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I think the problem comes from ambiguity of the question itself. Of course hobo can make a clock out of traveling photon, and claims that every passage of photon from front to rear and vice versa is for example 1 second. This hypothetical clock will measure the proper time of hobo himself though. What question is asking here imo is that does hobo measure ...


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You are asking if we can take space as a universal reference frame. Now what we usually use as universal reference frame, is the CMB. But in SR and GR, there is no universal frame of reference in theory. But let's disregard that, and say you want to move that bucket with water. First of all, how would you say if the bucket was in motion (constant speed) in ...


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Unfortunately, Dale's answer lacks sufficient intuition! Assume that, instead of explosive material, there is a thin screen at the midpoint of the rocket. From the viewpoint of the observer in the lab frame of reference, contrary to the observer in the rocket's rest frame, the wavelengths meeting each other on the screen are no longer equal, and thus it is ...


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I don't know if you came with this thought experiment by yourself but if you did you are crazy smart. This is actually very close to the argument made by Newton, usually called Newton's Bucket. He believed that absolute space was a real physical scenario where physical processes were to happen. And something similar to that is his main argument for it's ...


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Now from the point of view of the observer on ground what will happen? If the signals don’t arrive simultaneously the device must not explode. Constructive interference occurs at a given event when the phase, $\phi$, of the two waves differs by an even multiple of $\pi$ at that event. Destructive interference occurs when they differ by an odd multiple of $\...


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There is a very simple answer. The bomb will explode if and only if a detector on the ship detects constructive interference. Thus, the interference needs to be observed on the ship (by the detector), to explode the bomb. The explosion is based on that observation on the ship. It is a local observation on the ship that triggers the bomb. Now you are ...


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Suppose we choose some coordinates. These can be any coordinates that are convenient such as Schwartzschild, Gullstrand-Painleve, Kruskal-Szekeres or whatever. If we denote your position in these coordinates $(x^0, x^1, x^2, x^3)$ then we can differentiate twice to get your acceleration in these coordinates: $$ \frac{d^2x^\alpha}{d\tau^2} $$ This is called ...


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Imagine a series of concentric paper thin onion skins (spherical shells) surrounding the earth and centered on the center of mass of the earth. These skins extend all the way to the center of mass point. There is one special shell which is the surface of the earth itself (assume a perfect non rotating sphere). The free falling observer will not be able to ...


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The outcome depends on the method, how A (or B) measures and which clock he compares to which clock. The problem is that A and B can only directly compare readings of their clocks when they are at the same point. If they are at some distance from each other, to say what "another clock" shows they must make some assumptions about the one-way speed of light ...


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I really wish more books used spacetime diagrams to teach relativity, because 90% of confusion in relativity problems can be resolved by drawing a careful spacetime diagram. The idea is to superimpose the $t$ and $x$ axes for one observer (call them observer B) and the $t'$ and $x'$ axes for a moving observer (observer A) on the same diagram. All events ...


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'How old is B from his own (B's) frame of reference at the moment A made the above observation?' Your problem lies in the very moment you are talking about. In SR there isn't an unique moment for universe. A moment will be meaningful only if you specify your refrence frame of that moment. i.e you should have asked something like this: 1.'How old is B ...


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It's all in the Lorentz Transform: $t'=\gamma (t-v x/c^2)$ In your case $\gamma=2$, $t=60$ and as $A$ is presumably at the origin, $t'=120 $y, as @WillO says. However different values of $x$ would give different $t'$. So this is not 'a particular moment in the first inertial frame' which is what your question asks about. At the $t=60$ moment there are ...


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Since the situation is symmetric there are 2 answers, one for each frame of reference. If we take the relative velocity to be v=0.866c for a gammafactor of γ=2, when A is 100 years old, in A's frame B is only 50 years old. In B's frame, when B is 50 years old, A is only 25 years old. If they could beam information to each other they could build an ...


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It's a little hard to interpret your quoted question: "How old is B from his own frame of reference at the moment A made the above observation?" I'm interpereting this to mean "According to B's frame of reference, how old is B at the moment when A makes his observation?" If you meant something else, then the following might not apply: I'm assuming that ...


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Both the distance traveled and the time elapsed are multiplied by $\gamma$, so if you were to just divided the distance between the two ships by the time elapsed, you would get .5c. However, Lorentz boosts don't simply scale space and time, they convert some time to space and some space to time. Imagine at time $t_0$ you were to measure the positions of $A$...


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As is often the case, the "culprit" is the relativity of simultaneity. In the $S$ frame, the events of A being at location $.75ct$ and B being at $.25ct$ are simultaneous, but that's not the case in the $A$ frame or the $B$ frame. You can't just use the $\gamma$ separately on distance & time and combine them, you need to use the full Lorentz ...


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The phenomenon called gravitational red shift tells you most of what you want to know. What happens is that if the camera is on a planet where one hour corresponds to 7 years on Earth, then a viewer on Earth finds that the video stream of the distant events looks really slow. The pictures show the distant people walking around really slowly, and breathing ...


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You could go to Venus or Mercury and set up a video camera there. Both Venus and Mercury are deeper in the gravitational potential field of the Sun, contributing to time on those planets to "slow down" as compared to Earth. Both planets also moves faster with respect to the Sun then the Earth does, contributing to time on those planets to slow down as ...


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The way to think about problems in relativity is to avoid reference frames and think in terms of invariants, in this case proper time. Proper time is just path length in Minkowski space. So if the twins travel equal path lengths their clocks will measure equal durations. It's not acceleration per se that produces the paradox, it's the fact that a straight ...


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As objects fall into black holes the wavelength of the light they reflect, and that your eyes collect, gets longer and longer. This means, its quickly passes the infrared region and is effectively black to your eyes. As the light gets longer, measurement devices can't detect the object anymore. So at the same time it gets 'stopped in time', it becomes part ...


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