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Thread: The roundtrip time of light travel and how it really works!

  1. #201  
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    Quote Originally Posted by KALSTER View Post
    Your diagram demonstrates what would happen if you were to conduct the experiment with a pond, a moving photo frame and a pebble.
    You are misunderstanding the pic.

    The cube IS the pond. It's just that nobody threw a pebble in it. Do you not understand the pic? Of course a person, or spider, or waves in the cube of water would be relative to the cube, but that is NOT what I am talking about. I am talking about the velocity of the cube in space. Would you like it better if I showed the water waves in the cube at every time t?
     

  2. #202  
    Brassica oleracea Strange's Avatar
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    As this thread is a complete waste of everyone's time... Is that a Menger Cube as your avatar Markus?

    Have you seen this: What to do with 66,000 business cards - Mental Floss
    ei incumbit probatio qui dicit, non qui negat
     

  3. #203  
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    So, how about the experiment in post #175?

    Scaredy cat!
    ei incumbit probatio qui dicit, non qui negat
     

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    Quote Originally Posted by Motor Daddy View Post
    Pythagorean Theorem isn't general?
    Wow, so you know how to use the Pythagorean Theorem. Amazing. Keep up the good work MD, perhaps one day you will have a chance to glimpse the higher mysteries of SR !
    At the moment unfortunately all we are seeing from you is complete ignorance of even the most basic principles.
     

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    Quote Originally Posted by Markus Hanke View Post
    Quote Originally Posted by Motor Daddy View Post
    Pythagorean Theorem isn't general?
    Wow, so you know how to use the Pythagorean Theorem. Amazing. Keep up the good work MD, perhaps one day you will have a chance to glimpse the higher mysteries of SR !
    At the moment unfortunately all we are seeing from you is complete ignorance of even the most basic principles.
    Still working on the equation? Tell ya what, keep working on it, maybe you'll figure it out someday.
     

  6. #206  
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    Quote Originally Posted by Strange View Post
    As this thread is a complete waste of everyone's time... Is that a Menger Cube as your avatar Markus?

    Have you seen this: What to do with 66,000 business cards - Mental Floss
    It is indeed, well spotted Strange. I generated this myself using a 3D fractal generator capable of producing volumetric lighting. Pretty neat, ey ?
    As for the business cards...errr well, maybe one day, when I'm really bored, and there are no crackpots online...
     

  7. #207  
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    Quote Originally Posted by Motor Daddy View Post
    Still working on the equation? Tell ya what, keep working on it, maybe you'll figure it out someday.
    So, chicken, how about the experiment in post #175?

    cluck, cluck, cluck.
    ei incumbit probatio qui dicit, non qui negat
     

  8. #208  
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    Quote Originally Posted by Markus Hanke View Post
    It is indeed, well spotted Strange. I generated this myself using a 3D fractal generator capable of producing volumetric lighting. Pretty neat, ey ?
    Very cool.
    ei incumbit probatio qui dicit, non qui negat
     

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    Hey Markus, Maybe I should dumb it down for ya and make it the 1 dimensional version to start with.

    Here, v=(ct-l)/t

    Can you prove that wrong?
     

  10. #210  
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    Troll Troll Troll Troll Troll Troll Troll Troll Troll Troll

    this is in trash, right?
     

  11. #211  
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    Quote Originally Posted by Motor Daddy View Post
    Still working on the equation? Tell ya what, keep working on it, maybe you'll figure it out someday.
    Pretty lame try. Anyway, see post 176. I figured that one out decades ago...
    Strange that, since you are so convinced of your case, you seem to be unable to refute the general proof given...
     

  12. #212  
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    Quote Originally Posted by Motor Daddy View Post
    Hey Markus, Maybe I should dumb it down for ya and make it the 1 dimensional version to start with.

    Here, v=(ct-l)/t

    Can you prove that wrong?
    See post 176.
     

  13. #213  
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    Quote Originally Posted by Motor Daddy View Post
    Hey Markus, Maybe I should dumb it down for ya and make it the 1 dimensional version to start with.

    Here, v=(ct-l)/t

    Can you prove that wrong?
    How about the experiment in post #175?

    Is this you? Motor Daddy Christmas Song 2011_0001.wmv I do not own copyrights to the melody. - YouTube
    ei incumbit probatio qui dicit, non qui negat
     

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    Quote Originally Posted by Markus Hanke View Post
    Quote Originally Posted by Motor Daddy View Post
    Hey Markus, Maybe I should dumb it down for ya and make it the 1 dimensional version to start with.

    Here, v=(ct-l)/t

    Can you prove that wrong?
    See post 176.
    Bwahahahahaahahahahaha

    Keep working at it, maybe you'll understand it someday.

    Still rounding up the link to proof of length contraction??
     

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    Quote Originally Posted by Motor Daddy View Post
    Quote Originally Posted by KALSTER View Post
    Your diagram demonstrates what would happen if you were to conduct the experiment with a pond, a moving photo frame and a pebble.
    You are misunderstanding the pic.

    The cube IS the pond. It's just that nobody threw a pebble in it. Do you not understand the pic? Of course a person, or spider, or waves in the cube of water would be relative to the cube, but that is NOT what I am talking about. I am talking about the velocity of the cube in space. Would you like it better if I showed the water waves in the cube at every time t?
    If you were to sketch out the pond/photo frame experiment with the same wave front speeds and frame dimensions plugged in to it, you would get the exact same results. You might as well have the cube travelling in some medium like water and have the wave front started by a vibration. You'll get the same qualitative results.

    In your pic, the wave front stays centred around a fixed point relative to the observer, exactly like if you dropped a pebble into a pond. In your pic, the cube moves to the right at a certain speed, just like the photo frame. The wave front moves faster than the cube and catches up to it, with the expanding front lining up with each side at different times. Then in your pic the light is reflected from the leading side and creates a new wave front that eventually lines up with the centre of the cube. With the photo frame the same happens, with a new wave front created by dropping a new pebble into the water right at the point and time that the first wave catches up to the leading side.

    Exactly the same results, with some of the same premises. You imagine light to move at constant speed relative to some preferred reference frame, represented by the pond on my side. In the mean time, experiments have shown that there is no preferred frame for light and that in that scenario from the perspective of the cube, the light would hit all sides at the same time. Again, people are not making this up. It is decidedly weird and counter-intuitive, but the results of experiments show just that. It doesn't matter how little we like it, that seems to be the reality and relativity was developed to try and explain and describe and predict what goes on. It does so exquisitely.
    Disclaimer: I do not declare myself to be an expert on ANY subject. If I state something as fact that is obviously wrong, please don't hesitate to correct me. I welcome such corrections in an attempt to be as truthful and accurate as possible.

    "Gullibility kills" - Carl Sagan
    "All people know the same truth. Our lives consist of how we chose to distort it." - Harry Block
    "It is the mark of an educated mind to be able to entertain a thought without accepting it." - Aristotle
     

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    Quote Originally Posted by Strange View Post
    Quote Originally Posted by Motor Daddy View Post
    Hey Markus, Maybe I should dumb it down for ya and make it the 1 dimensional version to start with.

    Here, v=(ct-l)/t

    Can you prove that wrong?
    How about the experiment in post #175?

    Is this you? Motor Daddy Christmas Song 2011_0001.wmv I do not own copyrights to the melody. - YouTube
    Bwahahahahahahaahaha

    Not even close!
     

  17. #217  
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    Quote Originally Posted by MeteorWayne View Post
    Troll Troll Troll Troll Troll Troll Troll Troll Troll Troll

    this is in trash, right?
    It is in pseudoscience. Which is like real science but wrong. And refuses to submit hypotheses to experiment in case those nasty facts get in the way.

    (I see MD has already been banned from other science forums. Presumably for being annoying, cowardly and ignorant)
    ei incumbit probatio qui dicit, non qui negat
     

  18. #218  
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    Quote Originally Posted by Motor Daddy View Post
    Bwahahahahahahaahaha

    Not even close!
    How about the experiment in post #175?
    ei incumbit probatio qui dicit, non qui negat
     

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    Quote Originally Posted by Strange View Post
    Quote Originally Posted by Motor Daddy View Post
    Bwahahahahahahaahaha

    Not even close!
    How about the experiment in post #175?
    How about a raped ape!

    http://www.youtube.com/watch?v=JKnBxvN3tZk
     

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    Quote Originally Posted by Strange View Post
    (I see MD has already been banned from other science forums. Presumably for being annoying, cowardly and ignorant)
    Hey, here's an idea, go to a religious site and try to convince them that there is no god and see how long you last before getting banned!

    Presumably you'd be banned for being annoying, cowardly and ignorant!
     

  21. #221  
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    Quote Originally Posted by Motor Daddy View Post
    How about a raped ape!
    I really don't want to know.

    How about the experiment in post #175?
    ei incumbit probatio qui dicit, non qui negat
     

  22. #222  
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    Quote Originally Posted by Motor Daddy View Post
    Hey, here's an idea, go to a religious site and try to convince them that there is no god and see how long you last before getting banned!
    How about the experiment in post #175? Or are you afraid of what it might show?
    ei incumbit probatio qui dicit, non qui negat
     

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    Quote Originally Posted by Strange View Post
    Quote Originally Posted by Motor Daddy View Post
    How about a raped ape!
    I really don't want to know.
    Of course you don't, because you're only interested in illusions.

    How about you, can you post a link to the proof of length contraction?
     

  24. #224  
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    Quote Originally Posted by Strange View Post
    Quote Originally Posted by MeteorWayne View Post
    Troll Troll Troll Troll Troll Troll Troll Troll Troll Troll

    this is in trash, right?
    It is in pseudoscience. Which is like real science but wrong. And refuses to submit hypotheses to experiment in case those nasty facts get in the way.

    (I see MD has already been banned from other science forums. Presumably for being annoying, cowardly and ignorant)
    Which is sort of the definition of a Troll
     

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    Quote Originally Posted by MeteorWayne View Post
    Quote Originally Posted by Strange View Post
    Quote Originally Posted by MeteorWayne View Post
    Troll Troll Troll Troll Troll Troll Troll Troll Troll Troll

    this is in trash, right?
    It is in pseudoscience. Which is like real science but wrong. And refuses to submit hypotheses to experiment in case those nasty facts get in the way.

    (I see MD has already been banned from other science forums. Presumably for being annoying, cowardly and ignorant)
    Which is sort of the definition of a Troll
    No, a troll is someone like you, that has no real input to the task at hand other than to simply call names and disrupt the thread. Speak to the pic or exit stage left, Troll.
     

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    Quote Originally Posted by KALSTER View Post
    Exactly the same results, with some of the same premises.
    No it is NOT exactly the same results. Instead of waves let's just say a man starts at the center of the cube at t=0 and walks at a constant speed relative to the cube, to the mirror, and then turns around and walks at a constant speed relativve to the cube back to the center. The speed of the man is relative to the cube. But that is something ENTIRELY different than what my pic shows. Do you want to talk about how far the man is from the point of origin of the light sphere at every time t, or do you want to talk about how far the man is from the center of the cube at every time t? Do you want to talk about the distance that the light sphere is away from the man at every time t?

    Put those numbers together for yourself and you will see something very wrong with what you are saying.
    Last edited by Motor Daddy; February 16th, 2012 at 11:36 AM.
     

  27. #227  
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    Quote Originally Posted by Motor Daddy View Post

    Still rounding up the link to proof of length contraction??
    Refer back to post 198, which in turns refers you to post 181, which then gives a link to the proof you are looking for...
    Can you not see how foolish you look ? Of course you can't, or else you wouldn't be doing this...
     

  28. #228  
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    Quote Originally Posted by Motor Daddy View Post
    No it is NOT exactly the same results.
    Hmmm.... We seem to have a difference of opinion. What can we do to resolve this. We need some sort of test.

    How about an experiment!

    I have heard that is what "scientists" do. How about the one in post #175? Would that prove you correct? It must do surely? Shall we set it up and see what happens?
    ei incumbit probatio qui dicit, non qui negat
     

  29. #229  
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    Hey MD, I got to leave you one thing at least - you have the best entertainment value since that guy who said elementary particles are micro vortices in a perfect solid...
    Almost half way to your target of 500 posts now, keep it up !
     

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    Quote Originally Posted by Markus Hanke View Post
    Quote Originally Posted by Motor Daddy View Post

    Still rounding up the link to proof of length contraction??
    Refer back to post 198, which in turns refers you to post 181, which then gives a link to the proof you are looking for...
    Can you not see how foolish you look ? Of course you can't, or else you wouldn't be doing this...
    Still trying to prove SR using SR, eh? Still no link to the proof of length contraction.

    Heck, I can do that too. God said let there be light, and there was. No need to wonder where light came from anymore. Since god said let there be light, we can talk about light with no proof required, because it is assumed. (rolls eyes)
     

  31. #231  
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    Quote Originally Posted by Strange View Post
    Quote Originally Posted by Motor Daddy View Post
    No it is NOT exactly the same results.
    Hmmm.... We seem to have a difference of opinion. What can we do to resolve this. We need some sort of test.

    How about an experiment!

    I have heard that is what "scientists" do. How about the one in post #175? Would that prove you correct? It must do surely? Shall we set it up and see what happens?
    Funny the way he completely ignores your experiment, as well as the mathematical proof already presented.
    Turns out you were right Strange - he really is aiming for the 500 post mark !!
     

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    Quote Originally Posted by Markus Hanke View Post
    Hey MD, I got to leave you one thing at least - you have the best entertainment value since that guy who said elementary particles are micro vortices in a perfect solid...
    Almost half way to your target of 500 posts now, keep it up !
    See, I disagree with you again, it is you who is entertaining. People that actually believe there is no simultaneity. People that actually believe length contracts. People that actually believe that they are rightfully entitled to their own facts about motion, because since they are ignorant to their own motion in space, they might as well be ignorant to everyone else's motion in space. See how that works? Damn that's entertaining!
     

  33. #233  
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    Quote Originally Posted by Motor Daddy View Post
    Quote Originally Posted by Markus Hanke View Post
    Hey MD, I got to leave you one thing at least - you have the best entertainment value since that guy who said elementary particles are micro vortices in a perfect solid...
    Almost half way to your target of 500 posts now, keep it up !
    See, I disagree with you again, it is you who is entertaining. People that actually believe there is no simultaneity. People that actually believe length contracts. People that actually believe that they are rightfully entitled to their own facts about motion, because since they are ignorant to their own motion in space, they might as well be ignorant to everyone else's motion in space. See how that works? Damn that's entertaining!
    People that actually believe in experimental evidence...
    People who can actually do the maths needed...
    People who actually understand the concepts...

    I could go on, but sure...
     

  34. #234  
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    Go on now, don't let up, only a few more posts to the half-way mark !
     

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    Quote Originally Posted by Markus Hanke View Post

    People that actually believe in experimental evidence...
    People who can actually do the maths needed...
    People who actually understand the concepts...

    I could go on, but sure...
    Still rounding up the link to the proof of length contraction? When should I expect you to post it? Today? Tomorrow? Next week?
     

  36. #236  
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    Both already answered long ago. This thread is now only good for its entertainment value. The OP does not engage in any meaningful discussion, and refuses to accept any evidence presented.
    I say lock it.
     

  37. #237  
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    Quote Originally Posted by Motor Daddy View Post
    Quote Originally Posted by Markus Hanke View Post

    People that actually believe in experimental evidence...
    People who can actually do the maths needed...
    People who actually understand the concepts...

    I could go on, but sure...
    Still rounding up the link to the proof of length contraction? When should I expect you to post it? Today? Tomorrow? Next week?
    And the chain becomes longer : 235->229->198->181->Link with evidence !

    Don't you understand ? Every single experiment performed in particle accelerators is also evidence for length contraction, because the numbers don't add up any other way. Here is an excerpt from the "Tests of SR" Wikipedia page :

    "for example, the behavior of colliding heavy ions can only be explained if their increased density due to Lorentz contraction is considered. Contraction also leads to an increase of the intensity of the Coulomb field perpendicular to the direction of motion whose effects already have been observed. Consequently, both time dilation and length contraction must be considered when conducting experiments in particle accelerators."

    Happy now ? You better be, coz I'm off to do the school run now.
    See ya ! And when I come back you better be at the half way mark !
     

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    Quote Originally Posted by Markus Hanke View Post
    I say lock it.
    I'd want it locked too if I was you, since you have failed to prove length contraction, and I seriously doubt that you can. My numbers add up perfectly without length contraction or time dilation, so why is it needed in SR? I'll tell you why, because when you start with a ridiculous second postulate like SR does, it requires a box of band-aids to make it work, which still leaves you back to where you started, YOU DON'T KNOW THE VELOCITY OF THE FRAME!!!
     

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    Breaker one nine, break, this is source 1, can everyone tell me their speed in space, over.

    Source 1, this is source 2, my speed is zero
    Source 1, this is source 3, my speed is zero.
    Source 1, this is source 4, my speed is zero
    Source 1, this is source 5, my speed is zero.
    Source 1, this is source 6, my speed is zero
    Source 1, this is source 7, my speed is zero.
    Source 1, this is source 8, my speed is zero
    Source 1, this is source 9, my speed is zero.



    Bwahahahaahahahaahahaaaaaaaaaaaaaa
     

  40. #240  
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    Hey Motor Mouth, do you want to propose your own experiment to test your idea and prove you are correct?

    My suggestion in post #175 was based on your drawing. Do you want to suggest a modification? What do you think? Should we do it? When the experiment confirms what you say, we will all have to bow down before you. It's got to be worth it, no?

    Why so reluctant to discuss an experiment? Surely you aren't secretly worried it might show you wrong?
    ei incumbit probatio qui dicit, non qui negat
     

  41. #241  
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    No it is NOT exactly the same results. Instead of waves let's just say a man starts at the center of the cube at t=0 and walks at a constant speed relative to the cube, to the mirror, and then turns around and walks at a constant speed relativve to the cube back to the center. The speed of the man is relative to the cube. But that is something ENTIRELY different than what my pic shows.
    Who gave that scenario? Not me. The ripples in the pond move exactly as the wave front in your pic does. The photo frame moves exactly as your cube does.
    Disclaimer: I do not declare myself to be an expert on ANY subject. If I state something as fact that is obviously wrong, please don't hesitate to correct me. I welcome such corrections in an attempt to be as truthful and accurate as possible.

    "Gullibility kills" - Carl Sagan
    "All people know the same truth. Our lives consist of how we chose to distort it." - Harry Block
    "It is the mark of an educated mind to be able to entertain a thought without accepting it." - Aristotle
     

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    Quote Originally Posted by Strange View Post
    Hey Motor Mouth, do you want to propose your own experiment to test your idea and prove you are correct?

    My suggestion in post #175 was based on your drawing. Do you want to suggest a modification? What do you think? Should we do it? When the experiment confirms what you say, we will all have to bow down before you. It's got to be worth it, no?

    Why so reluctant to discuss an experiment? Surely you aren't secretly worried it might show you wrong?
    Here is my proposal:

    You go into deep space with an accelerometer. You make sure you are not accelerating according to the accelerometer. When you are not accelerating you measure the one-way time of light travel from one end of a meter stick to the other end of a meter stick, and then measure the time of light travel in the opposite direction. Adjust your speed accordingly until the one-way times are EXACTLY the same, and the times are 1/299,792,458 of a second. Double check and triple check to make sure nothing changed. At that point you are SURE you have an absolute zero velocity. From there you are at rest in the preferred frame. You coordinate system is valid for the entire infinite volume of space. ALL objects travel in your coordinate system, and DISTANCE is determined by light travel time!

    Get a clue, Bucko!
     

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    Quote Originally Posted by KALSTER View Post
    The ripples in the pond move exactly as the wave front in your pic does. The photo frame moves exactly as your cube does.
    Not according to the light sphere they don't. You have no clue about what you are talking about. Construct a diagram such as mine and see for yourself. The ripples are in the frame of the cube, and that means they are relative to the point of origin of the light sphere at the same time.
     

  44. #244  
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    Quote Originally Posted by Motor Daddy View Post
    Here is my proposal:

    You go into deep space with an accelerometer. You make sure you are not accelerating according to the accelerometer. When you are not accelerating you measure the one-way time of light travel from one end of a meter stick to the other end of a meter stick, and then measure the time of light travel in the opposite direction. Adjust you speed accordingly until the one-way times are EXACTLY the same, and the times are 1/299,792,458 of a second. Double check and triple check to make sure nothing changed. At that point you are SURE you have an absolute zero velocity. From there you are at rest in the preferred frame. You coordinate system is valid for the entire infinite volume of space. ALL objects travel in your coordinate system, and DISTANCE is determined by light travel time!

    Get a clue, Bucko!
    How about an experiment we can practically do here on Earth? Why do have to propose something which is either impractical or, at the very least, ridiculously expensive. It should be fairly straightforward to set up a lab experiment equivalent to your drawing. What do you think? Is post #175 close enough? Why are you avoiding the issue?
    ei incumbit probatio qui dicit, non qui negat
     

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    Quote Originally Posted by Strange View Post
    [How about an experiment we can practically do here on Earth? Why do have to propose something which is either impractical or, at the very least, ridiculously expensive. It should be fairly straightforward to set up a lab experiment equivalent to your drawing. What do you think? Is post #175 close enough? Why are you avoiding the issue?
    The reality of light traveling in the preferred frame is not concerned with your inability to measure accurately. Too bad that you can't afford the experiment or that you don't have the capability to measure that accurately! TOO BAD FOR YOU! Nature doesn't change how it works because your capabilities are limited. (rolls eyes)
     

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    Quote Originally Posted by Motor Daddy View Post
    The reality of light traveling in the preferred frame is not concerned with your inability to measure accurately. Too bad that you can't afford the experiment or that you don't have the capability to measure that accurately! TOO BAD FOR YOU! Nature doesn't change how it works because your capabilities are limited. (rolls eyes)
    But reality is something we can measure. Are you saying that you are right even if an experiment were to show you wrong? Surely not. That wouldn't be rational.

    We can easily measure things accurately enough to check your hypothesis in a realistic (lab-scale) set up. I'm wondering why you don't want to consider doing that and proving yourself correct. Odd...

    maybe you are just here to wind people up (i.e. trolling). Surely that is not the case, either.

    But, unless you are willing to perform an experiment, you must be either irrational or trolling. Or a geocentric nutcase?
    ei incumbit probatio qui dicit, non qui negat
     

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    Quote Originally Posted by Strange View Post
    But reality is something we can measure.
    Do you measure length contraction? Post the link.

    Heck, while you're at it, post the link to the measurement of the one-way speed of light.
     

  48. #248  
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    Quote Originally Posted by Motor Daddy View Post
    Quote Originally Posted by Strange View Post
    But reality is something we can measure.
    Do you measure length contraction? Post the link.

    Heck, while you're at it, post the link to the measurement of the one-way speed of light.
    I was thinking something much simpler: measuring the time for light to reflect off the sides of a moving box, rather like your diagram. What is your objection to that?
    ei incumbit probatio qui dicit, non qui negat
     

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    Quote Originally Posted by Strange View Post
    Quote Originally Posted by Motor Daddy View Post
    Quote Originally Posted by Strange View Post
    But reality is something we can measure.
    Do you measure length contraction? Post the link.

    Heck, while you're at it, post the link to the measurement of the one-way speed of light.
    I was thinking something much simpler: measuring the time for light to reflect off the sides of a moving box, rather like your diagram. What is your objection to that?
    Post the link to the measurement of length contraction and the measurement of the one-way speed of light. Why are you avoiding those issues? You seem to deny simultaneity, and are quick to implement length contraction into your method, but you ignore my requests.
     

  50. #250  
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    Quote Originally Posted by Motor Daddy View Post

    Here is my proposal:

    You go into deep space with an accelerometer. You make sure you are not accelerating according to the accelerometer. When you are not accelerating you measure the one-way time of light travel from one end of a meter stick to the other end of a meter stick, and then measure the time of light travel in the opposite direction. Adjust your speed accordingly until the one-way times are EXACTLY the same, and the times are 1/299,792,458 of a second. Double check and triple check to make sure nothing changed. At that point you are SURE you have an absolute zero velocity. From there you are at rest in the preferred frame. You coordinate system is valid for the entire infinite volume of space. ALL objects travel in your coordinate system, and DISTANCE is determined by light travel time!

    Get a clue, Bucko!
    My friend, this is has been done. All the way back in 1932. It is called the Kennedy-Thorndike experiment. The results are in perfect agreement with the predictions of SR :

    Phys. Rev. 42, 400 (1932): Experimental Establishment of the Relativity of Time
     

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    Quote Originally Posted by Markus Hanke View Post
    My friend, this is has been done. All the way back in 1932. It is called the Kennedy-Thorndike experiment. The results are in perfect agreement with the predictions of SR :

    Phys. Rev. 42, 400 (1932): Experimental Establishment of the Relativity of Time
    See, there you go again. I ask for proof of God and you post a link to the Bible.

    Post the link to the proof of length contraction and the measurement of the one-way speed of light!
     

  52. #252  
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    Quote Originally Posted by Motor Daddy View Post
    Post the link to the measurement of length contraction and the measurement of the one-way speed of light. Why are you avoiding those issues? You seem to deny simultaneity, and are quick to implement length contraction into your method, but you ignore my requests.
    Hang on. We are supposed to be discussing your diagram, remember. You named the thread "roundtrip time of light". You created a diagram showing the speed of light is the same in all directions. You asked about the reflection of light from point x.

    I'm simply suggesting we actually do this to demonstrate that you are correct. Then we can discuss the real measurements. That will convince all the doubters, surely.
    ei incumbit probatio qui dicit, non qui negat
     

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    Quote Originally Posted by Strange View Post
    Hang on. We are supposed to be discussing your diagram, remember. You named the thread "roundtrip time of light". You created a diagram showing the speed of light is the same in all directions. You asked about the reflection of light from point x.
    I showed you the round trip time of light from a source to the x and back to the source. I asked for your numbers, where are they?
     

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    Quote Originally Posted by Motor Daddy View Post
    Quote Originally Posted by Strange View Post
    Hang on. We are supposed to be discussing your diagram, remember. You named the thread "roundtrip time of light". You created a diagram showing the speed of light is the same in all directions. You asked about the reflection of light from point x.
    I showed you the round trip time of light from a source to the x and back to the source. I asked for your numbers, where are they?
    And I am suggesting we actually measure it and see what happens. What is your objection?
    ei incumbit probatio qui dicit, non qui negat
     

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    Quote Originally Posted by Strange View Post
    And I am suggesting we actually measure it and see what happens. What is your objection?
    Maybe you don't understand my position so let me restate it.

    There need not be any measurement. Light travels at a constant speed in space. We define the meter to be the length of the path that light travels in a vacuum in 1/299,792,458 of a second. That makes the speed of light 299,792,458 m/s, BY DEFINITION! It is impossible for light to travel away from the point it is emitted in space at any different speed than 299,792,458 m/s. That means the light sphere expands its radius at the rate of c, 299,792,458 meters per second.

    If a source emits light at coordinate (0,0,0), the radius of the light sphere expands at c away from the point of origin in every different direction, That means the center of the light sphere is ALWAYS the point of origin. It is IMPOSSIBLE for the light sphere to travel in space, it simply expands in space from the point of origin at c. The source was at (0,0,0) (the point of origin) when it emitted light at t=0. The source IS capable of traveling in space away from the point of origin, which means the source is not in the center of the light sphere if it travels away from the point of origin. That means the wave front (outer edge of the sphere) is closer to the source in one direction, and further away from the source in the opposite direction.

    This is not debatable. It is a rock solid fact set in stone, because the DEFINITION of the meter is the path that light travels in a vacuum in 1/299,792,458 of a second.

    Let me repeat that one more time in case it went in one ear and out the other. This is not debatable. It is a rock solid fact set in stone, because the DEFINITION of the meter is the path that light travels in a vacuum in 1/299,792,458 of a second.
     

  56. #256  
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    Quote Originally Posted by Motor Daddy View Post
    Quote Originally Posted by Markus Hanke View Post
    My friend, this is has been done. All the way back in 1932. It is called the Kennedy-Thorndike experiment. The results are in perfect agreement with the predictions of SR :

    Phys. Rev. 42, 400 (1932): Experimental Establishment of the Relativity of Time
    See, there you go again. I ask for proof of God and you post a link to the Bible.

    Post the link to the proof of length contraction and the measurement of the one-way speed of light!
    There you go again, you didn't even read the link. This experiment is a measurement of the one-way speed of light. When are you going to start reading our posts and follow the links provided ?
    The length contraction measurement on the trajectories of atmospheric mu-mesons is right here :

    A Brief Discussion on Participation of \mu-mesons (muons) based upon Relativistic Dynamics MY DIGITAL NOTEBOOK

    And here are the exact details of the experimental setup and results in numbers :

    http://www.physics.umt.edu/physics141/frisch-smith.pdf
     

  57. #257  
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    Quote Originally Posted by Motor Daddy View Post
    You're correct, I didn't have to fudge any numbers with a bunch of band-aids like the unproven length contraction, time dilation, or the notion that there exists no concept of simulatenity. Those were Einstein's band-aids because he couldn't figure out how to maintain the constancy of the speed of light and get the numbers to add up.
    *sigh* not another one!

    You do know we test SR every day in particle accelerators, don't you? And we have overwhelming evidence, from many experiments performed and repeated over the past century, that time-dilation is real. The GPS system, for instance, relies on the fact that time-dilation occurs and wouldn't work properly if time-dilation didn't exist. The GPS system is built around Einsteins equations.
    Markus Hanke likes this.
     

  58. #258  
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    Quote Originally Posted by Motor Daddy View Post
    because the DEFINITION of the meter is the path that light travels in a vacuum in 1/299,792,458 of a second.
    Have you ever asked yourself whose clock is used to measure these 1/299,792,458 s ?
     

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    Hey hold on a minute !
    You've just passed the half-way mark...
     

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    Quote Originally Posted by Motor Daddy View Post
    Quote Originally Posted by Strange View Post
    Hang on. We are supposed to be discussing your diagram, remember. You named the thread "roundtrip time of light". You created a diagram showing the speed of light is the same in all directions. You asked about the reflection of light from point x.
    I showed you the round trip time of light from a source to the x and back to the source. I asked for your numbers, where are they?
    In post 176.
     

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    Quote Originally Posted by Motor Daddy View Post

    Maybe you don't understand my position so let me restate it.
    We understand your position perfectly well - you are saying there is a preferred frame of reference in the universe, in contradiction to SR.
    So where's your experimental evidence for this ?
     

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    Quote Originally Posted by SpeedFreek View Post

    You do know we test SR every day in particle accelerators, don't you?
    I'm afraid he doesn't, otherwise this thread would not have grown to 261 posts.
     

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    Quote Originally Posted by Markus Hanke View Post
    Quote Originally Posted by Motor Daddy View Post
    because the DEFINITION of the meter is the path that light travels in a vacuum in 1/299,792,458 of a second.
    Have you ever asked yourself whose clock is used to measure these 1/299,792,458 s ?
    Have you ever asked yourself how it's possible to separate distance from time when speaking about light travel?
     

  64. #264  
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    Quote Originally Posted by Motor Daddy View Post
    Quote Originally Posted by Markus Hanke View Post
    Quote Originally Posted by Motor Daddy View Post
    because the DEFINITION of the meter is the path that light travels in a vacuum in 1/299,792,458 of a second.
    Have you ever asked yourself whose clock is used to measure these 1/299,792,458 s ?
    Have you ever asked yourself how it's possible to separate distance from time when speaking about light travel?
    You can't, that's exactly my point. That's where contraction and dilation come in - the ratio between them is always constant for all observers.
    You didn't answer my question - whose clock do you use to measure your time that defines the meter ?
     

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    Allow me to summarize the current state of this thread.

    We have :
    - given you experimental evidence for contraction and dilation
    - shown you the correct calculations for your picture
    - pointed out to you where the error in your reasoning lies

    You have :
    - refused to acknowledge any of the evidence presented, in fact you have not even responded to most of it, come to think of it
    - not presented any evidence of your own which is based on experimental evidence
    - not responded to the calculations shown in post 176
    - refused to engage with the request be Strange for a possible experiment.

    The readers of this thread as well as the moderators of this forum should draw their own conclusions.
     

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    Quote Originally Posted by Markus Hanke View Post
    You didn't answer my question - whose clock do you use to measure your time that defines the meter ?
    A clock in the preferred frame, of course. Light travel time defines distance in the preferred frame. Since all object travel in the preferred frame and distance and time are inseparable in the frame, then all objects distance traveled is according to the preferred frame, which means light travel time, which is the preferred frame time, because when speaking about light travel, distance and time are INSEPARABLE!
     

  67. #267  
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    Quote Originally Posted by Strange View Post

    I was thinking something much simpler: measuring the time for light to reflect off the sides of a moving box, rather like your diagram. What is your objection to that?
    Apart from a couple of details in experimental setup, this is precisely the aforementioned Kennedy Thorndike experiment. It has been done.
     

  68. #268  
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    Quote Originally Posted by Motor Daddy View Post
    Quote Originally Posted by KALSTER View Post
    The ripples in the pond move exactly as the wave front in your pic does. The photo frame moves exactly as your cube does.
    Not according to the light sphere they don't. You have no clue about what you are talking about. Construct a diagram such as mine and see for yourself. The ripples are in the frame of the cube, and that means they are relative to the point of origin of the light sphere at the same time.
    Really? How would my scenario behave differently from yours?
    Disclaimer: I do not declare myself to be an expert on ANY subject. If I state something as fact that is obviously wrong, please don't hesitate to correct me. I welcome such corrections in an attempt to be as truthful and accurate as possible.

    "Gullibility kills" - Carl Sagan
    "All people know the same truth. Our lives consist of how we chose to distort it." - Harry Block
    "It is the mark of an educated mind to be able to entertain a thought without accepting it." - Aristotle
     

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    Quote Originally Posted by Markus Hanke View Post
    Allow me to summarize the current state of this thread.

    We have :
    - given you experimental evidence for contraction and dilation
    - shown you the correct calculations for your picture
    - pointed out to you where the error in your reasoning lies

    You have :
    - refused to acknowledge any of the evidence presented, in fact you have not even responded to most of it, come to think of it
    - not presented any evidence of your own which is based on experimental evidence
    - not responded to the calculations shown in post 176
    - refused to engage with the request be Strange for a possible experiment.

    The readers of this thread as well as the moderators of this forum should draw their own conclusions.
    Allow my summation:

    Nobody has shown the SR numbers for the pic I posted.
    Nobody has provided a link to the proof of length contraction.
    Nobody has refuted my numbers in the pic.
    People are linking the bible when asked for evidence of God.
    There are trolls that just get a few jabs in once in a while, that are basically just an annoyance to this thread.
    I've asked people to provide numbers for their justifications of different example with no response.
    People put words in my mouth.

    etc, etc, etc...
     

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    Quote Originally Posted by Motor Daddy View Post
    Quote Originally Posted by Markus Hanke View Post
    You didn't answer my question - whose clock do you use to measure your time that defines the meter ?
    A clock in the preferred frame, of course. Light travel time defines distance in the preferred frame. Since all object travel in the preferred frame and distance and time are inseparable in the frame, then all objects distance traveled is according to the preferred frame, which means light travel time, which is the preferred frame time, because when speaking about light travel, distance and time are INSEPARABLE!
    Oh yeah, of course, I forgot...in your preferred imagined frame, for whose existence there is no experimental evidence whatsoever.
    Or would you care to provide this evidence in the form of references to a proper, repeatable experiment ? I seem to remember you have been asked for this before.
     

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    Quote Originally Posted by KALSTER View Post
    Really? How would scenario behave differently from yours?
    How about you construct a diagram and prove me wrong if you are so sure. Why should I waste my time drawing up your mistake? I've showed you my example, now show me yours. A misunderstanding on your part doesn't constitute as mistake on my part.

    Show me what you got!
     

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    Quote Originally Posted by Motor Daddy View Post
    Quote Originally Posted by KALSTER View Post
    Really? How would scenario behave differently from yours?
    How about you construct a diagram and prove me wrong if you are so sure. Why should I waste my time drawing up your mistake? I've showed you my example, now show me yours. A misunderstanding on your part doesn't constitute as mistake on my part.

    Show me what you got!
    How many times...?
    I have provided all of this in post 176.
    For a more technical treatment with real-life experimental evidence you can refer here :

    Phys. Rev. Lett. 64, 1697 (1990): Improved Kennedy-Thorndike experiment to test special relativity
     

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    Quote Originally Posted by Markus Hanke View Post
    How many times...?
    I have provided all of this in post 176.
    For a more technical treatment with real-life experimental evidence you can refer here :

    Phys. Rev. Lett. 64, 1697 (1990): Improved Kennedy-Thorndike experiment to test special relativity
    You don't even know what we are talking about. Go back and read the thread between Kalster and myself.
     

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    Nobody has shown the SR numbers for the pic I posted.
    Yes we have - post 176.

    Nobody has provided a link to the proof of length contraction.
    Yes we have - post 256.

    Nobody has refuted my numbers in the pic.
    Yes we have - post 176.

    People are linking the bible when asked for evidence of God.
    And others close their eyes and refuse to acknowledge clear evidence that threatens their view of the world.

    I've asked people to provide numbers for their justifications of different example with no response.
    Wrong, you got your response in post 176 ( gosh, how many more times...? ), you just refuse to acknowledge it.
     

  75. #275  
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    Quote Originally Posted by Motor Daddy View Post
    Quote Originally Posted by Markus Hanke View Post
    How many times...?
    I have provided all of this in post 176.
    For a more technical treatment with real-life experimental evidence you can refer here :

    Phys. Rev. Lett. 64, 1697 (1990): Improved Kennedy-Thorndike experiment to test special relativity
    You don't even know what we are talking about. Go back and read the thread between Kalster and myself.
    No, the problem is that you really don't understand the subject at hand. The Kennedy-Thorndike experiment is a direct experimental refutation of your assertion that a preferred frame exists.
     

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    This discussion is pointless. You are talking to a Troll who will repeat the same thing againandagainandagainandagainandaganandagain, never read or understand ony of our replies, or follow the links we provide, because it makes no difference. He will repeat the same thing againandagainandagainandagainandaganandagain.
     

  77. #277  
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    I am asking you again : where is your experimental, verifiable, repeatable evidence for the existence of a preferred frame ?
    Either provide it, or put this thread out of its misery.
     

  78. #278  
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    Quote Originally Posted by MeteorWayne View Post
    This discussion is pointless. You are talking to a Troll who will repeat the same thing againandagainandagainandagainandaganandagain, never read or understand ony of our replies, or follow the links we provide, because it makes no difference. He will repeat the same thing againandagainandagainandagainandaganandagain.
    You are right of course, MeteorWayne, no doubt whatsoever.
    But then again, he couldn't possible get to 500 posts...or could he ?
     

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    Quote Originally Posted by Markus Hanke View Post
    [
    Yes we have - post 176.
    I must have missed the round trip time for the light from the source to the x and back to the source in your 176 post.

    Please tell me the round trip time. Just the round trip time, nothing more. Save the BS.

    Oh, let me guess, 1 second?

    Bwahahahahahaahahahaha
     

  80. #280  
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    Quote Originally Posted by Motor Daddy View Post
    Quote Originally Posted by KALSTER View Post
    Really? How would scenario behave differently from yours?
    How about you construct a diagram and prove me wrong if you are so sure. Why should I waste my time drawing up your mistake? I've showed you my example, now show me yours. A misunderstanding on your part doesn't constitute as mistake on my part.

    Show me what you got!
    Have you not read a word I said? According to me, my diagram would look exactly like yours. I am asking why it wouldn't.
    Disclaimer: I do not declare myself to be an expert on ANY subject. If I state something as fact that is obviously wrong, please don't hesitate to correct me. I welcome such corrections in an attempt to be as truthful and accurate as possible.

    "Gullibility kills" - Carl Sagan
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    Quote Originally Posted by Markus Hanke View Post
    I am asking you again : where is your experimental, verifiable, repeatable evidence for the existence of a preferred frame ?
    Either provide it, or put this thread out of its misery.
    Metre - Wikipedia, the free encyclopedia

    The metre (meter in the US), symbol m, is the base unit of length in the International System of Units (SI). Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole (at sea level), its definition has been periodically refined to reflect growing knowledge of metrology. Since 1983, it is defined as the length of the path travelled by light in vacuum in 1 ⁄ 299,792,458 of a second.
     

  82. #282  
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    Quote Originally Posted by Motor Daddy View Post
    Please tell me the round trip time. Just the round trip time, nothing more. Save the BS.
    Oh, let me guess, 1 second?
    I can't believe it, he finally got it !!!!!!
    See, if you just keep at it they will eventually understand...
     

  83. #283  
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    Quote Originally Posted by Markus Hanke View Post
    Hey hold on a minute !
    You've just passed the half-way mark...
    In your frame of reference, maybe!
    ei incumbit probatio qui dicit, non qui negat
     

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    Quote Originally Posted by KALSTER View Post
    Have you not read a word I said? According to me, my diagram would look exactly like yours. I am asking why it wouldn't.
    Because my diagram was constructed from the actual times in the cube, recorded at the receivers. I was in the cube, the source emitted light and it took that much time for the light to reach the receivers. According to you, and SR, you say the time is always .5 seconds to each receiver, and that is simply not true. The only reason you say that is because you have NO WAY OF KNOWING the velocity of the cube on space.
     

  85. #285  
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    Quote Originally Posted by Markus Hanke View Post
    Quote Originally Posted by Strange View Post

    I was thinking something much simpler: measuring the time for light to reflect off the sides of a moving box, rather like your diagram. What is your objection to that?
    Apart from a couple of details in experimental setup, this is precisely the aforementioned Kennedy Thorndike experiment. It has been done.
    Shhh... I know that. And obviously so does Motor Mouth, otherwise he wouldn't avoid the issue so ... "devoutly".
    ei incumbit probatio qui dicit, non qui negat
     

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    Quote Originally Posted by Motor Daddy View Post
    Quote Originally Posted by Markus Hanke View Post
    I am asking you again : where is your experimental, verifiable, repeatable evidence for the existence of a preferred frame ?
    Either provide it, or put this thread out of its misery.
    Metre - Wikipedia, the free encyclopedia

    The metre (meter in the US), symbol m, is the base unit of length in the International System of Units (SI). Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole (at sea level), its definition has been periodically refined to reflect growing knowledge of metrology. Since 1983, it is defined as the length of the path travelled by light in vacuum in 1 ⁄ 299,792,458 of a second.
    Precisely - this is why your round trip time is 1s exactly...because c is the same for all observers, whether moving or not. Thus c does not depend on the observer, thus there is no preferred reference frame. All frames measure c equally to obtain the standard meter in their own frame.
    Thank you, you have just proven yourself wrong.
     

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    Quote Originally Posted by Markus Hanke View Post
    Quote Originally Posted by Motor Daddy View Post
    Please tell me the round trip time. Just the round trip time, nothing more. Save the BS.
    Oh, let me guess, 1 second?
    I can't believe it, he finally got it !!!!!!
    See, if you just keep at it they will eventually understand...

    Absolutely not .5 seconds each way, or 1 second round trip!! Absolutely NOT!
     

  88. #288  
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    Quote Originally Posted by Motor Daddy View Post

    Because my diagram was constructed from the actual times in the cube, recorded at the receivers. I was in the cube, the source emitted light and it took that much time for the light to reach the receivers. According to you, and SR, you say the time is always .5 seconds to each receiver, and that is simply not true. The only reason you say that is because you have NO WAY OF KNOWING the velocity of the cube on space.
    The person inside the box has no way of knowing, but the guy outside at rest does. However, he still gets the same value for c.
     

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    Quote Originally Posted by Markus Hanke View Post
    Precisely - this is why your round trip time is 1s exactly...because c is the same for all observers, whether moving or not. Thus c does not depend on the observer, thus there is no preferred reference frame. All frames measure c equally to obtain the standard meter in their own frame.
    Thank you, you have just proven yourself wrong.
    So, you are 1 meter away from a light source (a lamp post). Just as the light is emitted you run away from the lamp. Are you saying it takes exactly 1/299,792,458 of a second for the light to reach you?
     

  90. #290  
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    Quote Originally Posted by Motor Daddy View Post
    Quote Originally Posted by Markus Hanke View Post
    Quote Originally Posted by Motor Daddy View Post
    Please tell me the round trip time. Just the round trip time, nothing more. Save the BS.
    Oh, let me guess, 1 second?
    I can't believe it, he finally got it !!!!!!
    See, if you just keep at it they will eventually understand...

    Absolutely not .5 seconds each way, or 1 second round trip!! Absolutely NOT!
    Absolutely yes, and the evidence has been presented in the form of the aforementioned Kennedy Thorndike experiment.
    1 second. Precisely. Exactly. On the Dot.

    See if you can come up with a few more posts to get you closer to those 500...I'll check back on your progress tomorrow. Here in my part of the world it is night now, so off I go. Good night.
     

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    Quote Originally Posted by Markus Hanke View Post
    The person inside the box has no way of knowing, but the guy outside at rest does. However, he still gets the same value for c.
    Wrong. What you really mean is that in SR, nobody can know the velocity of a cube from inside the cube, because the cube is considered at rest and the times are always .5 seconds to the receivers. That is the biggest load of crap I've ever heard!

    Here is what you are saying. "I am in a cube and I am not traveling in space, it is everyone else traveling in space, but I am not." According to you in your box, every other object is in motion, but you are not.

    Bwahahahahahahahahahah
     

  92. #292  
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    Quote Originally Posted by Motor Daddy View Post
    Quote Originally Posted by Markus Hanke View Post
    Precisely - this is why your round trip time is 1s exactly...because c is the same for all observers, whether moving or not. Thus c does not depend on the observer, thus there is no preferred reference frame. All frames measure c equally to obtain the standard meter in their own frame.
    Thank you, you have just proven yourself wrong.
    So, you are 1 meter away from a light source (a lamp post). Just as the light is emitted you run away from the lamp. Are you saying it takes exactly 1/299,792,458 of a second for the light to reach you?
    If you start running the instant the light is emitted, then you are accelerating relative to the lamp - your frame is no longer inertial. In fact, the entire setup is completely different from your initial OP.
    This entire discussion was based on strictly inertial frames, so lets keep it this way.
     

  93. #293  
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    Quote Originally Posted by Motor Daddy View Post

    Wrong. What you really mean is that in SR, nobody can know the velocity of a cube from inside the cube, because the cube is considered at rest and the times are always .5 seconds to the receivers. That is the biggest load of crap I've ever heard!
    Sorry that you don't like it, but unfortunately it is experimental fact.
    This is indeed the case so long as the box doesn't accelerate.
     

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    Quote Originally Posted by Markus Hanke View Post
    If you start running the instant the light is emitted, then you are accelerating relative to the lamp - your frame is no longer inertial. In fact, the entire setup is completely different from your initial OP.
    This entire discussion was based on strictly inertial frames, so lets keep it this way.
    I don't have a problem with that. My method has no problem with be inertial or not. I can post a diagram of numbers as the cube accelerates too. Your problem is not mine.

    But, since you have problems with your BS method and can't deal with acceleration, then let's just say you are running at a constant speed from the lamp post, and when you get to a premeasured meter away from the lamppost the light is emitted. How much time does it take the light to reach you?
     

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    See if you can come up with the experimental evidence for your preferred frame until tomorrow. This is the third time I am asking you for this. I have provided the evidence you wanted, now show us yours.
    Good night.
     

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    Quote Originally Posted by Motor Daddy View Post
    Because my diagram was constructed from the actual times in the cube, recorded at the receivers.
    No it wasn't. It was based on what you think happens. Which you are strangely reluctant to test in the real world.

    I was in the cube
    No you weren't. Don't lie (isn't that sin in your fundie church?).
    ei incumbit probatio qui dicit, non qui negat
     

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    Quote Originally Posted by Motor Daddy View Post
    The metre (meter in the US), symbol m, is the base unit of length in the International System of Units (SI). Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole (at sea level), its definition has been periodically refined to reflect growing knowledge of metrology. Since 1983, it is defined as the length of the path travelled by light in vacuum in 1 ⁄ 299,792,458 of a second.
    You know what? That bold, embiggened and underlined text is almost convincing.

    Shame the actual measurements (not your fantasy ones) contradict you.
    ei incumbit probatio qui dicit, non qui negat
     

  98. #298  
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    Quote Originally Posted by Motor Daddy View Post
    Quote Originally Posted by Markus Hanke View Post
    If you start running the instant the light is emitted, then you are accelerating relative to the lamp - your frame is no longer inertial. In fact, the entire setup is completely different from your initial OP.
    This entire discussion was based on strictly inertial frames, so lets keep it this way.
    I don't have a problem with that. My method has no problem with be inertial or not. I can post a diagram of numbers as the cube accelerates too. Your problem is not mine.

    But, since you have problems with your BS method and can't deal with acceleration, then let's just say you are running at a constant speed from the lamp post, and when you get to a premeasured meter away from the lamppost the light is emitted. How much time does it take the light to reach you?
    How high is the lamppost ?
     

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    Quote Originally Posted by Markus Hanke View Post

    How high is the lamppost ?
    Same height as your head. How much time does it take for the light to reach your head?
     

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    Quote Originally Posted by Motor Daddy View Post
    Quote Originally Posted by Markus Hanke View Post

    How high is the lamppost ?
    Same height as your head. How much time does it take for the light to reach your head?
    So long as they are at the same height it still takes exactly 1s as measured in the same frame of reference your "pre-measured meter" was determined in.
    I don't know what you are getting at ?? The running person will see the length of the meter contracted, which is offset by the time dilation of his own watch. The ratio is again constant at c.
    Seriously I'm off now. I'll check in on you tomorrow.
     

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