Bob & Ted See Different Ages for Alice on Earth

[RandyD123]

TL;DR Summary

What is Alice's age?

Bob, Alice and Ted are all on earth. Bob leaves Earth traveling at .08 light speed for 6 months out then turns around and heads back to earth. Effectively he has been traveling for a total of 1 light year. Ted leaves Earth at the same time as Bob but only travels at .04 the speed of light for 3 months then turns around to head back to earth. Both Bob and Ted should arrive back at Earth at the same time. How do they both view Alice?

 

[Ibix]

Edit: this is a response to an older version of the OP.

You can't travel at the speed of light, so Bob's part of this experiment is impossible, and no useful discussion can be had about it.

Ted will return home in six months (three months out, three months back), unless he travels at a very different speed on his return leg. This is not the same as Bob, even if we modify Bob to be doing something possible, since his journey is a year long.

Can I suggest that you check the details of your experiment? Then you may wish to look through the many twin paradox threads here for the Doppler effect resolution of the twin paradox, since it directly discusses what twins see of each other.

One comment: if you define the travel times of the travellers in the Earth frame, as you appear to have done, the answer to "how old is the stay at home" is trivial - the amount of time you chose.

 

[RandyD123]

I will edit the post...

 

[phinds]

I will edit the post...

You should also do some calculations.

 

[Ibix]

So Alice is experiences a year while Bob and Ted are travelling. What's the problem?

Edit: no, you still have the problem that one twin travels for half the time the other one does. You need to fix that.

 

[Janus]

Summary:: What is Alice's age?

Bob, Alice and Ted are all on earth. Bob leaves Earth traveling at light speed for 6 months out then turns around and heads back to earth. Effectively he has been traveling for a total of 1 light year. Ted leaves Earth at the same time as Bob but only travels at half the speed of light for 3 months then turns around to head back to earth. Both Bob and Ted should arrive back at Earth at the same time. How do they both view Alice?

To reiterate what @Ibix has said, travel at the speed of light is not possible.
But even if we change to the speeds to 98% and 49% of light speed, your analysis makes no sense.
How can Ted, who leaves at the same time as Bob and makes a round trip in half the time that Bob does return at the same time as Bob?

In addition, you don't specify who's clock is measuring the trip time. Is it being measured by the Earth, or by Bob and Ted themselves?

If you are going by each ship's time, then it is possible for Bob and Ted to leave Earth at the same time, meaure different trips times, and return to Earth at the same time.
For example, let's assume that Bob's round trip time ( according to Earth) is 6 mo, and he is traveling at 0.98c relative to the Earth. Then Bob will measure the trip as taking just under 1/10 of a year (36.3 days) by his clock.
Ted is traveling a 0.49c, again with a round trip time of 6 mo ( according to the Earth), so he returns at the same time as Bob. However, he will measure his trip as taking something over 4/10 of a year (159 days) by his clock