Can Symmetry Guarantee Equivalence or Equality?

chandru_iyer

Let us consider two clocks, clock A and clock B. Let us say that A is running correctly, whereas clock B runs fast and slow. For one second clock B runs fast, that is it runs up two seconds; then for the next two seconds clock B runs slow and runs only one second. In a total of three seconds both the clocks run up three seconds.

A mapping of the times shown by the two clocks is given as below.

Sl No Clock A (seconds) Clock B (Seconds)
1 0 0

2 1.0 2.0

3 3.0 3.0

4 4.0 5.0

5 6.0 6.0

With the above data, clock A is convinced that clock B is running incorrectly.

Now, in the above table, the two clocks are synchronized at sl no 1, 3, 5. Let us assume we wish to synchronize the clocks at sl no 2. In order to do this we subtract 1 from all readings of clock A and 2 from all readings of clock B. The resultant table is as below.

Sl No Clock A (seconds) Clock B (Seconds)
1 -1 -2

2 0.0 0.0

3 2.0 1.0

4 3.0 3.0

5 5.0 4.0

6 6.0 6.0

Now we interchange the columns “Clock A” and “Clock B”

Sl No New Sl No Clock B (Seconds) Clock A (seconds)
1 0 -2 -1

2 1 0.0 0.0

3 2 1.0 2.0

4 3 3.0 3.0

5 4 4.0 5.0

6 5 6.0 6.0

Now, we see that the first mapping of clock A to clock B is identical to that of the second mapping seen from clock B to clock A.

Can we say both these clocks are equivalent?

-Chandru website -> www.easyrelativity.com

Eugene Shubert