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If you’re on Alpha Centauri 4 light years away and head home to earth at 80 percent of the speed of light ?
Before you head straight for earth at 80 percent of C, you will see the earth as it looked 4 years ago as earth light 4 light years away.
But the instant you hit 80 percent of Light speed and head for Earth from the star ....your Lorentz transformation is 1/0.60
I think the line of simultaneity jumps 3.2 years into the future for traveler at the velocity change and the distance between you and earth contracts by 60 percent to 2.4 light years instead of 4?
At the moment does this mean you will see the light of earth not 4 years ago but now the light of 3.2 minus 2.4 light years instead of 4 drip so a 4.8 years skip ? What am I missing?
- DixonLv 71 month ago
There seems to be some disagreement here, so check out the short and very readable Wikipedia paragraph explaining exactly what you suggest as the resolution to the twins paradox. It has a nice diagram and ends with,
"When one transfers from the outgoing inertial frame to the incoming inertial frame there is a jump discontinuity in the age of the Earth-based twin"
I haven't checked the numbers but that sounds generally correct to me, ie there are a bunch of Earth events you just never see and Earth skips ahead for you. Of course this doesn't actually happen due to the impossibility of an instantiations step change in velocity.
The “line of simultaneity” for the traveler is the locus of spacetime events at a constant time for the traveler. This is a space-like (ds^2 < 0) line.
The traveler doesn’t have causal connectivity along that line and CANNOT see anything or get information about anything along that line as they travel.
The speed of light as a limit to information travel prevents anything weird happening such as causal access to the past or future of any other reference frame, even though the traveler’s ‘present’ intersects the past or future of other frames.
Nothing "jumps" in the timeline. On the way back you would witness history faster is all.
- MorningfoxLv 71 month ago
You can see only the things right close to you. You can't see the Earth, you can only see the light from Earth. The only jump is in the RATE of events on Earth, as the light reaches your eyes. Before you left Alpha C, that rate was the "normal" 1 second (Earth time) per 1 second (your time). When you hit 80% c, that rate jumps so that you see 9 years of Earth events, in only 3 years of your time.
4 light years at 0.8 c = 5 years of Earth events while you travel
+ 4 years of light traveling to you from previous events
= 9 years of events.
4 light years at 0.8 c at Lorentz 1/0.60 = 3 years travel time, subjective to you.
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- billrussell42Lv 71 month ago
no, when you start your journey, you will see light from earth 4 years ago. Nothing to do with your speed.
you velocity and contraction has nothing to do with how long it takes light to travel 4 LY. That time is fixed at 4 years.
now as you travel, you will see a blue shift in the light and the 4 years will be compressed to 4/1.67 = 2.4 years.
at 0.8c, 2.4e8 m/s, γ = 1.67