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Daedalus

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Everything posted by Daedalus

  1. Time dilation has nothing to do with how often photons are emitted or detected. It doesn't matter if the second photon was detected in a negligible amount of time or instantaneously from the first photon. Furthermore, it doesn't matter if the passage of time occurs in increments of Planck time. When considering time dilation in special relativity, the only things that matters are the constancy of the speed of light, the relative speed of the object being observed in the chosen coordinate system, and that the passage of time occurs. Look, I understand that you have an idea about what time "actually" is but, before you make claims that time dilation is busted, you really need to understand what time dilation is and how to derive the equations mathematically. Otherwise, you end up with a bunch of statements that make no sense at all. First, we need to agree on a few things before we can actually understand what scientists are referring to when they talk about time dilation. The passage of time occurs. How it occurs is not important; only that is does. We can always choose a coordinate system where the object being observed changes position through space. The speed of light is constant regardless of the chosen coordinate system. Now, let's consider two identical light clocks where the reflector plates are separated exactly one-half the distance defined by the Planck length. Light clocks measure time by "bouncing" a photon between two reflectors. Because the speed of light is constant, it will take exactly one Plank time for the light to go from the bottom plate to the top plate and from the top plate back to the bottom plate when the clocks are at rest relative to the observer. Figure 1 illustrates the path that photons traverse when the light clock is at rest relative to the observer. Figure 1: A light clock at rest relative to the observer. Let [math]\mathcal{L}[/math] equal the distance between the reflective plates of the light clock. Because photons traverse the distance between the reflective plates at the speed of light, the total amount of time it takes for photons to go up and back down is equal to [math]\Delta t=\frac{2\mathcal{L}}{c}=\frac{\sqrt{\frac{\hbar G}{c^3}}}{\sqrt{c^2}}=\sqrt{\frac{\hbar G}{c^5}}[/math]. As we can see, when the light clock is at rest relative to the observer, each tick of the clock occurs at intervals of Planck time. So far, everything is easy to understand, and we've managed to capture part of your idea that time occurs at discreet intervals of Plank time as defined by how our light clocks actually measure time. Now, let's consider a light clock that is moving with a constant speed relative to the observer. Figure 2: A light clock in motion relative to the observer. As illustrated by Figure 2, the distance light has to traverse between the two plates has increased because the clock is in motion relative to the observer. Photons can no longer move up and down and remain between the reflective plates of the light clock in motion. The path the photons traverse must also consider that the plates have moved through space with a speed of [math]v[/math] for every interval of time measured. Because we know how fast the clock is moving relative to the observer, the distance the clock has moved for each interval of time is equal to [math]v\Delta \tau[/math]. Using the distance between the plates and the distance the clock has moved for each interval of time, we can apply the Pythagorean theorem to calculate the total distance, [math]\mathcal{R}[/math], photons must traverse between each plates. [math]\mathcal{R}=\sqrt{\left(\frac{1}{2}v\Delta \tau\right)^2+\left(\mathcal{L}\right)^2}[/math] The total distance the photons have to traverse for each tick of the clock that is in motion as measured by the observer at rest is equal to [math]2\mathcal{R}[/math]. However, the speed of light is constant. So, the total amount of time the photons take to bounce between the plates is equal to [math]\Delta \tau=\frac{2\mathcal{R}}{c}[/math], [math]\Delta \tau=\frac{2\sqrt{\left(\frac{1}{2}v\Delta \tau\right)^2+\left(\mathcal{L}\right)^2}}{c}[/math]. Solving for [math]\Delta \tau[/math] we get: [math]\Delta \tau^2=\left(\frac{2\sqrt{\left(\frac{1}{2}v\Delta \tau\right)^2+\left(\mathcal{L}\right)^2}}{c}\right)^2=\frac{v^2\Delta\tau^2+4\mathcal{L}^2}{c^2}[/math] Multiply both sides by [math]c^2[/math]: [math]c^2\Delta \tau^2=v^2\Delta\tau^2+4\mathcal{L}^2[/math] Move the [math]\Delta \tau[/math] terms to the left side: [math]c^2\Delta \tau^2-v^2\Delta\tau^2=4\mathcal{L}^2[/math] Factor out [math]\Delta \tau^2[/math] from the left side: [math]\Delta \tau^2\left(c^2-v^2\right)=4\mathcal{L}^2[/math] Divide both sides by [math]c^2-v^2[/math]: [math]\Delta \tau^2=\frac{4\mathcal{L}^2}{c^2-v^2}[/math] Factor out [math]4\mathcal{L}^2/c^2[/math] from the right side: [math]\Delta \tau^2=\frac{4\mathcal{L}^2}{c^2}\frac{1}{1-\frac{v^2}{c^2}}[/math] Take the square root of both sides: [math]\Delta \tau=\frac{2\mathcal{L}}{c}\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}[/math] Because [math]\Delta t=2\mathcal{L}/c[/math], we can substitute in [math]\Delta t[/math] and arrive at the equation for time dilation in special relativity: [math]\Delta \tau=\frac{\Delta t}{\sqrt{1-\frac{v^2}{c^2}}}[/math] This is a mathematical definition for what time dilation is according to special relativity, and our experiments confirm that this form of time dilation does, in fact, exist! Pretty cool huh? As you can see, time dilation doesn't depend on any of these crazy notions you keep repeating, and relativity didn't change.
  2. Finally, I'll be having my hip replacment surgery April 21st. I'm not looking forward to having the operation but, if it will stop all this pain, then I'm all for it.

    1. Show previous comments  3 more
    2. Sriman Dutta

      Sriman Dutta

      Hope you recover soon.

    3. Daedalus

      Daedalus

      I appreciate the comments everyone! I'm definitely looking forward to getting around and being able to sit at my desk longer than a few hours.

    4. Daedalus

      Daedalus

      Woot! My doctor has bumped my surgery up to Tuesday, April 18th.

  3. Well, the core decompression surgery did not work. I now have to get a hip replacement. At least I'll be able to sit down at my PC for more than an hour after having the surgery. As it stands now, I'm in constant, excruciating pain. :'(

    1. Show previous comments  6 more
    2. Moontanman

      Moontanman

      I hope you surgery goes well.

    3. Raider5678
    4. StringJunky

      StringJunky

      It's a mechanics cum carpenters kit isn't it Daedalus?

  4. That was the best research paper I've ever read, it really is. It has lots of facts, tons of alternative facts you know. The best facts filled with the best numbers and alternative data, but the best data... ROFL...
  5. Ah... I survived another trip around the sun!

    1. Show previous comments  1 more
    2. Daedalus

      Daedalus

      Thank you imatfaal. Oh, I also solved that problem I was telling you about. Now I have to rewrite my paper...

    3. Raider5678

      Raider5678

      I have passed 14 times.

  6. Happy Birthday Sirona!!!

  7. Happy New Year SFN!!!

    1. Show previous comments  3 more
    2. StringJunky

      StringJunky

      I'll light a match to 2016 with you; it was shit... 1977 all over again for... another annus horribilis.

    3. jimmydasaint

      jimmydasaint

      What happened in 1977? It was the year of punk rock wasn't it? Amazingly high energy tunes with exactly the right amount of rebellion. Never mind the bollocks...

    4. jimmydasaint
  8. I've seen his stone lifting technique performed by researchers on a show about Stonehenge on NatGeo about a year ago. I don't remember the name of the show, but we've known about these techniques for millenia thanks to Archimedes. It's not a far stretch of the imagination to think that ancient architects were aware of them too.
  9. The surgery went good, and I'm now back at home fully medicated hehehe. I appreciate all the support and comments. Thank you everyone.

    1. Show previous comments  2 more
    2. StringJunky

      StringJunky

      I......eeeee have become comfortably numb. :)

    3. Daedalus

      Daedalus

      Hehehe... he's got me on 10mg oxycodone. So, I'm feeling good, but I didn't sleep at all last night.

    4. koti

      koti

      That's some strong hehehe right there but the dosage seems to be low so you should sleep tonight.

  10. The core decompression surgery I'm having on my left hip is just one week away...

    1. Show previous comments  2 more
    2. imatfaal

      imatfaal

      Good Luck with the OP. Hope to see you back soon

    3. Moontanman

      Moontanman

      Hope you get well soon!

    4. Daedalus

      Daedalus

      Well, tomorrow is the big day... I appreciate all of the comments. Hopefully, I'll be back in action and walking normally in about 6 weeks :D

  11. The Cosmic Watch app is really awesome!!! Check it out: http://cosmic-watch.com/

  12. One million years is still a considerable amount of time when compared to our own life span. So, colonization of the planet would still be worth the effort. Furthermore, a million years is more than enough time to build structures and colonize the solar system itself and not just the planet. The value of the resources throughout the solar system would also make it a viable and worthwhile endeavor.
  13. Sitting at the doctor's office waiting on the results of my MRI...

    1. Show previous comments  3 more
    2. Moontanman

      Moontanman

      Whoa! Sorry to hear that dude!

    3. koti

      koti

      That sucks, sorry to hear that Daedalus. On the bright side, I have a friend who had the same condition, he's 4 years after the operation (65 years old) and he's good as new. Also be thankful that it's a ball in the hip. Could have been a lot worse ;)

    4. imatfaal

      imatfaal

      jeez thats bad news

  14. I finished another composition and, I must say, it's a very beautiful piece of music! Enjoy!!! http://www.scienceforums.net/topic/98721-a-concert-by-deadalus/?p=949577

  15. I finished another song where I take the theme from the beginning of the song, transpose it in key, and then vary the music. I finished this composition October 14, 2016, and It turned out as beautiful and as lovely as the woman I wrote it for. Enjoy!!!
  16. First my brother and now me rofl... I went to step off the porch and my left ankle gave out and I fell. So, I put my hands out to break my fall and end up getting a radial head fracture in my left and right elbow. The right elbow isn't too bad but my left arm is in a splint for a few weeks.

    1. Function

      Function

      Ouch ... Have a good recovery!

    2. imatfaal

      imatfaal

      Jeez - nasty. Hope recovery quick

  17. The lady who taught me how to read and write music retired this year. Without Mrs. Wood, I wouldn't be able to write the music that I do today. Great teachers are hard to find and, although we are in their lives for a brief period of time, their teachings remain with us forever. I wrote this song April 8, 2016 and posted it here at SFN. Enjoy!!!
  18. This next song is one that my brother wrote for his daughter, Alizah. He plays the guitar on this one and I orchestrated the rest. We finished this song December 28, 2014 and I posted it here at SFN. Enjoy!!!
  19. This next song is called "Endless Night". I wrote it November 1, 2015 and posted it here at SFN. The melody is a little melancholy, and it's one of my slower pieces but still beautiful nonetheless. Enjoy!!!
  20. This next song is my first concerto for oboe and is called "Tranquility". This is one of those times where I wished I had much better sounds to record with, but the song is still pretty. I wrote it August 12, 2015 and posted it here at SFN. Enjoy!!!
  21. I wrote the first part of this song in high school, but I didn't have the skill back then to finish it the way I heard it in my mind. Seventeen years later, I was able to complete it on August 20, 2015 and posted it here at SFN. This song is probably the happiest song that I've ever written and reminds me of something you would hear in a Disney movie. Enjoy!!!
  22. I wrote this next song for a very good friend of mine who was there for me after I went through my divorce back in 2009. I'm so happy that she finally found love again because her last husband passed away, but I do miss hanging out with her and all the fun we had. This song is called "Missing You". I wrote it for her September 5, 2015 and posted it here at SFN. Enjoy!!!
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