Therefore, you need general relativity which explains it by the acceleration that is inevitable if the brother on the ships ever wants to come back.
This is a very common misconception.
The problem is that the brother's reference frame is not an inertial frame at the time where he turns around. Thus, you can't work in his frame. You don't need general relativity to show how acceleration and forces work - General relativity is really more concerned about masses and how it curves spacetime. Electromagnetism, in the form of the electro-magnetic field strength tensor, is one of the nicest examples to show the advantages of "relativistic notation", so to speak, and would be more than capable of providing acceleration. Of course, do that, and the brother's frame won't be an inertial frame anymore.
But special relativity has proven to be very capable of solving this "problem" - it's been done dozens of times in this thread already. The trick is: Solve the equation in an inertial frame, and that would be the one of the brother back on earth.
It may seem difficult who and who isn't in an inertial frame (i.e., to see who of the two got accelerated). But it isn't impossible to find out - unless that acceleration is due to gravity. This, the strong equivalence principle, is what lead Einstein to formulate general relativity.
To illustrate that point, imagine being in a box that is freely falling in the vicinity of a massive object. You'd note that you're accelerating, since it seems to you that forces act on small test particles you throw around. But you cannot tell if you are in a gravitational field, or if you're otherwise getting accelerated.
Now consider the situation not in a gravitational field, but an electromagnetic one. Again, you could measure the effects by using (this time charged) particles. But this time, you'd see that the particles behave DIFFERENTLY if they're charged differently. The reason is that this force is *NOT* proportional to mass, but rather to (electric) charge. Therefore, this force seems "different". (Of course, the situation may be more DIFFICULT to approach in a more "realistic" situation, but there's no physical reason that would make it impossible)
In may opinion the twin paradox is a direct consequence of the special relativity only but Joey posted some articles whereas it seems the time shift entails a change of speed
I can't remember those articles in question, or Joey claiming that, but it's been a while. Do you have a link ready? I don't want to go through this thread again.
I agree though that the twin paradox can be completely solved in special relativity.
This post should get a huge
disclaimer, because I've done these calculations quickly, and thus may have done mistakes.
When the starcraft reaches the cruise speed V = 0.95 C the instrumentation on board start transmitting the pilot's heart beats
On the earth the frequency is f = 60 beats / minute
The twin brother, a doctor, doesnt know the theory of relativity therefore he would expect to receive the beats at a time interval T = 1 + 0.95 = 1.95 secs but he gets
T = 1 + 3.20 = 4.20 secs
He makes the false but consistent assumption that his brother's heart, on board, beats at a frequency f = 18.75 beats / minute
Same consideration on his return
Conclusion : The doctor would not be surprised if his brother twin looks younger than him
I'm not sure I got the problem completely. I think there are three ways to look at this problem:
ASSUME c IS CONSTANT FOR ALL OBSERVERS, BUT IGNORE TIME DILATION(
which is nonsense in a way - after all, time dilation and length contraction can be DERIVED from this assumption - but let us assume this doctor is careless, perhaps, and dangerously misinformed)
0.95 seconds corresponds to what is in essence how long light takes to travel the additional distance, right?
Therefore, he used: v*1s/c
However, at this point, he already realized that c is the same for all observers - after all, he did
not assume that the light only travels with speed (1-0.95)c, as you'd do if you naively add the velocities (as we'd do in classical mechanics, if we were to calculate, for instance, the speed of a ball thrown inside a train observed from outside - just adding velocities).
NO RELATIVITY AT ALLIf he
actually didn't know about relativity, he'd expect:
the first term being the actual time difference due to the heartbeat (here, we may use an "absolute time and space", since we're ignoring relativity on purpose :)), the second the time our now "slow light" needs to travel the additional distance the second heartbeat has to travel more (which is 0.95*c*1s).
Note please that the first lightray now also takes much longer, but since we're calculating DELTA t, the term vanishes.
Of course, he does not measure 20 seconds, but 6.24s (I get the 3.20 seconds if the doctor corrects those 6.24 seconds UNDER THE ASSUMPTION that c is constant for all observers, but we don't do that here :)). He assumes that the error lies in a different time difference between two heartbeats, that is to say, he assumes a formula of this type:
Solving for t_<3 gives us:
\Delta t_<3 = 0.312 s
Which implies 192.31 heartbeats per minute.
So this particular doctor would be very surprised indeed to find his brother didn't age at all!
... Also, perhaps, that his brother is still alive.
SPECIAL RELATIVITYTime dilation tells us that the time intervall between two heart beats, observed from the lab frame (=earth, here) would be
\gamma * 1s = 3.20 seconds.
In the lab frame, the ship travels an additional distance of v*c*3.20s in that time, and light travels (for us, and everyone else) at c. So all told, we'd expect a time difference of
Where the first term is just the time between two heartbeats in our reference frame, whereas the second is an additional time difference we get since the second heartbeat has to travel additional distance. This time, it travels at "c" (not 0.05c, as the naive doctor assumed). So we end up with 6.24 seconds.
If our doctor was uneducated (didn't know about relativity at all), he'd get the wrong result - and would assume that his brother would either be dead (due to his crazy heartbeat), or, at the very least, be much older (if he also assumes that, uhm, life speed grows if heartbeat frequency rises).
If our doctor was careless (knew about c=const., but not the rest of it), he'd find from the measured 6.24 seconds a heartbeat-time-difference of 3.20 seconds (which is actually completely right in his rest-frame. A lucky "coincidence", if you will - it is not really a coincidence, granted - this thing is "constructed" to work out like this, but from his wrong assumption, the right thing followed). From there, he'd find the new heartbeat that you've given above.
Another thing to consider is that while time transforms with \gamma, frequency does not (it goes with 1/time, after all). A more complicated transformation may be needed, I do not know right now.
So yeah, that was my slightly longish take on it.
This may actually be a standard problem (the nice result of 20 seconds if done classically, and the still nice result of 3.20 seconds if done in special relativity implies someone chose those numbers with great care ;)), but I didn't know it before, and I didn't google results. What fun is life if there is no risk to embarrass oneself in physics-replies
