Dave, thank you for humoring my skeptical take on the idea that the person in the inertial frame can experience an acceleration that indicates that they are traveling faster than the speed of light, even if to observers he appears only to be approaching c. About the muons -- I don't have enough confidence in statements in the wiki article or in your derivation from them to conclude with much confidence that the muon perceives its acceleration to have integrated up to 10x c. I'm going to have to ponder on that idea.
I've read the wiki article you link to and some others as well. What I've found so far is inconclusive, but following are some details that are relevant (some points just mentioned for fun): - The faster you go, the more energy you're going to need to maintain constant acceleration (because of gain in mass) [1, 2], and this could potentially lead to a need for infinite energy at the limit of light speed. - The limit of time dilation as the pilot in the inertial frame approaches c is a freezing of time in his frame [3], but the question of what one would experience traveling at light speed is thought to be meaningless (see the other answers). - The experience of the person in the inertial frame is that the surroundings speed up and approach the speed of light (and that their clocks slow down!), while he just continues to accelerate in the normal way [2]. The difference between his frame and the reference frame is that he's accelerating and the surroundings are not. So his clock is the only one that undergoes time dilation. - The pilot would be subject to intense x-rays, as oncoming light in the visible range is blue-shifted into the x-ray range [4]. Eric [1] http://www.spaceanswers.com/q-and-a/2049/would-a-ship-travelling-at-the-speed-of-light-have-its-own-gravity/ [2] http://en.wikipedia.org/wiki/Space_travel_using_constant_acceleration(see "A Half Myth: It gets harder to push a ship faster as it gets closer to the speed of light") [3] http://physics.stackexchange.com/a/29114 [4] http://io9.com/5976041/this-is-what-it-would-really-look-like-to-travel-at-near+lightspeed On Mon, Nov 18, 2013 at 2:17 PM, David Roberson <[email protected]> wrote: > Here is a start. Wikipedia has an article about time dilation and > particles: http://en.wikipedia.org/wiki/Time_dilation_of_moving_particles In > it is a description of an experiment by Frisch-Smith where they measured > the travel time for muons of relatively high energy as they propagated over > a distance of 1907 meters. They state that it takes these particles 6.4 > microseconds to complete the journey according to clocks at rest on the > Earth. That means they are moving at a velocity of approximately .995 > times c according to that observer. > > I reversed the usual square root of (1 minus (v/c) squared) where v was > equal to .995 times c to eventually calculate the effective velocity of the > particle within its own reference frame. The final calculation yields a > speed of 10.0125 times c. This is the speed that the muon would think that > it is traveling through a distance of 1907 meters that it could have > measured just prior to it's immense acceleration due to the cosmic ray > impact. All observers at rest on the Earth would measure the distance as > 1907 meters. > > If you take the 1907 meters and divide it by the particle determined > velocity of 10.0125 times c you get a travel time in its reference frame of > .6349 microseconds. These muons are normally measured to decay with a half > life of 2.22 microseconds. This half life allows a calculation of the > number of muons remaining after any given amount of time so in this case > you expect to see 563 muons per hour at the beginning of the trip being > reduced by a factor of e raised to the negative .6349/2.22 which is > .75125. The total should be 563 times .75125 or 422.96 muons per hour. > The actual experiment yielded 412 muons per hour. The error bars are at > plus and minus 10 %. > > The muon appears to be moving at approximately 10 times c according to its > internal clock, etc. We all realize that an Earth bound observer sees it > moving at .995 times c and that its apparent internal clock seems to be > slowed down by the SR relationships. This is an analogy to the spaceman > that we are considering in the discussion. > > Dave > -----Original Message----- > From: Eric Walker <[email protected]> > To: vortex-l <[email protected]> > Sent: Sun, Nov 17, 2013 12:00 pm > Subject: Re: [Vo]:Local Calculated Velocity of Space Ship > > On Sun, Nov 17, 2013 at 7:57 AM, David Roberson <[email protected]>wrote: > > I am confident that the world he sees before him will appear warped by his >> velocity when he compares notes to other spacemen traveling at a different >> clip. > > > To compare notes, they will have to send him photons that are emitted > from charged particles accelerated from pulsars and now in the TEv > spectrum, so that he can detect them in the radio wave spectrum. > Generations of descendants of the pilots of the near-light-speed observer > that he passed will have come and gone in a nanosecond for him as he > listens to Steely Dan on his tape cassette player and eats freeze dried > astronaut food. His family and thousands of generations of their progeny > will have passed away in a split second 6.022E23 earth years ago, while he > whacks the 100Mz onboard flight computer to get the green phosphor screen > to come back on. > > It is very interesting thought experiment. He's trying to approach an > asymptote, which is always a losing proposition for practical people. > Perhaps something on the planck scale is going to start getting in the way > -- some fundamental constant is going to make it so that space is no longer > continuous but is now big and blocky and no longer makes smooth flight > possible. > > >> The meson experiment confirms that this occurs as well if you view the >> world from its point of view. Perhaps we should chew on that one next. >> > > Can you elaborate? > > Eric > >
