How Much Does Samantha Age During Her Trip to Zircon?

[Heidi M]

I'm fulfilling my life-long dream of learning relativity theory by working through Taylor and Wheeler's Spacetime Physics. I've successfully made it through the first three chapters except for one problem, 1-10 on p. 23:

Samantha is beamed from Earth via a transporter to the planet Zircon (stationary with respect to the Earth) orbiting a star in the Andromeda Nebula, two million light-years from Earth. The time required for disassembling Samantha on Earth and reassembling her on Zircon is negligible as measured in the common rest frame of Transporter and Receiver.
Question: How much does Samantha age during her outward trip to Zircon?

Using the spacetime interval, the only (seemingly ridiculous) answer I can come up with is two million years. I would have guessed her to not have aged at all. I'm confused. Any help would be appreciated.

This is not homework. (I only wish I were back in school...)

 

[George Jones]

I'm fulfilling my life-long dream of learning relativity theory by working through Taylor and Wheeler's Spacetime Physics. I've successfully made it through the first three chapters except for one problem, 1-10 on p. 23:

Great!

How is Samantha beamed?

 

[yuiop]

Using the spacetime interval, the only (seemingly ridiculous) answer I can come up with is two million years. I would have guessed her to not have aged at all. I'm confused. Any help would be appreciated.

The spacetime interval for information beamed at the speed of light is zero. Assuming Samantha is disassembled and only the information that is required to reassembler her is transmitted in the form of light waves, then your original hunch that she does not age at all is correct. That makes sense because she would be reassembled in the exact same state as when she was disassembled (if all goes to plan). So, as George said "How is Samantha beamed?".

P.S. The spacetime interval ds is (essentially if we ignore the c^2 scale factor) the proper time measured by a (possibly hypothetical) clock that is transported a distance dx in a time interval dt. When dx = dt as is the case for something moving at the speed of light, the spacetime interval ds = sqrt(dt^2-dx^2) = 0.

 

[Heidi M]

The problem states: "Assume that one thousand years from now a Transporter exists that reduces people and things to data (elementary bits of information) and transmits the data by light or radio signal to remote locations. There a Receiver uses the data to reassemble travelers and their equipment out of local raw materials."

I was thinking that the time between events in the Earth frame is zero (I misinterpreted the problem), but now I see that there would be 2 million years between Samantha's disassembling and reassembling. And in Samantha's frame the time is zero.

 

[Heidi M]

Thanks for all of your help and for your clear explanations. I appreciate it.

 

[yuiop]

I believe I've answered my own question.

But, I don't know...I'm just learning...

For what its worth, I believe you have too

Thanks for your help. It's all clear to me now.

Your welcome :)

 

[Heidi M]

By the way, I am so impressed with the expert advice and prompt responses on this site. Thanks again, and thanks a million!

 

[yuiop]

By the way, I am so impressed with the expert advice and prompt responses on this site. Thanks again, and thanks a million!

Ah, it was nothing really. You should see some of the technical responses by real experts like George. Now that would blow your mind!