Twin Paradox: Travel at Fractional Speed & Instantly Return ##v##

[m4r35n357]

A traveler visits a location (or doesn't!) $x$ light years away at fractional [EDITED] speed $v$ and instantly returns at the same speed. After this her clock has progressed by $\frac {2 x} {v} \sqrt {1 - v^2}$ years. [EDITED]

That really is all there is to be said.

If the poster mentions time dilation, the question is a B.
If the poster mentions acceleration, the question is a B.

Thoughts?

 

[phinds]

A traveler visits a location (or doesn't!) $x$ light years away at speed $v$ and instantly returns at the same speed. After this her clock has progressed by $\frac {2 x} {v} \sqrt {1 - v^2}$ light years.

That really is all there is to be said.

If the poster mentions time dilation, the question is a B.
If the poster mentions acceleration, the question is a B.

Thoughts?

Yeah, my off-the-cuff thought is that clocks don't "progress by light years". That's like saying that my clocked reading moved forward by x meters

 

[Orodruin]

I understand your frustration, but it is in the nature of the forum structure that we deal with many novices who will inevitably ask similar questions. If you need a break from them, my advice is to take one and return to them if you feel the urge.

Yeah, my off-the-cuff thought is that clocks don't "progress by light years". That's like saying that my clocked reading moved forward by x meters

The units should not be there at all. They are part of the variables. See https://www.physicsforums.com/threads/differentiation-with-units-related-rates-problem.957356/

That being said, light years is a perfectly fine unit of time in a system of units where $c = 1$. It just happens to be the same unit as a year.

 

[m4r35n357]

Yeah, my off-the-cuff thought is that clocks don't "progress by light years". That's like saying that my clocked reading moved forward by x meters

Ouch! I re-read that so many times.

 

[.Scott]

With these notes:
x is measured in light-years
v is measured as a fraction of c (speed of light)
unit for the final result are year, not light years

 

[m4r35n357]

That being said, light years is a perfectly fine unit o time in a system of units where $c = 1$. It just happens to be the same unit as a year.

I really meant years of course. I think leaving the (correct) units in is helpful.

 

[phinds]

Ouch! I re-read that so many times.

Yeah, I sympathize. It's amazing the way the human brain, having once overlooked a mistake becomes blind to it.

 

[m4r35n357]

I understand your frustration, but it is in the nature of the forum structure that we deal with many novices who will inevitably ask similar questions. If you need a break from them, my advice is to take one and return to them if you feel the urge.

Not a problem, I'm just passing some time trying to distill what I consider the essentials of the scenario, that can be used to explain not just the TP, but all the so-called "variations", in a consistent way and in the absolute minimum of words and equations. Thanks to the feedback here I have already managed to delete one more word!

 

[Orodruin]

unit for the final result are year, not light years

Again, in units where $c = 1$, they are the same unit.

 

[.Scott]

If the poster mentions time dilation, the question is a B.
If the poster mentions acceleration, the question is a B.

I'm not sure what those statements mean.
It sounds as though you are responding to an exam question and that the answer should be graded down to a "B" if time dilation or acceleration is mentioned.

 

[Orodruin]

I'm not sure what those statements mean.
It sounds as though you are responding to an exam question and that the answer should be graded down to a "B" if time dilation or acceleration is mentioned.

Those are references to thread levels.

 

[m4r35n357]

I'm not sure what those statements mean.
It sounds as though you are responding to an exam question and that the answer should be graded down to a "B" if time dilation or acceleration is mentioned.

As @Orodruin pointed out, I was referring to the thread labels. I say this on the grounds that the two aspects indicate a need to understand the fundamentals properly before proceeding. I've been there myself and the only way out of that frustration is to go back and learn it properly!

 

[stevendaryl]

Off-topic, but I wonder if mathematical physicist John Baez has ever explained to his cousin, Joan, that "light-year" is a unit of distance, rather than time.

Well I'll be damned
Here comes your ghost again
But that's not unusual
It's just that the moon is full
And you happened to call
And here I sit
Hand on the telephone
Hearing a voice I'd known
A couple of light years ago
Heading straight for a fall

From "Diamonds and Dust"

 

[George Jones]

Continuing off-topic sub-thread ...

Off-topic, but I wonder if mathematical physicist John Baez has ever explained to his cousin, Joan, that "light-year" is a unit of distance, rather than time.

"A couple of light years ago"

Well, I think it works if "Hearing a voice I'd known A couple of light years ago" is replaced by "Hearing a voice I'd known So many many miles ago", so I do not have a problem with the original lyrics.

This could refer literally to a vast physical distance between two people, or, quite possibly, the author uses a physical distance as a metaphor for psychological/relationship distance between two people. Good lyrics of poetry and songs do this type of thing regularly.

 

[PeroK]

Off-topic, but I wonder if mathematical physicist John Baez has ever explained to his cousin, Joan, that "light-year" is a unit of distance, rather than time.

Well I'll be damned
Here comes your ghost again
But that's not unusual
It's just that the moon is full
And you happened to call
And here I sit
Hand on the telephone
Hearing a voice I'd known
A couple of light years ago
Heading straight for a fall

From "Diamonds and Dust"

It's called poetic licence!

 

[Sorcerer]

A traveler visits a location (or doesn't!) $x$ light years away at fractional [EDITED] speed $v$ and instantly returns at the same speed. After this her clock has progressed by $\frac {2 x} {v} \sqrt {1 - v^2}$ years. [EDITED]

That really is all there is to be said.

If the poster mentions time dilation, the question is a B.
If the poster mentions acceleration, the question is a B.

Thoughts?

Oh...now I get it. for a second I thought I wasn't the only one approaching inebriation tonight. (note: I can eternally approach that state, but never quite arrive there, due to the fact that I have too much mass)