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Opinion/discussion/advice on a simple thought experiment please

  1. Apr 13, 2008 #1
    I am not a physics expert but have been having a discussion about the effects of the Special Theory of Relativity with a friend.

    I came up with an example where time does not actually alter at high speeds, although it can be perceived to by a stationary observer because of the time it takes an image (light) to reach that observer. I am just wondering whether this example is "correct" ie - if somebody staged this experiment for real, would it work in a logical way as I am suggesting, or would there be some sort of strange result becuase of the effects of SR?

    Nb. for this example you have to assume that (i) it is possible to travel at ridiculously high speeds, (ii) someone has invented an amazing telescope and (iii) a month is exactly 1/12th of a year.
    I think that one of the reasons this is supposed not to work as I have described is because of Length Contraction. ie if Dude B is travelling really fast, the distance between him and Dude A becomes less during the period he is travelling. If he keeps moving for 6 months and travels a distance of 1/4 of a light year, then he when he comes to a standstill and looks back, he has actually travelled further than that. Also, apparently according to SR theory, time is running slow for him - he will also have been travelling for longer than a "stationary" 6 months - so there are 2 factors causing him to have travelled further then simple logic would suggest.

    Length Contraction is an almost impossible concept for me to grasp though. One of the reasons is that, to my mind, it really complicates what the speed of light itself is. I read that (using approximation here) if something travels at around 90% of the speed of light, length contracts by 50% - what appeared to be 2 light years to a stationary object becomes just 1 light year to the object travelling at 90% the speed of light. This is basically how I understand the Twin Paradox is explained. So what happens when you apply this principal of Length Contraction to light itself? Say there is a star that is 10 light years away from me. Obviously that means it takes light 10 years to travel that distance and I am seeing the star as it was 10 years ago. But, while light is travelling (at the speed of light), doesn't that distance become almost nothing... meaning that the light should arrive almost instantly? Obviously not, as we still have a concept of distance and time based on the speed of light, but it seems in my non-expert mind to defeat the theory of Length Contraction.

    Sorry, I know I haven't really given a question to answer here. I have given an example of what I would expect to happen based on my logical understanding of the world then tried to explain to myself how Einstein's theory would mean the outcome is different, but not been able to grasp it because it seems to be self defeating somehow.

    Any input would be appreciated -what am i getting wrong etc - but please try and keep in fairly simple terms for me!
  2. jcsd
  3. Apr 13, 2008 #2
    I will talk only about that distant star and 10 years. So - photon would think that no time has passed.

    You measure time and distance so that a photon gets away from you 300 000 000 meters per second. If you start chasing the photon from the distant star very fast, and after your observations and calculations it gets 300 000 000 meters away from you only once you have reached the earth then you and your wristwatch would say that one second has passed. Time would have slowed down.

    As to the Length Contraction - as you would have traveled at some 299 999 999.99... meters per second then seeing earth after one second the whole distance would seem like being 299 999 999.99... meters away from your starting point. As on earth's and your star's world the distance was much higher (10 light years) that whole world would seem to be contracted for you.

    But I am not a physics expert as well and I currently have problems with understanding the light traveling to the opposite direction - so maybe some or all of this my reasoning is somehow wrong:)
  4. Apr 13, 2008 #3

    Ken G

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    The way you've set it up does in fact get messed up by special relativity when the stationary observer (Dude A) looks at Dude B's calendar. Time progresses normally for Dude A's own calendar, but Dude B seems to be flipping through the pages at a strange rate, and it is not the rate that your thought experiment gets because you imagine that time is progressing the same for B as for A. It is a very common misconception about time dilation that it is purely some kind of optical illusion due to the finite light travel time. So here's what you have to replace that notion with:

    All of the weird/bizarre/interesting effects of special relativity appear after you have already corrected for the finite light travel time.

    So what that means is, Dude A does the calculation you mention, expects to see Dude B flipping at a certain rate, but that's not what he will actually see when he does the experiment! The only way to make the experiment work is for A to conclude that time was "running slowly" for B. B will not think his own time was running slowly, so there is a disagreement here, even after all light travel times are corrected for. That's relativity.

    It gets even weirder. Dude B, while he is approaching A at c/2, will do the same experiment looking at Dude A's calendar-- and will have to conclude that Dude A's time is running slowly (not quickly as you might expect from A's result). So if A thinks B's trip takes 2 years, and A thinks B's time was running slowly all the while, then A will say 2 years elapsed for A and less than that elapsed for B. But B thinks it took 2 years for B to make the trip, so less than 2 years must have passed for A! How can they both think that?

    The only way is if they can't agree on "what date it was" when B started the trip! (I'm imagining B was always moving at c/2. If you accelerate B, you will change how B perceives things.) This is called the "relativity of simultaneity", and unless you include it, you will run into paradox after paradox (like the twin paradox). Time dilation alone will never be enough-- you will also need the relativity of simultaneity to make sense of it all.

    So in summary, these are all the things you need for special relativity:
    1) first correct for all light time-of-flight effects, then you still get:
    2) time dilation (this is all many people get)
    3) length contraction (you won't always need it, but watch out if you forget it)
    4) relativity of simultaneity (observers in relative motion can't agree what "now" means, so if you think they do, nothing will work out right)

    Leave out any of these at your peril. If you want a one-step mathematical tool that automatically includes steps 2-4, then look up "Lorentz transformation". You still have to do step 1 manually, but you already showed you can do that.
    Last edited: Apr 13, 2008
  5. Apr 13, 2008 #4
    No, Ken G, I would disagree that during B's trip both would see slowed down images. It's exactly the opposite. It's quite directly explained in the twin paradox.

    As soon as B starts the trip (01/01/2008) he starts seeing A's time running faster. B still sees the 01/01/2007 when he looks into the telescope. B trips for his personal 6 months at half the speed of light and all the time sees A's time running much faster. When A starts seeing B's time running much faster? After one year - i.e. - when it's 01/01/2009 for him and he gets an image of B getting into the ship on B's 01/01/2008.

    I.e. if you travel away from each other only then you see each other's time slowed down.
    If you travel towards each other you will see each other time flowing faster. You get the other guys photons faster if you travel towards him.

    And when you travel towards each other it becomes important who is traveling and who is not. The guy that is not traveling will get older sooner. When they meet, the traveler will be younger.
    Last edited: Apr 13, 2008
  6. Apr 13, 2008 #5
    So - anony-mouse: once B turns the callendar to 01/07/2008 and looks at A he will see that he has almost reached him and that during the last 6 months somehow he has reached, e.g., 06/01/2009 (when B started the trip he saw A celebrating 01/01/2007). And what B will see A doing? He will see A baking a cake - for it will be 6 days since he has seen his friend B travelling to him at half the speed of light, aging 1 month per day and getting to be here any moment.

    The number here of course are not correct but an approximate image of what would happen.
  7. Apr 13, 2008 #6
    jviksne you are confusing me a little with the dates you are using there.

    In my example, B sets off on 01/01/2007 and stops travelling on 01/07/2007 (Nb. for clarity I am using UK, not US date format.)

    Can't understand why you think time is elapsing quicker for the traveller as that is the exact opposite of what I thought is expected to happen under SR theory.

    Not quite sure what the cake has to do with it either :/
  8. Apr 13, 2008 #7
    Hello jviksne.

    Time dilation makes a clock moving relative to you appear to you to run slowly in whatever direction it moves. What you are describing is the optical effect which you would see if the clock moved in different directions. Time dilation is not an optical effect which has different results depending on whetehr a clock is moving towards or away from you.

  9. Apr 13, 2008 #8
    Anony-mouse: sorry about the start date, I somehow misunderstood that B started off on 01/01/2008. So for your situation I would say that it would be the following way:

    1) A on 01/01/2008 sees B leaving his planet on 01/01/2007.
    2) A sees B travelling towards A. B's clock seems to be running much faster. B also seems to be covering the distance much faster. I am not sure about the numbers, but let's say that A sees that B is aging one month per A's day. As well as his speed seems to allow him to cover that 1 lightyear distance in 7 days (optical illusion).
    3) After 6 days A sees B turning his callendar to 01/07/2007, i.e., A will see that during the last 6 days, B has aged for 6 months. He will also have covered 6/7th of the distance.

    What if B would not stop:
    4) After one day B lands and shakes hand with A. B's callendar shows 01/08/2007. A's callendars shows 07/01/2008. A is older. (fine, no silly cake:))

    Please note that the rates could be a bit different but approximately this is how it would happen.

    Hello Matheinste - not sure but I think I agree. Does it somehow contradicts with what I have stated? B's time actually is running slower when he moves towards A, but A gets an optical illusion that it moves faster.
    Last edited: Apr 13, 2008
  10. Apr 13, 2008 #9
    Anony-mouse: sorry again - discard completely my previous post. I just noticed you were talking about 6 A's months.

    So during those 6 months all the time he really would have observed B's time running faster.

    As soon as B started the trip, distance between the planets became shorter for him.
  11. Apr 13, 2008 #10
    Helo jviksne.

    """I.e. if you travel away from each other only then you see each other's time slowed down. If you travel towards each other you will see each other time flowing faster. You get the other guys photons faster if you travel towards him."""

    I agree that this is this is what you see. But this is not what actually happens. If this is what you mean and i have misread or misunderstood what you said then the fault is mine and i apologise.

  12. Apr 13, 2008 #11
    Matheinste - actually there was a mistake in the idea of the very last sentence of that post, but not to go into an off-topic and as I guess I have been spamming here too much I won't go into details. Your comment was correct. (that does not change the validity of what I said to Anony-mouse in my two last posts as well as to Ken G that in this case both would see each others clocks running faster).
  13. Apr 13, 2008 #12
    Hello jviksne.

    No harm done.

    Thanks Matheinste.
  14. Apr 13, 2008 #13

    "The date is now 01/07/08. Dude A looks at Dude B's calendar and sees the date 01/10/2007. (6 months have gone by and Dude B has turned the page on his calendar "

    B's clock slows (5 months), his calendar is 01/06/07, but A will not see it until 9 months later at 1/3/08.
  15. Apr 13, 2008 #14

    Ken G

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    You are misreading my post if you think I said anything at all about "images", I was referring entirely to the concept of time as reconstructed after correcting the images for time of flight effects.
    Time running faster is never "seen", it is calculated. This is a crucial misconception we are trying to help Anony-mouse get away from, not underscore. While the distance between A and B is closing at a constant rate, both A and B infer that the other's time is running slow, that's the crux of time dilation.
    Taken literally, that statement is very misleading, as it appears to violate the main axioms of relativity. You must be imagining that both A and B start at rest, and one of them accelerates toward the other, thereby defining "who is traveling". If you don't specify that, you can create more confusion than you erase.
  16. Apr 13, 2008 #15

    Ken G

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    I think you mean 2008, yes? The crucial point you will need to recognize is that if B is stationary with A on 01/01/2008, seeing 01/01/2007 on A's calendar, then B suddenly accelerates to c/2, when he does that acceleration, he instantly thinks a great deal of time has elapsed for A, and he also instantly thinks A is a lot closer. That is the "relativity of simultaneity" and the "length contraction" here, that everyone who is having trouble wants to overlook, but nothing makes sense if you overlook them.

    I'll let you work out the numbers (there's a lot of calculating to do), but the key point is, if B accelerates toward A, B will think the distance to A has suddenly contracted. A will not think that. So right away you have broken the symmetry. Also, B will think a great deal of time has passed for A (the relativity of simultaneity), and A will not think any time has gone by for either A or B during that quick acceleration. Another symmetry break. Finally, both A and B will think the other's time is going slowly (actual time, not calendar images) during transit, and that is the only part that preserves the symmetry. But the symmetry is already shot to bits, and sure enough, if A and B were the same age before B accelerated toward A, then B will arrive younger than A.
    jviksne is confusing the way time of flight plays with what you see looking through a telescope, and what you infer is actually happening to time. You are right, time is inferred to be elapsing slowly for the other dude-- except while B accelerated, as a whole lot of time is inferred by B to have elapsed for A during that acceleration.
  17. Apr 14, 2008 #16
    No, I mean 01/01/2007.
    Again, as per my original post, It is 01/01/2008 and A sees B begin his journey on 01/01/2007, because B's starting point is 1 light year away.

    I don't think that this alters the basic concepts explained in your reply, but just wanted to clear that up.

    This is one of the points raised in my initial post (the comments after the quoted example). I have read about the principal of length contraction but don't understand how they can be true because of one, seemingly huge, contradiction that defeats the theory:

    If, when you travel at near-light speeds, length contracts then how can we measure the speed of light?

    ie - A star is ten light years away from our stationary perspective so the light from that star must take ten years to reach us. That is why we measure the distance in light years, right?

    But, according to the principal of length contraction, as the light is travelling to us really fast, that distance has shrunk massively, so it will not take then light years to reach us at all. We will see the light from that star almost as it is now.

    But that is not the case is it? So how can the theory of lenth contraction be true. Or does it not, for some reason, apply to light? If not, why not?
  18. Apr 14, 2008 #17
    Ok, sorry KEN G, I thought you meant that Anony-mouse statement that "The image Dude A is seeing of Dude B's calendar has sped up" is wrong. And that my one statement really is misleading. I agree that the image will be sped up but calculations will show that time goes slower.

    Sorry Anony-mouse for messing things up here!
  19. Apr 14, 2008 #18

    Ken G

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    There's your problem, you are thinking in terms of "absolute distance" somehow shrinking. When the light is emitted, we still think it's 10 LY away, and we still think it takes 10 years to get here-- but the light thinks there is no distance at all, and the light will take no time to get here from "its own perspective". Neither the distance traveled, nor the time it took, is the same for us as for the light. All we agree on is the value of c, though for the light it's a "singular" ratio of no distance to no time (so think of 0.99999c instead).

    The key points are that two obervers disagree on 3 things: how much time the trip took, how far the trip was, and what was the date at A when the accelerated speed was reached for B. You need all 3 of these to avoid paradoxes, they are all equally important to relativity.
  20. Apr 14, 2008 #19

    The rate of a moving clock slows as a result of its speed, agreed.
    The rate of perception depends on direction, i.e. doppler effect, agreed.
    A clock is a frequency, therefore it shifts the same as light as jviksne noted.
  21. Apr 15, 2008 #20
    Gotcha. That's cleared it up a bit for me now, cheers.

    I think I have a vague understanding of the basic principals of SR now. (I'm not worried about getting into the complext maths and calculations behind it, just the concepts).

    What I want to do next is look into what evidence there is supposting the theory... I am a sceptic by nature and these concepts seem a bit "out there" so I am wondering if there is any proof.
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