Settle a bet on time and distance.

[hazzatori]

Hear is my first post and go easy Hawkins i aint! but its to settle a little bet at work.

Lets say i am stood in a Universe that obeys all of the laws of physics as our own, no differences at all,

but all that is in this Universe is

1 Platform with a 12 hour clock face on it

and

1 Giant 12 hour clock face

both are synced to same time.

(oh and and some light so we can see, O2 so we can breath etc)

when i stand on the platform for the first time time starts, when i step off time stops

The distance from the platform to the clock face is exactly 1 Light Year, but the clock is so large all i can see in my peripheral vision is the clock face.

Am i right in believing that firstly, it would take me one year from stepping on the platform to even see the clock face?

then as i do see it and as it is precisely 1 light year away, i would see the time on both clock faces as exactly the same time in fact they should even tick over precisely.

then if the platform moves closer to the large clockface the times would not stay synced or would they?

 

[jbriggs444]

This probably belongs in the Special Relativity forum.

So you have two clocks. They are one light-year apart. The far clock is big enough to be seen from that distance. The two clocks are synchronized.

By convention, we take this to mean that the clocks are synchronized in the frame of reference within which they are both at rest. Also, by convention, the synchronization is such that the measured speed of light, timed with the use of the two clocks is judged to be the same going from near clock to far as from far clock to near.

You step on the platform with the near clock. No, it does not take you a year to see the far clock. You see it immediately. It had been illuminated a year ago and light reflected from past illumination is continuously arriving at the near platform. The light is all ready for someone to step up and start seeing it.

You would see the time displayed by the far clock showing a date and time as of one year ago. That's when the light from that year-ago reading left from the far clock's face.

The fact that the clocks are synchronized does not mean that you _see_ both displays showing the same time. It means that _once you account for speed of light delays_, both displays would show the same time. That's part of the standard convention for synchronization.

If the one clock is moved _slowly_ to the other you would find that the two clocks show the same time when they meet and that it does not matter which is moved to the other.

If one clock is moved _rapidly_ to the other you would find that the clock that was moved shows a time that is one year stale as compared to the clock that was not moved.

"slowly" is in the limit as the clock transport speed decreases toward zero.
"rapidly" is in the limit as the clock transport speed increases toward light speed.

In between the high speed and low speed limits you would find that the clock that moved is stale, but not a whole year stale.

 

[Naty1]

What does this mean:

1 Platform with a 12 hour clock face on it...

The distance from the platform to the clock face is exactly 1 Light Year...

 

[mrspeedybob]

when i stand on the platform for the first time time starts, when i step off time stops

This is a little ambiguous, and the different ways it should be interpreted affect the answer.

It could be interpreted to mean that each clock starts when it's detector sees you step onto the platform. In this case you will see the distant clock 2 years behind. It takes 1 year for the signal that you stepped onto the platform to reach the clock, and another year for the light from the clock to reach you after it starts ticking.

Now suppose there is a big "go" light on the far clock. The clock starts ticking at the same time the "go" light turns on. You step onto the plate when you see the go light turn on. In this case you see both clocks tick in sync.

Now you did leave the option to interpret the whole thing as a trick question. You stated the distance to be exactly 1 light year and you specified a 12 hour clock face. Based on a year that is exactly 365 days long you would see the clocks tick in sync regardless. It would depend on the specific interpretation weather you see the far clock start ticking at the same time, 730 hour hand revolutions later, or 1460 hour hand revolutions later. In any case, once you see them both start ticking they should read the same time and tic in sync.

 

[pmacias]

Thank you for your interesting question! Based on the scenario you have described, it appears that the platform and the large clock face are both stationary in this universe. In this case, time and distance are completely relative to the observer's perspective.

To answer your first question, yes, it would take you one year from stepping on the platform to even see the clock face. This is because light travels at a constant speed of approximately 186,282 miles per second, which is equivalent to one light year in distance. So, it would take one year for the light from the clock face to reach your eyes.

As for the second question, yes, you would see the time on both clock faces as exactly the same time. This is because time is also relative and is affected by the observer's frame of reference. In this case, since both the platform and the clock face are stationary, the time would appear to be synchronized and would tick over precisely.

Now, if the platform were to move closer to the large clock face, the times would still appear to be synchronized to the observer on the platform. However, to an outside observer, the times may appear to be slightly different due to the effects of time dilation. This is a phenomenon in which time appears to slow down for an object in motion, as predicted by Einstein's theory of relativity.

In conclusion, in this universe where everything is stationary, time and distance are relative to the observer's perspective. The times on both clock faces would appear to be synced and would tick over precisely, regardless of the platform's distance from the large clock face. I hope this helps settle your bet at work!