Dale's latest activity
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Dale replied to the thread A Is the constancy of c a postulate or a derivable theorem?.An alternative approach is to just write the most general affine transformation between inertial frames and determine the coefficients... -
Dale reacted to cianfa72's post in the thread I How do non-diagonal indices of a metric allow for local flatness? with
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In Anderson coordinates the expression of the flat spacetime metric ##ds^2## includes mixed term in ##\kappa dtdx##. For ##\kappa=0##... -
Dale replied to the thread I Transformation for Lemaitre coordinates.Yes, so I think I need to go back and be more careful with both equations 4 and 6. I will try to do that sometime later this week
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Dale reacted to PeterDonis's post in the thread I Transformation for Lemaitre coordinates with Like.
This will be true in general for any transformation between the Schwarzschild chart and a chart that doesn't have a coordinate...
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Dale replied to the thread I How do non-diagonal indices of a metric allow for local flatness?.Yes. Also, any four-velocity is a 4D tangent vector to a worldline. So that vector is the same vector in different frames, although its...
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Dale reacted to Ibix's post in the thread I How do non-diagonal indices of a metric allow for local flatness? with Like.
Which, incidentally, means that "locally flat" is a bit of a misnomer. The analogue in spherical geometry is that you can lay your...
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Dale replied to the thread I Transformation for Lemaitre coordinates.Playing around with this a little more, it looks like this only works for ##r<R## inside the horizon. For outside the horizon with...
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Dale replied to the thread I How do non-diagonal indices of a metric allow for local flatness?.As @PeterDonis mentioned also the coordinate two way speed of light can vary in non-inertial charts. Although that does also depend on...
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Dale reacted to PeterDonis's post in the thread I How do non-diagonal indices of a metric allow for local flatness? with Like.
No, he doesn't. For example, if you transform to Rindler coordinates, the round trip speed of light is not always ##c## in those...
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Dale reacted to Ibix's post in the thread B What reference frame is used for the velocity v in the Lorentz transformation? with Like.
For that, you'd have to do the experiment.
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Dale reacted to sophiecentaur's post in the thread I Energy of Electromagnetic Waves in Destructive Interference with Like.
Yes. Whatever diffraction pattern you manage to produce with your source (and you can design a source to produce any pattern you want -...
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Dale replied to the thread I Transformation for Lemaitre coordinates.Excellent, thanks @renormalize. It was just not occurring to me to eliminate one of the variables algebraically before integrating.
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Dale reacted to renormalize's post in the thread I Transformation for Lemaitre coordinates with
Informative.
Yes you can! Inspired by https://en.wikipedia.org/wiki/Lema%C3%AEtre_coordinates, note that your two... -
Dale replied to the thread I Transformation for Lemaitre coordinates.Ok, so the Jacobian would be $$ \left( \begin{array}{cc} \frac{\partial \tau}{\partial t} & \frac{\partial \tau}{\partial r} \\...
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I think the general approach is to use the differential transforms to write the Jacobian (or is it Jacobean?) and use that to write the...