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[help] Special relativity, reference frames and timekeeping - Lakeshore — LiveJournal
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Jay Lake
Date: 2010-12-01 18:12
Subject: [help] Special relativity, reference frames and timekeeping
Security: Public
Tags:help, science
So I'm noodling a bit more of special relativity into my poor, ageing, liberal arts educated brain, via (among other things), posts such as this one. (The first few dozen comments are excellent, btw. After that the thread starts breaking down.)

What got me rattling down this track was the problem of timekeeping across astronomical distances. Since reference frame is a critical concept, is it reasonable to have your clock so far away that it stands outside significantly enlarges your reference frame?

For example, let us posit a pulsar 30,000 light years distant. Let us further posit that its periodicity is slowly lengthening, by a degree both measurable and predictable. Say that I know from a certain zero point, say, Earth on a given day and time, what the periodicity is. Then, some arbitrary amount of time later, having moved at relativistic or supraluminal speeds to an astronomical distance, I measure my beacon star's periodicity again. I then calculate backwards (or, potentially forwards) from my known zero point reference.

Have I in my new, arbitrary location now established the time at my zero point? Ie, have I synchronized my clocks?

I am absolutely certain there is at least one serious error here, but I can't see it yet. I'd appreciate comments that might correct this idea, or references to more successful examples of this kind of thinking.

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David D. Levine
User: davidlevine
Date: 2010-12-02 02:41 (UTC)
Subject: (no subject)
My relativity-fu is not all that strong, but in this case I think that yes, you can calculate the "current" time at the zero point, but that information is not useful. (I put scare quotes around "current" because there's no such thing as simultaneity in an Einsteinian universe.)

Here's what I think is a comparable example, which doesn't require relativistic or superluminal speeds and thus might be easier to grok: if you measure the distance between here and a certain star as exactly 40 light-years, you know that the time "now" at that star is exactly 40 years earlier than your current clock-calendar. But so what? You can't use this information to communicate, and it doesn't tell you anything about the current state of affairs on that distant star other than what time it would have been on your clock-calendar if you'd been there then. (The star could already have exploded or gone out; you won't know for another 40 years.) This is part of why there's no such thing as simultaneity -- because no information can be exchanged faster than light, distant objects are always seen as they were and never as they are.

Does this help?
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Jay Lake
User: jaylake
Date: 2010-12-02 03:01 (UTC)
Subject: (no subject)
Yes, it does help. Thank you.

I also realize that I left out a problem condition, however. This is a universe with FTL, so there is simultaneity/causality violation implicit in the story. Ie, it may be useful to know what the time is back at the zero point.
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(no subject) - (Anonymous)
Jay Lake
User: jaylake
Date: 2010-12-02 04:01 (UTC)
Subject: (no subject)
[second try at reply, LJ ate my last one]

Handwaving is the SF writer's best friend. And thank you for the comment on the interval timing.
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Max Kaehn: Science!
User: slothman
Date: 2010-12-02 02:42 (UTC)
Subject: (no subject)
Keyword:Science!
You also need to measure the spectrum of the pulsar (for red or blue shift) to make sure that you have the same relative velocity to the pulsar after as before, or your measurement of the pulses is going to vary due to time dilation and skew your results. (There may also be very subtle general relativistic effects if you’re in differing gravity wells, but I don’t know if the magnitude of that effect is going to matter for this.) Once you’ve done that, you know the time at which the light left the pulsar. You can triangulate against other features to get your distance to the pulsar, so you know when you are as well.
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Tom
User: voidampersand
Date: 2010-12-03 03:28 (UTC)
Subject: (no subject)
Roughly, yes. You need to account for the fact that all stars are moving, including the beacon. Over longer periods of time, the movements are less predictable. You should be able to get your relative velocity from the red/blue shift in the spectra of the star. Then you can normalize the periodicity and figure out when and how far away you are (those being the same). Repeat with several beacon stars in different directions and you should be able to eliminate errors due to imprecision and unexpected changes in the location, velocity, and periodicity of the stars.

This is assuming the beacons are not moving relativistically. Let's say that while you are traveling, some joker accelerates your beacons to relativistic speeds back and forth at a 90° angle to your path. When you come out, it appears that the star's periodicity has slowed (because of its time dilation) and you think you are farther away than you really are. Then when it stops moving, it appears to speed up and you seem to be closer than you really are.

Does it matter what the universal time is? The time you get up for breakfast is local shipboard time, or planet-side it's going to be sometime around local dawn. The next time you need to get your teeth cleaned is when enough local shipboard time has elapsed. (I have an awesome idea for a story called "Semle's Dentist" but nobody wants to buy it.) The time you meet that other ship is whenever you're both in the same place. The time that the interest has been accruing on your savings account is going to be the local time measured by the banker. Try to convince her otherwise -- she's not going anywhere.
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