Delta1212

Oh don't worry. I'm actually a history buff and rather agree with you on the subject. I still found it funny, though.

e. holds if you fail to account for Doppler shift, but that's fine. The ban on faster than c travel applies to objects actually traveling at c. Things are allowed to look like they're traveling faster than c, as long as they don't actually travel faster than c. In this case, it's an optical trick caused by Tom's direction of travel. You can't take an accurate measurement if Tom's velocity until that optical effect has been accounted for. Likewise, you could point a laser at the moon and move it such that the dot on the moon's surface would travel across the lunar surface at faster than c. You can do this because it is merely a succession of images that create apparent motion that is faster than c. Nothing is actually moving faster than c. ----- If you're still not convinced, try reversing your assumed position. Let's say that Earth looks through its telescopes at t=2 and sees Tom turning around. Where is Tom actually at that point, and when did the light that Earth is seeing leave Tom's ship?

It would be far more efficient to use a fan without a sail to supply thrust than to use a fan blowing into a sail, though. And very easy to set up the sail such that it almost entirely negates any thrust supplied by the fan, which would, in any case, be in the opposite direction that the fan was blowing. The situation as conceived in the original question, for instance, would result in a net thrust in the opposite direction desired, but a very minuscule one as the sail actually acts to blunt the already tiny thrust supply by the fan.

You are underestimating the comparative size of protons and dust particles. One microgram is approximately 1,000,000,000,000,000,000 protons, give or take a power of ten. That many raindrops is equivalent to a hell of a lot of trucks.

Maybe flipping it will make this more intuitive: On Tom's return trip, a photon leaves his ship heading toward Earth. One second later, another leaves his ship and heads toward Earth. During that 1 second, the first photon will have traveled 1 light second. The ship, moving at 0.5c will have traveled half a light second. Therefore the second photon, released 1 second later, is released only half a light second behind the first photon. It will arrive on Earth half a second behind the first photon, but will represent 1 second's worth of Tom's travel time. In effect, Earth will be receiving Tom's light more frequently than it was released (I.e. blue shifted) which will make Tom appear to be moving faster than he is if you don't correct for Doppler shift.

They "see" him travel 1 ly in 1 year, but they measure him traveling 1 ly in 2 years. There is no prohibition on something looking like it is traveling FTL. There is only a prohibition on actually traveling FTL. They see the image of his ship turn around and say "This happened 1 lightyear away, therefore it took 1 lightyear for the light to reach us. Tom turned around 1 year ago." One year after that, Tom arrives and Earth says "One year ago, it was one year since Tom turned around, therefore it took two years for Tom to return 1 ly. He must have been traveling at 0.5c." Those two years of reflected light will arrive over the course of one year because it is being blue shifted by Tom's approach velocity.

Ok, let's do this in increments. At the moment Tom turns around, he is 1ly away from Earth. At the same time Tom starts traveling back toward Earth, a photon bounces off Tom and travels toward Earth as well. This is one of the photons that will allow Earth to see Tom turnaround when it reaches Earth. The photon is traveling at c. Tom is traveling at 0.5c. 6 months after beginning the trip back to Earth, the photon has traveled half a light year towards Earth. Tom has traveled a quarter of a light year. The photon has half a light year remaining. Tom has three quarters of a light year remaining. 6 months after that, the photon has traveled another half a light year and reaches Earth. Earth now sees Tom turn around. During the same 6 months, Tom travels another quarter of a lightyear towards Earth, and is now half a light year away. 6 months later, the Earth saw Tom turn around 6 months ago. In the intervening period, Tom has traveled another quarter of a light year and is now a quarter of a light year from Earth. 6 months after that, the Earth saw Tom turn around one year ago, and Tom travels another quarter of a light year, ending up at Earth. Thus two years have elapsed since Tom turned around, and one year has elapsed since the light from Tom turning around has reached Earth.

The blue-shifted image of Tom's ship will appear to be approaching faster than c, but c is a restriction on massive objects, not images. If Tom's ship turned around and suddenly accelerated to the speed of light traveling towards Earth (in violation of the laws of physics) he would arrive simultaneously with the light from his turnaround (seeing as he is traveling at the same speed). The Earth would therefore see Tom arrive back at Earth at the same time they see him turn around 1LY away. Because Tom takes 1 year longer than his light to travel the same lightyear, the people on Earth will know that he was, in reality, traveling at half the speed of light.

Actually, they'd look out of their telescopes at t=3 and observe that Tom turned around 1 year ago at t=2, but otherwise yes.

I suspect that confusion was common to most of the participants, whether we all realized it or not.

The Earth will not see something that is 1LY away until a year later. So anything the Earth sees at 1LY distant, the Earth concludes to have happened one year previous. The calculates the ship to be traveling at 0.5c and going 1LY, hence taking 2 years. Upon arrival however, it will then take 1 year for the light from the spaceship to reach Earth, for a total of 3 years between the ship leaving and the light from its arrival reaching Earth, but 2 years between the time the ship leaves and the arrival as measured by Earth, because Earth knows to correct for the time delay. So the image of the ship would recede at less than 0.5c, but Earth is smart enough to know that the location of the ship and the location of the ship's image as seen from Earth are not the same thing at any given moment, and the difference can be calculated based upon the distance and velocity. On the return trip, any light emitted from the shit at 1LY will take 1 year to reach Earth. 6 months after the ship turns around, the light showing that it has turned around will be 6 months from Earth, while the ship will be six months closer. In effect, it is "chasing its own light" because they are both moving in the same direction. The ship will therefore be much closer to Earth than the turnaround point by the time the Earth actually sees the ship turn around.

The sentence "Acceleration is not important in the twin paradox" is not here being used to mean "acceleration is not a necessary aspect of the classic twin paradox" because clearly you can't have an observer leave and then return without accelerating. It is rather being used to mean "acceleration is only necessary to switch frames for one observer but itself is otherwise incidental to the time dilation effect, which can be demonstrated by the fact that the same path through spacetime can be accurately measured by two inertial observers." Or stated another way, if disagreement of proper elapsed time is the demonstrated effect of the twin paradox, then the cause of the twin paradox is the path through spacetime through two inertial frames, while the acceleration has no direct contribution to the effect except that a single observer cannot switch frames without first accelerating. It is necessary to, but not the cause of, the time dilation. In other words, the point of the thread is, as Iggy said, to illustrate the clock postulate by setting up a thought experiment that will measure an equivalent time over an equivalent path to the twin paradox sans acceleration. It is not to set up a physically identical experiment to the twin paradox, but without acceleration, as this is clearly impossible. Md appears to be learning about relativity at the moment because I've noticed that he frequently makes topics about it as he discovers/learns new aspects of it, apparently in an effort to both work through the information himself as we'll as to receive input and help demonstrate the information to others. I don't think it has much objective beyond that, but this is an assumption about md that I have made. If I am wrong, I'm certain that I'll be corrected.

I'm pretty sure at this point that this whole thread has been an argument over semantic differences and ambiguous language, but I guess I'll wait to see how md and Iggy respond to my view of the thought experiment. I've been assuming they both basically agree with what I said above, but I suppose it's possible they don't and there really is more meat to the disagreement.

I hope the history joke was intentional, because it was hilarious.

Ok, so here's where the disconnect is happening. I didn't interpret md's claim that way. I'm assuming Iggy and md didn't either. I was working under the assumption that the equivalence of transferring B's reading to C's clock with an acceleration of one of the clocks was understood, and that md wasn't attempting to demonstrate a discrepancy between the elapsed times of inertial frames, but rather demonstrate that you could measure the elapsed time of an accelerated frame using observers in two different inertial frames making up different legs of the trip, without having to accelerate the actual observers. The final measurement would then not correspond to either inertial observer, but to the accelerated path that would be made up of their component paths. For that to be the case, the equivalence with an accelerated observer is, in fact, integral to md's entire premise. The acceleration of the measurement isn't hidden, it's the entire point. The acceleration that isn't important is that of the individual clocks, none of which measure an elapsed time in agreement with the final accelerated time measurement that is read by C at the end of the experiment. Edit to be extra clear: No one (I believe) thinks that the time on C at the end of the experiment is reflective of C's elapsed proper time since the beginning of the experiment.

xyzt, if you're defining acceleration as changing the frame in which a measurement is being conducted, then yes, there is acceleration present in this experiment. Is that what you're looking for? I feel like you think md is trying to claim that, because clock B is inertial, and clock C is inertial, and clock C's reading (which was set to B's at BC partway through the experiment) is equivalent to that of the accelerated twin in the twin paradox, that he must have then produced an example of the twin paradox that shows a discrepancy in elapsed time between inertial frames. You are then stating that this is inaccurate because upon switching the measurement from B's clock to C's clock, you are changing frames and, in effect, accelerating in the same way that the accelerating twin does in the typical version of the experiment. Is that accurate or am I mistaking your view of this thread?

Except you're not exposing anything. Demonstrating this equivalence was md's entire point, and was presumably understood by everyone arguing in his favor. I don't believe anyone here believes you can measure the time of an accelerated frame on a single inertial clock. The point wasn't that the twin experiment doesn't require undergoing a change in direction in order to create time discrepancy. It's that this discrepancy is entirely dependent upon the use of two (or more) different inertial frames. If you define switching frames as acceleration, then absolutely, the twin paradox is impossible without acceleration. A better understanding of the point of the thread is that there is nothing about experiencing acceleration that creates the twin paradox other than the fact that it causes the observer to change frames, and it is this use of two different frames which results in the discrepancy. The reason that "Acceleration is unimportant" is being claimed is solely because the effect can be measured using two clocks that, themselves, do not have to actually accelerate. The time they measure is understood to be the time in an accelerated frame and not reflective of either clock's individual proper time over the course of the experiment.

The entire point of this thread is that a coordinate transformation provides equivalent results to acceleration. You are trying to disprove this by stating that the coordinate transformation present in the experiment is... equivalent in effect to acceleration. Edit to elaborate: The thought experiment states that transferring B's time to C at BC will end the experiment with the C reading a time at the end of the experiment as if a single clock had started the experiment at B's velocity and accelerated to C's velocity at point BC. None of the clocks need actually undergo acceleration to accomplish this and the time at the end will not reflect the proper time experienced by either B or C over the course of the experiment.

There are a lot of things that are grossly wrong with this post, and I'm not just talking about the factual misconceptions of how genetics works or the way attractiveness is determined.

You would not find a twin paradox in the sense that no clocks will measure a different elapsed time between two events at which both clocks were present (since, seeing as they're all in uniform motion, no two clocks will ever be present at the same two events). Would you agree that you could set up the clocks to measure the elapsed time of the two paths taken in the twin paradox, one inertial and one non-inertial, without accelerating any of the clocks? The final elapsed time for the non-inertial path made up of the paths of two of the clocks would represent the elapsed time of a hypothetical accelerated twin, but would not represent the elapsed time measured by any one of the clocks in the experiment.

Whoops. I thought my numbers seemed a bit small. Must have missed a zero somewhere or something.

Yes, basically.

I know that "splitting the atom" is generally associated with nuclear weapons, but you don't actually get all that much energy out of one atom. To get the amount of energy released by a bomb, you need a fairly good sized chunk of specially prepared material. To use an example, a lot of smoke detectors use the radioactive isotope Americium-241. Based on the amount used, I think you wind up with an Americium atom splitting about once a month or so in the detector. Note that your house doesn't blow up once a month.

It's important to emphasize that a black hole is not actually a hole, and it does not suck things in. Unless your definition of "hole that sucks things in" also happens to include the Earth. Being slightly more technical than ajb, but still trying to avoid being too technical: The strength of something's gravitational pull increases the closer you are to its center point. As you get further away, the strength gradually fades. There is one caveat, however: once you reach the surface of something, the strength stops increasing as you move to the center. This is because, once you start moving through the object, you start decreasing how much of it is below you pulling you down. When a star collapses, it gets very, very small, but it still has all that gravity that the star had before. Only now, the surface of the star is very, very close to the center of the star. This means that you can get extremely close to the star's center, to an area that used to be inside the star, without reaching the star's surface. Gravity will be very strong here. This area where gravity is so strong that nothing can escape is always smaller than the size of the star before it collapsed. Anything further away will not, as ajb said, be able to tell the difference. This is because the strength of a black hole's gravity does not increase from when it was a star, it's just that you can get much closer because it is smaller, and the closer you get, the more you feel the pull.

The point of the experiment isn't to measure C's time. Changing C's time doesn't yield a false measurement of C's time at the end, because no one thinks that that is the time as measured by C since the beginning of the experiment...