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7

Why do you assume the length needed to "span the cyclic space" would be the same in different frames? With cyclic universes it helps to think of them as equivalent to an infinite universe where matter just repeats cyclically, see the "tiling diagram" with the bee and the spider on this page. From this perspective, it's clear the width of a given tile shrinks ...


5

It's my understanding that when something is going near the speed of light in reference to an observer, time dilation occurs and time goes slower for that fast-moving object. According to the 'something', it is the observer's clock that runs slower and it is the observer's rulers that are contracted. That is to say, the time dilation and length ...


3

Your starting point is incorrect. You say: The point is, Rindler's observer shows us that the "action" of an accelerated observer on space-time is non trivial (there exists a black hole behind a uniformly accelerated observer). You're correct that there is a singularity, but it is only a coordinate singularity. The Riemann tensor is everywhere zero in ...


2

This is the answer for the "continuum" bit of your question or what happens if Bob leaves for Vogon on a sublight spaceship. I've assumed that Alice and Charlie are one light year away from each in the rest frame of either and that they are at rest with respect to each other (ie the separation will remain one light year for the entire experiment). In ...


2

In relativity there's no objective frame-independent way to compare the rate two clocks at different locations are ticking--different coordinate systems can give different answers (ultimately this is due to the relativity of simultaneity). There is also no frame-independent notion of speed, so you can't say in any objective sense that clocks moving at high ...


2

"First, is my problem formulation correct with respect to special relativity, and second am I correct in how I'm solving the problems?" Your equations are perfectly ok. However, your scenario 1 seems suspect. Why would the sum of the rest masses be conserved in a relativistic inelastic collision? Scenario 2 seems fine to me. I like your quest for ...


2

The only naturally occurring symmetry breaking radiation of this kind is the CMB. Unless you are talking about charged particles of more than approx. 1e19eV energy (in the CMB rest system), the effects are negligible, as far as I know. For those ultrahigh energy particles, however, this so called Greisen–Zatsepin–Kuzmin limit (GZK limit) forms a cosmic fog ...


2

Time dilation is a comparison of rates. When an object is moving fast with respect to you, it's clock rate is slow, and when it comes to rest with respect to you its clock rate returns to normal. The time difference between the two clocks at this time is due to the accumulation due to these different time rates. That is the leftover effect of the time ...


1

Yes, you could make it permanent if you could move backwards in time. But apparently we cannot, so the answer is no. To see why you need to travel backwards in time remember the twin paradox. In the twin paradox the symmetry is broken when the traveler changes of inertial reference frame (see the figure below) Now relabel the graph $ct$ to $x$ and $x$ to ...


1

Length contraction effects may be permanent in the same way as time dilation! You just have to choose the right example. Example: An astronaut is traveling at v=0,99 c to an exoplanet, according to Earth frame he is traveling 198 light years in 200 years. According to his frame (reciprocal gamma = 0,141) he is traveling 27,9 light years in 28,2 years. ...


1

The explanations involving clocks ... Textbook examples or explanations of relativity that involve clocks are often about time-dilation. ... Is valid only if the clocks is ticking ... These examples/explanations generally assume that any clock they mention is a working clock. It doesn't have to be a clock that ticks. It could be any type of clock ...


1

There is actually an equivalent to "total elapsed proper time" along a time-like curves in spacetime (which can represent the worldlines of particles moving slower than light), and that is the "proper distance" along a space-like curve (which cannot be any real particle's worldline). See the spacetime wikipedia article for more on time-like vs. space-like, ...


1

I believe that one could rephrase the question as "if the limit of the speed of sound in a medium must be the speed of light in vacuum, what does that mean for the limit on rigidity of an object?" Speed of sound is given by $$c=\sqrt{\frac{E}{\rho}}$$ - it depends on both density and Young's modulus. I would consider "rigidity" to be just the modulus, and ...


1

All you need to do is conserve energy and momentum in the lab frame. Firstly you conserve energy in lab frame: \begin{equation} E_{\gamma 1} + E_{\gamma2} = E_{\pi} = 1.3GeV \end{equation} Then you work out what the pion's momentum was (still in the lab frame) using the mass-energy-momentum relation where the $E_\pi$ is the total kinetic and mass energy: ...


1

Alice: 2 years Bob: No time has passed Charlie: 2 years There are a couple of things to point out: First two planets aren't likely to be stationary with respect to each other, they will be rotating at different rates around different suns that are themselves in a solar system with it's own movement. But for a realistic scenario (e.g. another planet in ...


1

Assuming a direct hit - so traveling through about 50 km of atmosphere - at 0.1 c that would take about 2 ms if it didn't get slowed down too much by the atmosphere. What about drag force? Let's assume a radius $r$, density $\rho$, mass $m = \frac43 \pi r^3 \rho$. If it is a sphere, it experiences a drag force $F=\frac12 \rho_a v^2 C_d A$. Putting $\rho_a=1 ...


1

Consider the following results: From the definition of scalar product of four vectors, $$ \tag{1}(p_1 p_2)^2 \equiv (p_{1\mu}p_2^\mu )^2 = (E_1E_2 - \textbf{p}_1 \cdot \textbf{p}_2 )^2.$$ The usual dispersion relations: $$ \tag{2} E_i = \sqrt{ | \textbf{p}_i |^2 + m_i^2}.$$ The velocity $\textbf{v}_i$ in terms of momentum and energy: $$ \tag{3} ...



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