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An apparent speed paradox

  1. Apr 25, 2006 #1
    Suppose you are travelling from Earth to a distant planet, few light years away. Assuming you have enough energy for your ship (and Eistein's theory is correct), I was wondering what is the optimal speed you need to travel at (in the interval (0,c)), in order to reach the planet in the minimum amount of time (as perceived from an Earth observer). I believe this speed is not very close to the speed of light, as time passes at a slower rate on the ship, than on Earth.
     
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  3. Apr 25, 2006 #2
    apparent paradox

    do you consider that the statement contains all the elements in order to be solved?
     
  4. Apr 25, 2006 #3

    HallsofIvy

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    You said "as perceived from an Earth observer". Why would the rate at which time passes on the ship be relevant? Clearly to the earth observer, the ship will get to the planet fastest if it is moving at the greatest possible speed- as close to the speed of light as possible.
     
  5. Apr 25, 2006 #4
    Isn't the time that passes on the ship a linear function of speed? That is, 0.99c is about twice as fast as 0.5c. But on Earth, the time is altered by a Lorentz factor, which is not a linear function.
    As an example, suppose you travel a light year with 0.5c. It takes you 2 years to get to the destination, and on Earth about 2.3 years have passed.
    Now suppose you travel the same light year with 0.99c. It takes you a little more than a year, but on Earth more than 22 years have passed. So you actually went slower!

    What is wrong here?
     
  6. Apr 25, 2006 #5
    The Pioneer Anomaly seems to indicate that time may not pass exactly as we have been led to believe. The Earth observer perceives a ship which appears to alter its speed, does a passenger on the ship experience this variation, or does he measure time (velocity) at a constant rate?
     
  7. Apr 25, 2006 #6

    Janus

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    What is wrong is that you are mixing frames. At .5c it will take 2 yrs Earth time to travel the distance and 1.732 years for you.

    At .99c it takes a little more than a year Earth time but about only 1.7 months for you.

    From your perspective, the reason it takes a shorter time is that the distance between the Earth and destination undergoes length contraction and is shorter than that as measured by the Earth.
     
  8. Apr 25, 2006 #7

    ZapperZ

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    Could you point a legitimate source that connects the pioneer anomaly with "time"? All the reports so far have more to do with how we treat the gravitational forces on this vessel. Did someone look at the clock on Pioneer?

    Zz.
     
  9. Apr 25, 2006 #8
    The query was related to the fact that the Pioneer craft appear to be short of where they should be, in the 30+ years they have been travelling they are about 10 hours travel time from where they were expected. Speed has as much to with time as with distance so the question becomes a bit two part, if Pioneer was aware would it know it was not where it should be or would it believe it had travelled the right distance?
     
  10. Apr 25, 2006 #9

    ZapperZ

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    That is a BIG leap of faith to connect that anomaly with "time". I would still like to see any legitimate references to back your claim of being able to make such a connection.

    Zz.
     
  11. Apr 25, 2006 #10
    I have a publication in the works, which links several unexplained phenomena to the manner in which time passes. It should be due for release in a couple of weeks. It runs to about 200 pages so is a bit long to post here but as soon as it is released I will prepare a precise of the principles and main formulae so that it can be argued over/against.
     
  12. Apr 25, 2006 #11

    ZapperZ

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    Where are you having this published?

    Zz.
     
  13. Apr 25, 2006 #12
    This one is coming out as book, I have previously had some stuff published in Australia and Europe (books and magazines) but this one is being done in the USA as well. I will get the details going as quickly as possible and if I am right in all my calculations there is a lot more work to be done but there should be some interesting results at the end. I am updating my website at the same time so that everyone can get a handle on the concept.
     
  14. Apr 25, 2006 #13

    ZapperZ

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    Sorry, but I think you need to re-read our Guidelines regarding over-speculative posting (in case you forgot).

    It is why I asked you for legitimate references here. I do not intend to discredit your book, but unless you have peer-reviewed articles to base this on, I'm afraid this would be considered as speculative. You are welcome to discuss this in the IR forum is you wish per the instruction given there.

    Zz.
     
  15. Apr 25, 2006 #14

    Aether

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    J.D. Anderson et al., Phys. Rev. D, 082004 (2002); http://arxiv.org/abs/gr-qc/0104064. See section XI E "Quadratic in time model": "There was one model of the above type that was especially fascinating. This model adds a quadratic in time term to the light time as seen by the DSN station...it mimics a line of sight acceleration of the spacecraft, and could be thought of as an expanding space model...This model fit both Doppler and range data very well..."
     
  16. Apr 25, 2006 #15

    ZapperZ

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    No, I don't believe this is the same thing. That term has more to do with different interaction of the spacecraft with other external forces. It is obvious that if the spacecraft isn't where it should be, then there are different time of flight involved[1]. This isn't what Tzemach is claiming, specially when it was said that ... "... The Pioneer Anomaly seems to indicate that time may not pass exactly as we have been led to believe. The Earth observer perceives a ship which appears to alter its speed, does a passenger on the ship experience this variation, or does he measure time (velocity) at a constant rate?.. "

    As far as I know, no one has measured the "time" on the spacecraft, nor is that the current puzzle. Even Anderson's later paper with Nieto reiterates the claim that a more careful study of the systematics needs to be done to make sure this is an anomolous effect[2].

    Zz.

    [1] M.M. Nieto and S.G. Turyshev, Class. Quant. Grav. v.21, p.4005 (2004).
    [2] M.M. Nieto and J.D. Anderson, Class. Quant. Grav. v.22, p.5342 (2005).
     
  17. Apr 25, 2006 #16

    Aether

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    There is a mission in the planning stages to measure the Pioneer anomaly with much greater precision (three orders of magnitude greater) than has already been done to date. Do your "precise of the principles and main formulae" yield a prediction for the Pioneer anomaly of greater precision than has already been measured to date?
     
  18. Apr 25, 2006 #17
    Length contraction seems to expalin this phenomenon, thanks for the tip. It looks like if near light-speed travelling is ever to become viable, it may not even be the need for special training facilities or criogenic chambers for the ship astronauts.

    Edit: Ah, I remembered mass also increases with speed. This might be a problem :)
     
    Last edited: Apr 25, 2006
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