Comparing the time of two moving clocks

[Mike_bb]

Hello, PF!

I just understand that people couldn't fully understand me in my old topic because many terms in English have another senses in Russian and vice versa. Because of the language barrier I couldn't explain what I meant. Moreover, my vocab is poor and I speak English badly. Please, sorry me!

Now I'll try to explain what I want to find out but I don't know if people will understand me correctly.

I have an example on the Russian. It sounds like this:

1) If observer A will look at the clock B then he will see that clock B is running slowly. E1: clock A = 100sec, E2: clock B = 80sec
2) If observer B will look at the clock A then he will see that clock A is running slowly. E3: clock B = 100 sec, E4; clock A = 80 sec

My question is: How is it possible that the clock B can read two different values (slowed time (80sec) and proper time (100sec))?

I've thought about it and I conclude that clock B (or clock A) never read slowed time.

My explanation:

If observer A will look at the clock B then he will see that clock B is running slowly. Therefore clock B read slowed time for observers A, B, since events E1 and E2 are simultaneously. But if it so then we have 80sec on the clock B. If we'll look at the clock B at the frame B we'll see 80sec. Well, it leads us to the fact that clock B is running slowly at the frame B. It can never be because this is violates Postulate 1 and break symmetry. Then we'll see 100sec on the clock B at the frame B in accordance with Postulate 1.

If two clocks are moving we can try to compare their time but as I mentioned above we'll see that clock A read 100sec and clock B read 100sec. (I see such explanation in Russian).

 

[Matterwave]

I guess so we don't just rehash the exact same explanations as the previous thread, I'll ask some different questions.

Do you use AI to translate between English and Russian and vice versa? Have you tried asking an AI to give you some of the explanations from the previous thread in Russian?

Are you able to get some good textbooks on Special Relativity in Russian? There are many excellent Russian scientists. Landau and Lifshitz were some of my favorite authors but they might be a bit too advanced. Unfortunately I don't know more basic Russian textbooks.

 

[Mike_bb]

I guess so we don't just rehash the exact same explanations as the previous thread, I'll ask some different questions.

Do you use AI to translate between English and Russian and vice versa?

No.

Have you tried asking an AI to give you some of the explanations from the previous thread in Russian?

I use Google AI that provides example with link to the sources.

Are you able to get some good textbooks on Special Relativity in Russian?

I tried to read Landau&Lifshitz.

 

[Matterwave]

There are some excellent answers to your question in the previous thread. If the English --> Russian barrier is blocking you from understanding, I think a good translation AI can help. Use the higher tier ones so they don't hallucinate.

I tried to read Landau&Lifshitz.

This is perhaps too advanced. Landau and Lifshitz are excellent authors but they basically assume you already took some courses in those topics so they skip over a lot of steps. It would be worth while to find a more gentle introduction to the topic. Preferably one with good space time diagrams.

 

[Mike_bb]

There are some excellent answers to your question in the previous thread.

Robphy gave good diagram and as I understand it corresponds to my explanation above ( He wrote that E1 and E4 are distinct).

 

[Ibix]

Robphy gave good diagram and as I understand it corresponds to my explanation above ( He wrote that E1 and E4 are distinct).

They are. All four of your nunbered events are distinct. Your problem is that you keep thinking of "at the same time" as if it were an absolute truth. But it isn't.

Train yourself to say "at the same time according to A's rest frame" (or B's, or the primed frame or whatever) and never exclude the italicised bit. When you've learned to do that you'll be able to see immediately what the solution to your problem is, which is:

• E1 and E2 are simultaneous according to A's rest frame
• E3 and E4 are simultaneous according to B's rest frame

When you stop thinking of "simultaneous" as a concept the frames must share, the apparent contradiction goes away. Relativity still has a sense of causality, but it has more flexibility than pre-relativistic physics.

 

[Mike_bb]

They are. All four of your nunbered events are distinct. Your problem is that you keep thinking of "at the same time" as if it were an absolute truth. But it isn't.

Train yourself to say "at the same time according to A's rest frame" (or B's, or the primed frame or whatever) and never exclude the italicised bit. When you've learned to do that you'll be able to see immediately what the solution to your problem is, which is:

• E1 and E2 are simultaneous according to A's rest frame
• E3 and E4 are simultaneous according to B's rest frame

When you stop thinking of "simultaneous" as a concept the frames must share, the apparent contradiction goes away. Relativity still has a sense of causality, but it has more flexibility than pre-relativistic physics.

If you compare two clocks on the fly, you'll see that both clocks show 100sec.

 

[Mike_bb]

Matterwave,

Let we have frame C with stationary clock C that shows some time. Compare clocks A , B on the fly at the time of clock C. We see that both clocks A , B show the same time in accordance with Postulate 1.

 

[Dale]

I just understand that people couldn't fully understand me in my old topic because many terms in English have another senses in Russian and vice versa. Because of the language barrier I couldn't explain what I meant. Moreover, my vocab is poor and I speak English badly. Please, sorry me!

This is not the issue. We are used to dealing with language barriers. The main problem is making incomplete statements. Every time you speak about simultaneity you must include the reference frame. This is required in both Russian and English. It is not a language barrier, it is incomplete thinking in every language.

You must use complete statements.

 

[Dale]

1) If observer A will look at the clock B then he will see that clock B is running slowly. E1: clock A = 100sec, E2: clock B = 80sec

A more clear way to say this is:

In observer A’s frame clock B is running slowly. E1 (clock A = 100 s) is simultaneous with E2 (clock B = 80 s) in A’s frame.

2) If observer B will look at the clock A then he will see that clock A is running slowly. E3: clock B = 100 sec, E4; clock A = 80 sec

A more clear way to say this is:

In observer B’s frame clock A is running slowly. E3 (clock B = 100 s) is simultaneous with E4 (clock A = 80 s) in B’s frame.

How is it possible that the clock B can read two different values (slowed time (80sec) and proper time (100sec))?

Every clock reads different values at different events. That is what a functioning clock does. Why do you think it is a problem for a clock to read 80 s at one event and then to read 100 s at a later event?

Well, it leads us to the fact that clock B is running slowly at the frame B.

This is false. Nothing that you stated leads to this conclusion. Please do not just make up your own things here.

If two clocks are moving we can try to compare their time but as I mentioned above we'll see that clock A read 100sec and clock B read 100sec. (I see such explanation in Russian).

Russian clocks work the same as English clocks. Time dilation is an experimentally established fact of nature. You cannot just wish it away in any language.

If you compare two clocks on the fly, you'll see that both clocks show 100sec.

This is an incomplete statement. In which frame will both clocks read 100 s? There is a frame where this is true, but it is neither A’s frame nor B’s frame.

No more incomplete statements, please. Any time you compare clocks you must state the reference frame.

 

[Ibix]

If you compare two clocks on the fly, you'll see that both clocks show 100sec.

As stated, this is not true.

A correct statement would be "according to a frame in which both clocks are moving at the same speed (possibly in different directions), if both clocks were started simultaneously according to this frame they will always read the same time, which will be lower than the time elapsed according to clocks at rest in this frame". Other frames will not describe the circumstances this way.

 

[Mike_bb]

As stated, this is not true.

A correct statement would be "according to a frame in which both clocks are moving at the same speed (possibly in different directions), if both clocks were started simultaneously according to this frame they will always read the same time, which will be lower than the time elapsed according to clocks at rest in this frame". Other frames will not describe the circumstances this way.

Ok. Each of observers think that time in another frame is running slowly. And each of observers is right.
This is proved by experiment:
"Two observers fly to each other on the rockets and send light signal to each other every 2sec. Light signal every rocket receive with delay and this explain why clock of observer B run slowly than clock of observer A and vice versa."

Slowed time isn't showed on the clock because otherwise it violates Postulate 1.

 

[Mike_bb]

Dale,

Sorry, but I can't provide complete sentence because I have no complete sentences in Russian examples.

 

[Dale]

Dale,

Sorry, but I can't provide complete sentence because I have no complete sentences in Russian examples.

Yes you can. Simply state the reference frame in each sentence that you compare times on two different clocks. This is not a language issue. You have done it occasionally. You just need to do it consistently.

 

[Mike_bb]

Thanks to all! I catch an insight and now I understand how reciprocal time dilation works!

 

[robphy]

Strong suggestions:

• The position-vs-time graph of a situation (also known as a spacetime diagram)
  [like the ones I have been drawing] tells a story of the situation
  that is often more clear than a series of casually written sentences.
  - In relativity, as you have been reminded, sentences must be stated clearly and completely.
  Assumptions based on our everyday common-sense based on Galilean physics can't be assumed.
  Spell out the details, although it may seem tedious to be unambiguous.
• Minkowski's idea of spacetime was developed by the mathematician Minkowski in 1907, a few years after Einstein's 1905 papers. I think this helped Einstein's special relativity gain more acceptance. It makes Einstein's ideas more tangible and provides a geometric framework one can use to scaffold a developing intuition.
  
  
• I think you need to learn to express your situations using spacetime diagrams.
  I personally use spacetime diagrams more than textbook formulas for time dilation, length contraction, Lorentz transformation, etc... often because the word problem, the symbols (prime vs unprime), etc... are unclear to me until I draw a spacetime diagram. Even then, I analyze the diagram as a geometric problem in hyperbolic trigonometry. If needed, I translate into the textbook formulas (after I decode the notations used in the context of the problem).
  (For optics, I draw ray-tracing diagrams first, then translate into a textbook formula after I decode the notations.)
• It takes practice to translate back and forth between words and spacetime-diagrams. Practice!

Possibly helpful:

• (i have only glanced at this)
  https://www.amazon.com/What-Relativity-L-D-Landau/dp/0486428060?tag=pfamazon01-20
  What Is Relativity?
  by L. D. Landau
• (i have only glanced at this)
  https://mirtitles.org/2012/07/07/special-theory-of-relativity-ugarov/
  Special Theory Of Relativity
  by V. A. Ugarov
  - This has a discussion of Bondi's k-calculus.
• https://www.amazon.com/Relativity-Common-Sense-Approach-Einstein/dp/0486240215?tag=pfamazon01-20
  Relativity and Common Sense: A New Approach to Einstein
  by Hermann Bondi
  - I think this is the best short introduction to relativity, using Bondi's k-calculus (which uses geometry and algebra but no calculus)
• https://www.amazon.com/General-Relativity-B-Robert-Geroch-ebook/dp/B01EPVY276/?tag=pfamazon01-20
  General Relativity from A to B
  by R. Geroch
  - This develops spacetime thinking.
  When I first read it in college as an optional assignment, I thought it was verbose and not very useful. When took his classes in grad school, I realize I was mistaken. I found this book had deep insights and perspectives in relativity that I have not seen anywhere else.
  (more advanced but the introductory chapters may be useful:
  his 1972 General Relativity notes from https://home.uchicago.edu/~geroch/Course Notes ,
  which were written long before I took his class...
  and I didn't know about them until much later)
  
  
• https://www.amazon.com/Simple-Non-Euclidean-Geometry-Physical-Basis/dp/0387903321?tag=pfamazon01-20
  A Simple Non-Euclidean Geometry and Its Physical Basis: An Elementary Account of Galilean Geometry and the Galilean Principle of Relativity
  by I.M. Yaglom
  - I found a used copy in a bookshop during a vacation thirty years ago.
  It inspired my "Spacetime Trigonometry" line of research trying to unify how to think about special relativity using geometric analogies with Euclidean and Galilean geometry as Cayley-Klein geometries.
  
  
• https://www.amazon.com/Ideas-That-Shaped-Physics-Frame-Independent/dp/0072397144?tag=pfamazon01-20
  Six Ideas That Shaped Physics: Unit R - Laws of Physics are Frame-Independent
  by Thomas Moore
  
  
• I recently stumbled upon these videos on spacetime diagrams that I think are worth watching
  - (2026) "I wish I was taught RELATIVITY this way!" by More in Depth
  - (2025) "Understanding Relativity with Spacetime Diagrams" by More in Depth
  I like the approach taken. (I wish I had the time and skills to make such presentations.)
• Have a look at some of my Physics Forums Insights.

"A spacetime diagram is worth a thousand words"
- robphy

 

[Nugatory]

I've thought about it and I conclude that clock B (or clock A) never read slowed time.

This is wrong, and we can try one more time to explain why

1) If observer A will look at the clock B then he will see that clock B is running slowly. E1: clock A = 100sec, E2: clock B = 80sec
2) If observer B will look at the clock A then he will see that clock A is running slowly. E3: clock B = 100 sec, E4; clock A = 80 sec

My question is: How is it possible that the clock B can read two different values (slowed time (80sec) and proper time (100sec))?

Using the frame in which A is at rest, events E1 and E2 are simultaneous - that's what A means when they say that B is running slowly. But when we use the frame in which B is at rest, we find that E1 and E2 are not simultaneous. Instead E2 and another event E5 (A's clock reads 64) are simultaneous. That's how both can conclude that the other clock is running slow.

So far you haven't involved proper time at all, but there are some proper times: proper time between E1 and E4 is 20 seconds, proper time between E2 and E3 is 20 20 seconds, proper time between E1 and E2, E1 and E3, E3 and E4 is undefined because we're comparing different clocks.

 

[PeterDonis]

people couldn't fully understand me in my old topic

I don't think this is true. You're asking the same question here that you asked in your previous threads (of which there have been more than one), and we understood it just fine in those threads, and we understand it just fine here:

My question is: How is it possible that the clock B can read two different values (slowed time (80sec) and proper time (100sec))?

The answer is that clock B does not read different values at the same event. There is an event where clock B reads 80 sec. There is an event where clock B reads 100 sec. These are two different events. The second event occurs after the first in any frame.

Until you grasp what I have just said, and realize that the question you keep asking is based on a false premise, we are never going to get anywhere. Many of our best PF experts on this topic have been extremely patient in trying to get across to you that your question is based on a false premise. But you still don't appear to get it.

Note that everything I've just said relates to clock B's proper time. Which is not the same as coordinate time in any frame in which clock B is not at rest. That is another point which we are not sure that you understand, and you need to.

 

[PeterDonis]

This is proved by experiment:
"Two observers fly to each other on the rockets and send light signal to each other every 2sec. Light signal every rocket receive with delay and this explain why clock of observer B run slowly than clock of observer A and vice versa."

Where is this quote taken from? Please give a reference.

 

[PeterDonis]

"Two observers fly to each other on the rockets and send light signal to each other every 2sec. Light signal every rocket receive with delay and this explain why clock of observer B run slowly than clock of observer A and vice versa."

No, this is not correct as a description of what each observer actually sees--the timing of the light signals they receive.

If the two observers are flying towards each other, each one sees (if they just look at the incoming light signals and don't adjust for light travel time) the other's clock running faster than theirs, not slower. The relativistic Doppler factor for motion towards each other is

$$\frac{\sqrt{1 + v / c}}{\sqrt{1 - v / c}}$$

That's the factor by which each observer sees the other's clock running faster.

If the two observers are flying away from each other, each one sees (again if they just look at the incoming light signals and don't adjust for light travel time) the other's clock running more slowly than the relativistic $\gamma$ factor would imply. The relativistic Doppler factor for motion away from each other is

$$\frac{\sqrt{1 - v / c}}{\sqrt{1 + v / c}}$$

That's the factor by which each observer sees the other's clock running slower in this case.

The relativistic $\gamma$ factor, which is what is usually referred to as "time dilation", is what each observer calculates by adjusting what they actually see in the incoming light signals for light travel time.

Failure to take proper note of these crucial facts is a common cause of confusion for people trying to understand relativity scenarios.

 

[kuruman]

1) If observer A will look at the clock B then he will see that clock B is running slowly. E1: clock A = 100sec, E2: clock B = 80sec
2) If observer B will look at the clock A then he will see that clock A is running slowly. E3: clock B = 100 sec, E4; clock A = 80 sec

Observers at separate locations moving relative to each other just can't look at each other's clock and decide whether they run slow or fast. The best they can do is to communicate with each other by radio at the speed of light and report to each other what their onboard clock reads.

However, if they have a basic understanding of special relativity, they can calculate where the other person is and what the other person's clock reads at that position. So let's do some sample calculations that pair positions and times using the Lorentz transformation equations $$\begin{align} & x'=\gamma\left(x-vt\right)~;~~~t'=\gamma\left(t-\frac{vx} {c^2}\right) \nonumber \\
& x=\gamma\left(x'+vt'\right)~;~~t=\gamma\left(t'+\frac{vx'}{c^2}\right) \nonumber \\
& \text{where}~~\gamma=\frac{1}{\sqrt{1-v^2/c^2}}. \nonumber
\end{align}$$Unprimed observer A stays on the Earth. Primed observer B, moving with velocity $v$, passes by observer A. Each observer has a clock at rest with respect to him. Observer A's clock reads time $t$ and B's clock reads time $t'.$ Two events happen.

Event 1: Observer B passes by Observer B. Times and positions are
$t_1=0~;~~t'_1=0~$ and $~x_1=0~;~~x'_1=0.$

Event 2: Observer A looks at his clock and sees that it reads $t_2=T$.

Question 1
Where is Observer B according to A when A's clock reads $t_2=T$?
Observer A says "B has been traveling with velocity $v$ from time zero to time $T$ by my clock."
Answer 1: Therefore, B's position must be $x_2=vT~$ at time $t_2=T.$

Question 2
Observer A now asks himself, "What time must Observer B's clock show if B is looking at his clock?"
He uses the Lorentz transformation equations to find out.
$t'_2=\gamma\left(t_2-\dfrac{vx_2} {c^2}\right)=\gamma\left(T-\dfrac{v^2T} {c^2}\right)=\gamma T\left(1-\dfrac{v^2} {c^2}\right)=\gamma T\left(\dfrac{1}{\gamma^2}\right)=\dfrac{T}{\gamma}.$
Answer 2: Therefore, A's calculation shows that when $t_2=T$ by his clock, B's clock must read $t'_2=\dfrac{T}{\gamma}.$

The final conclusion of A is that B's clock must be running slower than his by a factor of $\dfrac{1}{\gamma.}$

Question 3
Where is Observer A according to B when B's clock reads $t'_2=\dfrac{T}{\gamma}$?
Observer B says "A has been traveling with velocity $-v$ from time zero to time $\dfrac{T}{\gamma}$ by my clock."
Answer 3: Therefore, A's position must be $x'_2=-\dfrac{vT}{\gamma}~$ at time $t'_2=\dfrac{T}{\gamma}.$

Question 4
Observer B now asks himself, "What time must Observer A's clock show if A is looking at his clock?"
He uses the Lorentz transformation equations to find out.
$t_2=\gamma\left(t'_2+\dfrac{vx'_2} {c^2}\right)=\cancel{\gamma}\left(\dfrac{T}{\cancel{\gamma}}-\dfrac{v^2T} {\cancel{\gamma} c^2}\right)= T\left(1-\dfrac{v^2} {c^2}\right)=\dfrac{T}{\gamma^2}.$
Answer 4: Therefore, B's calculation shows that when $t'_2=\dfrac{T}{\gamma}$ by his clock, A's clock must read $t_2=\dfrac{T}{\gamma^2}.$

The final conclusion of B is that A's clock must be running slower than his by a factor of $\dfrac{1}{\gamma.}$

Bottom line: Based on their calculations, both observers conclude that the other observer's clock is running slower by the same factor $1/\gamma.$

 

[Sagittarius A-Star]

Ok. Each of observers think that time in another frame is running slowly. And each of observers is right.
This is proved by experiment:
"Two observers fly to each other on the rockets and send light signal to each other every 2sec. Light signal every rocket receive with delay and this explain why clock of observer B run slowly than clock of observer A and vice versa."

Slowed time isn't showed on the clock because otherwise it violates Postulate 1.

That's not correct. Each rocket sees the relativistic Doppler effect. The formula for it can be written as a product of the time-dilation-factor and the non-relativistic Doppler formula for the receiver at rest:

$f_r = {f_s \over \gamma (1-v/c)}$

From $f_r/f_s$, the time-dilation factor for the sender in the receiver's frame can be calculated for the usual definition, that the one-way-speed of light is $c$.

Relativistic Doppler effect:
https://en.wikipedia.org/wiki/Relativistic_Doppler_effect

Non-relativistic Dopper effect, receiver at rest (signal source moving):
https://de.wikipedia.org/wiki/Doppler-Effekt#Beobachter_in_Ruhe,_Signalquelle_bewegt

The Ives–Stilwell experiment (1938) was a confirmation of the time-dilation factor, based on the relativistic Doppler effect:
https://en.wikipedia.org/wiki/Ives–Stilwell_experiment

 

[Gavran]

My question is: How is it possible that the clock B can read two different values (slowed time (80sec) and proper time (100sec))?

Mermin, N. David. Space and Time in Special Relativity
Chapter 10 (pages 87-90)
“Why He Says My Clocks Go Slowly Although I Know that His Go Slowly”
https://dokumen.pub/qdownload/space-and-time-in-special-relativity-1stnbsped.html