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Very simple relativity questions

  1. May 20, 2007 #1
    I've only just started reading on this topic at a very basic level, i just have a few questions which im uncertain about.

    If one is to travel at 99.99% the speed of light in a rocket car on earth, a day for the person traveling at this speed would seem to be a week for everybody else on earth. Will the person in the car feel time pass quickly or it will everything seem normal. Secondly, if the time passes quicker inside the car, will the person age at the same rate as everyone else outside but just die at a younger age or when the car stops the person will be much younger than everybody else?
     
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  3. May 20, 2007 #2
    The whole point of relativity is that the same exact laws of physics apply to anyone in any frame of reference. So the person in the rocket car, as long as he doesn't have any windows to see the outside world, has no idea that he is even moving. All the usual laws of physics apply from his point of view, so nothing seems unusual or indicates to him that he is moving, let alone that his time is different from everyone else's time.

    Of course when he gets out of the car he will be younger than the rest of us. Relativity isn't just some effect on human biology, it's a real physical principle.
     
  4. May 26, 2007 #3
    I guess this is what usually goes by the name of the 'twin paradox'. Given that from the point of view of the guy in the rocket car the rest of the world is speeding by, the question arises why, after he stops, ehem, the world stops speeding by, he is indeed younger than all the rest. If they were speeding, they should be yonger.:confused:

    The usual killing answer in any forum then is that due to the acceleration and deceleration involved, this is not covered anymore by Special Relativity. Instead General Relativity is needed and consequently I have to learn what a tensor is before I can understand why it is as it is.

    Nevertheless I venture to ask if there is a way to understand the twin paradox without learning tensors first.

    Harald.​
     
  5. May 26, 2007 #4
    Yes, this is the twin paradox, and no, I don't think you need to know what a tensor is to have at least some understanding of it. I don't know what a tensor is (well, OK, I do, but I'm not enough of a math-head to actually be able to approach GR), but I think I have some understanding.

    Since one of them is accelerating and decelerating, it actually doesn't look from his point of view like the whole world is moving and he is standing still. He can't say that. He feels acceleration and deceleration, so he knows that he is moving. He doesn't just "see the world slow down and stop", he actually feels himself slow down and stop, like you would if you were in a speeding car that slammed on the brakes. The rest of the world feels no such acceleration and deceleration, so they actually can claim they aren't moving.

    The golden rule of SR is that all reference frames are valid, except reference frames that are accelerating, decelerating, or feeling gravity. So Earth is a valid reference frame in the twin paradox (if we assume Earth's gravity is so weak it can be considered "about 0" in cosmic terms), but the spaceship moving the other guy around the planet is not a valid reference frame. SR can't really say anything about "his point of view" during the time he is accelerating and decelerating. However, Earth's point of view on the whole situation, can be described, rock solid, using SR.

    This is no big deal, it just means if you want to understand what's happening, you have to analyze the whole thing from Earth's point of view to get the right answer. Looking at it from Earth's POV, he is younger. So that's what happens. And whatever happens from the traveller's point of view, we know it must be some kind of situation that ends up in "everyone else being older" when he stops and steps off the spaceship, because we know (by using a valid reference frame to do the physics) that that is what needs to happen.
     
  6. May 26, 2007 #5

    Chris Hillman

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    http://www.math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html
     
  7. Jan 20, 2010 #6
    If a traveller from the earths frame of reference takes an atomic clock with him, the atomic clock will show less time has passed upon the travellers return compared to an identical clock left on earth. Hence the vibrations of the atoms constituting the travellers clock have slowed down during the journey in this instance from an earth Frame. Therefore relative motion slows atomic activity. Is this correct? Also at the approach to light speed does atomic activity not also approach zero.
     
  8. Jan 20, 2010 #7
    If a person is travelling at any speed there time is going slower. The only reason you say at the speed of light is that the difference would be noticable. For instance, if observer A was stationary- if earth was the inertial frame- and another person, or B, was moving faster than that person over the earth, even if it was only slightly, there time would be going slower.

    Also, time goes slower if the person is further away from the gravitational force. For instance, the earth. If someone was on the 100th floor and someone else was on the ground, the person on tthe grounds time would be going slower, assuming that they were both stationary.

    Hope this helps.
     
  9. Jan 20, 2010 #8
    Yes thanks - as I thought.

    Any idea on the mechanism for how the changed velocity causes the slowing in atomic activity for the traveller WRT the earth frame.
     
  10. Jan 21, 2010 #9
    From the perspective of the earth's rest frame everything at rest in the rocket's rest frame is happening more slowly ... even the rate of an onboard Cesium clock. But from the perspective of the ship's rest frame, everything at rest in the earth's rest frame is happening more slowly. These effects can be measured, using the clocks and measuring rods in one's rest frame. But note that when the rocket changes rest frames, and comes to rest in the earth's rest frame, then an onboard astronaut must reassess his position. Believing now that the measuring rods and clocks at rest in his new (earth) rest frame give correct measurements, he realizes that it was himself who was actually aging more slowly while he was moving relative to earth's rest frame. When he comes to rest in earth's rest frame, his onboard clock will read less than the earth rest frame clock at that location. And, since all the clocks at rest in earth's rest frame are presumably synchronized, he concludes that he's aged less than his counterpart who remained "back home" permanently at rest in earth's rest frame. (He can verify that this is the case by returning to his starting point.)
     
  11. Jan 21, 2010 #10
    I can accept that the travellers has aged more slowly.
    But why is this, or how did this happen. How does relative motion or increased gravity cause a slowing of clocks?. Or is this a naieve question to ask.
     
  12. Jan 23, 2010 #11
    Regarding time dilation and relative speed, you might find it useful to go to www.maxwellsociety.net and then click on the "Learning To Love The Lorentz Transformation" link (about 6 lines down on the home page).
     
  13. Apr 2, 2010 #12
    This question has puzzled me for years. Can anyone give an answer that makes sense?

    Two spacecraft, A and B are next to each other in space. They synchronise their clocks.
    They both start moving away from each other at immense speed.
    From the point of view of spacecraft A, it is standing still, while from their point of view spacecraft B is moving at close to the speed of light, and the clock on spacecraft B is moving slower.
    From the point of view of spacecraft B, it is standing still, while from their point of view spacecraft A is moving at close to the speed of light, and the clock on spacecraft A is moving slower.

    They then both stop and start moving towards each other in the same way.
    From the point of view of spacecraft A, it is standing still, while from their point of view spacecraft B is moving at close to the speed of light, and the clock on spacecraft B is moving slower.
    From the point of view of spacecraft B, it is standing still, while from their point of view spacecraft A is moving at close to the speed of light, and the clock on spacecraft A is moving slower.

    So it made no difference whether one stood still and the other moved, or both moved. The time dilation occured because of relativity.

    When they meet they compare their clocks.
    Spacecraft A sees their clock is showing a later time than slower clock B.
    Spacecraft B sees their clock is showing a later time than slower clock A.

    Are they forever arguing about what time both clocks are displaying? Do they perceive a different value is displayed on both clocks depending which spacecraft they were in?

    What if an observer stayed in between them, and watched them travelling at the same speed, do they see a third value on both clocks that says the same time?
    And the same for their own clock, do they see one value while those who went in both spacecraft see a different value on their clock, but at least can agree between them that they see the same value?

    And if all this craziness is true, what if the clocks are a part of a time bomb? Do the clocks explode for some people, and not explode for others?
     
    Last edited: Apr 2, 2010
  14. Apr 2, 2010 #13

    JesseM

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    What do you mean by "point of view"? Normally in relativity if you talk about an observer's point of view you're talking about the inertial frame where they're at rest, but if spacecraft A turns around, there is no single inertial frame where it was at rest both before and after the turnaround (likewise with B), because an inertial frame is defined as one moving at constant velocity for all time (constant speed and constant direction). The idea that moving clocks run slow only applies in inertial frames, it wouldn't apply in a non-inertial coordinate system. And if you want to switch what inertial frame you use in the middle of the journey--switching from the frame where A was at rest during the outbound trip to the frame where A was at rest during the inbound trip, for example--then you have to take into account the relativity of simultaneity, which says that different frames have different opinions about which pairs of spatially-separated events happened at the "same time". So in this case, the first frame's opinion about what clock-reading on B was simultaneous with the event of A turning around will be different than the second frame's opinion on that question. In this section of the twin paradox FAQ there's a diagram showing lines of simultaneity for an observer ('Stella') that turns around at the midpoint of her journey, the downward-sloping blue lines being lines of simultaneity in the frame where she was at rest during the outbound leg, and the upward-sloping blue lines being lines of simultaneity in the frame where she was at rest during the inbound leg--you can see there's a large gap between the event on the worldline of the other observer ('Terence') that was simultaneous with the turnaround in the first frame, and the event on his worldline that was simultaneous with the turnaround in the second frame.

    [​IMG]

    Anyway, in your scenario if the move apart and come together in a perfectly symmetrical way (from the perspective of the frame that sees them moving apart and coming back together at equal speeds in opposite directions), they will both be the same age when they reunite, and all inertial frames will agree on this prediction.
     
  15. Apr 2, 2010 #14
    By "point of view" I mean "in the experience".

    Forget about the turning around and coming back then. But that should make no difference anyway, only the relative speeds and the fact time time slows down for moving objects relative to stationary ones.

    People claim if a spaecraft travels away from Earth, then turns around and comes back it is the same as if it had just travelled twice the distance in a straight line. Time has slowed down for it during the time it is travelling, no matter what the direction.

    From the point of view of A: A is stationary, B is moving. Time moves slower for B.
    From the point of view of B: B is stationary, A is moving. Time moves slower for A.

    Does time move slower for A or B when the clocks are compared?

    (And for C, that sees both A and B moving and itself standing still?)


    Is this true, a spacecraft leaves Earth very fast, returns, it seems to have travelled into the future. The occupant is younger than his twin brother who stayed on Earth?

    If so then the reverse should also be true: The one in the spacecraft stayed in the same place and the Earth leaves very fast, returns, it seems to have travelled into the future. The occupant of Earth is younger than his twin brother in the spacecraft.
     
    Last edited: Apr 2, 2010
  16. Apr 2, 2010 #15

    JesseM

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    What does "experience" mean? Are you talking about what they see visually with their eyes? Because that's not what time dilation in relativity is about (for example, if a clock is moving towards you you'll actually see it ticking faster rather than slower, it's only when you adjust for the different time the light from each tick had to take to reach your eyes that you conclude it was 'really' ticking slower in your frame)
    "Relative to stationary ones" is too vague, you can only judge whether a clock slows down by picking a particular spacetime coordinate system (reference frame) and looking at how much coordinate time passes between ticks of a clock. In a non-inertial coordinate system, the usual time dilation formula doesn't apply, clocks which are moving in the rest frame of a non-inertial observer might even speed up rather than slowing down. Only if you're talking about a purely inertial observer does it make sense to say that clocks moving relative to that observer are guaranteed to slow down (and 'relative to that observer' is just shorthand for 'in that observer's inertial rest frame').
    Who claims that, exactly? It's true that if you're calculating the time dilation of the spacecraft in the Earth's rest frame, then the speed is all that matters, it doesn't matter whether the ship turns around or not. But if you're interested in calculating the time elapsed on the Earth's clock from the point of view of a frame where the ship has an unchanging position coordinate, it certainly does matter whether the ship moves inertially or whether it accelerates at some point in its journey, because the normal time dilation equation only works in inertial frames.
    Not if "from the point of view of" = "in the non-inertial rest frame of", in that case it's no longer guaranteed that the clock of a moving observer ticks slower than the clock of a stationary observer. This would be true if A and B were moving apart in a purely inertial manner, though.
    You can only "compare" the clocks at a single location if one or both of them moves non-inertially, you have to specify whether this happens.
     
  17. Apr 2, 2010 #16
    You seem to be avoiding the questions I am asking!

    Xezlec claimed "Of course when he gets out of the car he will be younger than the rest of us." Speaking of a very fast car instead of a spacecraft, but the same applies. Is this true?

    But from the point of view/experience/frame of reference of the one in the car/spacecraft, they stayed still, while the Earth was moving very fast. It was in fact the Earth that was accelerating instead of the car/spacecraft. Is this true?

    There doesn't even have to be ANY acceleration, just two bodies moving relative to each other.

    And in the case of the two spacecraft moving away from each other, which one sees time slowed down when looking at the other moving relative to it?

    The clocks do not have to be at a single location if you do not want them to be!
     
    Last edited: Apr 2, 2010
  18. Apr 2, 2010 #17

    JesseM

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    No, I'm pointing out the ambiguity in your wording, and asking for clarification. If you don't answer my questions I can't help you--for example, can you address my first question about whether "experience" means what an observer sees visually or what is true in their rest frame or something else?
    Xezlec implied the car was moving inertially the whole time with the statement "So the person in the rocket car, as long as he doesn't have any windows to see the outside world, has no idea that he is even moving" (if the car was moving non-inertially, the person in the car would feel G-forces and therefore know he was accelerating). If "we" are also assumed to be inertial observers, then it is true in our frame that the guy in the car has aged less at the end of the journey, but in the inertial frame where the car was at rest throughout the journey, the opposite will be true, it will be we who have aged less than the guy in the car. Since the end of the car's journey happens far away from us, this is just an illustration of how different frames disagree about simultaneity for events which happen far apart. If both we and the guy in the car are aged 20 when the car departs us, and the car moves away at 0.6c, then if the end of the journey is defined as the point where the guy in the car turns 28, in our inertial rest frame this event is simultaneous with the event of us turning 30 but in the car's inertial rest frame this event is simultaneous with the event of us turning 26.4, so the two frames disagree about who has aged less.
    If they are not at a single location, then there is no single frame-independent answer to which clock has elapsed more time, because different frames disagree about the simultaneity of distant events.
     
  19. Apr 2, 2010 #18

    jtbell

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    If one of the bodies doesn't accelerate, they can't re-unite in order to compare their clocks directly. There's no physical contradiction caused by each body's clock "running slow" in the other body's rest frame, after you take relativity of simultaneity into account.

    (This is in the flat spacetime of special relativity; if the bodies are in free-fall along different paths under the influence of gravity, such that they can re-unite without having to fire rocket engines or whatever, then you have to analyze the results using general relativity.)
     
  20. Apr 3, 2010 #19
    The clocks do not have to be next to each other, just their values compared, wherever they are. There is no gravity, no firing of rocket engines, etc.

    It seems people are trying to create confusion where there is none. I will start again and simplify the question...

    There are two twins in spacecraft flying through empty space. Relative to each other each one is standing still from their own point of view, while the other is moving close to the speed of light.

    Spacecraft A observes time passing normally, but since spacecraft B is moving very fast then time is moving slower for them, their clock shows an earlier time and the twin is younger.
    Spacecraft B observes time passing normally, but since spacecraft A is moving very fast then time is moving slower for them, their clock shows an earlier time and the twin is younger.

    Which twin is younger, which clock shows the earlier time?
     
  21. Apr 3, 2010 #20
    In the above scenario they are both the same age. Their clocks show the same exact elapsed time.
     
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