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Light Puzzle

ynot

Philosopher
ynot
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A laser in space fires one second long beams of light at one second intervals. You are 10 light seconds away from the laser and you receive the beams of light 10 seconds after they were emitted and measure them to be one second long with one second intervals. You then travel toward the laser at half c and continue to measure the light beams and intervals to be one second long because light travels relative to you at c regardless. It takes you twenty of your seconds to reach the laser but as your time has been time dilated relative to laser time 30 seconds may have passed in laser time. When you reach the laser you have counted and measured 20 light beams and intervals but the laser has created 30. What has happened to the extra 10 light beams and intervals?

A non-mathematical answer would be appreciated.
 
I think you have it backwards - the Doppler shift would cause you to encounter the laser pulses more frequently than the rate at which they are emitted, not less, if you're moving towards the laser source. How did you come up with 30 seconds passing in laser time as opposed to 20 seconds for your time?

ETA: In addition, according to your assumptions, the laser "clock" would be running at a faster rate than your "clock" (i.e. measurement of laser pulses) but this is incorrect. If the relative motion is at a constant velocity, which I assume it is, then from your frame of reference on the ship you would measure the laser "clock" to run at a slower rate.
 
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ynot said:
A laser in space fires one second long beams of light at one second intervals.
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In other words, the laser is emitting light continuously, without interruption.

There are no pulses, just one continuous stream.
 
MattusMaximus said:
I think you have it backwards - the Doppler shift would cause you to encounter the laser pulses more frequently than the rate at which they are emitted, not less, if you're moving towards the laser source. How did you come up with 30 seconds passing in laser time as opposed to 20 seconds for your time?

ETA: In addition, according to your assumptions, the laser "clock" would be running at a faster rate than your "clock" (i.e. measurement of laser pulses) but this is incorrect. If the relative motion is at a constant velocity, which I assume it is, then from your frame of reference on the ship you would measure the laser "clock" to run at a slower rate.
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It’s a basic postulate of the theory of relativity that the speed of light is constant and independent of the motion of the observer. A second long beam of light is therefore a second long to all observers regardless of time or place or motion.

30 seconds is an aribitary figure. The point is that your time is dilated (slower) relative to laser time. Which is equivalent to laser time being faster than your time. In 20 seconds of your time the laser produces more than 20 light beams and intervals.
 
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Complexity said:
In other words, the laser is emitting light continuously, without interruption.

There are no pulses, just one continuous stream.
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Don’t know how you arrive at that conclusion. The laser is on for one second then off for one second repeatedly. How is that “continuously, without interruption”?
 
ynot said:
It’s a basic postulate of the theory of relativity that the speed of light is constant and independent of the motion of the observer. A second long beam of light is therefore a second long to all observers regardless of time or place or motion.
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No. The speed will be the same, but the frequency, wavelength, duration and spatial extent of the pulses will be different to observers at different velocities.
 
ynot said:
It’s a basic postulate of the theory of relativity that the speed of light is constant and independent of the motion of the observer. A second long beam of light is therefore a second long to all observers regardless of time or place or motion.

30 seconds is an aribitary figure. The point is that your time is dilated (slower) relative to laser time. Which is equivelent to laser time being faster than your time. In 20 seconds of your time the laser produces more than 20 light beams and intervals.
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No, you have that mixed up. It sends out 14 billion sine waves of light. The receiver picks up 14 billion as well, but they are half the wavelength (blue shifted), so they only last .5 second altogether.
 
shadron said:
No, you have that mixed up. It sends out 14 billion sine waves of light. The receiver picks up 14 billion as well, but they are half the wavelength (blue shifted), so they only last .5 second altogether.
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If the beams of light “shrink” to half their size do the intervals between them shrink as well? If so why?
 
RecoveringYuppy said:
Because frequency times wavelength is the velocity and the velocity of light is constant.
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Yes but do the intervals between the light beams (the void of space) have a frequency, wavelength and velocity? When the light beams “shrink” wouldn’t the intervals between them be increased?
 
ynot said:
Yes but do the intervals between the light beams (the void of space) have a frequency, wavelength and velocity? When the light beams “shrink” wouldn’t the intervals between them be increased?
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No, the voids in your example have the same length as the pulses. All observers will measure the lengths of the pulses and breaks between the pulses as being the same length as each other but they won't necessarily agree on what that length is.
 
I can see how a Doppler effect could “shrink” or “expand” the light beams depending whether you were travelling against or with their direction of motion. I can’t see however how a Doppler effect could “shrink” or "expand" the distances between things, but I could see how time dilation might. To keep the length of the light beams and distances between them equal they would both have to “shrink” the same amount when you were travelling toward the laser and “expand” the same amount when you were travelling away from it. How could time dilation both shrink and expand distance?
 
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ynot said:
I can see how a Doppler effect could “shrink” or “expand” the light beams depending whether you were travelling against or with their direction of motion. I can’t see however how a Doppler effect could “shrink” or "expand" the distances between things, but I could see how time dilation might. To keep the length of the light beams and distances between them equal they would both have to “shrink” the same amount when you were travelling toward the laser and “expand” the same amount when you were travelling away from it. How could time dilation both shrink and expand distance?
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Length contraction is something above and beyond time dilation.
 
ynot said:
I can see how a Doppler effect could “shrink” or “expand” the light beams depending whether you were travelling against or with their direction of motion. I can’t see however how a Doppler effect could “shrink” or "expand" the distances between things, but I could see how time dilation might.
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Doppler effect is a result of shifting of the times of receiving events caused by the change of your distance and thus change of the time that it takes light (which travels at constant speed) to reach your position.

When you measure the intervals between pulses, you measure the intervals between specific events (stopping the emitter and restarting the emitter) which are transmitted to you at the speed of light. If you are moving with respect to the source that transmits these events to you, the interval between these events will change by the same factor as the interval between any two events transmitted by that source (including the intervals between the events corresponding to the wave peaks, which is another way of saying that the frequency changes).

The fact that nothing travels towards you while the transmitter is off is of no consequence, because you are not measuring any characteristic of the non-transmitted silence - you are measuring the interval between events that are transmitted to you at the speed of light (start and end of the pause).
 
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Roboramma said:
Length contraction is something above and beyond time dilation.
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Yes but - “Length contraction, according to Hendrik Lorentz, is the physical phenomenon of a decrease in length”.

What increases the length of the distances between the light beams to keep the beam and distance lengths the same when you are travelling in the same direction as the light beams?
 
ynot said:
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Yes but - “Length contraction, according to Hendrik Lorentz, is the physical phenomenon of a decrease in length”.

What increases the length of the distances between the light beams to keep the beam and distance lengths the same when you are travelling in the same direction as the light beams?
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Both the beam length and void length decrease by the same amount according to length contraction.

The distance between any two events decreases by the Lorentz factor in the direction of travel. It doesn't matter whether each event is the start or end of a pulse.
 
Did anyone catch the other length contraction error?

You are 10 light seconds away from the laser ... You then travel toward the laser at half c ... It takes you twenty of your seconds to reach the laser ...

The distance to the laser (assuming instantaneous acceleration to 0.5c) is no longer the same as before (to you), it has contracted, and the time for you to arrive at the source will be less than 20 of your seconds.
 
ynot said:
A laser in space fires one second long beams of light at one second intervals.
Click to expand...

I'll assume you meant one second on, one second off - so 5 pulses in 10 seconds.

You are 10 light seconds away from the laser and you receive the beams of light 10 seconds after they were emitted and measure them to be one second long with one second intervals.
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I'll assume you begin at rest with respect to the laser, and those statements are valid in that frame.

You then travel toward the laser at half c and continue to measure the light beams and intervals to be one second long because light travels relative to you at c regardless.
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No. As others have pointed out, neither the beams nor the intervals will be one second long according to your clock. Your statement wouldn't be true even for sound waves because of the standard Doppler effect.

It takes you twenty of your seconds to reach the laser but as your time has been time dilated relative to laser time 30 seconds may have passed in laser time.
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If my assumptions about what you meant were right, it would take 20 laser seconds to arrive, and less than that of your seconds. To make it 30 laser seconds and 20 of yours, the initial setup (10 light seconds distance) must have been measured in a frame moving with respect to the laser. Is that what you meant?

When you reach the laser you have counted and measured 20 light beams and intervals but the laser has created 30. What has happened to the extra 10 light beams and intervals?
Click to expand...

In all cases both you and the laser will agree on how many pulses were sent and received. Clarify what you meant and we can see how it works.
 
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