Right now I’m learning about relativity, and I have a specific question about the Twin Paradox.
In the Twin Paradox, one twin is an astronaut that takes a flight at near the speed of light to a distant star and returns, while the other twin stays home. Because of time dilation, the twin on the rocket ages less than the twin on earth. Relativity says it is equally reasonable from the rocket twin’s frame of reference to say he stays at home, while the earth-bound twin speeds away in the opposite direction and returns. Hence, the earthbound twin should be younger, which is a contradiction.
The book explains the paradox by saying the fact that the rocket twin turns around is what makes it clear he is the one that is traveling. His reference frame changes when he reverses direction while the twin’s frame has remained the same the entire time. I understand the Twin Paradox up to this point.
My question is what happens if the rocket twin only travels one-way? What if his rocket breaks down at the distant star so he stops there but is unable to return? Does this mean it is no longer possible to say he has aged less than his earthbound twin?
I think the answer may have something to do with the relativity of simultaneity (where events that are simultaneous in one frame are not simultaneous in another), but that’s just speculation on my part.
personally, I think all this theory about “time slowing down as you approach the speed of light” is a misunderstanding of sometihng much simpler…
I think when Einstein explained that a clock would slow down as you approach the speed of light, what he meant was that if you were flying away from the clock at the speed of light, the image of it would slow down, because, as you reach a point one ‘light minute’ away from the clock, the image you see of the clock is a minute old… as opposed to the image someone near the clock sees…
you see, I’m seeing people equating ‘speed of light’ with ‘speed of time’
Time is instantaneous… as proof of that, all speed is measured against it. No matter how fast you can travel, be it the speed of light, or 5 times the speed of light, you won’t be moving faster than time…
<<Glenoled Again steps off his soap box and puts it back in the depths of the garage, where it will sit for another decade or three>>
Unfortunately, you’re incorrect. Time really does slow down when you travel near the speed of light. Remember, the speed of light is constant to all observers, no matter how fast they move.
I believe the resolution to the one-way twin paradox comes from the fact that the rocket has to start and stop. This is acceleration, and the “frames of reference” argument doesn’t apply any more.
Suppose you take a one-way trip to a planet 10 light-years away, travelling at 98% c. (I’ve forgotten the special relativity conversion for time dilation, so I can’t use specific numbers.) You will arrive shortly after a radio message beamed from Earth at the time of your launch toward the same planet – 10 years later. For you, however, the voyage will have seemed to take a short time (hours or days, I can’t remember). You set up camp and radio home that you’ve arrived.
20 years after your launch from Earth, your message is received (you, of course, are 10 years older as well). The image they see is one of you nearly the same age as when you left.
The image (“I’ve made it!”) would be nearly the same as if you had travelled back yourself at relativistic speed.
I’m not confident in my understanding of the original paradox, i.e. whose intertial reference frame is stationary. It seems intuitively obvious, but I don’t know how it is proved. Just thought I’d offer an illustration; someone else can do the math.
ultrafilter beat me to it. And I also figured out another way to think around the paradox. Carry a flashlight with you on your voyage. If the beam can barely squeeze out in front of you, you’re the one travelling near c. Or your batteries need changing.
Hmm…that would seem to violate the central dogma (so to speak) of relativistic theory, that the speed of light is constant in any reference frame.
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Exactly. As long as you’re in an inertial refernece frame, the beam of light will move away from you at c. If you twin turned on his flashlight, the exact same thing would happen.
My meanderings through Special Relativity have taught me that any time you think you’ve found an easy answer, you’re wrong.
My flashlight example (I’ll claim now that it was offered facetiously) also fails because it doesn’t account for how one might hypothetically see the subtracted speed of the beam. Yeah, that’s it. Facetiously.
w/r/t the OP, my understanding is as follows: If the accelerated twin’s (twin 2’s) rocket broke down and he/she ended up in an inertial reference frame, twin 2 would be demonstrably younger than twin 1, and they both would agree after transmitting clock readings to each other and then adjusting for transmission travel time. The twins do not have to end up in immediate proximity for the results to hold. Put another way, the paradox does not depend on one twin accelerating “away” and then “back,” merely that one accelerates and the other does not.
To resolve the “twin paradox”, you have to invoke General Relativity. General Relativity takes into account acceleration and gravity (in fact, it says that they’re ultimately the same thing), and is broader in scope then Special Relativity- special in the sense that it only covers the special case of uniform linear motion.
The reason one twin is younger is that one undergoes acceleration and the other does not. To preserve the “no privileged frame of reference” rule, General Relativity predicts that you would observe the same difference in time passing if you presumed that the twin in the rocket was holding still and the entire universe, including the stay at home twin, was accelerating. In that case you would have to calculate the gravitational effect of the movement of the entire universe on the twin in the rocket, and it is the same as if you presume that the rocket is moving and everything else is holding still (or any combination of relative motions).
Actually, you were right the first time, Jet Jaguar. It’s the breakdown of simultaneity. If you want to compare the ages of the two twins, you need to say when you’re measuring. I could look at a baby picture of my mother, and my high school graduation picture, and claim that I’m older than her… But I’d be laughed at. To say who is older, you need to look at both at the same time, but you can’t do that when the twins are travelling at different speeds and are separated by a great distance. In Alice’s frame, she’s older than Bob right now, and in Bob’s frame, he’s older than Alice.
Yes and no. The twin paradox arose, not as a paradox, but as a “peculiar consequence” of special relativity, early on. Special relativity can indeed be applied to accelerated objects, if you’re careful. General relativity assumed that gravity and acceleration were the same effect.
