[jeffreyH (OP)]

If we have an observer standing on the top of a skyscraper and another observer freefalling past how do they both experience time with respect to each other?

[PmbPhy]

If we have an observer standing on the top of a skyscraper and another observer freefalling past how do they both experience time with respect to each other?

The free-fall frame will have a local time which runs faster or slower hen the top of skyscraper frame due to gravitational effects. There will also be time dilation effects due to the speed of the falling frame.

[jeffreyH (OP)]

If we have an observer standing on the top of a skyscraper and another observer freefalling past how do they both experience time with respect to each other?

The free-fall frame will have a local time which runs faster or slower hen the top of skyscraper frame due to gravitational effects. There will also be time dilation effects due to the speed of the falling frame.

That doesn't answer the question properly. Is the falling frame's time faster or slower than that of the observer on the skyscraper?

[PmbPhy]

That doesn't answer the question properly.

I disagree. It sure does explain it properly.

Is the falling frame's time faster or slower than that of the observer on the skyscraper?

This is where you're confused and what led you to believe that time throughout the falling frame should all run faster and all slower than the skyscraper frame. That's not true. The relation ship is more complicated than that because what I said that came to believe is not true.

[jeffreyH (OP)]

That doesn't answer the question properly.

I disagree. It sure does explain it properly.

Is the falling frame's time faster or slower than that of the observer on the skyscraper?

This is where you're confused and what led you to believe that time throughout the falling frame should all run faster and all slower than the skyscraper frame. That's not true. The relation ship is more complicated than that because what I said that came to believe is not true.

I am very well aware that it is complicated but at the point where the two observers are at the same instantaneous elevation how is time behaving for each one with respect to the other? It is a simple enough question. If relativity can't answer it what use is it?

[PmbPhy]

...at the point where the two observers are at the same instantaneous elevation how is time behaving for each one with respect to the other? It is a simple enough question.

You didn't mention in previous posts that they had the same location at the moment when you compare clocks. That makes things much easier. At that moment the two rates are related by the same expression given in SR.

If relativity can't answer it what use is it?

I never suggested that relativity can't answer it. Of course it does.

[jeffreyH (OP)]

...at the point where the two observers are at the same instantaneous elevation how is time behaving for each one with respect to the other? It is a simple enough question.

You didn't mention in previous posts that they had the same location at the moment when you compare clocks. That makes things much easier. At that moment the two rates are related by the same expression given in SR.

If relativity can't answer it what use is it?

I never suggested that relativity can't answer it. Of course it does.

Are there any experimental observations to back that up?

[PmbPhy]

...at the point where the two observers are at the same instantaneous elevation how is time behaving for each one with respect to the other? It is a simple enough question.

You didn't mention in previous posts that they had the same location at the moment when you compare clocks. That makes things much easier. At that moment the two rates are related by the same expression given in SR.

If relativity can't answer it what use is it?

I never suggested that relativity can't answer it. Of course it does.

Are there any experimental observations to back that up?

If it wasn't true then the GPS system wouldn't work properly since it was designed using that fact.

I hope you know that when we explain something we're answering from a theoretical stand point which is based on the theory of general theory of relativity (GR) and GR has been widely confirmed to be true. It's not possible to have experimental observations to back that everything that GR predicts so it's unwise to assume that since we don't have experimental observations to back it up that it's not true and it's also not wise to assume that just because we have experimental observations to back up GR that it can be assumed that everything we predict using it is correct since a theory can be confirmed to be correct and still be wrong!

[jeffreyH (OP)]

Well a satellite is in orbit and moving through the gravitational field. In freefall an object is moving in the direction of the field. The time dilation for the satellite will not vary by a significant amount whereas the freefalling object is far different. It is an important question to answer correctly.

[JohnDuffield]

Jeffrey: the falling guy is moving fast, so he's subject to SR time dilation. In addition he's lower than the guy on top of the skyscraper, so he's subject to GR time dilation too. If you could contrive an experiment wherein the guy on top of the skyscraper hit his clock with a hammer at the same instant* that the other guy smashed into the ground, the two clock readings wouldn't be the same. The clock all smashed and broken on the ground would have the lower reading. Re what Pmb was saying, see Phil Fraundorf's chart plotting GPS time dilation:



Note that clocks on GPS satellites go slower because they're moving fast, and faster because they're higher up, and the latter effect dominates. 

* the same instant is problematical, but nevermind. 

[jeffreyH (OP)]

Jeffrey: the falling guy is moving fast, so he's subject to SR time dilation. In addition he's lower than the guy on top of the skyscraper, so he's subject to GR time dilation too.

There is the heart of the matter. I knew it would come up eventually. Time dilation squared or time dilation addition. It can't be squared surely.

[JohnDuffield]

No, it's just addition.

[jeffreyH (OP)]

No, it's just addition.

Well it has consequences for black hole cosmology.