Relative values & GPS

Stop bletherin' oan aboot ma hat .. what I really want to know is:

Can I sail my boat really fast round the world and sell it as a new one and then catch a plane the other way, buy an old boat and sail it back really fast the other way and have a new for old for new for old?

<hr width=100% size=1>.. whit way roon should it be again ..
 
ERRrrr,.....No but you can have a lie down in a quiet dark room until this star trek syndrome passes!! /forums/images/icons/wink.gif

<hr width=100% size=1>Someday my ship will come in, and with my luck I'll be at the airport!!
 
Jimi is correct, the difference in time between the two clocks will tell you your distance away from the one you left behind. So it would put you on a position circle. Add another fixed clock somewere else and you would have a fix - or actually 2 possible fixes where the circles cross. Decide which of the 2 possible places you are in by guesswork, or heads/tails with a coin.

What you are thinking of is that if you go at close to the speed of light, your distance from the clock you left behind is increasing so rapidly that the one you left behind will appear to you to be running slow compared to the one on the boat, as its delay is always increasing, so even though they are precise atomic clocks, it will appear to loose say a few seconds every day compared with the clock on the boat.

Would need to be a bloody fast boat maybe, something like what that Ellen McArthur sails, and not for us normal mortals.

Chris

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"Jimi is correct, the difference in time between the two clocks will tell you your distance away from the one you left behind. So it would put you on a position circle. Add another fixed clock somewere else and you would have a fix - or actually 2 possible fixes where the circles cross. Decide which of the 2 possible places you are in by guesswork, or heads/tails with a coin."

But why? You have no reference to your local time - you're locked in the cabin with the clock. The clock in your cabin doesn't give you local time, it gives you the time it was set to before it was given to you. You have no accurate method of working out what your local time is, and therefore calculating the difference between your local time and the reference time provided from the central atomic clock.

Furthermore, even if you could use this method, I don't see any method of working out latitude.

Think of it like this: you fly to New York, check into a hotel, and go to sleep. You wake up, the curtains are drawn, you look at your watch and see that it says 8am. You're a bit groggy, and you've forgotten where you are. Do you have any evidence from your watch that you're in NY? No. You fire up your laptop, and look at your homepage, which is a UK based homepage. The clock on this homepage gives you London time. From the time displayed on your laptop, and the time shown on your watch, is there any information that lets you work out where you are? Again, no. Only when you look at the bedside clock, which reads 3am, do you see that you're 5 hours, and therefore about 75 degrees west of London. And then, even if someone gives you another clock, which says "Pacific time" on it, and shows 11pm, you still have no idea whether you are in NY, Connecticut or Brazil - you have no method of determining latitude. You know that you're five hours behind London, and four ahead of California, but more than that you can't say.

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Possible but not probable

Or maybe you'd die from radiation sickness, carrying that atomic clock around with you all the time.

BTW - anyone hear Melvyn Bragg's radio prog about Rutherford this morning - good stuff for a peasant like me.

<hr width=100% size=1><A target="_blank" HREF=http://www.writeforweb.com/twister1>Let's Twist Again</A>
 
OK here goes with a long answer - Jimi said

"you are locked in a a cabin in a ship travelling at a constant speed with an atomic clock, and a sophisticated computer capable of receiving a land based atomic clock signal. "

The signal transmitted from the land based atomic clock is always travelling through the air at the speed of light to you. If you are further away from the land based clock, it will take longer for the signal from it to reach you than if you are close to it.

Using the hotel in New York analogy - as well as looking your watch on London time, you can phone the speaking clock in London. And lets suppose that you syncronised your clock with the speaking clock before you left London, and both clocks keep perfect time. If you called the London speaking clock from your hotel you would think that it was slow - because takes a certain amount of time for the signal to travel down the phone network and reach you.

If you measure how slow the London clock is, and know the speed phone signals travel at then distance = speed * time so you know how many metres the pip of the speaking clock in London has travelled to get to you. From the delay you can calculate the length of the path from London (OK with phones the path taken is quite unpredictable and can vary from call to call. There are also unpredictable repeaters and so on in the circuit so this won't really work very well in practice!).

Now you now know that you are a certain distance, lets say 2500 miles from London. Suppose that there was a 2nd speaking clock that you could phone in Sydney, then you could also measure your distance from that one in the same way, and suppose it comes out to be 9000 miles. Now you look up in your Atlas (assuming you remembered to pack one!) which places are 2500m from London, and also 9000m from Sydney and you find that New York is one of two (I think!) candidates in the world. If you knew also that the plane had been flying slightly south of west during the flight you could eliminate the other candidate. You have found out that you are in NY. You'd be doing well to do all of this with the jetlag though!!!

The practical problem with this is that many ways of transmitting the signals from the fixed clock introduce rather unpredictable paths to you - for example radio waves can curve around the earth or bounce off the ionosphere.

But I still think it can be done without local time, since reference points you are measuring are all on the earth, and therefore the earth's rotation doesn't matter.

Chris

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Chris, I think you're wrong. As I understand it if I keep on travelling around the world and arrive back at the atomic clock (which had been synchronised) the time will now be out of sync due to the fact that the moving clock has had accelerated motion applied to it relative to the static one and therefor would indicate a time and derived distance difference. Therefore the clocks have time travelled relative to each other although they are now back in the same place spatially.

Or is this all just bollocks?

<hr width=100% size=1>.. whit way roon should it be again ..
 
I propose an experiment!

Jeez, now you've got me worried. I did do a degree in Physics (perhaps shouldn't admit that here in case I am wrong!!!!) but have never used any of it and forgotten almost all that I ever learnt! So the chances of me being wrong are high... I have a nasty feeling what you are saying is correct. But I still have an alternative theory....

My understanding was that the slip depends on the relative speed betwen yourself and the starting point. So in the travelling around the world example, the fixed clock seems to slow down as you move away from it but then speeds up as you move back towards it, so that when you end up back at your starting point the clocks are back to being aligned again.

Anyway there is no way that we are going to resolve this with theory - the only way forward is to buy a couple of atomic clocks on Ebay and get that Paddy bloke with the Coribee to race around the world with one of them. We will of course hack off his slow old bilge keels and replace them with a fin to ensure sufficient speed. To make it more interesting, how about a little bet on the result?

Chris

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I have to admit that I had thought that this effect only really starts to show noticiably when you start to reach speeds near the speed of light, but it looks like I'm wrong on this.
http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/airtim.html

However, this brings us back to the other major problem - how do you know what time is shown on the reference clock? The signal being sent to you isn't arriving on instantaeously - its travelling at the speed of light. The thing is, you have to remove the time taken for the signal to arrive to you in order to show the difference between your clock and the reference clock. Given the size of the differences between the clocks - of the order of nanoseconds, or shorter, by the looks of things, the time the signal takes is significant.

You know the speed it's traveling - the speed of light, but you don't know how far its traveled.

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The assumption is that the two clocks were initially synchronised and are running at the same rate. If one sends out a radio signal at a pre-specified time, the other will receive it at a slightly later indicated time. The apparent delay is the time taken for the signal to travel at speed-of-light between the two stations. Since the delay and the speed are both known, the distance can be calculated.

Incidentally, I understand that the rate of the GPS satellite clocks is adjusted to allow for the effects predicted by relativity theory.

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Well, that's a new way of doing it - most of this thread seems to be thinking about time/space relativity type thinking.

The problem with your method though is that we don't know the exact altitude the HF beam is reflecting. Given that each band of the ionosphere is tens of kilometres thick, we can't tell if the beam is reflecting fewer times from a higher altitude, or more times from a lower one.

The very fact that caesium clocks have been around a while, but that nobody seems to have tried to put a method like this into practice makes me believe that it isn't practically possible. AIUI, nav for commercial shipping moved directly from celestial (and RDF/Loran/Decca when possible) to Satnav then to GPS.

Ah, well. I suppose the real question is: when we set off on this voyage, do we sail away from the shore, or does the shore move away from us?

And is the cat locked in the focs'le dead, alive, or some strange mixture of the two?

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Just strugging through "The Elegant Universe" by Brian Greene. Well recommended!

<hr width=100% size=1>.. whit way roon should it be again ..
 
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