Recent content by JD96

@bcrowell Thanks for your input! So to make sure I got it right, are you defining curvature as the coordinate acceleration in the momentarily comoving frame and it is problematic to obtain its direction due to the fact that only its norm is an invariant quantity?

Thanks for your response! I see that you are referring to the definition ##|\frac{d\vec u_{T}(t)}{dt}|##, where ##\vec u_{T}(t) ## is the unit tangent vector to a curve parameterized by ##t##. I think to apply this definition to minkowski space I could use proper time as a natural...

Hello, in this section of the wiki article on Rindler coordinates it is stated that the proper acceleration for an observer undergoing hyperbolic motion is just "the path curvature of the corresponding world line" and thus a nice analogy between the radii of a family of concentric circles and...

Thanks again for clearing that up to me, too. Then I will keep in mind that although one in principle could use the EP to explain why the weak field approximation for gravitational time dilation and the ratio of the proper times in Bell's setup have the same form, one should use the scenario...

I should have noticed the bad wording "observing unstressed length" in my previous post, but your answer nonetheless adresses what I had in mind, namely that unprimed K's explanation of the breaking of the string should involve the unstressed length being shortened by the lorentz factor. Ah I...

I am realizing I forgot to distinguish between unstressed and "actual" length as done in the insight post and probably that is where my confusion comes from. So when you write the length of the string stays constant in unprimed K, it's because each end of the string is always attached to one of...

Great article and since I am trying to get my head around this seeming paradox I found this insight to be very useful to get an overview. Nonetheless I would like to use this opportunity to ask a few additional questions: 1. Since forces are involved, why does the rest length of the string stay...

I will have a look at the link you gave me when I have a little bit more time to study it in greater detail. With correction I meant that when aiming to derive the 3+1d lorentz boost in matrix form as given here https://en.wikipedia.org/wiki/Lorentz_transformation#Boost_in_any_direction, but...

@bcrowell I would like to derive the 3+1d lorentz boost in matrix form using the one dimensional lorentz transformation (I haven't yet learned about differential geometry and group theory). Apart from the method mentioned in my OP what other ways are there? I now know that using several...

@bcrowell So from what I understand using the graphics in the wiki article: If I perform three lorentz transformations (where in each one the relative velocity is aligned with one of the axes), I have not simply transformed the coordinates between two frames whose relative velocity is...

Intuitively I would think that a set of three rulers that are orthogonal to each other in one frame are not in another one or does one have to distinguish between a rotation that is brought in manually with a rotation matrix and one that is "induced" by relativistic effects?

Hello, a derivation of the lorentz transformation for an arbitrary direction of the relative velocity often makes use of writing the spatial position vector of an event as the sum of its component parallel and perpendicular to the velocity vector in one inertial frame and then transforming both...

Mhh... I didn't consider the possibility that the error bound could cause problems and it really seems that it does, since I checked my result several times (and proving the taylor expansion converges for 1/2<x is not really satisfying). Thus I am considering your method, but I have a few...

I decided to work out the limit and keep getting the same result, namely \displaystyle\lim_{n\rightarrow +\infty} {\frac{a_{n+1}}{a_n}}=\frac{|x|}{1-x}. But instead it should be zero or am I wrong here? Clearly the result I got is wrong, since that limit doesn't exist for x>0,5. So is it true...

Thanks to both of you for your replies! @micromass I will try to get my head around your method after I had some sleep. I just tried to work it out using the ratio test and got a wrong result (I have fairly little experience with computing limits), but maybe I will find the error tomorrow :-)...