Could extreme time dilation ever be directly observed?

[Louis Philippe]

Hi Folks-I am interested in knowing whether, in actual practice, people on Earth would see their 99% of c colleagues moving around in fast forward motion and if the reverse would be true from the vantage point of the relativistic astronauts who are moving away from earth. I suspect that since there is no privileged observer, both would see the other in fast forward motion since the rocket ship could be said to be stationary and the Earth moving at the speed of light. If not, would the astronauts ever see their earthbound colleagues frozen by time dilation or would the loss of information due to red shifts prevent such a spectacle?

 

[Ibix]

You have to be a bit careful by what you mean by "see" in this context.

In terms of what they would literally see, it would depend on whether they were moving towards each other or away from each other. If they were moving towards each other then they would both see each other speeded up; if they were moving away from each other they would each see the other slowed down.

The reason you see different things depending on the direction is due to the Doppler effect. If you subtract out the Doppler effect, however, you are left with the effects of time dilation. That is the result of a calculation, though (and it ends up requiring you to make an assumption about how clocks were synchronised). In this case, both observers will determine that the other is moving slowly - as you say, there are no priviledged frames and you can consider either the ship or the Earth to be at rest.

Whichever approach you take, the situation is symmetric - what you see from Earth is the same effect you see from the ship.

 

[Mentz114]

To be pedantic, it is the relativistic Doppler effect which for approaching worldlines is $f_1/f_2=\gamma(1+\beta)$ and $f_1/f_2=\gamma(1-\beta)$ for receding WLs.

 

[Louis Philippe]

Thank you for elucidating that point. Still, it is hard to see how the ship's observation could be contrary to the clocks on Earth and the space craft. If time is whizzing by on earth, why would the telescope on board the craft see a world nearly frozen in time? If the craft came to an abrupt stop,now synchronized, after many years had passed on earth, what would they see ?

 

[Nugatory]

The doppler effect complicates any attempt to dir

Thank you for elucidating that point. Still, it is hard to see how the ship's observation could be contrary to the clocks on Earth and the space craft. If time is whizzing by on earth, why would the telescope on board the craft see a world nearly frozen in time? If the craft came to an abrupt stop,now synchronized, after many years had passed on earth, what would they see ?

One way to understand this problem is to imagine that the clocks are equipped with a little radio transmitter that broadcasts the clock reading with every tick: "I read 12:00:00", then one second later "I read 12:00:01", and a second after that "I read "12:00:02", and so forth. Watching the other observer's clock is equivalent to receiving these radio signals (the signals reach our radio receiver at the same time that light reflected from the hands of the clock reaches our eyes).

Now there are two factors that affect the time interval between the arrival of successive signals. One is time dilation, and it is the same as long as the relative velocity of the two observers is constant. The other is the travel time between clock and receiver, and it changes with every tick because the distance between the two observers is always changing.

Obviously if the two observers are at rest relative to one another, they will each receive one signal per second from the other clock. If we don't go to some extra work to also set the clocks to read the same time they won't agree about what time it is, but that's beside the point; what matters is that the interval between the arrival of successive signals is one second.

If the two observers are moving towards one another, both will receive more than one signal per second from the other clock. Each signal will have a shorter distance to travel than its predecessor, so will spend less time in flight. The visual experience, what is actually "seen", is that the other clock is running fast. Conversely, if they are moving away from each other, each signal will have to spend more time in flight than its predecessor, and both observers "see" the other clock running slow.

Time dilation only comes into the picture when the two observers subtract the light travel time from the arrival time to find the time when the signal left the source. When they do this calculation, they both find that the other clock is running slow relative to their own. However, that's a calculation, not something that they actually see with their eyes and their radio receivers.

 

[Janus]

Thank you for elucidating that point. Still, it is hard to see how the ship's observation could be contrary to the clocks on Earth and the space craft. If time is whizzing by on earth, why would the telescope on board the craft see a world nearly frozen in time? If the craft came to an abrupt stop,now synchronized, after many years had passed on earth, what would they see ?

According the ship, time is not "whizzing by" on Earth, it is actually running slower, (by about 1/7 the rate). The Earth, on the other hand will say that time is running slow for him. This is different from what they see in a telescope where each sees the other clock running at 1/14 their own rate when they are receding and 14 times faster when approaching. (the actual time dilation factor remains the same 1/7 rate regardless of whether they are approaching or receding.)

As far as what happens if the Ship stops. While they are separating, he will see the Earth clock running at a rate of ~1/14. So let's say that he travels for 14 hrs by his clock. He will see 1 hr elapse on the Earth clock. If he suddenly stops, he will continue to see a 13 hr difference between the clocks. Of course there is a great deal of distance between the Earth and himself now, which means that the time he sees on the Earth clock is old information. To figure out what time it really is on Earth, he has to account for this, and in doing so, will work out that the Earth clock will actually read 84 hrs ahead of his own. (his clock read 14 hours and the Earth clock reads 98 hours or 7 times more than his own.)

If we look at things from the point of view of the Earth, you will see this.

Again, as the ship travels away, you see their clock running 1/14 as fast as your own. Now remember, above we said that the spaceship came to a stop when its clock read 14 hrs. This means that the Earth observer won't see the spaceship come to a stop until 14x14= 196 hrs has passed on his own clock. Thus when he sees the spaceship stop ( the the clock on the spaceship starts to run at the same rate as his own), his clock will read 196 hours and he will see the spaceship clock read 14 hrs. Again, there is a large distance between the two, which means that the time he sees on the spaceship clock is old information. Once he takes this into account, he can work out that when the light left the spaceship ( when its clock read 14 hrs), his clock read 98 hours.This is the same answer the spaceship got.

 

[Louis Philippe]

I understand fully.I had forgotten to consider the time light needs to travel. Thanks.

 

[Stephanus]

[..]The reason you see different things depending on the direction is due to the Doppler effect. If you subtract out the Doppler effect, however, you are left with the effects of time dilation. [..]

That's what keeps me wondering. How can they say the other object is dilated, when we see it blue-shifted and the time ticks faster. So, it's when we subtract Doppler effect, then all we can see if time dilation. Thanks.

 

[aman patel]

yes..if the ship is moving at speed of light then man would see them as steadystate..and we will see that person fastly growing old...

 

[Stephanus]

yes..if the ship is moving at speed of light then man would see them as steadystate

That's almost true. not steady, but really slow going old. Nothing can travel at the speed of light. So, not steady, but really slow.

..and we will see that person fastly growing old...

Now, this is completely wrong. We will see that person fastly slowly growing old, too. The time dilation works both ways.
See this for explanation:

[Add by me]. When the ship travels, the ship will see that the Earth clock runs slower. And the Earth see the ship clock runs slower, too. Time dilation work both ways. After the ship stops, the ship immediately see the Earth clock runs at the same rate, as the ship. But what will the Earth see?
[This is by Janus]
Again, as the ship travels away, you see their clock running 1/14 as fast as your own. Now remember, above we said that the spaceship came to a stop when its clock read 14 hrs. This means that the Earth observer won't see the spaceship come to a stop until 14x14= 196 hrs has passed on his own clock. Thus when he sees the spaceship stop ( the the clock on the spaceship starts to run at the same rate as his own), his clock will read 196 hours and he will see the spaceship clock read 14 hrs. Again, there is a large distance between the two, which means that the time he sees on the spaceship clock is old information. Once he takes this into account, he can work out that when the light left the spaceship ( when its clock read 14 hrs), his clock read 98 hours.This is the same answer the spaceship got.

 

[aman patel]

i means the person who is watching us on ship is seen by us growing old quickly...

 

[Stephanus]

i means the person who is watching us on ship is seen by us growing old quickly...

No, Aman. We'll see them growing up slowly. And they'll see us growing up..., slowly, too.
Time dilation works both ways.
Look at Janus answer "This means that the Earth observer won't see the spaceship come to a stop until 14x14= 196 hrs has passed on his own clock."
Both party will see the other party growing up slowly, but...
Once the ship stops, the ship will see the Earth grows at the same rate, but the Earth still see the ship grows up slowly.

Imagine this.
You move away from earth
You---------------------------------------->
Earth 10 lys.
------------------------------------------->You
Earth

There are 10 lys between you and earth. So you will see the Earth time late by 10 years (LATE, NOT SLOW), and the Earth will see your clock 10 years late.
Add to that, you'll see the Earth growing up slow, and the Earth will see the same. Now one knows who is moving. Motion is relative, right.

Now, suddenly YOU stop.
-------------------------------------------||You
Earth

You'll see the Earth is still 10 years late, but time dilation effect stops for you. You'll see the Earth clock runs normally. If you STOP, you will KNOW if you stop. Doppler will tell you.

What will the Earth see if YOU stop? As I say the Earth will see you late by 10 yrs, so does you will see Earth late by years.
Supposed when YOU stop, you also light a red beam, just as in the car. When will Earth see the red light? Ten years later, right. And during that time when Earth haven't seen the red light. Earth will still think that you are moving. That's why Earth will see your time go slow.
The Earth will see your time go slow for another 10 years.
You'll see Earth time go slow, 10 years earlier.
There's 10 years different. That's why for moving object time goes slower because of this.

 

[Louis Philippe]

If an astronaut is falling into a black hole then her image would fade to red as she approaches the event horizon, as see from the ship hovering safely above. Before she passed the event horizon the command ship would lose her image all together. Would it be fair to say that the situation would be the same for a ship moving away from Earth at very near the speed of light? (Can we draw this comparison with GR?) Even with the strongest telescope capable of seeing inside the ship? would this be what astronomer's on Earth see, do to the Doppler effect? Let's say the ship is bathed in reflected light rather than producing it's own light source. It seems to me that this loss of information would equal an answer of no to my thread.

 

[Nugatory]

If an astronaut is falling into a black hole then her image would fade to red as she approaches the event horizon, as see from the ship hovering safely above. Before she passed the event horizon the command ship would lose her image all together. Would it be fair to say that the situation would be the same for a ship moving away from Earth at very near the speed of light? (Can we draw this comparison with GR?)

The comparison would be better if in the second case the ship were accelerating away from Earth instead of just moving away from earth. If it's just moving at a constant speed, the Doppler effect will be constant and the image won't fade - it will be redshifted, but the redshift will be constant, not increasing.

 

[vanhees71]

The original question has been answered already, but let's also answer the question in the headline of the thread. I think that the observation that unstable particles running at high speeds appear to live longer than when they are at rest is the closest observation that measures time dilation. This has been done with very high precision recently (relative error of only $2 \cdot 10^{-6}$!), using the ESR (experiment storage ring) at GSI (the Gesellschaft für Schwerionenforschung=Helmholtz Center for Heavy Ion Research) in Darmstadt:

https://www.tu-darmstadt.de/vorbeischauen/aktuell/news_details_103104.en.jsp

Of course, there are also more direct realizations of experiments to measure time dilation, like the famous Hafele-Keating experiment:

https://en.wikipedia.org/wiki/Hafele–Keating_experiment

However, as is well explained in the Wikipedia article, in addition to the purely kinematic time-dilation effect you also have gravitational, i.e., general relativistic time-dilation effects.

 

[newjerseyrunner]

The original question has been answered already, but let's also answer the question in the headline of the thread. I think that the observation that unstable particles running at high speeds appear to live longer than when they are at rest is the closest observation that measures time dilation. This has been done with very high precision recently (relative error of only $2 \cdot 10^{-6}$!), using the ESR (experiment storage ring) at GSI (the Gesellschaft für Schwerionenforschung=Helmholtz Center for Heavy Ion Research) in Darmstadt:

https://www.tu-darmstadt.de/vorbeischauen/aktuell/news_details_103104.en.jsp

Of course, there are also more direct realizations of experiments to measure time dilation, like the famous Hafele-Keating experiment:

https://en.wikipedia.org/wiki/Hafele–Keating_experiment

However, as is well explained in the Wikipedia article, in addition to the purely kinematic time-dilation effect you also have gravitational, i.e., general relativistic time-dilation effects.

The most straight forward display of time dilation I know of is the GPS system. They account for both special relativity and general relativity, and that their orbits are elliptical. They did experiments early on where they had a switch where they could turn that compensation on or off to observe whether it was needed and it's required to be altered by 5 parts per 10¹⁰.

Skip to about 29 minutes in, he's one of the engineers who works on it