




Simultaneity
in Visible Space-Time is often deceptive. After all, Absolute
Space-Time is the one to make the final decision whether the events are
simultaneous or not.
Reaching the correct information
is only possible with the transition
to Absolute Space-Time by using the information in Visible Space-Time.
We saw them in an orderly fashion that this transition requires a
period of analyses and calculations, (c+v) (c-v) mathematics can also
be involved in when there are frames that are in motion relative to
each other and also how to do the necessary calculations.
Simultaneity Rules: |
There are also Coexistence
Rules, which are like siblings to
Simultaneity Rules. We can call Coexistence Rules “Equidistance Rules”,
as well.
![]() Coexistence (Equidistance) Rules |
All these rules explain and
summarize the relationship between Absolute
Space-Time and Visible Space-Time. As we saw the mathematical equations
of these rules in parts before, I am not going to repeat them
here.
The
figure above represents the first rule of Simultaneity. TV station (the
place of incident) broadcasts an interview. There are reference systems
that are moving at different speeds and directions relative to the TV
station. If their distances to the TV station are the same for that
moment, the image that each reference system sees is different from the
others.
The figure below represents the
second rule. Let’s think that reference
systems are seeing the same image on their TVs. In this case, the
distances of each reference system to the TV station are
different.
As
I stated before, don’t just think that these situations that we saw in
the examples above take place on communication signals because
electromagnetic waves that carry images of objects are, just like
communication signals, subject to the rules of (c+v) (c-v) mathematics.
Imagine
we are watching a tennis match. Let’s take the point we see the ball as
the center and draw a circle of “r” radius in a way that it passes over
us and other spectators. Each spectator on the circle sees a different
“t” moment of the movement of the ball. In other words, when we saw the
ball at a specific point, the ball didn’t reach that point for some
spectators; and others had seen the ball reaching that point before we
did. It is not important how many nanoseconds or nanometers this
difference is for the rule. As the distance and speed between reference
systems increase, this difference becomes more evident. The important
thing is that we are aware of these rules.
By creating a problem, we can
easily see some results of these rules in
real life. Let’s think that two space probes are moving at 150.000 km/h
relative to the earth. Let’s say that one is approaching the earth and
the other is moving away from the earth. Assume that observers are
watching a TV broadcast from the earth in both probes. We are
discussing the situation when the probes are at the same distance to
the earth. In order to have a 5 seconds difference between the
broadcasts that observers watch, at what distance should the probes be
from the earth?
Answer: The difference between
the arrival times of the TV signals to
the probes should be 5 seconds. Based on this, we can find the
distances of the probes from the earth.
= 5.349.733.102 kilometters =
35,7841 AU
c: speed of light: 299.792,458 km/sec, v: speed of probes = 150.000
km/h = 42 km/sec
We
found a huge distance as a result of the calculation. 35.78 AU is
indeed a long distance; it is almost as much as the distance between
Pluto and the Sun.
(AU: An astronomical unit. It is based on the
distance between the center of the sun and the center of the earth and
it corresponds to 149.5 million kilometers.)
Let’s keep working on the same example with a second question. How far
away do the observers see the earth from themselves at that moment?
Answer: Now that we calculated the distances of the probes to the
earth, we can calculate the distances at which the observers in the
probes see the earth.
For the probe that is approaching the earth.
= 5.350.482.688 kilometers =
35,7892 AU
For the probe that is moving away from the earth:
= 5.348.983.726 kilometers =
35,7792 AU
Let’s ask a more interesting question now. What is the duration of
rotation of the earth around its own axis for the observers in the
probes?
Answer: The earth completes its rotation around its own axis in 24
hours. We can calculate this as we know the speeds of the probes.
The duration of rotation of the earth around its own axis relative to
the probe that is moving away:
23,99663767 hours = 23 hours 59 minutes 47 seconds
The duration of rotation of the earth around its own axis relative to
the probe that is approaching:
24,00336233 hours = 24 hours 0 minutes 10 seconds
The speed value 150.000 km/h that we chose in the questions above is
hard to reach even today’s world. Nevertheless, we see that there are
no serious differences in terms of Relativity Effects. For these
effects to be more obvious, we need to have a lot higher speeds. The
table below has been prepared based on 0.1c – 0.9c values for the
speeds of the probes, but for the situation where 1 second instead of 5
seconds of the broadcast shift. The questions are the same and the
answers are in the table. In the table, you can see how the values go
crazy as the speed goes up.
These were the questions:
Both probes are at the same distance from the earth.
1- In order to have 1-second difference between the broadcasts that
observers watch, at what distance should the probes be from the
earth?
2- How far away do the observers see the earth from themselves at that
moment?
3- What is the duration of rotation of the earth around its own axis
for the observers in the probes?
The answers are in the table:
The calculations are based on
1 second of the broadcast shift |
|||||||||
Probe Speeds |
|||||||||
In terms of c |
0,1c |
0,2c |
0,3c |
0,4c |
0,5c |
0,6c |
0,7c |
0,8c |
0,9c |
In km/s |
29.979 |
59.958 |
89.938 |
119.917 |
149.896 |
179.875 |
209.855 |
239.834 |
269.813 |
The distance of the probes from Earth at the moment when a
1-second signal delay occurs |
|||||||||
Kilometers |
1.483.973 |
719.502 |
454.685 |
314.782 |
224.844 |
159.889 |
109.210 |
67.453 |
31.645 |
AU |
0,00993 |
0,00481 |
0,00304 |
0,00211 |
0,00150 |
0,00107 |
0,00073 |
0,00045 |
0,00021 |
The distance of Earth relative to the observer in the probe
that is approaching Earth |
|||||||||
Kilometers |
1.648.859 |
899.377 |
649.550 |
524.637 |
449.689 |
399.723 |
364.034 |
337.267 |
316.448 |
AU |
0,0110 |
0,0060 |
0,0043 |
0,0035 |
0,0030 |
0,0027 |
0,0024 |
0,0023 |
0,0021 |
The distance of Earth relative to the
observer in the probe that is moving away from Earth |
|||||||||
Kilometers |
1.349.066 |
599.585 |
349.758 |
224.844 |
149.896 |
99.931 |
64.241 |
37.474 |
16.655 |
AU |
0,0090 |
0,0040 |
0,0023 |
0,0015 |
0,0010 |
0,0007 |
0,0004 |
0,0003 |
0,0001 |
The duration of Earth's rotation around its own axis
relative to the probe that is approaching |
|||||||||
Hour |
21,6 |
19,2 |
16,8 |
14,4 |
12 |
9,6 |
7,2 |
4,8 |
2,4 |
Hours:Minutes |
21:36 |
19:12 |
16:48 |
14:24 |
12:00 |
9:36 |
7:12 |
4:48 |
2:24 |
The duration of Earth's rotation around its own axis
relative to the probe that is moving away |
|||||||||
Hours |
26,4 |
28,8 |
31,2 |
33,6 |
36 |
38,4 |
40,8 |
43,2 |
45,6 |
Hours:Minutes |
26:24 |
28:48 |
31:12 |
33:36 |
36:00 |
38:24 |
40:48 |
43:12 |
45:36 |