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If mass is defined as a ratio of force and acceleration, it depends on the angle between force and velocity, and there would be a parallel mass, a transverse mass, or even a 30-degrees mass. So the standard (and I think the only) definition of mass is the rest mass measured at zero velocity.Well, I'm confused about "relativistic" mass. Is it a mass ...


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"If the Earth measures the dilated time then is the time it measures given by $t=t_0 \gamma$, with $t_0$ being the proper time? And the proper time would be the time as measured by the rocket, so simply $t_0 = d/v$?" If $d$ is meant to be the distance from Earth to the star in their own mutual rest frame, then $d/v$ would be the coordinate time in that same ...


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Here is the erroneous step: "Now, if Alice between the steps 3 and 4 (the ideal time would be as the photons get very close to 4, right before the double slit as expected from their synchronized clocks and known distance),measures the polarisation of her photons, the entanglement is broken before Bob's photons arrive at the double slit at step 4. Thus the ...


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I think you're kind of misunderstanding the notion of what proper time and dilated time is. Special relativity, at base, is a theory of four dimensional spacetime. It is always clearest when you think of things in terms of different points in spacetime, and paths between those points. So, if you have your spaceship travelling from earth to mars, you can ...


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Please keep in mind Dirac's dictum "a particle interferes only with itself" (I am not sure about the word "particle", it may be that he said "photon"). The polarization of Bob's photon is not relevant here. Be it vertically polarized, or horizontally polarized, the fringes will fall on the same places, because one photon doesn't care of the polarization of ...


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To be exact, time dilation refers to the difference in time between the two. Plus, usually, the dilation is measured in accordance to a reference clock, usually, Earth. But you are correct, both results are correct within their reference frame but they don't cancel out.


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Particles with zero rest-mass can only move at the speed of light, while massive particles can never reach it. This is a fact from special relativity and is independent of the source of said mass. The fact that the Higgs mechanism makes certain particles massive is not intrinsically related to this.


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First, note that there is no unified theory of QFT and gravity, so talking about geodesics and about the Higgs is really not possible within the framework of our current theories. Nevertheless, the confusion here seems to stem somehow from the idea that all particles are "initally" massless, and "then" the Higgs comes along and gives them mass. This idea of ...


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Ok I solved case 2. Let $t'=\tan^{-1}(\omega t)$ and $x'=x\sqrt{1+t'^2}$. Also observe that $x=A\cos \omega t + B\sin \omega t$ to represent simple harmonic motion. We get $x'=A+Bt'$. So only case 3 remains open. Also as u can see, I just did guesswork, without proper techniques for how to solve this in general.


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If you are allowing non-linear transformations of space-time (as you have done in your Case I), then I don't see why you can't write any motion of an object as x' = 0. i.e. Suppose the motion of the object in the (x,t) coordinates can be written as f(x,t) = 0 for some non-linear function f. Then, by setting x' = f(x,t), t' = t, the motion in (x',t') can be ...


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The Lorentz transformation simplifies to the classical transformation for all your cases since you took $c$ as infinity. There is no time dilation. The transform is just an identity multiplication for all 3 cases with: $$x' = x - vt$$ and $$t' = t$$ Now that you are in the classical world in one dimension, your first case is merely a tilted line with ...


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Due to the structure of reality, while within it, you cannot distinguish between absolute rest and uniform motion, you cannot distinguish between absolute length and apparent length. Due to these absolutes not being detectable, the absolute structure of reality itself also becomes undetectable. With this being the case, many folk conclude that the ...


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This is an extended comment on Valter's answer, so please upvote his answer not this one. In Relativity (General and Special) there is no unique way to divide spacetime into space and time. Different observers, using different coordinate systems, will disagree about whether a four vector is just a displacement in time or just a displacement in space. So to ...


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In contrast to coordinate time, proper time is independent from any geodesics geometry. Any clock is OK as long as it is in the same frame as the object whose proper time is measured. In order to recover the proper time information, the observer must ensure synchronization of his own clock with the clock of the observed object. Thus, your problem might be ...


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My point of view in physics is that, given any concept (in this case, proper time), there are always two notions: (1) the theoretical concept defined in the sense of mathematics, and (2) the experimental concept defined in the sense of experiment. We then hypothesize that these two concepts are equal, and of course, if experiment shows that this is wrong ...


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In a certain sense (regime) acceleration is caused by the curvature of time more than the curvature of space. Actually, the curvature is of the spacetime so that, making rigid distinctions has no much sense. However, if you consider the motion of a particle free falling in a region of spacetime, the equation of its story is the geodesical one: ...


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The "g-force" you would experience if you were to "hover" at Schwarzschild coordinate $r$ away from a spherical body of mass $M$ is given by: $$g=\frac{GM}{r^2 \sqrt{1-\frac{2GM}{c^2r}}}$$ (This only applies to bodies held at a fixed value of $r$. A body in freefall experiences no acceleration, for example. If $r$ is changing in some fashion then then ...


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I'm hardly a GR expert, so if you want a more technical analysis I'm sure others will be able to give you one. However, the answer to your apparent questions is fairly straight forward. It is not the curvature of space or the curvature of time that causes accelerations, it is the curvature of space-time. We live in a four dimensional universe (ignoring ...


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At first glance it might appear that the question about “reality” of length contraction in Special Relativity, is meaningless. To take the basic example, two 100 unit long spaceships A and B pass each other, at a respectable fraction of the speed of light. In A’s frame of reference B is much shorter than 100 units, say, only 70 units. And ...


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After checking various sources, including Einstein, this link, or this link, it seems that the length an observer measures for a rod in a reference frame where the rod is at rest is "real" (that term though seems to be usually avoided by physicists), but equally "real" is the contracted length of the same rod measured in another reference frame in uniform ...


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In special relativity, it is crucial to distinguish between frame independent (proper) quantities and frame dependent (coordinate) quantities. The proper length of a rod is frame independent, while the coordinate length of a rod is frame dependent. In a frame in which the rod is at rest, the proper length and coordinate length are equal. In a relatively ...


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Length contraction, as a consequence of Einstein's 1905 false constant-speed-of-light postulate, is ABSURD - it implies that unlimitedly long objects can be permanently trapped inside unlimitedly short containers: http://www.youtube.com/watch?v=uQHPAeiiQ3w "How fast does a 7 m long buick need to go to fit in a 2 m deep closet?" ...


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An observer cannot change the whole universe just by accelerating his spaceship. This is why "apparent" means "real for the observer". Spacetime is relative, and the relative spacetime diagram of an observer is changing. In short: The only absolute, undilated time value is the proper time of an object. Proper time is dilated by time dilation for observers ...


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The laws of physics have the same form for all, but there are different measurements which are equally "real"? Correct. Having said that, it is often sensible to differentiate between 'apparent' and 'proper' (or 'intrinsic') values, the latter normally measured in the rest frame of the object in question and giving an upper or lower bound for an ...



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