The discussion centers on the resultant time dilation experienced by an object in motion within a gravitational well, specifically using the Schwarzschild metric. The correct expression for time dilation is derived as \frac{d\tau}{dt}=\sqrt{1-\frac{r_s}{r}}\sqrt{1-\left(\frac{r\frac{d\phi}{dt}}{c\left(1-\frac{r_s}{r}\right)}\right)^2}, where r_s is the Schwarzschild radius. The conversation clarifies that the combined effects of gravitational and velocity-based time dilation are multiplicative rather than additive. This conclusion is supported by references to specific posts within the thread, particularly those by users kev and pervect.
Physicists, astrophysicists, and students of general relativity who are interested in the effects of gravity and motion on time perception, particularly in the context of black holes and high-velocity objects.
kev said:Let's start with this equation for the time dilation ratio:
\frac{{d}\tau}{{d}t}= \sqrt{1-r_s/r} \sqrt{1- \left (\frac{dr/dt}{c(1-r_s/r)} \right)^2 - \left (\frac{r d\theta/dt}{c \sqrt{1-r_s/r} } \right)^2 - \left(\frac{r\sin\theta d\phi/dt}{c\sqrt{1-r_s/r}} \right)^2 }
No, we are not talking about clocks on Earth's surface. You were talking about that in response to Dmitry67's post, not the OP by espen180 (you claim Dmitry67's post was originally on this thread and that it was later split, but I'm not even sure you're correct about that--given that you seemed to think Dmitry67's post was always the first one, it's quite possible the two threads were always separate and that you simply got confused and posted on this thread thinking you were still looking at the other thread, I don't remember Dmitry67's post ever being on this thread). The whole debate between you vs. everyone else got started because you claimed there was something dreadfully wrong with kev's derivation, which was meant to deal with the question of time dilation experienced by clocks in arbitrary circular orbits. The set of all valid circular orbits in Schwarzschild spacetime would include orbits with many different orbital planes, just like Pluto and Earth have different orbital planes despite orbiting the same Sun--some of these orbits would be ones where d\theta is equal to 0 (orbits in the \theta = \pi/2 plane), but others would be ones in a different plane where d\theta is not equal to 0. Do you disagree?starthaus said:You are making the same mistakes as JesseM, we are talking about the delay experienced by clocks on the Erath surface due to Earth rotation. What do you think I have been trying to explain to you starting with post 6?
JesseM said:No, we are not talking about clocks on Earth's surface. You were talking about that in response to Dmitry67's post, not the OP by espen180 (you claim Dmitry67's post was originally on this thread and that it was later split, but I'm not even sure you're correct about that--given that you seemed to think Dmitry67's post was always the first one, it's quite possible the two threads were always separate and that you simply got confused and posted on this thread thinking you were still looking at the other thread, I don't remember Dmitry67's post ever being on this thread). The whole debate between you vs. everyone else got started because you claimed there was something dreadfully wrong with kev's derivation,
I haven't been following the more recent posts between you and kev on this thread so I don't know if there were any "false starts" in his last few equations, but the original derivation I linked to was fine, and I pointed out in post 117 you could get the exactly the same formula from the equation you were using in post 6. If you want to use some minor error in a recent post by him as an excuse to avoid addressing all the flaws and confusions in your own arguments (in particular your own confused criticisms of my posts, not kev's), be my guest.starthaus said:Yes, look at the post above , kev finally got the right formula after a lot of false starts. Feel free to peruse all his false starts throughout this thread. I am done.
How about you tell us why instead? Or is this thread destined to exceed 300 posts, too?starthaus said:This is wrong. Since you are putting in results by hand again, try deriving it from the basics and you'll find out why.
Al68 said:How about you tell us why instead? Or is this thread destined to exceed 300 posts, too?
If kev made any "basic math errors" in his recent posts to you they are apparently minor ones which don't affect the final equation he derived for circular orbits, as I showed you in post 117 using your own equation to derive it. And of course you have made plenty of minor math errors yourself, like not including the factor of c in post #6.starthaus said:These are basic math errors
You keep accusing me of trolling, but you are the one who keeps destroying threads, making them completely worthless for most readers, with your shenanigans.starthaus said:These are basic math errors, if you can't see them all by yourself, you should find a different hobby. This does not include your current one :trolling.
I help people that are sincere, I don't help trolls. You contributted noothing to this thread.Al68 said:You keep accusing me of trolling, but you are the one who keeps destroying threads, making them completely worthless for most readers, with your shenanigans.
Back to the point, I'll take that as a NO, you either can't or won't explain (in any rational way) your claims.
LOL. Yep, that's why you can't substantiate your claims: because if I can't "spot the errors" I have "no business in this thread".starthaus said:If you can't spot the errors, you have no business (other than trolling) in this thread.
Al68 said:LOL. Yep, that's why you can't substantiate your claims: because if I can't "spot the errors" I have "no business in this thread".
Is that also why you're so rude and condescending?
So, you are unable to see the wrong variables. ...Seriously, dude, it might feel good to say something constructive and useful in your posts.
LOL. I was responding to your last post which contained nothing useful or constructive.starthaus said:I did, I put up quite a few solutions but you can only see the stuff that makes you tick, err troll.Al68 said:LOL. Yep, that's why you can't substantiate your claims: because if I can't "spot the errors" I have "no business in this thread".
Is that also why you're so rude and condescending?
Seriously, dude, it might feel good to say something constructive and useful in your posts.
Al68 said:LOL. I was responding to your last post which contained nothing useful or constructive.
I read them. They weren't the ones I was referring to. Was that not obvious? Can you read English?starthaus said:Try reading the other posts, the ones that contain formulas. Can you read formulas?