Recent content by Dylan H

Perfect, thanks.

Yes; I like that description. It seems that, as evidenced by various equations, this sort of phenomenon doesn't happen. I'm still trying to understand why the energy of the photon is irrelevant to the gravitational force. I would have expected that just as objects of increasing mass will deflect...

Thanks. I've been reading about gravitational redshift and Shapiro delay, and have some clarifying questions. Are photons affected by gravity? (To me, that seems to be how gravitational lensing works.) If photons are affected by gravity, then photons have gravitational mass. Is this...

Imagine a massive object emitting photons of various frequencies. Because the object is massive, it will exert gravitational acceleration on those photons. Because the energy of a photon is proportional to its frequency, it seems that higher-frequency photons will experience a higher magnitude...

Perhaps. So earlier we thought that some of the analytic solutions for ##\beta## were physically excluded. If that's still the case now that I've fixed the solution, what physical constraint would exclude them (e.g. if I plug in ##\bar{x}=\frac{x}{2}##, I get two possible answers for ##\beta##...

Gotcha. $$(\bar{x}^2 + x^2 - S^2)\beta^2 - (2x\sqrt{x^2 - S^2})\beta + (x^2 - \bar{x}^2) = 0$$ The quadratic formula explicitly yields (if I've done my arithmetic correctly): $$\begin{eqnarray}\beta &=& \frac{ 2x\sqrt{x^2 - S^2} \pm \sqrt{ 4x^2(x^2 -S^2) - 4 (\bar{x}^2 + x^2 - S^2) (x^2 -...

Thanks. To clarify: my question is why the result seems asymmetric with respect to ##x## and ##\bar{x}##. Since the problem didn't specify which is the primed frame and which is the unprimed frame, I would expect a result that would have some (anti)symmetry with respect to an exchange of ##x##...

Naturally I noticed, but there are several dead ends when deciding which equations to substitute into which others. Here is one of my more successful attempts: Start by expressing the Lorentz equation ##\bar{x} = \gamma(x-vt)## in terms of ##\beta##, then re-arrange: $$\begin{eqnarray} \bar{x}...

No worries. I've been trying a number of different ways to derive a function ##\beta = \cal{F}(\Delta x, \Delta \bar{x}, \Delta s^2)##; using the Lorentz transform along with the spacetime metric was just the first thing I tried. I thought about starting from other equations like the length...

Regarding (1), it shouldn't matter whether the events are timelike-separated, should it, when you're making the temporal interval arbitrarily large rather than arbitrarily small? As for (2), I've been trying something similar and hitting a dead end. Starting from $$\begin{eqnarray} x^2 - (ct)^2...

Regarding (1), my question is: by choosing the appropriate intertial reference frame, is it possible to make a spacetime interval seem like it spans an arbitrarily large interval of time (it doesn't matter to me what happens to the spatial separation)? Regarding (2), that's surprising! What's...

Thanks for your help. To clarify: suppose you ignore the object for now; all you have is a spacetime interval being viewed from two different inertial reference frames. (Maybe there are two lights in particular places being switched on at particular times, for example.) The length of the...

That makes some sense. You're telling me that because the (easiest?) way to measure length in a given reference frame is to use two simultaneous events located at the endpoints of the object, different reference frames will in general require different pairs of events for measuring the length of...

I'm trying to understand the relationship between the spacetime metric \Delta s^2 = \Delta x^2 - c^2\Delta t^2 and the simple formulas for time dilation and length contraction in special relativity x = \frac{1}{\gamma} \bar{x} and t = \gamma \cdot \bar{t}. Suppose from an inertial reference...