Relative death of people traveling at the speed of light

[grizzly]

Hello. So I always hear people say, "If someone flew in a ship at light speed to a far away star and then came back to earth, and it only took him two years to travel (the star being a light year away). When he came back all of his family/friends would have been dead for a long time." My question is about the people on earth... If instead we change our perspective to those on earth, and they observed the travel of this astronaut to the far-away star with a telescope, wouldn't relativity imply that the people on Earth would see the astronaut die in the same way the astronaut would observe his friends? The way I understand relativity is that while to the astronaut it seems that he had not aged more than 2 years, to the Earth observers they would see him age dramatically because of his travel at the speed of light? I hope I was clear in my question. I've never heard anyone discuss this thought experiment from the perspective of the earthians.

 

[PeterDonis]

The way I understand relativity is that while to the astronaut it seems that he had not aged more than 2 years, to the Earth observers they would see him age dramatically because of his travel at the speed of light?

No. How much the astronaut ages is invariant; it doesn't depend on who is doing the observing.

I've never heard anyone discuss this thought experiment from the perspective of the earthians.

Evidently you haven't read much of the extensive literature on the twin paradox. I recommend the Usenet Physics FAQ article on it:

http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html

It addresses all the issues you raise.

Oh, and welcome to PF!

 

[phinds]

Hello. So I always hear people say, "If someone flew in a ship at light speed to a far away star and then came back to earth, and it only took him two years to travel (the star being a light year away). When he came back all of his family/friends would have been dead for a long time." My question is about the people on earth... If instead we change our perspective to those on earth, and they observed the travel of this astronaut to the far-away star with a telescope, wouldn't relativity imply that the people on Earth would see the astronaut die in the same way the astronaut would observe his friends? The way I understand relativity is that while to the astronaut it seems that he had not aged more than 2 years, to the Earth observers they would see him age dramatically because of his travel at the speed of light? I hope I was clear in my question. I've never heard anyone discuss this thought experiment from the perspective of the earthians.

Quite the contrary. The people on Earth would see him, to the extend he COULD be seen, as aging almost not at all relative to them. During his son's entire lifetime of say 80 years, he would age only a few days (as seen from Earth) or a few weeks or a few months, depending on his exact speed. (You CAN'T travel at the speed of light, although theoretically you can get close and the time dilation depends on the speed).

 

[PeterDonis]

The people on Earth would see him, to the extend he COULD be seen, as aging almost not at all relative to them.

One thing should be clarified here: the word "see" has two possible meanings. One is the rate of aging that the people on Earth actually see, literally, as in "view through a telescope"; the other is the rate of aging that the people on Earth *calculate* for the astronaut, after correcting for light travel time.

The latter is always slower, as you say. However, the former is *not*; as the Usenet Physics FAQ article I linked to shows, what the people on Earth actually *see* through a telescope (we assume it's a very, very powerful telescope) is the astronaut aging more slowly than people on Earth on his outbound leg, but aging more *quickly* than the people on Earth on his inbound leg. This is because of the relativistic Doppler effect. The reason the astronaut ages less over the entire trip is that, as actually *seen* through the telescope, his outbound leg lasts a lot longer than his inbound leg (because the people on Earth see his turnaround time-delayed).

 

[phinds]

One thing should be clarified here ...

agreed

 

[ghwellsjr]

Hello. So I always hear people say, "If someone flew in a ship at light speed to a far away star and then came back to earth, and it only took him two years to travel (the star being a light year away). When he came back all of his family/friends would have been dead for a long time." My question is about the people on earth... If instead we change our perspective to those on earth, and they observed the travel of this astronaut to the far-away star with a telescope, wouldn't relativity imply that the people on Earth would see the astronaut die in the same way the astronaut would observe his friends? The way I understand relativity is that while to the astronaut it seems that he had not aged more than 2 years, to the Earth observers they would see him age dramatically because of his travel at the speed of light? I hope I was clear in my question. I've never heard anyone discuss this thought experiment from the perspective of the earthians.

I don't think you have heard exactly that story before. If the astronaut flew at just under the speed of light (because he can't actually go at exactly the speed of light) to a star just one light year away and returned at the same speed, the people on Earth will have aged only about two years but the astronaut will have aged must less, maybe only a few days or weeks, depending on his speed so the chances are most of his family/friends will still be alive and they probably won't even notice the difference in their ages.

If you want the difference in their ages to be at least a hundred years (so that all the earthlings will have died) then the astronaut will have to travel to a star that is more than fifty light years away, let's say, about 84 light years. And let's say he is traveling at 99% the speed of light so as not to be in violation of the maximum speed limit. This means that it will take him 85 years of Earth time to get to the star and another 85 years to get back.

As the earthlings watch the astronaut travel away, they will see him through their telescope aging at a much lower rate than themselves but since it takes the light just about as much time to get back to them as it took for the astronaut to get to the star, it will take about double the time for them to see him arrive as it took for him to get there, which, of course means that if it took him about 85 years of Earth time to get there, they will be dead before they see him arrive. Since the star is 84 light years away it will take 84 years for the image of him arriving to get back to them so the total time will be 169 years by the time anyone could see him arrive at the star.

But a new generation of people will be able to see him arrive and they will see him having aged just twelve years since he left. Then they will see him turn around and come back home but this time they will see him age at a higher rate than themselves, in fact, they will see him age 12 more years in just under one year of Earth time.

So when it's all over, the astronaut will have aged 24 years while 170 years will have gone by on Earth since he left. He will still be alive but his family/friends will be dead.

Now what does the astronaut see of the earthlings? Well he will see them age at the same low rate that they saw him aging during his trip out. So during the twelve years that he ages during his trip out, he will see the earthlings age a little less than one year. But as soon as he turns around, he will see the earthlings age at a much faster rate than himself, actually more than 14 times his own aging rate. So during the 12 years that he takes coming back, he sees the earthlings accumulate about 169 years for a total of 170 years.

I have attached a spacetime diagram to depict the scenario that I have just described. The thick blue line represents the people on the Earth while the astronaut is shown as the thick red line. The dots mark off one-year increments of time for both of them. The thin blue line down at the bottom shows the image of the earthlings after one year traveling to the astronaut at the point of his turn-around. The thin red lines show the images of the astronaut at one-year increments of time as seen by the earthlings.

Hopefully, this will help you understand what's going on.

 

[grizzly]

Wow guys. Thanks for all the wonderful answers apparently the people that I heard reference this don't actually know what they are talking about. I'm going to read the articles at once.

 

[ghwellsjr]

It occurred to me that there is another way to understand the problem. When you said that it only took the astronaut two years to travel to and from the far away star, you might have been talking about how long the trip took for the astronaut instead of for how long it took according to Earth time. It's very important when setting up a scenario that you state what frame the times and distances are specified in. So if the time and distance that you specified were in the astronaut's frame of reference during the first half of the trip, then it would be more correct to say that it was the star that traveled toward him from a distance of about one light year.

However, the principles that I and others have stated in previous posts apply either way, it's just the details that are different. I have made another spacetime diagram where the astronaut is traveling much faster, at 99.9898% of the speed of light. Then in one year of his time, it takes about 70 years of Earth time to get to a star about 70 light years away. The total trip takes 140 years of Earth time and 2 years of the astronaut's time.

At the beginning of the trip, each observer sees the other ones time progressing at 1/140 times their own which means the astronaut sees the earthlings have progressed through just 2.6 days by the time he turns around. Then during the last part of the trip, the astronaut sees the earthlings age at 140 times his own so they accumulate 140 years during his own time of one year. His total is one year plus one year or two years and their total is just over 140 years.

The earthlings would also see the astronaut age at 1/140 of their own rate during the first part of the trip. If they could live long enough, they would see the astronaut age just one year during 140 years of their time, then they would see him turn around and then they would see him age at 140 times their own rate so in just 2.6 days they would see him age one year. So, again, the astronaut's total age is 2 years while the Earth has gone through just over 140 years, guaranteeing that all of the astronaut's family and friends have died while he is gone.