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5

First off, we should take the wisdom of Jack Wisdom to heart: "Calculation of the history of the lunar orbit is fraught with difficulties." While calculating the history may well be fraught with difficulties, calculating the future is hugely problematic. For the sake of argument, I'll ignore that issue. The OP suggests the end of the planet is about 5 ...


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Whether or not time is continuous or has some sort of discrete time step, consider the following. Imagine you had a very powerful computer at your disposal, or that the laws of physics happened to be simple enough that we could simulate something as complex as a sentient, self-aware organism using it. Now, we hit "start" on our simulation, and wait a few ...


3

Energy is the name physicists give to the Noether Charge that is conserved when a physical system's description through its Lagrangian is unchanged by time shifts. Or, in more everyday language, most physics does not depend on where one puts the $t=0$ time co-ordinate origin. The laws are invariant when we shift our time origin back and forth. Noether's ...


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The site rules forbid us from giving the answers to homework problems, but this problem illustrates a fundamental issue in relativity so I think it's worth some general comments. Incidentally you may be interested to read the Wikipedia article on the ladder/barn paradox, though in it's efforts to be comprehensive I think the article gets a bit confusing. ...


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Don't confuse time dilation and length contraction,(even if length contraction is a consequence of time dilation) because there is no length contraction for the distance between two reference frames. The length (or distance) must be found in one reference frame, and the observer must be in another reference frame, he may not be part of the reference frame of ...


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A photon cannot be said to have its own inertial reference frame, because inertial reference are defined to be a family of coordinate systems that satisfy the two fundamental postulates of SR, one of which is that light moves at c in all frames. You could construct a coordinate system where the photon was at rest, but since this coordinate system wouldn't be ...


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Quite a philosophical approach. There is still the reliance on our four other senses in order to make sense of our physical world, however the same approach can be imply to those senses also with the delay in neurological impulses. One must also take into account, as you would call it, the in between frames of other people's perceptions, as well as those ...


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Fortunately for experiments in physics we have better proxies than the accuracies of our five senses. We have detectors and computers and .... With these tools a theory of how the universe is made has been developed, from elementary particles with the theory of quantum mechanics building up the observables around us, to the astrophysical models that fit ...


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Have a look at my answer to Time Dilation Effects from simply being on a spinning planet orbiting a star in a rotating galaxy in an expanding universe.. Compared to an observer far from the Earth, time at the Earth's surface runs more slowly by a factor of 0.9999999993. Over a 70 year lifespan this makes a difference of about 1.5 seconds. So the man in ...


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There are two types of time dilation: dilation caused by being near a large body, and dilation caused by traveling very fast relative to another observer. Relativistic time dilation plays a bigger role for astronauts aboard a space station similar to the ISS. Even though velocity and gravity produce opposite time dilation, in this scenario, time dilation due ...


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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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Well, Lorentz transformation and whole special relativity gives us short qualitative answer - time dilation and length contraction are very similar. Sitting on Earth we see muons with slower decay rate, because of time dilatation. Being a muon, we calculate time in our own frame of reference - so to keep calculations clear, we need to contract length ...


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Short answer: Yes, length contraction is a symmetric transformation between reference frames. However... You may not like this answer, but I think it's far easier to regard muon decay via the concept of time dilation rather than length of contraction. Reason is, from the standpoint of the muon it's not moving (and yes the Eath is moving but it's not ...


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We've already observed time dilation, so we know time isn't linear/constant. See the Experimental confirmation section of the Wikipedia page on time dilation.


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Length is contracted the other way, we just don't notice it because muons are pointlike particles (as far as anyone knows), and a length of zero is still zero no matter how much you contract it. If you had a beam of muons spaced a fixed distance apart (and yet somehow their "decay counters" only start at $50\text{ km}$ altitude), then it would be a ...


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I was doing a question about if a train fits in a tunnel. Did the question assignment include a specific consistent definition of what's meant there by "to fit", in the first place? Presumably, in the setup which is typically considered, the ends of the tunnel (say participants $A$ and $B$) are supposed to be at rest to each other, the ends of the ...


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Confusion about Length Contraction [...] if one object is moving at a speed relative to another object, shouldn't this movement affect [...] Talk about "length contraction" (or "time dilation") is inherently confusing; it is improper and should be avoided. In the typical "cosmic ray generated atmospheric muon" example we have the following unambiguous ...


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I looked at the previous discussion that you had about this here in the comments and I think I may have an idea about what is going on here, but I expect someone else will post a better reply here. First I want to quote three of John Rennie's comments. See this article on the block universe. Note that most us regard this as philosophy not physics ...


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The most helpful path to getting your mind wrapped around physics of your question is to examine how you pose the question itself. Most importantly, you write: "...with acceleration instead of a constant velocity, because one of you is experiencing time dilation" This is wrong on a few counts: Time dilation occurs whenever there is relative motion, whether ...


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This alleged problem falls apart as soon as you do a rigorous analysis. It should be clear that with such random accidents there is no causation. If event A really causes event B, then that's reflected in the state of the system. You'll have a state of the form 1/sqrt(1+|u|^2)[|A B> + u |not(A) not(B)>], so an entangled state containing information about the ...


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Tilting an object in space changes its apparent dimension (think of trying to get furniture through a door: the width of an object depends on its orientation). Objects in relative motion are tilted in space and time (or rather, spacetime), and different observers will see things unfold under different perspectives. Personally, I find relativity of ...



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