Not Understanding Time Dilation - mk 2.

[Dale]

One other thing to note, the separation of time dilation into kinematic and gravitational components is only an approximation, even in a non-time varying gravitational field. It is an approximation that works reasonably well for the GPS satellites, but not in general. The exact formula is not separable. See equations 3 and 4 at:
http://en.wikipedia.org/wiki/Time_dilation#Time_dilation_due_to_gravitation_and_motion_together

Generally you need to evaluate the integral I gave above in your coordinate system of choice.

 

[cmb]

One other thing to note, the separation of time dilation into kinematic and gravitational components is only an approximation, even in a non-time varying gravitational field. It is an approximation that works reasonably well for the GPS satellites, but not in general. The exact formula is not separable. See equations 3 and 4 at:
http://en.wikipedia.org/wiki/Time_dilation#Time_dilation_due_to_gravitation_and_motion_together

I'm looking at equation 4, in which the approximation separates out the terms, and it says underneath "For applications near the Earth this approximation will introduce an error on the order of .76 nanoseconds per century." In my examples, I'm discussing 7,200ns per DAY. So the approximation is entirely satisfactory and represents an effect less than one millionth of the effect I am discussing.

But thanks for directing me to that, as I now know that arguing that my scenario fails, on the basis that it is unreasonable to separate the terms, is not a legitimate argument.

I feel like I am asking reasonable questions, and I'm being thrown curve-balls back to dissuade me from enquiring into the detail. Well, thanks to that equation I can now see that the 'combined-effect-disargument' of gravitational and kinematic effects in my example is a red-herring.

 

[PAllen]

I'm looking at equation 4, in which the approximation separates out the terms, and it says underneath "For applications near the Earth this approximation will introduce an error on the order of .76 nanoseconds per century." In my examples, I'm discussing 7,200ns per DAY. So the approximation is entirely satisfactory and represents an effect less than one millionth of the effect I am discussing.

But thanks for directing me to that, as I now know that arguing that my scenario fails, on the basis that it is unreasonable to separate the terms, is not a legitimate argument.

I feel like I am asking reasonable questions, and I'm being thrown curve-balls back to dissuade me from enquiring into the detail. Well, thanks to that equation I can now see that the 'combined-effect-disargument' of gravitational and kinematic effects in my example is a red-herring.

Maybe it would help to describe exactly what you are asking. Since every responder has (in my opinion) tried to be helpful, your feeling that your questions are not being answered suggests a complete disconnect between what you think you are asking and what others understand of your questions. Try a fresh, complete, precise as possible, statement of what you are asking.

From my point of view, it seems that what I would see as direct answers produce responses: not what I was asking, misleading, etc.

One thing I can tell you is that outside of the specific application of GPS, no papers or books on GR I've read ever bother to separate kinematic and gravitational effects. It is not worth it, as straighforward integrations of the line element give you your measured quantities for arbitrary situations.

 

[cmb]

Maybe it would help to describe exactly what you are asking. Since every responder has (in my opinion) tried to be helpful, your feeling that your questions are not being answered suggests a complete disconnect between what you think you are asking and what others understand of your questions. Try a fresh, complete, precise as possible, statement of what you are asking.

Yes, I was thinking on trying to frame it as a different example. Seems I have introduced what are considered too many variables.

Indeed, I do appreciate all the comments so far. I am happy to say again; thanks for your time responding. I recognise there is no thought to try to dismiss my question, but that it looks like it is not a very obvious paradox. After all, if it were obvious it'd have already been discussed many times!

I'll chew it over and see if I can put it into a different form away from gravity or orbits.

Bear with me..Thanks again!

 

[ghwellsjr]

Maybe it would help to describe exactly what you are asking.

I think he did that in post #42 and I responded to him in post #45 and #49 but he has not reacted to my posts.

I'm guessing that he thinks the orbiting clock is like the traveler in the Twin Paradox whose age difference is indeterminate until he comes back to Earth and then all of a sudden there's this vast age difference. So even if the orbiting clock were adjusted so that it looks like it's keeping time with the Earth clock, when it comes down from orbit, he thinks, it will all of a sudden have this huge time shift.

 

[Dale]

I'm looking at equation 4, in which the approximation separates out the terms, and it says underneath "For applications near the Earth this approximation will introduce an error on the order of .76 nanoseconds per century." In my examples, I'm discussing 7,200ns per DAY. So the approximation is entirely satisfactory and represents an effect less than one millionth of the effect I am discussing.

Yes, which is why the approximation is used in GPS.

But thanks for directing me to that, as I now know that arguing that my scenario fails, on the basis that it is unreasonable to separate the terms, is not a legitimate argument.

I feel like I am asking reasonable questions, and I'm being thrown curve-balls back to dissuade me from enquiring into the detail. Well, thanks to that equation I can now see that the 'combined-effect-disargument' of gravitational and kinematic effects in my example is a red-herring.

Apparently you didn't read the very next sentence where it says "Unfortunately equation (4) is inconsistent with special relativity". Regardless of the accuracy in one frame (ground frame), if the equation is inconsistent with special relativity then you can get big errors in another frame (astronaut frame).

This is not a red-herring, you only feel like you are asking reasonable questions because you are unfamiliar with the material and seem to be completely unwilling to listen to the good advice and responses that you have received from multiple well-informed people.

 

[Dale]

cmb, pay attention to this comment:

One thing I can tell you is that outside of the specific application of GPS, no papers or books on GR I've read ever bother to separate kinematic and gravitational effects. It is not worth it, as straighforward integrations of the line element give you your measured quantities for arbitrary situations.

 

[cmb]

This is not a red-herring, you only feel like you are asking reasonable questions because you are unfamiliar with the material

Yes, that is a possibility and I'll see if I can provide a 'refreshed scenario'. I thought I'd been clear before, but it seems not. Maybe in doing so I will see my error and realize the issue for myself, if not I'll post it.

...and seem to be completely unwilling to listen to the good advice and responses that you have received from multiple well-informed people.

That's a bit unfair. What makes you say that if I disagree my point has been answered it means I am not listening? It might mean I am wrong and that I simply don't understand my own question, but I assure you I am reading every word to see if it answers my questions.

Better you say "..and it seems that you are prepared to be completely wrong on something just to see if there is something new to find out, even though everyone else is saying something different". I'd agree with that!

It is a non-sequitur to argue someone is not listening to you because they don't agree with you.

 

[cmb]

Apparently you didn't read the very next sentence where it says "Unfortunately equation (4) is inconsistent with special relativity". Regardless of the accuracy in one frame (ground frame), if the equation is inconsistent with special relativity then you can get big errors in another frame (astronaut frame).

OK, message heard! I'll see if I can reframe it away from any gravity.

 

[ghwellsjr]

OK, message heard! I'll see if I can reframe it away from any gravity.

Before you do that, would you please respond to my comments regarding your previous scenario in post #42. My comments are in posts #45, #49 and #55.

 

[PAllen]

OK, message heard! I'll see if I can reframe it away from any gravity.

Before you do that, would you please respond to my comments regarding your previous scenario in post #42. My comments are in posts #45, #49 and #55.

Also see my post #48. I threw in humorous wording, but the content is serious.

 

[Dale]

OK, message heard! I'll see if I can reframe it away from any gravity.

Thanks, I think that you can learn a lot that will help your understanding. I think that there are 3 scenarios that are worth considering here:
1) Two perpetually inertial observers
2) Standard twin's paradox
3) One clock at rest and one in uniform circular motion

The last one may be particularly interesting for you since it is pretty easy to use a rotating coordinate system where the circular-motion clock is at rest, and doing so allows you to gently introduce some of the very useful GR-related math without the complications of gravity and curvature. But I would approach them in order and not jump to 3) until you are comfortable with 1) and 2).

 

[cmb]

Before you do that, would you please respond to my comments regarding your previous scenario in post #42. My comments are in posts #45, #49 and #55.

#45 - I've no problem with that, but it isn't quite what I meant.

#49 - Sorry, I did indeed miss that one in the melee: "If so, then you have overlooked the fact that the orbiting clock is not inertial, it is always accelerating toward the earth.." This is an interesting point, and is why I initially shyed away from using accelerating ships in free space. However, if I drill down into this point, can you explain why 'inertial' differs from 'accelerating'? There is no 'acceleration' component in the equation given on wiki, just a gravity and a velocity term.

#55 - Almost, that is about it, but a slightly different flavour. If there is to be a noticeable time dilation effect once some time-piece/person/whatever returns to 'earth', then by how much is it? It doesn't appear to be objective, because if we watch a clock 'elsewhere' in some other frame, adjusted so it appears to keep time, then the time dilation when that clock returns to Earth should be a function of the path it takes to get back to earth, not how longit has been there building up a 'desynch'.

PAllen #48 - It seemed similar to an earlier reply. "the funny clock would now be going fast compared to the ground clock, with a time difference accumulating only from when the satellite's motion changed from what the funny clock was adjusted for" .. but what about the notion that as the guy on the satellite has been watching it, it has been gaining time over the clock on the ground? I thought we'd agreed that'd happen earlier, which'd make it 'time-in-orbit' dependent?

 

[PAllen]

PAllen #48 - It seemed similar to an earlier reply. "the funny clock would now be going fast compared to the ground clock, with a time difference accumulating only from when the satellite's motion changed from what the funny clock was adjusted for" .. but what about the notion that as the guy on the satellite has been watching it, it has been gaining time over the clock on the ground? I thought we'd agreed that'd happen earlier, which'd make it 'time-in-orbit' dependent?

That was all meant to be clarified with the introduction of an unadjusted clock. The adjusted clock is gaining time over the colocated unadjusted clock. It will not be seen as gaining time over the ground clock, by the satellite observer.

 

[ghwellsjr]

#45 - I've no problem with that, but it isn't quite what I meant.

If it's not quite what you meant, then what did you mean? Where did I go wrong?

#49 - Sorry, I did indeed miss that one in the melee: "If so, then you have overlooked the fact that the orbiting clock is not inertial, it is always accelerating toward the earth.." This is an interesting point, and is why I initially shyed away from using accelerating ships in free space. However, if I drill down into this point, can you explain why 'inertial' differs from 'accelerating'? There is no 'acceleration' component in the equation given on wiki, just a gravity and a velocity term.

In the context of Special Relativity (assuming no gravity), "inertial" and "accelerating" are opposites. Inertial means you are experiencing no acceleration which means you could be traveling in a straight line at a constant velocity. Non-inertial means that you are either changing your speed or changing your direction or both.

#55 - Almost, that is about it, but a slightly different flavour. If there is to be a noticeable time dilation effect once some time-piece/person/whatever returns to 'earth', then by how much is it? It doesn't appear to be objective, because if we watch a clock 'elsewhere' in some other frame, adjusted so it appears to keep time, then the time dilation when that clock returns to Earth should be a function of the path it takes to get back to earth, not how longit has been there building up a 'desynch'.

Time dilation is absolutely objective although it may be complicated to calculate but if you can be precise in exactly what happens to a clock, its time dilation with respect to any given Frame of Reference can be exactly calculated.

If in your scenario in post #42, an orbiting clock has to be adjusted so that it keeps time with an Earth bound clock, then when you return it to earth, there will be no sudden jump in time related to how long it was orbiting. If we can assume that the trip is done instantly, then there will be no change in the time and both clocks will match up. But from that point on, since the orbiting clock had been adjusted, it will start accumulating an increasing time difference.

I was just speculating in post #45 that it might be possible to put a clock in orbit around a planet such that no adjustment was necessary and that the two clocks would always remain in synch.

But I want to ask you again: are you thinking of the orbiting clock like the traveling twin in the Twin Paradox?