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TechBear_Seattle Donating Member (1000+ posts) Send PM | Profile | Ignore Sat Jan-10-09 11:54 PM
Original message
Question about light speed and relativity
I'm trying to work out some possible complications of relativistic sub-light travel for a story. Here is the scenario: A space ship is holding a position that is relatively stationary to you, 20 light minutes away. The beam from a comm laser -- a communications device using coherent light as a carrier wave -- will take 20 minutes to travel that distance.

Suppose the ship is moving directly away from you at 50% of the speed of light. If the laser is fired when the ship is 20 light minutes away, will it still take 20 minutes to reach the ship, correct? This despite the reasoning that for every one light minute the laser travels, the ship has gotten farther away by 30 light seconds. Likewise if the ship is moving directly towards you, correct?
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Orrex Donating Member (1000+ posts) Send PM | Profile | Ignore Sat Jan-10-09 11:58 PM
Response to Original message
1. I think it depends which way the wind's blowing
Other than that, I believe that you're right. Same time to cover the same distance.


Though I admit that I would be happy to be corrected, if wrong.
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man4allcats Donating Member (1000+ posts) Send PM | Profile | Ignore Sat Jan-10-09 11:59 PM
Response to Original message
2. My best guess is
you're not gonna get a lot of takers on this one. :D
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man4allcats Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Jan-11-09 12:23 AM
Response to Reply #2
15. Then again,
I could be wrong.
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Jamastiene Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Jan-11-09 12:03 AM
Response to Original message
3. Use a flashlight. n/t
:evilgrin:
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BrklynLiberal Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Jan-11-09 12:11 AM
Response to Original message
4. Excellent question. I think I will not give you the answer, but let you figure it out yourself..
:rofl: :rofl: :rofl: :rofl: :rofl: :rofl: :rofl: :rofl:



i.e.
I have no idea....
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Howzit Donating Member (918 posts) Send PM | Profile | Ignore Sun Jan-11-09 12:12 AM
Response to Original message
5. By the time the light gets to the ship,
wouldn't it have moved 10 light minutes further away? If so, the message will start reaching it after 30 minutes...
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Sinistrous Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Jan-11-09 12:13 AM
Response to Original message
6. I have a limited understanding of relativity, but I believe the answer is
yes. The speed of light is independent of the velocity of its source.
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RJ Connors Donating Member (679 posts) Send PM | Profile | Ignore Sun Jan-11-09 12:15 AM
Response to Original message
7. Let me see if I have this straight
In the first part of the question you are talking about a space station and a ship that are traveling at the same rate of speed so therefore holding a continual non moving position. But in the second part you are talking about a ship and a space station in which the ship is moving away from the space station.

So, if the ship fires the beam when it is at a point that is 20 light minutes away it doesn't make any difference that it is moving away from the space station as the demarcation point, the point where the beam is fired, is the sum total of the distance the wave will have to travel.

However, this is if we are talking a single burst of information that is being sent to the space station. If you are talking about an on-going conversation, while the ship is moving away, the time period of travel will become larger and larger. However, it is a know fact in interstellar communications of this type the the light wave carrier companies have built in buffers and dampeners into their signal so you will not experience any disruption or static in you service even though at the time you happen to be a body in motion.
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kristopher Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Jan-11-09 12:16 AM
Response to Original message
8. Don't know the answer, but shouldn't you specify where the clock is? nt
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Incitatus Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Jan-11-09 12:16 AM
Response to Original message
9. try here
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baldguy Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Jan-11-09 12:17 AM
Response to Original message
10. The signal will still take 20 min
but it will be red shifted due to the Doppler effect.
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Believing Is Art Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Jan-11-09 12:18 AM
Response to Reply #10
12. Doh!
You're right, redshifted
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TechBear_Seattle Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Jan-11-09 12:24 AM
Response to Reply #10
16. That is what I was missing!
Relative motion is irrelevant to the time interval, but it will compress or stretch out the frequency of the light. Thanks!
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anigbrowl Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Jan-11-09 10:20 PM
Response to Reply #16
44. And it's wrong - see #43. Although yes, it tiwll be red-shifted.
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Believing Is Art Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Jan-11-09 12:17 AM
Response to Original message
11. close enough
Neglecting negligible atmospheric effects, 20 minutes, I think the only difference moving would make would be blueshifting, but I could be wrong.
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Kurt_and_Hunter Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Jan-11-09 12:22 AM
Response to Original message
13. The light is independent of the ships movement
Edited on Sun Jan-11-09 12:22 AM by Kurt_and_Hunter
So no matter how fast a ship is moving away from you the light will travel at C... can't accelerate light. It will have a massive shift in wavelength from your perspective, but C is C.

So the moving ship to you will take 20 minutes.

But from you to the moving ship it would take longer--when the light reaches the 20 light minute mark the ship has gone another 10 light minutes away and that physical gap must be covered.

(The light-speed sequence in rendezvous with Rama is unforgettable when they disarm the bomb while the people watching on TV are trying to fire the bomb.)
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TechBear_Seattle Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Jan-11-09 12:26 AM
Response to Reply #13
18. That had to do with straight distance, not relative motion
The events were happening about 30 light minutes away from Mercury, if I recall, and half an hour is a half an hour. :hi:
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Kurt_and_Hunter Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Jan-11-09 12:34 AM
Response to Reply #18
20. Yes. Just remembering a nice plot effect, not drawing an equivalency
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BlooInBloo Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Jan-11-09 12:22 AM
Response to Original message
14. The Lorentz Transform is your friend here, I think.
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RandomThoughts Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Jan-11-09 12:25 AM
Response to Original message
17. This would be my guess.
I think you are asking if a Doppler effect would also work with light.

In each instance the light that is traveling will take the time it takes based on distance between the source and the receiver. If you think of it as many events like pearls on a string, with each pearl being a photon, you can still get a Doppler shift without the speed of light of any of the photons changing. When moving away, they are spaced further apart, when moving closer they are squished closer together.

so since the ship is in motion, the wavelength of the light will shift. Each photon of light takes the proper amount of time based on when it was emitted. But the com frequency would be Doppler shifted. Red moving away, blue moving closer I think.

So light never changes speed, but the emission source at different ranges creates a Doppler effect.

It should be noted, that both the sender and receiver will believe the photon of light took 20 minutes to travel.

But that will be in their own relative time.

look at formula distance = speed / time

since speed of light can not change, the time must change to make the formula work, the only way this can happen is if different things moving at different speeds have their own 'time'

So if the guy is moving away at 50% of speed of light, The only way light can reach target in his perception is for his time to be moving slower, or from his perception the time of the receiver is moving faster.

moving guy wants to think distance = (speed - his speed) / time. But the speed of light is constant. Normal laws would say that emitting light should be effected by his speed. But each photon still leaves his ship at same speed. so distance = speed / time modified.

The only way the assumed receiver watching this could also see the light moving at same speed as the guy moving away at 50% speed of light, is for them to be living in different measures of the passing of time.

There could be an argument that distance changes not time, interesting thought, but it would require a really wild interpretation of 'space' and I don't know if it would match other equations in his formulas, but it would be fun to try and visualize a reality where time does not get distorted but the actual distance between units is changed in perspective. So when things move they get smaller or bigger, giving the mover a different perspective of the distance, adjusting for the effect of time. Just a fun thought, thinking about it, there could be a fun story in this if done right. Doubt it would be mathematically sound, but that could be the story in it.

(His equations do equate a mass change, and a stretching, but I very much doubt he tried to say that actual distance changed based on a perception of one or the others size)

Anyway, fun question, but this is just my understanding of it, how I think about it, could be different then how others think about it.
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TechBear_Seattle Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Jan-11-09 12:30 AM
Response to Reply #17
19. I've seen hard sci-fi writers disallow relativistic communications completely
I'm finishing up Spin State by Chris Moriarty right now; inability to communicate with a ship travelling at relativistic speeds from Earth to Saturn is a minor but important plot point. I'm trying to decide whether to follow that course or to allow some types of comm.
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Kurt_and_Hunter Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Jan-11-09 12:39 AM
Response to Reply #19
21. Hmmmm... why couldn't you communicate?
If you painted a billboard on the sun they'd be able to see it, and that is really no different from any other electromagnetic signal.

Granted, there are speeds and distances where they'd be to Saturn already before a signal could overtake them, but assuming the time&distance are okay I don't know they couldn't get a signal.
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Gore1FL Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Jan-11-09 12:55 AM
Response to Reply #21
22. Of course the time it took for the sun's light to reach them
would be longer than from the earth (assuming the ship was on the same side as the earth) and you'd have to add another 8 mins to get the signal to the sun billboard.
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Gore1FL Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Jan-11-09 12:55 AM
Response to Reply #22
23. Of course you could use tachyons or subspace,
Then you get to write your own physics.
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TechBear_Seattle Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Jan-11-09 01:13 AM
Response to Reply #23
25. I'm trying to create as little of my own physics as possible
In my universe, a discovery about how the universe is constructed (well, probably constructed; we can't test it directly) has led to the three techs that I want: "cold" fusion, relativistic sub-light travel and FTL interstellar travel. Now that I have those, I would like to keep physics as standard as possible.
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qazplm Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Jan-11-09 12:16 PM
Response to Reply #25
32. if you have FTL travel
couldnt you send a "message in a bottle" that would end up being faster than a signal at light speed?

You'd simply build beacons with your message encoded and give it an FTL drive.

So you want to communicate with something say an hour away, but your FTL drive can get you there in say 20 minutes.

Record your message, put it in a FTL Beacon, fire it off, and it pops out and broadcasts it's message.

Doesn't violate any rules of your fictional universe and would seem to be a means of quasi-FTL communication.

My only other thought is that FTL drives might be very expensive or very large or both and thus could require such a thing to be saved for the greatest of needs but one would think you could re-use them for both ends of the trip.

In my example, you could have a message and reply and a re-reply in the time you'd receive the first message sent out at light speed.
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RandomThoughts Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Jan-11-09 01:08 PM
Response to Reply #32
34. You totally had the same idea as me.
I posted mine without reading yours.

But drop messaging between mini warps, was same thing I was thinking, even had the buoys like you did.
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TechBear_Seattle Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Jan-11-09 05:43 PM
Response to Reply #32
39. The smallest possible FTL ship would be 1.25 km in diameter
Basically, it would be a central sphere about 250 meters in diameter to hold the fusion reactor and a store of helium fuel. The reactor powers an energy "bubble" of altered dimensions a few Plank lengths thick above the surface scaffolding of the ship; this bubble defines the boundary of the universe inside the ship and the universe as a whole. When the ship is under way, normal spacetime kind of flows around the ship and reconnects without a ripple behind it.

It does happen that, occasionally, a piece of matter will go through the bubble, causing it to reconfigure briefly to match the altered dimension, then snap back to normal as it passes back into the normally formatted universe inside. Weird things happen when this occurs: it is not good for quarks to change from red, green and blue to vermillion, chartreuse and aqua. The resulting Yakazumi-Zellerhoff (or "why-zed") radiation is short lived but hazardous to a wide variety of materials. Because of this, safety protocols require a minimum of 200 meters of dead space between the inner surface of the bubble and anything other than internal scaffolding, and at least 500 meters between the inner surface and any organic materials, inhabited modules or essential systems such as the fusion reactor.

So basically, I want FTL travel to be expensive and somewhat dangerous, under the control of a mega corporation; think of the Spacer Guild from the Dune books. And I want the few inhabited systems (human habitable worlds are pretty rare) to be effectively on their own, isolated from all other human culture except for the regularly scheduled FTL vessels which park outside the star's heliopause to transmit and receive data and take on and dispatch cargo pods that will take another three to four weeks to transit the system.

And I want it this way because. :hi:
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TechBear_Seattle Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Jan-11-09 01:03 AM
Response to Reply #21
24. The usual rationale is differing timeframes
To a person on a craft travelling at relativistic speeds, time outside the ship seems to speed up. To a person outside the craft, time inside the ship seems to slow down. The net result is a craft that leaves earth for 50 years and returns with a crew that is only a few months older.

Everything that is in relative motion has a different timeframe. At "normal" speeds -- say, a jet flying from Seattle to London -- this difference is a few microseconds. At higher speeds, this difference becomes significant. Go fast enough, and things are too out of synch for communication to be possible.
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RandomThoughts Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Jan-11-09 01:15 PM
Response to Reply #24
35. Well if your talking
a ratio of 1 day to 1000 days, communication would be difficult. But still not impossible. It would just be Doppler shifted to the extreme.

If you can figure out how to go that fast, you could figure out how to adjust for that I would think. However, it could be said that sending a breakfast message to a guy on his first day out of college, and a dinner message when he is retiring, might not be called real communication.

Seriously if you were going to do a non FTL long trip at near light speeds, you would want to add a time jump to re-equalize the time so you could return to same generation you left. When you reach destination, jump back to day you left based on a earth clock, then do the same thing on return trip.
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TechBear_Seattle Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Jan-11-09 05:45 PM
Response to Reply #35
40. I think the real reason is author choice
The author makes a decision that ships travelling at relativistic speeds are incommunicado. Any rational, if given, is just an excuse.
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struggle4progress Donating Member (1000+ posts) Send PM | Profile | Ignore Sat Jan-17-09 04:51 AM
Response to Reply #24
56. Time dilation should be symmetric: if frame A is moving relative to frame B,
observers in frame A think clocks in frame B are running slow, but observers in frame B also think clocks in frame A are running slow
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RandomThoughts Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Jan-11-09 01:51 AM
Response to Reply #19
27. During sub light speeds
Communication would seem fairly practical. I would be interested in hearing the rational for no comms during sub light travel.

FTL flight is a completely different subject. But relay stations can fix this, communication is more of dropping messages back into sub light speed, then message pod broadcasting across network. Reception is more complicated.

Depends on what kind of FTL you use, many small warps, allows for pretty good reception, but requires excellent timing or repetition. Those that use single large warp seem to make the represented travel take to long, and they do not factor in diminishing returns based on the size of warp.

Battle Star Galactica gets the warp jumps down pretty good. I like there representation of FTL.
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TechBear_Seattle Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Jan-11-09 10:44 AM
Response to Reply #27
31. Under my physics, FTL comm is not allowed
In effect, interstellar craft detach from the universe and skid across its surface on the outside. Gravity is the only thing that gets through the barrier, and then only weakly, enough to navigate around large gravity wells. When a ship is in transit, it is completely incommunicado. Also, there is no FTL carrier wave technology (all evidence says it is impossible but hey, they were wrong about FTL travel so who knows?) so all comm traffic must be carried shipboard and narrow cast when the ship arrives.
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qazplm Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Jan-11-09 12:18 PM
Response to Reply #31
33. see my post above but
you have then effectively created FTL communication.

You could have "message ships" of some sort with FTL drives. Pop out, broadcast a message, pop back, broadcast a response.
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RandomThoughts Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Jan-11-09 01:27 PM
Response to Reply #31
36. Well the FTL
I am talking about is not one big warp where you do extra dimensional trip through folded space for a long time.

I am talking about many small jumps, the distance to power ratios are more efficient on small warps, (not real small, some initial loss at initialization.) But one big jump is inefficient, many quick small jumps that feel like one jump. Then just drop your message between jumps. Your really going between normal, and folded space.

So the folded space moves with you, imagine more of a wave of folding, and message fired off the back, quickly misses next jump.

Gravity does bleed off, thats why its used for navigation.

And actually if you understand the gravity loss, power of 2 instead of 3, its pretty easy to see why smaller jumps are better. you do not need to fold extra space you effectively are not using, since amount of space folding to move forward, also gets folded left right top and bottom. So for every extra x forward you jump, it cost like x^2 or x^3 power(forget math, but same as gravity leak) folding effects 3d, movement forward just 1d. Easy to figure.
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Vincardog Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Jan-11-09 10:13 PM
Response to Reply #31
42. Just invent the author's curious effect that disallows whatever you want.
Isn't that why you are the author?
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Hugabear Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Jan-11-09 01:47 AM
Response to Original message
26. My guess is that it wouldn't have any effect
Once you fire the laser, it's gone; on its way to its target. The fact that the source is moving away shouldn't affect the laser since it's already gone. If it's a continuous signal, then that might be different, not sure how that would work.

Of course, my answer could be wrong, I don't pretend to know everything about this sort of stuff.
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napoleon_in_rags Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Jan-11-09 02:33 AM
Response to Original message
28. That is my understanding.
But I am not a physicist. It comes from reading about a vexing experiment trying to measure the speed of light that set Einstein off.
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kurt_cagle Donating Member (294 posts) Send PM | Profile | Ignore Sun Jan-11-09 02:46 AM
Response to Original message
29. Yup - 20 min and red shifted
by about 15%. (F = f/sqrt(1-(v^2/c^2))) where f is initial frequency of the light, F is final frequency and v is the speed of the space-craft.

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RandomThoughts Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Jan-11-09 01:30 PM
Response to Reply #29
37. Hey kurt
Do you remember the formula for increased energy while folding, energy requirement versus distance jumped?
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ashling Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Jan-11-09 06:37 AM
Response to Original message
30. Is it farther to New York, or by bus?
This sounds like one of those questions in 7th grade that always drove me up a wall: If one train heading ... blah, blah, blah.

They say there are two universal languages: music and math. I guess that makes me illiterate.

:crazy:
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Ready4Change Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Jan-11-09 02:34 PM
Response to Original message
38. Is the message SENT when ship is 20 light minutes away?
Or, does the message reach the ship when it is 20 light minutes away?

Your message lasers will need to be aimed like a shotgun trying to hit a flying clay pigeon. In otherwords, they have to lead the target.

So the message the ship recieves when it is 20 light minutes away was actually sent 20 minutes AGO. ANnd it will be red shifted due to the ships velocity.

If you send a message to a ship which is already 20 light minutes out, you will have to lead the target, by aiming the message to the spot the ship will be, once the message gets out there. If the ship is travelling .5 lightspeed you'll need to aim MORE than 20, or even 30 light minutes ahead. When the message has travelled 20 lm, the ship has moved another 10 lm. 10 minutes later the message still isn't there, because the ship has gone another 5 lm. The message DOES eventually reach the ship, but since the ship is so fast, it takes quite a while.

It's more difficult though. You don't really know where the ship is NOW. When it's 20 lm out, you only know where it was 20 minutes ago, because that's how long it took for that light to reach you. If you 'see' the ship 20 lm out, and it's travelling .5 lightspeed, you can estimate that it's really 30 lm away now. BUt that estimate is only as good as the odds that the ship hasn't changed course since 20 minutes ago and won't change course during the 30+ minutes that the message will be playing catch up.

You'll need someone with stronger math than mine to figure out how long/far that game of catchup takes.
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Vincardog Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Jan-11-09 10:02 PM
Response to Original message
41. If the laser is fired when the ship is 20 light minutes away, will it still take 20 minutes to reach
whatever is 20 light minutes away when the laser is shone. Correct
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anigbrowl Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Jan-11-09 10:18 PM
Response to Original message
43. Argh, so many wrong responses. NO, it does NOT take 20 minutes.
The speed of light is invariant, regardless of the direction you're going in. But if you are moving away from the light source, as you specify, then of course the light will take longer to reach you. To believe it takes the same length of time exhibits a complete misunderstanding of relativity. It's basically Zeno's paradox of Achilles and the tortoise. Now when an observer at the departure point of the ship sees the light catch up with the ship is another matter entirely.

It will take 40 minutes for the light to reach the fleeing spaceship.


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RandomThoughts Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Jan-12-09 02:17 AM
Response to Reply #43
48. two different conditions.
Edited on Mon Jan-12-09 02:39 AM by RandomThoughts
At the moment the light reached you when you were 20 light minutes away, it took 20 minutes for it to reach you. and the guy seeing it saw it travel for 20 minutes. But both people see time differently.

You are right if the problem says the light was first emitted when ship was 20 light minutes away, because yes it would be further away when reached. The problem most people talk about is a continuous message where measurement starts at 20 light minutes, so it is saying it took 20 minutes, not it will take 20 minutes.

your comment that it would take 40 minutes might be true for the photon released when ship was 20 minutes away, but not the photon received when ship was 20 light minutes away.


* photon
- path in future.

your measurement is starting with first photon released when ship at 20 light minutes
0**------------ ship at 20 light minutes.
0*************************ship at futher distance, where you start measuring.

Some of us seem to have mearly began measurement when ship is at 20 light minutes
0************** ship at 20 light minutes.

And guy bellow saw problem as ship emiting light.
0-------------* ship at 20 light minutes.

Personally my point was dopler effect. However rereading question, initial measurement should have started with ship further away, since he said laser fired when ship 20 light minutes away, but after adjusting for when measurement begins, the rest seems correct.

I think my mental representation was galaxies moving away, so I was thinking like third example, but may have just been thinking of monitoring a continual light source not a comm laser turned on. Like looking at earth starting at 20 light minutes.

Either way, 1st example better matches question actually asked.

In a side note, example 1 and 3 show that you could find an absolute 0 movement in galaxy, there by not making all motion relative. In other words, if all motion is relative, then earth moving away, or ship moving away would be same thing, and which one is moving faster would be interpretation, thereby not being able to figure who moves faster or slower in time. So if nothing else, the mistake turns out to be a good proof of 0 speed space existing. Or there being a way to find the exact speed of every object in universe based on some hard 0 speed that exist. Which is interesting in itself.
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anigbrowl Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Jan-12-09 12:27 PM
Response to Reply #48
52. Indeed. I neglected to say that I was using the 'proper time'
and taking the origin of the laser beam as my reference frame. To be honest, I stopped thinking about it in terms of communication and instead visualized a death-star type laser beam, in order to answer the question of how long after the laser is fired could we say the ship is blown up.

Pic possibly related...


Ever since I saw this I have been musing the possibility of doing one in the shape of Vladimir Putin's head in order to fly it over Juneau. Apparently the balloon above is the creation of some Belgians, increasing that country's cool factor by an order of magnitude.
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Trajan Donating Member (1000+ posts) Send PM | Profile | Ignore Sat Jan-17-09 01:01 AM
Response to Reply #43
55. Yay ....
I knew the answers here were problematic ...

The speed of light is a CONSTANT, and the 'relative' frame of reference between observers will offer different views of time and distance ...

I do have a question for you: Will the light be 'red shifted' when it arrives ?

I believe it will be like the classic train whistle, moving away at lowered pitch ....
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Hanse Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Jan-11-09 10:37 PM
Response to Original message
45. It'd take 40 minutes.
At 20 minutes the message reaches the spot where the ship was at t = 0, another 20 minutes to catch up on its head start.

If you can't do calculus, you can easily do this with a piece of graph paper.

The x-axis is time in minutes. The y-axis is distance, in light minutes. Thus your message is a line with a slope of 1, and y-intercept at 0. Your ship, with its head start, has a y-intercept of 20, with slope of 0.5. The two converge at x = 40 minutes.
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anigbrowl Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Jan-11-09 10:46 PM
Response to Reply #45
46. Quite. I think confusion comes from...
the fact that relativity leads to time dilation. If the ship is traveling at 0.5 the speed of light, the clocks on that ship will seem to have slowed down compared to that of a stationary observer at the ship's departure point (or at the origin of the laser beam).

http://en.wikipedia.org/wiki/Time_dilation
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Hanse Donating Member (1000+ posts) Send PM | Profile | Ignore Sun Jan-11-09 10:56 PM
Response to Reply #46
47. Yes, ships clocks would read a bit less than 40 minutes.
Perhaps not enough for human perception. At 0.5 c relativistic effects are measurable, but huge.

Should be easy enough to figure out if someone wants to bother with the math.

I struggled at first with the wording of the problem. First time reading it I thought the signal was a pulse from the ship going back to the planet. That would take 20 minutes.
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caraher Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Jan-12-09 09:15 AM
Response to Reply #46
49. The question is somewhat ill-posed
Edited on Mon Jan-12-09 09:18 AM by caraher
The good news is that you can use Lorentz transformations to answer any reasonable question about "how long it takes" for the signal to arrive.

The bad news is that you need to pose your question with more precision. Anytime you ask a question about time, you need to frame it in terms of what an actual clock would measure. And you need to tell me what starts and stops this hypothetical stopwatch.

One tip on working with relativity: Always frame the problem in terms of "events," where by an event you must specify a location in space and moment in time (here, you do not need to specify who is measuring time). In this case, there are two events: A. Signal transmitted B. Signal received by spaceship. Each occurs at a well-defined location (A: the location of the transmitter; B: location of the ship) and time (A: when the message is sent; B: when the message is received)

The answer will not be 20 minutes. I'll come back later with the correct answer; the most precise way to get it involves using Lorentz transformations (simple equations to use, but you need to be very careful to understand what everything means). But one can use graphical methods to develop intuition... a very nice introduction we use in our first-semester course is in Tom Moore's "Six Ideas That Shaped Physics": Unit R. A used copy or other edition should be fine... anyway, it's chock-full of examples like this (this would be a very easy problem at the end of a chapter) and is extremely readable as physics texts go.

And yes, there will be a relativistic Doppler shift. The formula is different for light from other kinds of waves. In fact, this relativistic Doppler shift is the basis of many everyday applications of radar (you can thank it for many speeding tickets!).

<edited to clarify what I found ill-posed>
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TechBear_Seattle Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Jan-12-09 09:51 AM
Response to Reply #45
50. A train leaves the station travelling at 0.75 c...
I am beginning to realize where my confusion lies. I was thinking of an example I had read about some years ago, which involved a game of laser tag on a train travelling at relativistic speeds. But that illustration had to do with two players shooting at one another simultaneously: regardless of which player was in front of the other relative to the direction of travel, or whether only one was on the train, the beams of light from both guns would reach the other player at exactly the same time.

But that would be a special case: two beams shot at the same time between two objects, and trying to determine which beam would reach its target first. Not at all what I was asking.

Ok, so it seems that, at sub-light speeds, normal communications would be possible, although technically challenging due to Doppler shift. That is the key thing I was trying to figure out.
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anigbrowl Donating Member (1000+ posts) Send PM | Profile | Ignore Mon Jan-12-09 12:21 PM
Response to Reply #50
51. Yep...
where most people go wrong with relativity (and I had the same problem...until I read Einstein's own writing, which is much clearer than most of his commentators') is that they add the vector of the train/spaceship/whatever to the vector of the light emitted. And this would be justified if we were talking about shooting bullets rather than light, since bullets have mass and thus share the momentum of the platform from which they are fired. Prior to Michelson/Morley and then Einstein, the belief was that light traveled as a wave in some sort of electromagnetic medium in which conservation of momentum would obtain.

As you say, the light will be increasingly red or blue shifted depending on the direction of your spaceship, although I'd say the difficulties of keeping a laser beam exactly on target over such large distances dwarf the signal-processing requirements of correcting for frequency drift in the resulting signal, which are soluble with regular old vector math and calculus - that is, if the ship knows its own speed and direction of travel then the calculations for unshifting the incoming signal are trivial.

You might also wish to examine quantum entanglement as a method not for FTL communication (which it doesn't allow, contrary to popular belief) but for verification purposes...although this makes the relativistic stuff look lightweight be comparison. It's not just theoretical though; a test last year succeeded in transmitting a single entangled photon over 144km, the aim being to establish a basis for secure satellite communication. http://plato.stanford.edu/entries/qt-entangle/
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caraher Donating Member (1000+ posts) Send PM | Profile | Ignore Thu Jan-15-09 05:33 PM
Response to Original message
53. OK, so here's how this looks on spacetime diagrams
There are two events: transmission of the signal (event A) and receipt of the signal (event B).

First, as originally posed, neglecting the time it takes the spaceship to accelerate to 0.5 c:



In these diagrams, green is the worldline of the transmitter, red is the worldline of the spaceship and black is the worldline of the signal transmitted. The blue lines are for hypothetical return signals. There are two red lines, one corresponding to the case of the spaceship moving toward the transmitter and one for the spaceship moving away. The way to "read" them is from the bottom up; if one looked at it through a horizontal slit sliding from the bottom up, you'd see a "movie" of the 1-D motion.

What you can see is that, as measured at the transmitter, it would take 40 minutes for the signal to reach the spaceship if the spaceship were moving away and about 13.3 minutes if it were moving toward the transmitter.

From the rest frame of the spaceship, the picture is a little different. The time between the transmission and receipt of the message will be 20 minutes:



Note that in either case, events A and B have "lightlike" separation. That means that, for a given observer, the time between the events (in minutes) will have the same numerical value as the distance between the events (in light-minutes). For the transmitter, the signal reaches the ship when the ship is 13.3 or 40 light-minutes distant, and therefore the signal takes 13.3 or 40 minutes to get there. For the ship, event A occurs at a distance of 20 light-minutes and event B occurs at a distance of 0, so the time will always be 20 minutes as measured by the ship.

It's also worth noting that none of these - 13.3, 20 or 40 minutes - is a proper time between events A and B. A "proper time" is a time interval measured by a clock present at both events, and in this case neither the ship nor the transmitter is present at both events. Proper time is something that depends not only on the two events, but on the worldline traced by the clock between the events. Because there is lightlike separation between events A and B, the only worldline connecting them that does not involve superluminal speeds is the straight line shown for the signal. Along that worldline, the proper time equals the spacetime interval - zero!
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joshcryer Donating Member (1000+ posts) Send PM | Profile | Ignore Fri Jan-16-09 12:13 AM
Response to Reply #53
54. Those are so cool. Thanks for the post.
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