Iggy

No, that isn't what I said, and it's frankly a dishonest or mentally ill conclusion to make from what I said. I don't think you're mentally ill, so something else must be going on. The sane people who go to church on Sunday know very well that the crap preached to them isn't true, and that's exactly what makes them sane, but you didn't get that from what I said. You'll have to reread what I said. How old are you? I'm looking for an explanation for this miscommunication.

Mentally ill people don't know the delusion isn't true. Mentally sane people know things and profess opposite beliefs. People who know things and color them exactly as they see them are mostly autistic... and I could make an argument for autistic people being broken. "deciding to believe in something one knows is not true" isn't a sign of mental illness. It is a sign of humanity. If it is broken, then broken we are.

Our brains have made us the most powerful predators on the planet... with our fail and slow bodies and all. Anyone doubting the evolutionary benefit of that isn't just using 20% of their brain... they are extremely diluting that 20%

****Fourth Error: This is outright false, the symbolic formulas work for any [math]t_a[/math]. These are the run of the mill Lorentz transforms, I do not understand why you have so much difficulty with the fact. Keep trying. Do you need me to help?

Try again. Own your words.

Nope. Try again. This is your pitiful equation: [math]t_{e2}-t_{e1}=\gamma(t_a+v_2 x_a/c^2)-\gamma(t_a+v_1 x_a/c^2)=\gamma vx_a/c^2[/math] Plug some numbers into the left and right side and prove to me that ta doesn't have to be zero for your pitiful excuse for nauseating and exhausting math is correct. Go ahead and try to back up that claim. edit: by the way, please stop neg oneing all my posts. I've never given you a -1 no matter how much you deserve it (and frankly, no one deserves it more than you). Bother someone else with that crap, please!

Well, that was boring to read. ****Fourth Error: This is outright false, the symbolic formulas wort for any [math]t_a[/math]. These are the run of the mill Lorentz transforms, I do not understand why you have so much difficulty with the fact. Do it. Let's see some numbers big boy.

Yikes. I must have gone crosseyed. Sorry, Tar. I'm glad you liked it

I guess that's good. I just hope it isn't lost on you... I wasn't intending to write a poem. It's just that you asked the most cliched question ever to hit the airwaves. It has been answered so completely, in so many different ways, for hundreds of years -- I was just looking for some unique way of putting it. The current favorite way of answering your question is with pixie farts and pink unicorns. That should give an idea how worn out and slippery the handhold you're reaching for really is. How completely does a question need to be answered before you stop asking it... was the point there.

To keep things interesting, I'm going to answer alphabetically in iambic pentameter... The A-bao-a-qu lived in human dream. No less real than any god he did seem. The spirit Aatxe took the cavern's deep. The Abaasy sat atop heaven's heap. The thought that made these, one cannot deny, can just as easily make any god die. The Abada was a little unicorn. In guiltless dreams of children it was born, and survived by the thoughts they would adorn, but now they're gone with no one left to mourn. How could we invent the horn of Abath, without the aphrodisiac it hath? Our nature dreams up man-made frauds, imagining mighty and living gods. But, we don't get to ask from where they came. Our playful thoughts are only to blame. Ah... that went well ;-)

Yes, I rather prefer it that way.

I know you're suspended, but that shouldn't stop you from reading this reply and responding when and if you return. I'm afraid your explanation didn't do much for me. The trouble starts with the first thing you say in post 2 from the other thread: The Lorentz time transformation (which you're about to try to use) transforms from one coordinate system to another. But, you attribute these coordinates, above, to both earth observers. The point of the Andromeda paradox is that the t coordinate of an event at a significant distance is different in two different frames. Your most recent post in the other thread: The three velocities are [math]v_1[/math], [math]v_2[/math], and [math]v[/math]. If [math]v_2=v[/math] then it sounds like you're just being redundant. Ok... [math]t_{e2}-t_{e1}=\gamma(t_a+v_2 x_a/c^2)-\gamma(t_a+v_1 x_a/c^2)=\gamma vx_a/c^2[/math] What you just said means... [math]t_{e2} = \gamma(t_a+v_2 x_a/c^2)[/math] and [math]t_{e1} = \gamma(t_a+v_1 x_a/c^2)[/math] This could only make sense if you have a third frame. If [math]t_a[/math] is a coordinate in a third frame then [math]t_{e1}[/math] and [math]t_{e2}[/math] would be the same coordinate in two different frames. The third frame, however, would need to have its origin in the same place as the other two frames. So, now we have three earth observers. There is no need for that, I assure you. That doesn't help. If you evaluate your equation numerically, the only way it works is if [math]t_a[/math] is zero. The further from zero, the less correct. In fact, the left hand side and right hand side would disagree by exactly the value of [math]t_a[/math]. So, if [math]t_a[/math] is half c (ta = 150,000,000) then the equation would be off by 150,000,000 seconds. Nobody wants to be nearly 5 years off, so... If [math]t_a[/math] has to be zero then: [math]t_{e2}- \textcolor{red}{t_{e1}} = \gamma(t_a+v_2 x_a/c^2)- \textcolor{red}{\gamma(t_a+v_1 x_a/c^2)} =\gamma vx_a/c^2[/math] the red terms HAVE to be zero. No point in subtracting zero from anything, and you told us v = v2, so... [math]t_{e2} = \gamma(t_a+v_2 x_a/c^2) [/math] That would be the correct equation. Like I said, one variable for velocity and two for time. The second post in the other thread explains the variables and what they mean in the context of the Andromeda paradox: The equation simply transforms the t coordinate in one frame to the t coordinate in another (given distance and velocity). If t' is zero then t is the change in time between the two. When you say "Now, if one insists on having two observers, the math gets just a tad more complicated", it really doesn't. It is nothing more than one Lorentz transform. If you have one observer who changes velocity then the math and the equation is the same.

Quite a few posters have missed the fact that the above is a variant of the "Andromeda paradox", one with only one observer, NOT two. Nevertheless, the "paradox" works just the same and the above explanation is perfectly correct. You did *not* present the 'Wolfram variant'. You said this: [math]v[/math] represents the relative speed between the Earth and Andromeda. Wolfram said this: Assume, for simplicity, that the galaxy and the Earth remain momentarily at this fixed distance, with no relative motion. Those things are mutually exclusive.

I second that. All of the following posts as well. I feel bad for the OP, or anyone else bumping into this thread, looking for an honest explanation of the Andromeda Paradox. You have three variables for velocity (you should only have one). You have three variables for time (only need two). You don't say which velocity belongs in the gamma factor. Unless you explain every variable and give a sample scenario with numbers there is just no way to unravel what you are trying to do with that equation.

It isn't the best, but there is really nothing unusual about Wolfram's explanation. It doesn't make the mistake of thinking v is the velocity between earth and Andromeda. And, it does have two observers, in so far as this is two observers: To a stationary observer on Earth, the Supreme Galactic Council on Andromeda might be engaged in a debate on whether to attack Earth, whereas to an observer strolling at a leisurely pace of 2 feet per second, the Intergalactic Battle Fleet has already been launched toward Earth. -The Andromeda Paradox Just had to give Wolfram their props

Typo. I edited the post.

Not at all. The equation you gave works like this... [math]t = \frac{t'+vx/c^2}{\sqrt{1-v^2/c^2}}[/math] where, t is the time between present instants at a distance of x by the stationary earth observer x is the distance to the Andromeda galaxy (2.3 x 1022 meters) v is the velocity between the stationary earth observer and the earth observer who is walking past him toward the Andromeda galaxy (1.3 m/s) t' is zero (the present instant as defined by the walking earth observer) [math]t = \frac{0+(1.3)(2.3 \times 10^{22})/299792458^2}{\sqrt{1-1.3^2/(299792458)^2}}[/math] [math]t = 332682 \ \mbox{seconds} = 3.8 \ days[/math] 3.8 days separate the present instant in the Andromeda galaxy between two observers on earth who have a relative walking speed. That is the Andromeda paradox. The Andromeda galaxy is approaching our solar system at 130 km/s. When you say "v represents the relative speed between the Earth and Andromeda" that is simply untrue. Plugging 130 km/s into the above equation would give the wrong answer. That number doesn't enter into the above equation, or this scenario, or the Andromeda paradox.

But, that isn't the Andromeda paradox. There are two observers on earth who have a small relative velocity. The link you gave, which is pretty terse but pretty good, says the following,

Earth and Andromeda are in the same frame for the purpose of this thought experiment. They have no relative velocity. The two frames belong to two earthlings who have a small relative velocity. V, in that equation, represents their relative speed. Like Somanystylez says, walking speed. All of the events that are simultaneous for the one fella, and all the events that are simultaneous for the second fella, make two lines of a triangle in sapcetime. It's like the image on wikipedia. The further away something is, the greater the distance between the lines. It might be intuitive that two people right next to each other with a small velocity won't disagree much at all about the present time of a clock that is right next to them. The further away the clock gets, the more they disagree.

He made 365 trips. I multiplied the proper time of the round trip by 365. You didn't notice? I don't know what purpose that would serve. You're welcome to calculate it if you like. If you think it proves some point. The results certainly wouldn't disagree with anything I've done. Time dilation won't depend on acceleration. Whatever the velocity of the rotating twin -- that will give the time dilation. You're talking nonsense. All of my calculations have been correct and they have shown exactly what I've claimed they've shown. You're just throwing rocks now. I'm going to honestly stop feeding the... uh... yeah...

You said this: Yep I asked very explicitly because I knew you would try to take it back. The velocity of the rotating twin is constant in post 297. The point is that two different twins can experience 2g acceleration throughout the duration of a thought experiment (matching accelerometers) and their clocks will disagree upon reuniting. You claimed that this was a result of centripetal acceleration as opposed to linear acceleration. I have now given an example with linear acceleration.

Excellent. I shall use the same method to calculate the proper time of the pacing twin. Person A notes that C accelerates away from him for 1 day, decelerates for 1 day, turns around, accelerates towards him for 1 day, and decelerates for 1 day (all at 2g). According to A, this round trip takes C 4 days. The time according to C is: [math]\tau_C = 4 \frac{c}{a} \mbox{arcsinh} \left( \frac{at}{c} \right)[/math] (for one round trip) c = 1 lightyear / year a = 2.06314646 lightyears / year2 t = 0.002739726 years (i.e. one day @ 365 days/year -- A's proper time for one segment of the trip) [math]\tau_C = 4 \frac{1}{2.06314646} \mbox{arcsinh} \left( \frac{(2.06314646)(0.002739726)}{1} \right)[/math] [math]\tau_C = 0.010958846 \ \mbox{years}[/math] A watches C make this round trip 365 times taking four days each time for a total of four years. At the end of four years A and C both land. The proper time for each trip for C was 0.010958846 years. He made the trip 365 times. [math]\tau_C = 0.010958846 \ \mbox{years} \times 365 = 3.99997879 \ \mbox{years}[/math] (for 365 round trips) Person A (accelerating linearly at 2g) aged 2.853 years while person B (accelerating linearly at 2g) aged 3.99997879 years. Let me explain where you went wrong... The 4 in each equation refers to the number of segments of acceleration or deceleration. That equation assumes that only one trip is being made (accelerate / decelerate / accelerate / decelerate). Four segments. You assumed also that T is the same in both equations, but one trip (the pacing trip) is much shorter. One day versus one year undergoing constant acceleration makes a big difference as far as top speed. It does. Acceleration is 2.06314646 light-years / year2. It is in the equation you quoted.

All I did was use the relativistic rocket equation to solve the easiest acceleration / deceleration time dilation problem known to man. Is the number 2.853 correct? If not, please correctly calculate. If so, please say so. If you don't know, please say you don't know.

I can point out the error you made when giving those equations, but it will be too easy for you to dissemble and obfuscate. I need to pin you down with numbers. Can I proceed as if I have calculated the proper time of B correctly?

Acceleration is important in the classical twin paradox. Can I proceed with the pacing twin as if the numbers thus far are correct? The trip took the first twin 2.853 years? The one pacing back and forth is expected to take the same?