I recently asked this question...

When are events frame independent and why?

...on when it is that the simultaneity of events is frame independent. As I understand now, observers in every frame of reference will agree on the simultaneity of two events when those events happened at the same location.

However, besides this being an intuitive observation about our universe, I don't really see why it follows from Einstein's 2 postulates of special relativity:

1. The laws of physics are the same and can be stated in their simplest form in all inertial frames of reference.

2. The speed of light is constant in all frames of reference.

The loss of simultaneity at two different locations for two different reference frames (moving with respect to one another) can be shown with the above two postulates...but, I'm not quite sure how to show the "intuitive" observation above about events at the same location.

I'm definitely wrong...but it seems to me that there should be a third postulate...

3. Observers in every frame of reference will agree on the simultaneity of events that happen at the same location.

If not, what about the first two postulates is to stop observers in from seeing simultaneous events at a specific location in one reference frame, from not being simultaneous when viewed from a different reference frame?

Thanks!

I recently asked this question...

When are events frame independent and why?

...on when it is that the simultaneity of events is frame independent. As I understand now, observers in every frame of reference will agree on the simultaneity of two events when those events happened at the same location.

However, besides this being an intuitive observation about our universe, I don't really see why it follows from Einstein's 2 postulates of special relativity:

1. The laws of physics are the same and can be stated in their simplest form in all inertial frames of reference.

2. The speed of light is constant in all frames of reference.

The loss of simultaneity at two different locations for two different reference frames (moving with respect to one another) can be shown with the above two postulates...but, I'm not quite sure how to show the "intuitive" observation above about events at the same location.

I'm definitely wrong...but it seems to me that there should be a third postulate...

3. Observers in every frame of reference will agree on the simultaneity of events that happen at the same location.

If not, what about the first two postulates is to stop observers in from seeing simultaneous events at a specific location in one reference frame, from not being simultaneous when viewed from a different reference frame?