Is Simultaneity Absolute in Einstein's Theory of Relativity?

[MeJennifer]

As I see you consider that "coordinate time" is "what a clock reads". Then "coordinate time interval" is the difference between the readings of two such clocks?

Clocks read proper time not coordinate time.

Of course coordinate time and proper time could overlap for a particular group of observers, but they cannot be the same for two or more observers who are moving with respect to each other.

 

[bernhard.rothenstein]

clock and time

Clocks read proper time not coordinate time.

Of course coordinate time and proper time could overlap for a particular group of observers, but they cannot be the same for two or more observers who are moving with respect to each other.

Thanks. With all respect, I do not understand your point of view. IMHO when I speak about the time displayed by a clock I am not able to distinguish if it is proper or coordinate time. Please have a look at my post 47 and tell me where my point of view is wrong. A correct understanding of the problem is of big importance for me, not being very familiar with the Anglo-American nomenclature and probably for others as well. Also please comment the definitions given by Thomas Moore A Traveler's Guide to Spacetime according to whom:
"Coordinate time :The time measured between two events either by a pair of synchronized clocks at rest in a given inertial reference frame (one clock present at each event) or by a single clock at rest in that inertial reference frame (if both events happen to occur at that clock in that frame) is called the coordinate time between the events in that frame.

 

[MeJennifer]

Thanks. With all respect, I do not understand your point of view. IMHO when I speak about the time displayed by a clock I am not able to distinguish if it is proper or coordinate time. Please have a look at my post 47 and tell me where my point of view is wrong. A correct understanding of the problem is of big importance for me, not being very familiar with the Anglo-American nomenclature and probably for others as well. Also please comment the definitions given by Thomas Moore A Traveler's Guide to Spacetime according to whom:
"Coordinate time :The time measured between two events either by a pair of synchronized clocks at rest in a given inertial reference frame (one clock present at each event) or by a single clock at rest in that inertial reference frame (if both events happen to occur at that clock in that frame) is called the coordinate time between the events in that frame.

Some comments that hopefully clear things up.

I have learned from Einstein that time t is what a clock reads. That time is used in order to define the time coordinate of an event that takes place in front of the clock when it reads t. In order to become opperational the clocks of a given inertial reference frame should be synchronized in order to display the same running time.

This is certainly one way of setting up a coordinate system, but not the only way.
In the setup you mention it is true that for the clock, which we assume is inertial, proper time overlaps coordinate time.

Now consider another clock in relative motion with this clock, could we say that this clock measures coordinate time? I think the answer is no, the coordinate time and the proper time no longer overlap and we need a Lorentz transformation to calculate the difference.

The reason that the proper time direction no longer overlaps the coordinate time is that the second clock is semi-rotated in the first clock's space-time coordinate system and, as a consequence, the direction of the proper time line is now rotated away from the coordinate time direction. And due to the metric of space-time, such a rotation will shorten any line segment and thus the proper time interval will be smaller compared to the coordinate time interval.

It seems that Moore defines as coordinate time, the condition in which proper time and coordinate time overlap.

Note that the physical meaning of coordinate time becomes more problematic when we consider curved space-time as well. In curved space-time coordinate time is no longer guaranteed to be ortho-normal to the spatial coordinates.

 

[bernhard.rothenstein]

Some comments that hopefully clear things up.


This is certainly one way of setting up a coordinate system, but not the only way.
In the setup you mention it is true that for the clock, which we assume is inertial, proper time overlaps coordinate time.

Now consider another clock in relative motion with this clock, could we say that this clock measures coordinate time? I think the answer is no, the coordinate time and the proper time no longer overlap and we need a Lorentz transformation to calculate the difference.

The reason that the proper time direction no longer overlaps the coordinate time is that the second clock is semi-rotated in the first clock's space-time coordinate system and, as a consequence, the direction of the proper time line is now rotated away from the coordinate time direction. And due to the metric of space-time, such a rotation will shorten any line segment and thus the proper time interval will be smaller compared to the coordinate time interval.

It seems that Moore defines as coordinate time, the condition in which proper time and coordinate time overlap.

The physical meaning of coordinate time becoms more problematic when we consider curved space-time as well. In curved space-time coordinate time is no longer guaranteed to be ortho-normal to the spatial coordinates.

Thank you for your help and for the kind way to answer.

"Now consider another clock in relative motion with this clock, could we say that this clock measures coordinate time? I think the answer is no, the coordinate time and the proper time no longer overlap and we need a Lorentz transformation to calculate the difference."

My problem is related to the clocks of the same reference frame in a state of rest relative to each other and synchronized. I am confused by the fact that Authors make not a net distinction between time and time interval So far SR is not involved. It becomes when I consider a clock C' which moves with constant V relative to the clocks mentioned above, reading zero when it is located in front of a stationary clock which reads zero as well. After a given time of motion it reads t' being located in front of a stationary clock. Then by definition
t-0 represents a coordinate time interval
t'-0 represents a proper time interval
related by (t-0)=gamma(t'-0)
The Lorentz transformation becomes involved in the case when in both inertial reference frames the observers measure coordinate time intervals.
Do you consider that such a way of teaching a beginner is correct?

 

[MeJennifer]

My problem is related to the clocks of the same reference frame in a state of rest relative to each other and synchronized.

Then in this coordinate time overlaps proper time.

But note that, in general, this is not the case and certainly will give problems when you consider cases with curved space-time.

I am confused by the fact that Authors make not a net distinction between time and time interval

I agree with you that, when appropriate, adding the term interval is better.

So far SR is not involved. It becomes when I consider a clock C' which moves with constant V relative to the clocks mentioned above, reading zero when it is located in front of a stationary clock which reads zero as well. After a given time of motion it reads t' being located in front of a stationary clock. Then by definition
t-0 represents a coordinate time interval
t'-0 represents a proper time interval
related by (t-0)=gamma(t'-0)
The Lorentz transformation becomes involved in the case when in both inertial reference frames the observers measure coordinate time intervals.

Do you consider that such a way of teaching a beginner is correct?

It is certainly not incorrect.

If it is the best way of teaching, well, I certainly have an opinion on it, but I feel that it is not proper to "vent" my opinon here in this topic.

Note that in this case the coordinate system is only valid for a particular group of observers, namely those who are at relative rest to it.

 

[country boy]

Reply to post 47:

I have learned from Einstein that time t is what a clock reads. ...

In conclusion I think that besides the fact that we should or we should not synchronize clocks, it is important to have an unique conception about what they measure.
Please let me know your oppinion.

My idea of coordinate time is, I believe, more specific than what you describe. If two events happen at different locations and the coordinate times are recorded at both points, the difference of the two coordinate times is delta t. If the two events happen at the same location then only one clock is needed and delta t = delta tau.

The "time" of an event is equivalent to the "time interval" between two events, one of which is at the clock's zero reading.

"Proper time" is a special case of the invariant "space-time interval." Proper time refers to invariant intervals that are on or inside the light cone.

A lot of this discussion seems to be about definitions, but that is okay because it leads to clearer understanding (speaking for myself, anyway).

 

[bernhard.rothenstein]

clock and time

Reply to post 47:

My idea of coordinate time is, I believe, more specific than what you describe. If two events happen at different locations and the coordinate times are recorded at both points, the difference of the two coordinate times is delta t. If the two events happen at the same location then only one clock is needed and delta t = delta tau.
That is what I mentioned in one of my intervention. I consider that we should make a net distinction between coordinate time which IMHO represents the reading of a clock when an event takes place at its location abd I use it to define the time coordinate of the event. I would aggree with you if instead of using coordinate time would use coordinate time interval.

The "time" of an event is equivalent to the "time interval" between two events, one of which is at the clock's zero reading.
It is a little confusing for me. If the clock are synchronized that condition is automatically fulfilled.

"Proper time" is a special case of the invariant "space-time interval." Proper time refers to invariant intervals that are on or inside the light cone.
I would add: If in one of the reference frames dx=0

A lot of this discussion seems to be about definitions, but that is okay because it leads to clearer understanding (speaking for myself, anyway).
for me too

With thanks for the participation