How does reciprocal time dilation work?

[Matterwave]

Time doesn't depend on frames. Only time interval depends on the frames. (as in example above)

This statement suggest you still do not grasp the relativity of simultaneity. Consider for space like separated events $A,B$, I can always find 2 inertial reference frames, one in which $A$ has a coordinate time before $B$ and another one in which $B$ has a coordinate time before $A$.

 

[Dale]

[clock A = 80s] and [clock B = 100s]

In which frame? (And please use complete sentences)

[clock A = 100s] and [clock B = 80s].

In what frame? (And please use complete sentences)

clock a=80s -> clock a=100s - it's correct.

What is correct? Please use complete sentences.

But how is it possible that clock b = 100s -> clock=80s ?

So close to a complete sentence. What is the second clock here and what does the arrow mean?

The clock is running backwards.

Yay for a complete sentence. The sentence is false, but at least it is complete.

What makes you believe that any clock is running backwards? If you draw a spacetime diagram you will be able to see that neither clock ever runs backwards.

Even if you choose not to do the diagram, I am going to have to insist that you start writing in complete sentences.

 

[Sagittarius A-Star]

A simple explanation of the relativity of simultaneity is given in Morin's book "Special Relativity: For the Enthusiastic Beginner", chapter 1.3.1

Event 1 is “light hitting the left receiver”
Event 2 is “light hitting the right receiver”

In A's reference frame, E1 and E2 happen simultaneously.
In B's reference frame, E1 happened before E2 happens.

source:
https://davidmorin.physics.fas.harv...nuum12331/files/2025-10/relativity_chap_1.pdf
via:
https://davidmorin.physics.fas.harvard.edu/books/special-relativity

 

[robphy]

Case 1) Reference frame: A
E1: clock A shows 100s
E2: clock B shows 80s

Case 2) Reference frame: B
E3: clock B shows 100s
E4: clock A shows 80s

I think you need to write out...

• I'm going to use "reads" to avoid possible misinterpretations
  when using anything suggesting what it "visually looks like".

According to observer A, E1 (clock A reads 100) and E2 (clock B reads 80) are simultaneous.

According to observer B, E3 (clock B reads 100) and E4 (clock A reads 80) are simultaneous.

 

[A.T.]

Time doesn't depend on frames. Only time interval depends on the frames.

You have it exactly backwards:
- Time coordinates assigned to events depend on reference frames, because they assign them.
- Time intervals measured by clocks between events local to that clock are frame invariant.