Gravitational Time Dilation and Twin Paradox ?'s

[Apophenia]

Just to be clear: if you take two identically prepared radioactive samples, raise one in a gravitational field; let them decay a bit; then bring them together, the amount of decay products will different. However, someone next to each sample would find it normal; the lower observer would claim the upper sample is decaying fast; the upper observer would claim, no, the lower sample is decaying slow. Despite the clear difference at the end, I don't see any meaningful way to talk about one or both of them changing (except as measured by the other). At the end, they both agree on the difference; but you can't pick one that 'really change'; nor can you say both changed - changed in relation to what?

Makes sense. Again I don't know what you mean by an observer watching the process (next to the sample as it decays) but when you bring the samples together one will be decayed less and one more. The one that decayed more (farther away from the gravitational source) can undoubtedly be said to decay at a faster rate (if we establish that less material left means faster decay rate), no? (that is after the samples are brought together. I don't know what an observer watching one of the samples implies; like actually perception and neurology slow and I don't want to bring that into it)

 

[PAllen]

Makes sense. Again I don't know what you mean by an observer watching the process (next to the sample as it decays) but when you bring the samples together one will be decayed less and one more. The one that decayed more (farther away from the gravitational source) can undoubtedly be said to decay at a faster rate (if we establish that less material left means faster decay rate), no? (that is after the samples are brought together. I don't know what an observer watching one of the samples implies; like actually perception and neurology slow and I don't want to bring that into it)

One can be said to have decayed faster than the other; one can be said to have decayed slower than the other. The key thing is 'than the other'. You can't just say one decayed fast, without some specific reference. Other than that, maybe you've got it.

 

[Apophenia]

Intuition has little place in modern physics. Our intuition simply wasn't designed to handle the regimes that modern physics deals with. We must hold to two higher standards than intuition: logic and evidence.

You insist that the concepts are intuitively clear to you. I suspect that is not the case. When things are actually clear then they can be defined clearly. I suspect that you feel intuitive clarity simply because no one has ever challenged you on these topics. Having not had to define and explain them you simply have not noticed the problems.

The term "observer" in relativity is usually shorthand for "a coordinate system where a given person or measuring device is at rest".

Intuition in modern physics is a no. I understand where that comes from especially with quantum physics which Ill admit I am even more ignorant of. But take the example of posulated virtual particles "popping in and out of existence" as Krauss puts it. We intuitive know something can not come from nothing. I think the problem becomes intuitive when we observe what is really happening on a deeper level. Something from nothing is clearly not intuitive but virtual particles from interaction of something on a more fundamental level is. (something mechanistic would be my definition of intuitive). <- I am not going to say it has to be because I clearly dont/cant know.

Im not so sure about virtual particles and such. Some Krauss youtube videos are interesting but that's about the extent of what I know; I don't pretend to know much on it.

I challenge myself on the topic all the time and welcome constructive debate. I am actually glad moderators have not closed this one yet.
I seem to be getting somewhere.


Observer = coordinate system at rest (relative to what is being observed I am assuming)...
Thanks

 

[Apophenia]

One can be said to have decayed faster than the other; one can be said to have decayed slower than the other. The key thing is 'than the other'. You can't just say one decayed fast, without some specific reference. Other than that, maybe you've got it.

Well faster/ slower is how you define it I know. (i just go with the general thought that more material being decayed is 'faster').

But you are in fact saying there are differing amounts of radioactive material left in each clock?

I can make the somewhat superfluous example of:

take clock 1 in the middle of two clocks 2 and 3. 3 being closer to the source and 2 being farther. Define 1 as the arbitrary absolute sense of time (i.e., half the material decaying = 1 second). Now run all 3 clocks for that arbitrarily defined 1 second; until clock 1's material decays to half its original mass.

3 will have more radioactive material (time slows), 2 less (time speeds) in comparison to 1 which decayed to half of its original sample.

That is how I am seeing it. Is that flawed?

 

[PAllen]

Well faster/ slower is how you define it I know. (i just go with the general thought that more material being decayed is 'faster').

But you are in fact saying there are differing amounts of radioactive material left in each clock?

Yes, definitely. The radioactive block that was at higher altitude before they are brought together will have more decay products.

I can make the somewhat superfluous example of:

take clock 1 in the middle of two clocks 2 and 3. 3 being closer to the source and 2 being farther. Define 1 as the arbitrary absolute sense of time (i.e., half the material decaying = 1 second). Now run all 3 clocks for that arbitrarily defined 1 second; until clock 1's material decays to half its original mass.

3 will have more radioactive material (time slows), 2 less (time speeds) in comparison to 1 which decayed to half of its original sample.

That is how I am seeing it. Is that flawed?

That is fine except who gets to pick the absolute sense of time?

 

[Apophenia]

Yes, definitely. The radioactive block that was at higher altitude before they are brought together will have more decay products.

That is fine except who gets to pick the absolute sense of time?

It does not matter; the definition of a second is what's arbitrary.

Now you need to convince yourself (which you seem to have done) and DaleSpam that 1) and 2) (minus the ether stuff) are equivalent.

"detection" - The change of these mechanisms is precisely the detection of "mysterious, unknown" whatever we call gravity.

2) being essentially what I described to you and you saying "that is fine" with the addition of clear motive against it in the language (which I welcome to some extent as I have clear motive in mine to some).

I don't see a difference between the two (here in my words which are not the best):
1) Time slows down as predicted by relativity.
2) The mechanism which measures time slows down time as predicted by relativity.

Acknowledging that it takes a comparison of 2 clocks.

The Michelson Morely experiment.

Time dilation has been measured using gravity, the strong, weak, and electromagnetic forces. There are currently no other known forces to account for.

Apophenia: If the mechanism behind the clocks all slow accordingly, then there is NO experimental difference between saying time slows or saying the mechanism slows as you would suggest.

Exactly. There is no difference. You are free to adopt either of the following two propositions:

1) Time slows down as predicted by relativity.
2) Some mysterious unknown mechanism which cannot otherwise be measured or detected (e.g. the luminiferous aether) causes EM processes to slow down and coincidentally it just happens to slow down by the exact same amount predicted by relativity, AND a second mysterious unknown mechanism which cannot otherwise be measured or detected causes strong-force processes to slow down and doubly-coincidentally it just happens to slow down by the exact same amount as the EM processes and relativity, AND a third mysterious unknown mechanism which cannot otherwise be measured or detected causes weak-force processes to slow down and triply-coincidentally it just happens to slow down by the exact same amount as the previous two processes and relativity, AND a fourth mysterious unknown mechanism which cannot otherwise be measured or detected causes gravitational processes to slow down and quadruply-coincidentally it just happens to slow down by the exact same amount as the previous three processes and relativity.

I want to clear what seems like a discrepancy to further my own understanding of this all. 1) and 2) seem equivalent! Thanks to you both( and others...Nuggatory, and so on). Cheers

 

[PAllen]

At this point, arguing over 'all processes, whatever their nature, proceed according to relativistic predictions' versus 'time comparisons proceed per relativistic predictions' is silly. The two statements have the same content. It is like W.V.O. Quine's point that you can't distinguish 'undetached rabbit parts' from 'a rabbit'.

 

[Dale]

take the example of posulated virtual particles

Please stop randomly throwing in irrelevant topics. You posted about time dilation. Stick with that.

If you have questions about virtual particles please post them in the QM forum, and if you have questions about string theory please post them in the beyond standard model forum. When you post them here it seems that you are just trying to deflect the discussion.

 

[Dale]

I want to clear what seems like a discrepancy to further my own understanding of this all. 1) and 2) seem equivalent!

What is the discrepancy?

 

[Janus]

I don't see a difference between the two (here in my words which are not the best):
1) Time slows down as predicted by relativity.
2) The mechanism which measures time slows down time as predicted by relativity.

Maybe If we cleared up something about gravitational time dilation it will help.

It seems to me that so far you have been thinking of it as being the relative strength of the gravitational field at different heights that results in the clocks running at different rates. It isn't. It is the difference in gravitational potential.

So why does this make a difference? Let's consider the following scenario:

Imagine we have a uniform gravity field. By uniform, I mean one in the the strength of the field doe not change with height. An object at one height experiences exactly the same gravity force as an object at a different height.

Now let's say that we have two identical pendulum clocks. We put them side by side and they tick in perfect sync. Now we put one of these clocks at a different height from the other. The clock that is higher will tick faster.

The only thing that physically effects the operation of the mechanism is the force of gravity, but both clocks experience the same force of gravity. Yet, the clocks will tick at different rates from each other.

 

[Apophenia]

Please stop randomly throwing in irrelevant topics. You posted about time dilation. Stick with that.

If you have questions about virtual particles please post them in the QM forum, and if you have questions about string theory please post them in the beyond standard model forum. When you post them here it seems that you are just trying to deflect the discussion.

Deflecting is not my intent. I should just shut it sometimes. As for the discrepency: It seemed that some had the impression that you can say 1) and not mean 2) when now it seems 1) = 2) ... (until I read the next post). But other than that seeming to be an argument of semantics it is really saying that when you say 'time' you are inherently referring to all processes (anything that can be used to measure time) which I agree with you is seemingly too coincidental but how things 'seem' has no effect on what we observe. I think the next response clears this problem and put's me back into confusion though.

Maybe If we cleared up something about gravitational time dilation it will help.

It seems to me that so far you have been thinking of it as being the relative strength of the gravitational field at different heights that results in the clocks running at different rates. It isn't. It is the difference in gravitational potential.

So why does this make a difference? Let's consider the following scenario:

Imagine we have a uniform gravity field. By uniform, I mean one in the the strength of the field doe not change with height. An object at one height experiences exactly the same gravity force as an object at a different height.

Now let's say that we have two identical pendulum clocks. We put them side by side and they tick in perfect sync. Now we put one of these clocks at a different height from the other. The clock that is higher will tick faster.

The only thing that physically effects the operation of the mechanism is the force of gravity, but both clocks experience the same force of gravity. Yet, the clocks will tick at different rates from each other.

You are basically saying that there is NO physical effect on the mechanism which changes it's operation (other than gravity which is same for both so it does not matter within the context of what is being discussed). Get's back to my confusion of how the operation of a mechanism could change without something "physically effecting" (as you put it) it. You can simply say time changes (there is no physical effect) but I don't know what that means, anyone can't know what that means, but we may just have to take it and look at the whole thing mathematically. idk.

 

[Dale]

It seemed that some had the impression that you can say 1) and not mean 2) when now it seems 1) = 2) ... (until I read the next post).

1) and 2) are experimentally indistinguishable. Since they are experimentally indistinguishable there is no scientific way of choosing between the two. They are philosophically distinct, but many people regard experimentally indistinguishable positions as being the same in some sense.

Personally, I recognize them as being distinct, but feel that the distinction is unimportant.

 

[Apophenia]

1) and 2) are experimentally indistinguishable. Since they are experimentally indistinguishable there is no scientific way of choosing between the two. They are philosophically distinct, but many people regard experimentally indistinguishable positions as being the same in some sense.

Personally, I recognize them as being distinct, but feel that the distinction is unimportant.

...and certainly unimportant for GPS design. By the way, is there a straightforward method for calculating GTD? Also, a geosynchronous satellite would be considered a coincident frame with the Earth so are there exclusively GTD effects acting upon them?

I understand your sentiments.

 

[mfb]

By the way, is there a straightforward method for calculating GTD?

If you know the gravitational potential, yes.

Also, a geosynchronous satellite would be considered a coincident frame with the Earth

Something rotating together with Earth is not an inertial frame. No. You have to consider the velocity as well.

 

[Dale]

...and certainly unimportant for GPS design. By the way, is there a straightforward method for calculating GTD? Also, a geosynchronous satellite would be considered a coincident frame with the Earth so are there exclusively GTD effects acting upon them?

Where curvature is unimportant you can use this approach: http://hyperphysics.phy-astr.gsu.edu/%E2%80%8Chbase/relativ/gratim.html

If curvature is important and you are dealing with time outside a non-rotating spherically symmetric mass then you need to use:
http://en.wikipedia.org/wiki/Gravitational_time_dilation#Outside_a_non-rotating_sphere

In more complicated situations it is not generally possible to split the time dilation into a "gravitational" and "motion" part. In such cases, the overall time dilation can usually still be defined. There are two typical processes for doing that. One is to simply calculate the frequency shift of signals sent, and the other is to calculate the ratio of proper time to coordinate time. The first doesn't work when signals cannot be exchanged and the second doesn't work if your coordinate system doesn't have a timelike coordinate.

 

[A.T.]

Also, a geosynchronous satellite would be considered a coincident frame with the Earth so are there exclusively GTD effects acting upon them?

Something rotating together with Earth is not an inertial frame. No. You have to consider the velocity as well.

How would you combine the two TD effects. Is it just multiplication? The clean way to deal with the rotating common rest frame of Earth and geosynchronous satellite is to use the Schwarzshild metric for the rotating frame:
http://en.wikipedia.org/wiki/Geodetic_effect#Formulae
However, when I simply multiply the TD-factor from the non-rotating metric with the movement TD in the inertial frame, I get something else than the TD-factor from the rotating metric.

Also, what does dt in the rotating frame metric represent physically? In the non-rotating frame dt is the time of a clock at rest at infinity. But in the rotating frame we can't have an clock at rest at infinity. Is this still the time of an inertial clock.