Confused about this blueshift/redshift paradox

[kamenjar]

Confused about this blueshift/redshift "paradox"

Say you had a light probe with a sensor that converts light energy into electricity and and uses electricity generated to draft a chart of energy converted on paper.

Now you send the probe on a 1 LY round trip. The probe has an internal drive that accelerates it (fast) it to relativistic speeds, decelerates (fast) and the same thing on the way back. The probe spends most of the trip near light speed. The whole round trip takes time T in Earth time. The probe takes less but for it is also some probe proper time T and moment of turnaround is Tproper/2 (right?)

You send the probe and immediately start shining that green light at it.
After exactly T/2 time, you stop for one second and you continue to shine the light at the probe.
When the probe returns you see a chart like this (now correct me if I am wrong):
t=0 to t= T/2 (Low energy) - Most of the trip is redshifted light
T/2. (Normal energy) , stop, normal - probe turns around at 1LY away and registers you turning off the beam shortly and back on
T/2 to T. (High energy) - most of the trip is blueshifted light

Is this assumption correct? If so, what does it tell us?
If the paradox is not obvious - The total energy registered on the way back is more than the energy on the way to the destination.

 

[JesseM]

Say you had a light probe with a sensor that converts light energy into electricity and and uses electricity generated to draft a chart of energy converted on paper.

Now you send the probe on a 1 LY round trip. The probe has an internal drive that accelerates it (fast) it to relativistic speeds, decelerates (fast) and the same thing on the way back. The probe spends most of the trip near light speed. The whole round trip takes time T in Earth time. The probe takes less but for it is also some probe proper time T and moment of turnaround is Tproper/2 (right?)

Right, as long as the probe's speed relative to Earth is the same on both legs of the trip.

You send the probe and immediately start shining that green light at it.
After exactly T/2 time, you stop for one second and you continue to shine the light at the probe.
When the probe returns you see a chart like this (now correct me if I am wrong):
t=0 to t= T/2 (Low energy) - Most of the trip is redshifted light
T/2. (Normal energy) , stop, normal - probe turns around at 1LY away and registers you turning off the beam shortly and back on

But the probe is a great distance away, it won't register you turning the light off and on until that gap in your beam has traveled at the speed of light to reach the probe, which won't happen until after T/2 in your frame (and after Tproper/2 for the probe).

If the paradox is not obvious - The total energy registered on the way back is more than the energy on the way to the destination.

This is true but not really a paradox--if you were sending out regular pulses rather than a continuous light, the probe would receive more signals on the way back than the way out, so it'd also receive more energy on the way back. Look at the right-hand diagram in this image from the twin paradox FAQ:

 

[kamenjar]

Ahh right, the guy on Earth would have to flicker the beam earlier than T/2, which brings me to the original idea I had:

If you wanted to use Beam Propulsion for interstellar travel, you could do something like this:
- Send a tiny nanobot that can replicate to the target (you can accelerate it pretty well due to low mass)
- Have it build more nanobots from some resource to build a Dyson sphere or mirrors.
- Harvest the target stars energy to start a beam of parallel directed light and send it then, wait for it to reach the source

As opposed to sending a beam from source, to travel to the target it would be much easier for the payload to accelerate - because the beam's energy over say 20 years for 20 LY distance will be stored in space like a capacitor. As the payload accelerates drastically as it benefits more from the blueshifted beam, so acceleration would be probably be linear or exponential in its proper time.

Makes sense?

 

[JesseM]

Ahh right, the guy on Earth would have to flicker the beam earlier than T/2, which brings me to the original idea I had:

If you wanted to use Beam Propulsion for interstellar travel, you could do something like this:
- Send a tiny nanobot that can replicate to the target (you can accelerate it pretty well due to low mass)
- Have it build more nanobots from some resource to build a Dyson sphere or mirrors.
- Harvest the target stars energy to start a beam of parallel directed light and send it then, wait for it to reach the source

As opposed to sending a beam from source, to travel to the target it would be much easier for the payload to accelerate - because the beam's energy over say 20 years for 20 LY distance will be stored in space like a capacitor. As the payload accelerates drastically as it benefits more from the blueshifted beam, so acceleration would be probably be linear or exponential in its proper time.

Makes sense?

Well, if the issue with long-term space travel was just power, having a blueshifted beam would be useful, but I always thought the issue was with propulsion--to accelerate forward you have to either expel matter out the back (bringing a lot of fuel on board) or be pushed by something traveling in the same direction as you hitting you from the back. In this sense I don't think having a beam sent towards you from the target you're trying to get to would be helpful.

 

[Mentz114]

In this sense I don't think having a beam sent towards you from the target you're trying to get to would be helpful.

Too right. If you're flying into it, it will resist your motion.