must be passing faster than for me. What is wrong with this picture I painted? I understand that I have to view his clock as ticking slower than mine.

    Sorry for the dumb questions, but I am new to this, and having some trouble understanding what is going on.
     
  5. Aug 11, 2011 #4

    Janus

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    This deals with what is known as the Relativity of Simultaneity. Imagine that your space ship also has a 10 light second ruler extending in front of Him. according to him, his light pulse reaches the ends of both rulers at the same time. According to you however, the light will reach the end of the trailing ruler first and then the end of the leading ruler. IOW, Events that are simultaneous in one frame will not be so in the other and vice-versa.
     
  6. Aug 11, 2011 #5

    pervect

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    I very much suspect that you're having the usual problem with the relativity of simultaneity. But it's a bit hard to interpret your scenario without a space-time diagram. Furthtermore, there's a good chance that drawing up the space-time diagram would help you to clear up your confusion.

    The basics of drawing a space-time diagram are simple: chose a scale such that light always moves at a 45 degree angle on the space-time diagram.

    Time goes in the vertical direction, so non-moving objects on the space-time diagram are represented with vertical lines, as below.

    attachment.php?attachmentid=37922&stc=1&d=1313088245.png

    Moving objects always move less than 'c', so they tilt slightly to the left or right, but never as much as 45 degrees.

    attachment.php?attachmentid=37923&stc=1&d=1313088643.png

    To actually measure lengths and time intervals, use 3/4/5 triangles, and remember that the lorentz interval is the square of the time or distance interval and is equal to [itex]| \Delta T^2 - \Delta X^2 | [/itex], so the distance between a point at (t=0,x=0) and (t=4,x=5) is sqrt(5^2 - 4^2) = 3, the distance being space-like.

    Finally, and this is the important point - and the main motivation for using the space-time diagrams. Events that are simultaneous are connected by lines of simultaneity, but the slope of the line depends on the observer.

    If you aren't familiar with how to draw lines of simultaneity, you can create them from the Einstein midpoint definition, and it's a worthwhile exercise.

    To wit - in the stationary frame, you need the worldline of three stationary observers, one is the "midpoint". At some time, the midpoint observer emits a flash of light, we know it arrives "at the same time" by definition on the other two worldlines. The result looks like this - it's no surprise, A and B are two simultaneous events, the thin red line is the "line of simultaneity".

    attachment.php?attachmentid=37925&stc=1&d=1313089588.png

    But in the moving frame it looks like this. Again, we use the notion of synchronizing clocks by emitting a light pulse from the co-moving midpoint observer, we know that the signal received from the midpoint arrives "at the same time" in the moving frame.


    https://www.physicsforums.com/attachment.php?attachmentid=37926&stc=1&d=1313090496

    So, when you talk about two events that occur "at the same time", if they are separated by any distance, you need to pick the right line. The concept of "simultaneity" for the stationary observer is a different concept than that of the moving observer, i.e. it depends on the frame.

    If you draw everything perfectly to scale, you'll find that the angle between the lines of simultaneity of the moving and stationary observers is the same as the angle between the wordlinles of the moving and stationary observers.
     

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    Last edited: Aug 11, 2011
  7. Aug 11, 2011 #6
    Once again, thanks for the answers. I feel like I am starting to get a better idea of how relative time, simultaneity, and space work together to preserve the speed of light from all reference frames. However, as can be expected from a confused new guy, your answers lead to more questions.

    The question I have now leads somewhat back to my original question, and it is: if relative simultaneity corrects to preserve the speed of light simply by saying that two things that happen simultaneously for one person will not happen simultaneously for somebody in relative motion, why is it that time dilation is a necessary thing? I guess what I am getting out of this is that the relativity of simultaneous events is what actually preserves the speed of light in all reference frames, and that length contraction is a consequence of relative simultaneity, and that time dilation is a consequence of length contraction, so to speak . . . Am I even close here?
     
  8. Aug 11, 2011 #7
    "Relative simultaneity" is observed because of dilated time and contracted lengths. I would suspect it can't be said one is a "consequence" of the other, they are mutually inclusive.

    time dilation / length contraction is a consequence of c being constant, which maybe a result of spacetime properties.
     
  9. Aug 11, 2011 #8

    ghwellsjr

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    You need all three: time dilation, length contraction and relativity of simultaneity. Let me work our your problem in a way that may make it obvious to you.

    You stated you have a ruler 10 light seconds long so that when the laser fires, it will take 10seconds for the light to get to the end. However, you cannot see that happening. What you need to do is put a mirror at the end of your ruler so that the light can be reflected back to you and then you will measure 20 seconds elapsing on your watch, confirming that the light did indeed travel the 20 light seconds in 20 seconds.

    Now the guy on the spaceship has a similar mirror on the end of his ruler which you say is scunched down to 5 light seconds. You can work the Lorentz factor equation backwards to determine that he is traveling at 86.6%c, correct?

    Now if he is traveling at 86.6%c to the right, his mirror is also traveling at that same speed, correct? So now it won't be too hard to figure out how long it will take for the laser beam traveling to the left at c to meet the mirror traveling to the right at 0.866c. It's a simple ratio and it turns out to be 2.68 seconds. Can you figure that out? This also means that the mirror and the spaceship have traveled 2.32 light seconds to the right.

    Next we notice that the laser beam is changing direction and the difference in speed between the laser beam and the mirror tells the relative speed between them and that is 0.134c, correct? Now at this speed, the laser beam has to travel 5 light seconds to get to the other end of the ruler and that will take 37.31 seconds, correct? And that is when the guy on the spaceship sees the return laser flash just like you did on the ground. The total elapsed time for him, according to ground time, is 39.99 seconds, but according to him, since his clock is running at half speed is just about 20 seconds, the same as you measured. (The slight error is caused by rounding off the numbers.)

    Remember, he thinks his ruler is 10 light-seconds long, so his measurement of the speed of light is the same as yours.

    I think you can see the parts that length contraction and time dilation play in this analysis. Simultaneity has to do with the fact that for you, the two halves of the round trip for the laser beam took the same time but as far as you are concerned they were way different for the spaceship guy. If we had done the analysis from his point of view, he would say that the two halves were equal for his ruler and mirror but yours were the ones that were way different.

    One last thing: we can calculate how much farther the spaceship had to travel before the reflected laser beam was detected and that is 32.31 light seconds for a total of 34.62 light seconds which is the distance the spaceship traveled in 40 seconds (according to you) at 86.6%c (ignoring round off errrors).

    I'm not sure where you got the 25 seconds or why you thought time must be progressing faster for him but hopefully this explanation will clear everything up for you.
     
  10. Aug 11, 2011 #9
    You know, ghwellsjr, I think you may have totally solved my confusion, but not in the way that you expected to solve my confusion. Let me explain. When you stated “You stated you have a ruler 10 light seconds long so that when the laser fires, it will take 10seconds for the light to get to the end. However, you cannot see that happening. What you need to do is put a mirror at the end of your ruler so that the light can be reflected back to you and then you will measure 20 seconds elapsing on your watch, confirming that the light did indeed travel the 20 light seconds in 20 seconds.” you cleared up a lot for me. For whatever crazy reason, I had it in my head that where you see that beam of light, that is where it actually is. I totally neglected the fact that when you are talking about light, you are always talking in terms of round trip. When you see light someplace, you don’t actually see it there. You see it when it comes back to you. As it turns out, my entire problem had nothing to do with relativity. It was actually a simple issue with the nature of light that classical mechanics could have, and did, predict.

    When you think it terms of the round trip, it doesn’t matter if the space ship that you are observing from a distance is traveling towards an oncoming beam of light, or if it is running away from beam of light that is chasing it. Either way, you (on the ground) witness the light traveling at 0.134c relative to the space ship one direction, and 1.866c relative to the space ship the other direction. Where I was stuck was when I was for some reason thinking that it didn’t have to come back to the space ship. You probably could guess this, but I feel pretty stupid right now!

    Also, just to make sure that I had a grasp on the subject, I ran the same calculations that you made, only in the assumption that the laser was fired from the front of the space ship. It worked out exactly the same, just like it should.

    Thanks a bunch for all the help, guys! I know how frustrating it can be when you try to explain something in the best way you know how, and the guy you are explaining it too just doesn’t get it. Thanks for having patience with me.
     
  11. Aug 11, 2011 #10
    Oh yeah, one more quick question about relativity, but this one shouldn’t prove frustrating. Suppose that Planet Neptune considers itself to be perfectly round. Also suppose that we here on Earth are capable of observing Neptune from a telescope, and also capable of making precise measurements of Neptune’s diameter from here on Earth. Now, let’s say that we got into an orbital pattern such that Neptune was moving relative to us in a crossways direction. In that case, we would actually measure Neptune to be slightly oval shaped due to length contraction, right?
     
  12. Aug 11, 2011 #11

    ghwellsjr

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    When viewed through a telescope a spherical body, even when traveling at a very high speed will appear to be perfectly round. However, with proper measurements, it would be determined to be oval shaped. See:

    http://en.wikipedia.org/wiki/The_Terrell-Penrose_Effect
     
  13. Aug 12, 2011 #12
    Wow! That is facinating. I never would have thought of it. I actually googled the Terrell-Penrose Effect, and found this site <http://th.physik.uni-frankfurt.de/~scherer/qmd/mpegs/lampa_terrell_penrose_info.html> [Broken] It really helped me to visualize what was going on here. Thanks for the help!
     
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  14. Aug 12, 2011 #13
    Newguy: You should take a look at Einstein's original RELATIVITY....The book is available for free online and Einstein explains special relativity using high school algebra...

    Also you should recognize

    is an issue (for everyone) because relativity (and quantum mechanics, and a number of other areas of physics) requires new rules, new ways of thinking, new LOGIC, and our everyday day experience does NOT reveal those to us. For example, while you cannot expect the clock of a rapidly moving friend to agree with your stationary clock...who would have expected that from our everyday experience?? It took an "Einstein"!!!!

    For example black holes are NOT logical in everyday thinking....but even Einstein refused to believe they could exist. Is quantum mechanics "logical" : again, even Einstein refused to believe the imprecision, the statistical limitations, it imposes.
     
  15. Aug 12, 2011 #14
    Yes. http://www.bartleby.com/173/
    But see also:
    http://www.fourmilab.ch/etexts/einstein/specrel/www/
    That earlier and more precise formulation about SR is sometimes clearer. :tongue2:
    I disagree! Although our everyday day experience is different, every time that people told me (and almost convinced me!) that I should use "new logic", it turned out that some subtle aspect was not well understood. There are no other "logics": either our thinking is logical and correct in principle, or illogical and therefore in principle wrong. In particular SR does not require a new way of thinking (indeed, much to my surprise).
    Not really :wink:
    Larmor, Lorentz-Poicare, Einstein ...
    - http://en.wikipedia.org/wiki/History_of_special_relativity
    Unexpected is different from illogical. And the biggest remaining issue is, IMHO, not free will vs. predestination, but Bell's theorem (and it's still not solved!).

    Cheers,
    Harald
     
  16. Aug 13, 2011 #15
    Thanks for the input, guys! I will not argue whether relativity and QM require new logic or not. I will, however, say that it is much harder to learn about relativity and QM because the effects are nothing like we experience in everyday life; although, with the right equipment you can observe wave-particle duality in QM. As far as relativity goes, it sure would be great if I could jump into a space ship and accelerate to 0.9c so that I could actually observe the effects. Everybody learns better by actually observing things. Some of the physics that we observe in everyday life is totally second nature to us, but yet, if it was not observable it would be very difficult to in vision. For example, if you set a hammer down on a slanted rooftop, it might stay right there, but yet, if you give it any little push to start it moving, it will never stop until it hits the ground. I can’t imagine trying to explain that to somebody who has never seen it and doesn’t understand it. However, that is kind of the mission when it comes to learning about relativity and QM.

    I will have to take a look at that book. Special Relativity in terms of algebra is something that I could understand. I am a college student right now, and will be taking calculus this semester, but for now, I know no calculus. Most of the equations that you run into in relativity don’t require anything special beyond algebra to manipulate, but that is only if you are plugging numbers into them and solving. If you actually want to understand where most of the equations were derived from, you need to know calculus. I'm anxious to see how Einstein explains it in terms of algebra.
     
  17. Aug 13, 2011 #16
    I have read through the thread, and I am still having trouble understanding how it is possible for a physical object to age slower near the speed of light than it's still counterpart, even after it has slowed down and observed from any frame of reference. I understand the light clock, but how would that principle apply to for example, a watch, that doesn't use light pulses to calculate time.
     
  18. Aug 14, 2011 #17
    In really simple terms the faster you move through space-time that faster time passes for you. The real question is what if you could stop moving have zero speed what would time do.
     
  19. Aug 14, 2011 #18

    WannabeNewton

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    Not quite correct. In your reference frame time never passes "faster" or "slower" for you. Remember that in your reference frame you are at rest so the components of your 4- velocity are zero except for the one corresponding to the time basis. However, other objects that are not at rest relative to you will experience a time dilation as measured in your frame.
     
  20. Aug 14, 2011 #19
    Well, it's all the same no matter what the nature of the time piece used. So wrist watch vs lightclock vs planetary motion vs atomic clock, doesn't matter. Everything is governed by the rate at which time itself goes by. Just as the photon bounces slower per the moving observer, so too do the arms of a mechanical clock attached to the lightclock revolve slower. As someone here already mentioned, you can replace the bouncing photon with a steadily bouncing ball. The result is the very same. A steady bounce is just to say "a steady cyclic activity" of any kind. No matter what the activity, if it's of material nature, then it ages because time goes by. The ticking of a time-piece is the aging of a time-piece.

    There's much more to it than that, but to go into that opens up many more cans of worms that you are likely not ready for yet. Technically, the rate at which time passes by me per me is the same rate at which time passes by you per you. That's called "the rate of proper time". Wrt the interval between 2 defined events, the LTs relate a duration of a moving clock (per you) to the duration of your own clock (per you), which yields a "relative rate of time" in which the moving clock always runs slower. It's a frame-to-frame relation.

    GrayGhost
     
  21. Aug 14, 2011 #20
    You are right newton but if you put a man on a space ship and his speed was 99% of the speed of light for 5 years when he gets off his ship a lot more then 5 years will have passed when compared to someone on earth as we are only traveling 0.1933% of the speed of light. So it would seem that faster you move through space-time the faster time travels for you, but only when you have a reference point to compare it to that is moving slower.
     
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