How can time dilation be the same for both observers?

[Prem1998]

Here, I'm not talking about the twin paradox in which one of the observer's frame gets accelerated. I'm talking about the case in which they just move relative to each other without accelerating. I'm having some confusion. Please tell me where I'm wrong:
1.There are two people, Dick and Jane on Earth. Dick goes on space travel on a spacecraft which moves with a velocity 0.8c relative to Earth.
2. He leaves when both their clocks read 07:00 AM, and Dick takes one clock along with him. Both of them have telescopes by which they can observe the time elapsed on another clock. When the time is 07:05 AM on Dick's clock, he views Jane's clock from his telescope and sees that it is reading 07:03 AM.
3. So, when Jane's clock reads 07:03 AM, Dick's clock reads 07:05 AM.
4. So, if Jane views Dick's clock from her telescope when her clock reads 07:03 AM, she should see 07:05 AM on Dick's telescope.
5. But Dick is also moving at 0.8c for Jane, so by applying time dilation formula, so when Jane's clock reads 07:03 AM, i.e. 3 minutes have passed on her clock, only 1.8 minutes should pass on Dick's clock, so she should see 07:1.8 AM on Dick's clock.
6. So, when Jane's clock reads 07:03 AM, Dick's clock reads 07:1.8 AM. But this contradicts my third point.
Please explain this to me. Thanks.

 

[Jonathan Scott]

The main missing factor here is that the definition of "at the same time" (that is, simultaneity) depends on the velocity of the observer, so events which are the same time according to one observer may be at different times according to another observer.
Also, any observation using a telescope or similar has to be adjusted for the light speed delay according to the reference frame of the observer.

A way of visualising this is to imagine two people walking in different directions. Each observes that the other one is going slower than themselves in their own direction, but there is no contradiction in this.

 

[Prem1998]

The main missing factor here is that the definition of "at the same time" (that is, simultaneity) depends on the velocity of the observer, so events which are the same time according to one observer may be at different times according to another observer.

I'm still not getting this. Can you please just explain the problem I've written here? I mean, how can Dick's clock read both 07:05 AM and 07:1.8 AM at the same time when Jane's clock reads 07:03 AM ? I'm putting this another way like this:
Let's just pause the universe when Jane's clock reads 07:03 AM. At this instant, Jane is seeing 07:1.8 AM on Dick's clock while Dick is seeing 07:05 AM on the same clock. And, let's just forget about the telescope part. Let's just assume they can see each others' clock instantaneously ( I know it's impossible, but let's just suppose).

 

[jbriggs444]

I'm still not getting this. Can you please just explain the problem I've written here? I mean, how can Dick's clock read both 07:05 AM and 07:1.8 AM at the same time when Jane's clock reads 07:03 AM ?

Because "at the same time" is not an invariant concept. It depends on one's choice of reference frame.

 

[Orodruin]

I suggest reading my Insight article https://www.physicsforums.com/insights/geometrical-view-time-dilation-twin-paradox/

 

[Prem1998]

Okay, so when Jane sees 07:03 AM on her clock is not 'the same time' when Dick sees 07:03 AM on the same clock. Then, what is the time on Jane's clock according to Jane when there is 07:03 AM on her clock according to Dick?

 

[Prem1998]

Okay, so when Jane sees 07:03 AM on her clock is not 'the same time' when Dick sees 07:03 AM on the same clock. Then, what is the time on Jane's clock according to Jane when there is 07:03 AM on her clock according to Dick?

 

[Jonathan Scott]

There is no problem with defining "at the same time" at the same location. The complication comes when trying to define whether two events at different locations are at the same time. The usual definition of "at the same time" for a given observer is effectively that if the observer sent a light-speed signal to a remote event and received a light-speed signal back again, the event where the signal was reflected is assumed to occur at a time half way between the time when the signal was sent and when it was received back. However, when this situation is viewed from a frame where the observer is moving, the two light trips will not be equal, so from that point of view the events are not at the same time.

 

[Prem1998]

There is no problem with defining "at the same time" at the same location. The complication comes when trying to define whether two events at different locations are at the same time. The usual definition of "at the same time" for a given observer is effectively that if the observer sent a light-speed signal to a remote event and received a light-speed signal back again, the event where the signal was reflected is assumed to occur at a time half way between the time when the signal was sent and when it was received back. However, when this situation is viewed from a frame where the observer is moving, the two light trips will not be equal, so from that point of view the events are not at the same time.

If we suppose that the two persons are able to see each others' clocks instantaneously without any light pulse being sent, then will it be the same time when Dick sees 07:03 AM on Jane's clock and Jane sees 07:03 AM on Jane's clock? If not, then, what is the time on Jane's clock according to Jane when there is 07:03 AM on her clock according to Dick?

 

[Jonathan Scott]

If we suppose that the two persons are able to see each others' clocks instantaneously without any light pulse being sent, then will it be the same time when Dick sees 07:03 AM on Jane's clock and Jane sees 07:03 AM on Jane's clock? If not, then, what is the time on Jane's clock according to Jane when there is 07:03 AM on her clock according to Dick?

"Instantaneously" is not a valid concept when two events are at different locations. There is no global definition of "same time".

 

[A.T.]

If we suppose that the two persons are able to see each others' clocks instantaneously

Then relativity would be wrong, so it's pointless to ask what it would predict.

 

[Prem1998]

"Instantaneously" is not a valid concept when two events are at different locations. There is no global definition of "same time".

Just tell me what is the time on Jane's clock according to Jane when there is 07:03 AM on Jane's clock according to Dick.

 

[pervect]

I'm still not getting this. Can you please just explain the problem I've written here? I mean, how can Dick's clock read both 07:05 AM and 07:1.8 AM at the same time when Jane's clock reads 07:03 AM ? I'm putting this another way like this:
Let's just pause the universe when Jane's clock reads 07:03 AM. At this instant, Jane is seeing 07:1.8 AM on Dick's clock while Dick is seeing 07:05 AM on the same clock. And, let's just forget about the telescope part. Let's just assume they can see each others' clock instantaneously ( I know it's impossible, but let's just suppose).

"At the same time" is an ambiguous statement, as others have mentioned. You need to distinguish between "at the same time according to Dick" and "at the same time according to Jane". You also need to distinguish "what Dick sees" from "at the same time according to Dick". So there are four different concepts here which you are confusing and combining:

1) What Dick sees on Jane's clock through a telescope/
2) "At the same time" according to Dick, which is what Dick sees with the propagation delays compensated for.
3) What Jane sees on Dick's clock.
4) "At the same time" according to Jane.

It's hard to reword your example because I'm not sure what you meant due to the ambiguity of your language. So if you'd care to re-write it unambiguiously, we can give you a definite answer for all four observations.

 

[Prem1998]

Just forget all the above things. What I want to ask is: do both observers age at the same rate when they are moving at 0.8c relative to each other and Dick never comes back to Earth? If so, then how?

 

[PeroK]

Just forget all the above things. What I want to ask is: do both observers age at the same rate when they are moving at 0.8c relative to each other and Dick never comes back to Earth? If so, then how?

Ageing is the passing of elapsed time. So, ageing according to whom?

 

[jbriggs444]

Just forget all the above things. What I want to ask is: do both observers age at the same rate when they are moving at 0.8c relative to each other and Dick never comes back to Earth? If so, then how?

As has been suggested by @pervect previously, this is an ambiguous question. What would you mean by a rate at which someone ages?

You could firm up the question by considering Jane aging from 20 to 21 [by her personal biological clock] and Dick aging from 20 to 21 [by his personal biological clock] and how you could match these intervals up using frame-relative notions of "at the same time".

 

[Jonathan Scott]

"Age at the same rate" assumes global time.

This is like the following question:
Dick and Jane start from the same spot.
If Dick walks 100m north and Jane walks 100m north-east, which one is further ahead?

 

[Prem1998]

As has been suggested by @pervect previously, this is an ambiguous question. What would you mean by a rate at which someone ages?

You could firm up the question by considering Jane aging from 20 to 21 [by her personal biological clock] and Dick aging from 20 to 21 [by his personal biological clock] and how you could match these intervals up using frame-relative notions of "at the same time".

Let me say it like this:
'Three years have passed on Earth since Jane's twin Dick went to space travel. Now, God pauses the universe and visits Earth to see Jane and then visits the spacecraft to see Dick. Now, which one will God find more older?'
I'm sorry if I'm asking stupid questions. But I'm not getting the concept.

 

[PeroK]

Let me say it like this:
'Three years have passed on Earth since Jane's twin Dick went to space travel. Now, God pauses the universe and visits Earth to see Jane and then visits the spacecraft to see Dick. Now, which one will God find more older?'
I'm sorry if I'm asking stupid questions. But I'm not getting the concept.

You're not listening. There is no universal "now". In your mind, you probably have the Earth's reference frame as God's reference frame in this case. But, you need a reference frame to define "now".

 

[Ibix]

Let me say it like this:
'Three years have passed on Earth since Jane's twin Dick went to space travel. Now, God pauses the universe and visits Earth to see Jane and then visits the spacecraft to see Dick. Now, which one will God find more older?'
I'm sorry if I'm asking stupid questions. But I'm not getting the concept.

Depends which frame God used when he defined the "now" at which he paused the universe. Assuming such a concept makes any sense. There's no way around the fact that "at the same time" is only unambiguously defined for two things at the same place, no matter how much you wiggle.

 

[jbriggs444]

Let me say it like this:
'Three years have passed on Earth since Jane's twin Dick went to space travel. Now, God pauses the universe and visits Earth to see Dick and then visits the spacecraft to see Dick. Now, which one will God find more older?'
I'm sorry if I'm asking stupid questions. But I'm not getting the concept.

God has a choice. He can pause the universe in a configuration where Jane is older than Dick. He can pause the universe in a configuration where Dick is older than Jane. And we cannot tell which one is "right". That is because we have no way to measure "at the same time" unambiguously to be sure that he paused all parts of the universe "at the same time".

 

[Prem1998]

Depends which frame God used when he defined the "now" at which he paused the universe. Assuming such a concept makes any sense. There's no way around the fact that "at the same time" is only unambiguously defined for two things at the same place, no matter how much you wiggle.

Let's just say, I, as a person on Earth, have power to stop everything, stop the time. I use my power and everything, wherever it was, whatever it was doing, whatever reference frame it was in, just stops. The spacecraft in which Dick is, stops, whatever process was going on, just stops. Except me. Now, I watch go to watch Dick and Jane separately. Who will I find older?

 

[jbriggs444]

Let's just say, I, as a person on Earth, have power to stop everything, stop the time. I use my power and everything, wherever it was, whatever it was doing, whatever reference frame it was in, just stops. The spacecraft in which Dick is, stops, whatever process was going on, just stops. Except me. Now, I watch go to watch Dick and Jane separately. Who will I find older?

You may need to take a step back. What do you think a reference frame is?

 

[Ibix]

Let's just say, I, as a person on Earth, have power to stop everything, stop the time. I use my power and everything, wherever it was, whatever it was doing, whatever reference frame it was in, just stops. The spacecraft in which Dick is, stops, whatever process was going on, just stops. Except me. Now, I watch go to watch Dick and Jane separately. Who will I find older?

Depends which frame's simultaneity convention you decided to use when you stopped everything.

 

[Prem1998]

I used Earth's simultaneity convention. Now, please, who will I find older?

 

[PeroK]

Let's just say, I, as a person on Earth, have power to stop everything, stop the time. I use my power and everything, wherever it was, whatever it was doing, whatever reference frame it was in, just stops. The spacecraft in which Dick is, stops, whatever process was going on, just stops. Except me. Now, I watch go to watch Dick and Jane separately. Who will I find older?

That's not a bad definition of your reference frame. You pick a time and then wander round the universe looking at everything. That's your refernce frame.

Things are not in a particular reference frames. All things are in all reference frames at all times.

For example, if a particle at CERN could stop the universe and wander round, they would find you massively length contracted in the direction that you are moving at near light speed relative to it.

 

[PeroK]

I used Earth's simultaneity convention. Now, please, who will I find older?

In the Earth's reference frame Dick is younger. That's easy!

 

[Prem1998]

That's not a bad definition of your reference frame. You pick a time and then wander round the universe looking at everything. That's your refernce frame.

Things are not in a particular reference frames. All things are in all reference frames at all times.

For example, if a particle at CERN could stop the universe and wander round, they would find you massively length contracted in the direction that you are moving at near light speed relative to it.

I think I'm getting this now. So, when the particle at CERN resumes the universe on finding me, then it'll find me of my normal length suddenly, right? So, it depends on who pauses the universe and what was his motion relative to things he is observing now when he paused the time.
Another, very very stupid question: if two people in different reference frames (moving with a non zero velocity with respect to one another) pause the universe, and meet me together, will they see both see different lengths of me and will they see different events occurring in the same place of the universe?

 

[jbriggs444]

I think I'm getting this now. So, when the particle at CERN resumes the universe on finding me, then it'll find me of my normal length suddenly, right?

When the particle at CERN pauses the universe, the frozen "you" will be short. But then you always were short as viewed from the reference frame where that particle is at rest. Pausing the universe did not change that. Nor does resuming the universe change it. Your "length" as viewed from a particular reference frame is the length of a snapshot of you taken at an instant in time using the simultaneity convention for that reference frame.

 

[robphy]

(If you want to talk about length contraction, maybe that should go in a different thread...
Though there is a relation, it's convoluted to discuss time dilation and length contraction concurrently while trying to clarify one.)

A spacetime diagram may be helpful here.

https://www.desmos.com/calculator/ti58l2sair [my t axis is horizontal ]
Tune v1 and v2 and you can see that their senses of simultaneity disagree in general... and that the time dilation is symmetrical in the sense that each observer's dashed line of simultaneity cuts off the other observer's 4-velocity (unit vector) by the same fraction. [Slide E to -1 to see the Euclidean version, and 0 for the Galilean version.]