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Thread: Question on time dilation and length contraction

  1. #1 Question on time dilation and length contraction 
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    Hi,

    If a person standing still measures the length of an object moving at relativistic speeds the object will seem shorter in the direction of motion. If the person moving at near light speed measures an object standing still it will seem shorter in the direction of motion. Right.

    If a person standing still looks at a clock moving near light speed, that clock will appear to move slower. If a person moving at near light speed looks at a clock standing still it will appear to move faster. Right?

    In the first case each sees the same thing.
    In the second case each sees the opposite thing.
    Right?

    Thanks,
    Rusty


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  3. #2  
    Moderator Moderator Janus's Avatar
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    Both observers would measure the other clock as running slow. Again, there is no way to tell if you are the observer "moving" or "Standing still". The is no absolute frame of reference against which motion can be measured.


    "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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  4. #3  
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    Let's say the thing moving always accelerated to get up to speed. In a previous example somehow the space ship only sees 6 years while the stationary thing sees 8 years. The stationary object sees a longer time somehow. If both clocks move slower, how does that happen?

    Rusty
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  5. #4  
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    Quote Originally Posted by rrw4rusty View Post
    Let's say the thing moving always accelerated to get up to speed. In a previous example somehow the space ship only sees 6 years while the stationary thing sees 8 years. The stationary object sees a longer time somehow. If both clocks move slower, how does that happen?

    Rusty
    Which example? Which thread and which post?
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    "So as far as the Earth in concerned, the spaceship leaves Earth at 0.8 c, takes 10 years to reach the other planet while the spaceship clock only ticks off 6 yrs."
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    Quote Originally Posted by rrw4rusty View Post
    "So as far as the Earth in concerned, the spaceship leaves Earth at 0.8 c, takes 10 years to reach the other planet while the spaceship clock only ticks off 6 yrs."
    You need to review your earlier posts. You have asked essentially the same question 3 times and received the correct answer.
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    Moderator Moderator Janus's Avatar
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    Quote Originally Posted by rrw4rusty View Post
    Let's say the thing moving always accelerated to get up to speed. In a previous example somehow the space ship only sees 6 years while the stationary thing sees 8 years. The stationary object sees a longer time somehow. If both clocks move slower, how does that happen?

    Rusty
    If this is the example for which I did a break down, we were talking about a ship traveling from the Earth to a distant planet, the Earth measured ten years for the trip and the ship 6. In this case we are measuring the interval between two events: When the ship is next to the Earth, and when the ship is next to the other planet. We then compare how both the Earth and ship measure this interval. The Earth measures it as taking being 10 yrs. (8 ly at 0.8c) The ship measures it at taking 6 yrs (distance between Earth and planet length contracted to 4.8 ly, which take's 6 yrs to cover at 0.8c.

    The thing you need to accept is that it doesn't matter which of the two, Ship or Earth, that we treat as "stationary" we still get each of these observers measuring the same answers as above for the time interval.

    In the case of acceleration, our non-accelerated frame will measure a time dilation for the accelerated clock which only relies on the velocity difference between the frame and clock. An observer accelerating with the clock will measure additional effects beyond that caused by relative velocity. They will measure clocks in the direction of the acceleration as running fast, the further "ahead" they are the faster they run. Clocks in the other direction will run slow. (even if there were no relative velocity difference between them and another clock, that clock would run fast if in the direction of the acceleration and slow if in the opposite direction.
    "Men are apt to mistake the strength of their feelings for the strength of their argument.
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    Quote Originally Posted by Bufofrog View Post
    Quote Originally Posted by rrw4rusty View Post
    "So as far as the Earth in concerned, the spaceship leaves Earth at 0.8 c, takes 10 years to reach the other planet while the spaceship clock only ticks off 6 yrs."
    You need to review your earlier posts. You have asked essentially the same question 3 times and received the correct answer.
    Give the man a gold cup. I just can’t get this one idea sorted out. I feel like my son when he asked how a rocket worked in space when the rocket exhaust did push against anything like the ground. I couldn’t explain it in a way that made sense to him. In this case, somehow both clocks run slower, both view the other as accelerating away, then traveling away at the same speed, yet one (the one that accelerated using power) sees less time. I guess I’ve worn out this forum on the question but I’ll keep hammering away until I get it. I will re-read everything again.

    Rusty

    Edit: I want to thank the forum for being so patient with me. I want to understand.
    Last edited by rrw4rusty; February 3rd, 2019 at 11:56 AM.
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    Quote Originally Posted by Janus View Post
    If this is the example for which I did a break down
    I think it does not break down. You are only employing SR's change in planes of simultaneity without introducing Rindler observer or equivalence principle of GR. From traveller’s point of view in your plane simultaneity approach you also have 12.8 years of discontinuity, but it is not distributed like in the standard approach.

    Your discontinuity is not around the middle point of the trip i.e. you do not have lack of 6.4 years of Earth twin equally at both sides around the middle point of the trip like in standard approach. You have discontinuity and lack of the first 6.4 years of the Earth twin, and another 6.4 years from the middle point of the trip. It is still 12.8 years of the trip covered by the plane jump + 7.2 retardation clock years from the traveller’s perspective. Numerically it is equal to 20 years from the traveller’s perspective like in the standard plane simultaneity approach.

    It is worth noting that Einstein was introduced with plane simultaneity approach for resolving twin paradox. He did not like discontinuity in the age of Earth win, and jumping planes reminded him to non-locality of QM. So, he employed equivalence principle of GR.

    Regards,
    Zlatan
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    Quote Originally Posted by Zlatan Stojanovic View Post
    Quote Originally Posted by Janus View Post
    If this is the example for which I did a break down
    I think it does not break down.
    English is difficult. He didn't say it (relativity? nature?) breaks down -- he specifically says that he did a break down. To break something down means to break something into its parts, as in to explain the steps in a chain of reasoning, which is what he is referring to.
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    Forum Freshman Zlatan Stojanovic's Avatar
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    This is for those who do want to see my argumentation and the point I am making:

    To depict how SR's solution of the twin paradox has problems by employing the plane of simultaneity and the reciprocal time dilation, just put twin paradox experiment in the comoving frame of cosmic fluid of FLRW metric. Imagine the balloon analogy. Earth twin corresponds to the twin comoving with cosmic fluid. Travelling twin by employing clock retardation to Universe time puts himself forward in time than the rest of Universe. By changing to other reference frame of the trip he will now be backward in regards to comoving cosmic fluid time (the plane jump). Like plane of simultaneity mentioned in the reference, he travels forward and then jumps backward in time comparing to comoving cosmic fluid frame! How much of the dynamics of GR is needed for the Universe to reach the same forward traveler’s point in time, comparing to the one simple relativity change of traveler perspective? The last also applies to the twins' reciprocal time dilation in the GR's conventional interpretation of twin paradox. The absence of the aforementioned is the advantage of the Einstein’s relativized ether interpretation of GR. Following the Lorenz-Poincaré track in twin paradox, the pair: time dilation and length contraction of travelling twin is actuality, so, the twin does not go ahead of cosmic time during entire trip. Proper time of Lorenz/Poincaré's travelling twin is less than the maximal proper time of comoving cosmic fluid along the entire trip, which is in accordance with the results of authors.

    Recall the words:

    "What is fundamentally new in the ether of the general theory of relativity as opposed to the ether of Lorentz consists in this, that the state of the former is at every place determined by connections with the matter and the state of the ether in neighbouring places, which are amenable to law in the form of differential equations; whereas the state of the Lorentzian ether in the absence of electromagnetic fields is conditioned by nothing outside itself, and is everywhere the same. The ether of the general theory of relativity is transmuted conceptually into the ether of Lorentz if we substitute constants for the functions of space which describe the former, disregarding the causes which condition its state. Thus we may also say, I think, that the ether of the general theory of relativity is the outcome of the Lorentzian ether, through relativization." Albert Einstein, 1920.

    The same is applicable to the Universe not just in places/space, but in the time as well. I have earlier depicted the path toward it.

    Regards
    Zlatan
    _______________
    Reference edit:
    Zlatan Stojanovic. On the Twin Paradox and Ether. J Space Explor. 2019;8(1):153.
    Last edited by Zlatan Stojanovic; March 8th, 2019 at 06:50 AM.
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  13. #12  
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    I suspect that the difficulty people have with time dilation and length contraction is that they try to understand it within a three-dimensional context instead of the four-dimensional context in which it occurs. One is prevented from understanding it within a three-dimensional context because when two observers are at constant velocity relative to each other, they no longer share the same three-dimensional space. This is the same as saying that they do not agree about simultaneity, but not sharing the same three-dimensional space allows the two observers to measure different values for ostensibly the same thing. It is important to note that all observers do observe the same four-dimensional reality irrespective of the apparent differences due to time dilation or length contraction. There is no inconsistency in relativity. Given reality from any one observer's point of view, the reality from any other observer's point of view is determined.

    Four-dimensional spacetime is properly understood as a geometric notion. That is, one considers distances between points in spacetime using generalised Pythagorean formulae. Thus, one can create analogues of time dilation and length contraction using distances in ordinary three-dimensional space. For time dilation, consider two straight paths diverging from the same location at 45°. If from either path, one looks perpendicularly from their own path towards the other path, then the length of the other path will be the length of one's own path. Note that each person's path is shorter than the other person's path, yet there is obviously no inconsistency in this three-dimensional analogue. For the twin-clock paradox, there are two different paths between the same two locations. One of the paths is straight, while the other path is not straight. The shortest distance between two points is a straight line. Therefore, the straight path is shorter than the other path. Note that this is not in conflict with the time dilation analogue. For length contraction, consider the width of the paths. For the person's own path, the width is the distance perpendicularly across the path. But if the person on the other path looks perpendicularly from their path towards the other path, the width they see of the other path will be the distance obliquely across the path and will be the distance perpendicularly across the path.

    However, it should be noted that there is an important difference between the geometry of four-dimensional spacetime and the geometry of ordinary three-dimensional space. This difference leads to moving clocks being slower instead of faster, and moving rulers being shorter instead of longer. It also leads to the existence of a fundamental speed such as the speed of light.
    There are no paradoxes in relativity, just people's misunderstandings of it.
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  14. #13  
    Forum Freshman Zlatan Stojanovic's Avatar
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    I have read your post KJW, and as usual, I find it very interesting.

    I would very appreciate if you could do pinpoint in my argument where I have problems, so that I can think more about it.

    Regards,
    Zlatan
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