Light Puzzle

[Thabiguy]

The pulses of light could be considered a tick-tock of a clock, right?

Kind of... if you account for the effect of the finite speed of light propagation. Namely, the rate at which the Receiver sees the pulses arrive is not the rate of the Sender's clock in Receiver's reference frame.

If so, then what the moving Receiver is observing is that the Sender's clock has slowed down.

That's what Receiver observes - i.e. can carefully conclude from observation. But what he sees is pulses arriving at an accelerated rate, giving a first (incorrect) impression of a faster-ticking Sender's clock.

Now, here's where the mind-**** happens for me. While stationary relative to Sender, Receiver puts a rod behind him that is one light-second long. That means they both agree it is 186,000 miles long from A (Receiver's ass) to B (end of the rod). Correct?

So, while still stationary relative to one another, both will agree that the laser will hit points A and B one second apart. Correct? If we imagine the laser beam looking like a Star Trek phaser, they will be the same length.

With you so far.

When Receiver is moving at 0.5c relative to Sender, then Sender will observe it hitting points A and B 0.87 seconds apart. Thus, the length of the rod has shortened due to length contraction. Sender still measures light moving at c.

Actually, no. The rod is indeed shortened in Sender's frame and measures 0.866 light seconds, but Sender will not observe the light hitting points A and B 0.866 seconds apart, because the rod is moving.

Sender will observe the light hitting points A and B 0.577 seconds apart.

Now, if there was a mirror at point B, and the light was reflected, Sender would see that it takes light 1.732 seconds to get from B to A, because the 0.866 light seconds long rod is "flying away" from the returning beam of light.

Altogether, Sender will see that it took 2.309 seconds for light to get from A to B to A. (The asymmetry of the legs' durations in Sender's frame is due to tilting of the plane of simultaneity over the length of the rod.)

What about the Receiver? The rod is stationary relative to Receiver, so he still measures it as 186,000 miles long. It will still take one second for it to go from point A to point B.

Yes. And one second to go back again, if there's a mirror at point B.

Thus, if Receiver times how long it takes the light to return to him, he measures 2 seconds, while Sender observes that it took 2.309 seconds (which happens to be 2/0.866) - and that Receiver's clock has slowed down, advancing only by 2 seconds during those 2.309 seconds.

(Just for completeness: Receiver's take would be that Sender, when measuring those 2.309 seconds, did not start and stop his stop-clock at the correct moments that light passed through A. If Sender had started and stopped his stop-clock at the moments that Receiver would consider simultaneous with light passing through A, Sender's clock would have measured 1.732 seconds. Receiver would therefore observe that Sender's clock has slowed down, advancing only by 1.732 seconds during a 2 second interval.)

Only now when it reaches point B, the "tail end" of the laser beam will have passed point A 0.13 seconds ago as observed by Receiver.

I'm not completely sure what you mean here. In general, relativity causes different-moving observers to disagree about the simultaneity of events that are not colocal (that occur at different places).

 

[ynot]

If light travels at c relative to everything then when it’s either emitted or received I can’t see how it receives or gives any motion or time property from or to the emitter or receiver. In other words c is c and it can’t be c plus or c minus anything. If light never shares or interacts with other times or motions I don‘t see how it can be affected by other times or motions.

Hint - I have difficulty accepting the claims of Relativity (this isn’t saying Relativity is wrong).

 

[Reality Check]

If light travels at c relative to everything then when it’s either emitted or received I can’t see how it receives or gives any motion or time property from or to the emitter or receiver. In other words c is c and it can’t be c plus or c minus anything. If light never shares or interacts with other times or motions I don‘t see how it can be affected by other times or motions.

Hint - I have difficulty accepting the claims of Relativity (this isn’t saying Relativity is wrong).

I am not sure what you mean by this post but "motion or time property from or to the emitter or receiver" seems to be about the Doppler effect. This does not change the speed of light, just its frequency.

Hint - you do not have to accept the claims (math?) of SR - you can accept the experimental evidence that the universe acts as if SR works.

 

[sol invictus]

If light travels at c relative to everything then when it’s either emitted or received I can’t see how it receives or gives any motion or time property from or to the emitter or receiver. In other words c is c and it can’t be c plus or c minus anything. If light never shares or interacts with other times or motions I don‘t see how it can be affected by other times or motions.

Speed isn't the only characteristic of light. It also has a frequency, and its frequency determines its energy. If the emitter or receiver is in motion, the frequency of the light it emits or receives will be altered.

That's how light can be affected by motion even thought it always moves at c.

 

[ynot]

Speed isn't the only characteristic of light. It also has a frequency, and its frequency determines its energy. If the emitter or receiver is in motion, the frequency of the light it emits or receives will be altered.

That's how light can be affected by motion even thought it always moves at c.

I can’t see how relative motion could change the frequency because it’s the same being emitted and received (c). I assume therefore it must be the difference in the “local times” of the emitter and receiver. The problem I have with this is I don’t see that that light can ever exist in any other time but it’s own. Does this mean it’s only being observed as being at a different frequency?

As well as being measured as distance/time from emitter and receiver is the speed of light also “reverse engineered” from it’s frequency? Normal frequency light comes from a “stationary” emitter and red or blue shifted light comes from a “moving” emitter and the amount of frequency change determines the speed?

 

[sol invictus]

I can’t see how relative motion could change the frequency because it’s the same being emitted and received (c).

c is not a frequency, it's a speed. c has units of length/time. Frequency has units of 1/time.

There is a relation between frequency and c: it's that c = f*l, where f is frequency and l is wavelength. When the emitter is moving, f and l both change, in such a way that that relation remains true.

As well as being measured as distance/time from emitter and receiver is the speed of light also “reverse engineered” from it’s frequency? Normal frequency light comes from a “stationary” emitter and red or blue shifted light comes from a “moving” emitter and the amount of frequency change determines the speed?

No. You measure the speed by measuring distance and time.

 

[Roger Ramjets]

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?

As has already been pointed out, in reality nothing odd 'happened' to the extra 10 light beams, as they would have been detected. Your 'thought experiment' is a failure.

Hint - I have difficulty accepting the claims of Relativity (this isn’t saying Relativity is wrong).

You appear to be having difficulty accepting classical Doppler effect. Perhaps you should try to understand that first...

IMO, once you accept the fact that c is constant for all observers, Relativity is quite obvious and easy to understand (even if the math to prove it isn't). Unfortunately, effects such as time dilation and length contraction are often promoted as being 'magical' properties of Relativity, with no attempt to logically explain the reasons why they occur. This has caused a lot of confusion and unwarranted disbelief.

My post count isn't high enough to include links, but you can find 'relatively' math-free explanations on Wikipedia (search for 'Doppler effect', 'Time Dilation', 'Length Contraction').

 

[Uncayimmy]

Actually, no. The rod is indeed shortened in Sender's frame and measures 0.866 light seconds, but Sender will not observe the light hitting points A and B 0.866 seconds apart, because the rod is moving.

Thank you. This was the (now) obvious piece I was missing. Shame on me.

 

[MattusMaximus]

If light travels at c relative to everything then when it’s either emitted or received I can’t see how it receives or gives any motion or time property from or to the emitter or receiver. In other words c is c and it can’t be c plus or c minus anything. If light never shares or interacts with other times or motions I don‘t see how it can be affected by other times or motions.

Once again, no one here is saying the speed of light is affected. What is affected is the rate at which the flashes are observed (i.e., the passage of time due to the "ticking" of the laser clock) from different frames of reference. That difference in the observed rate at which two different laser clocks "tick" is the effect called time dilation.

You are mixing apples & oranges. Speed of light does not equate to the frequency of the observed flashes.

Hint - I have difficulty accepting the claims of Relativity (this isn’t saying Relativity is wrong).

Me too, and I have an advanced degree in physics, I teach high school & college physics, and I've studied this particular subject for well over a decade.

Join the club

 

[ArmillarySphere]

Situation #2: Receiver is moving toward sender at 0.5C. Sender turns on his light for one second according to his clock. What does my device read as the duration of the pulse?

I think I did my derivations wrong - I forgot to compensate for normal Doppler shift.

Let's use normal letters for the sender (S) frame and primed for the receiver (R) frame.
(Coordinates oriented so that the light pulse is moving at -c along the x axis)
If t=t'=0 is the moment when the pulse arrives at the receiver, then the tail end of the pulse will arrive at t=2/3 s, x=1/3 ls (due to the relative motion)
The equivalent time in the R frame is t' = 1.15 * (2/3 - 0.5 * 1/3) = 0.58 s.

As far as the sender is concerned, the receiver got the tail end of the pulse at 0.67 s, but the receiver clock is running slow, causing it to register less time than "actually" happened.

As far as the receiver is concerned, the sender is moving along with the emitted pulse. If nothing else was involved, the pulse would be 0.5 s long, but the sender clock is running slow as well, lengthening it.

(The time dilation factor here is 1/sqrt(0.75), or 1.15)

 

[Alferd_Packer]

If the beams of light “shrink” to half their size do the intervals between them shrink as well? If so why?

Think of it this way. Imagine that you have two lasers. Each one is on for one second and off for one second, but they alternate. When one is on, the other is off.

Thus you would see the same "shrinkage" efect in both beams.

turn one beam off, and the interval between the light bursts of the remaining beam does not change.

 

[Towlie]

To help me understand the Doppler effect, I picture myself standing near one end of a long conveyor belt. At the other end, a person takes objects out of a basket and sets them on the belt at a rate of one per second. The belt carries the objects to me and I take them back off the belt as they arrive, also at a rate of one per second.

Then the person at the other end begins to walk toward me with his basket while continuing to place objects on the belt at a rate of one per second. The result is that after an amount of time elapses that depends upon the speed and length of the belt, I begin removing objects at a faster rate than they're being placed on the belt.

Of course you can also picture what happens with variations such as the distance between the two of you increasing instead of decreasing, or you walking along the belt instead of the other person.

 

[ynot]

In the conveyor belt example the belt effectively speeds up or slows relative to the sender or receiver when either move against or with it’s direction of motion. This doesn’t happen with light however because it’s always moving at c regardless. Effectively this is like the whole conveyor belt apparatus moving to match any motion of the sender and/or receiver. At the same time it would have to move with the moving yet remain stationary with the stationary. If the sender and receiver moved toward each other the whole conveyor apparatus would have to compress, and stretch if they moved apart.

As I understand it a Doppler effect has a shortening or lengthening effect depending whether the relative movement is with or against. If this is so, and a Doppler effect is part of time dilation, wouldn’t the amount of time dilation be dependant on the directions of the relative movements? Wouldn’t it be as AmillarySphere said - “As far as the receiver is concerned, the sender is moving along with the emitted pulse” in one case but “As far as the receiver is concerned, the sender is moving away from the emitted pulse” in the other case?

 

[ynot]

Think of it this way. Imagine that you have two lasers. Each one is on for one second and off for one second, but they alternate. When one is on, the other is off.

Thus you would see the same "shrinkage" efect in both beams.

turn one beam off, and the interval between the light bursts of the remaining beam does not change.

I can imagine how a light burst can be “shrunk” due to time dilation because the length between the peaks and troughs of the frequency waves have been effectively “shrunk” . In the gaps between the light bursts however exactly what in the void of space has been “shrunk”? In your double laser scenario why can't each lot of light bursts be shrunk and each lot of void gaps between them be effectively lengthened accordingly?

 

[Ziggurat]

As I understand it a Doppler effect has a shortening or lengthening effect depending whether the relative movement is with or against. If this is so, and a Doppler effect is part of time dilation

The Doppler effect is not part of time dilation. It happens in addition to time dilation. Time dilation is direction-independent. Doppler shift is not.

 

[Reality Check]

...As I understand it a Doppler effect has a shortening or lengthening effect depending whether the relative movement is with or against. If this is so, and a Doppler effect is part of time dilation, wouldn’t the amount of time dilation be dependant on the directions of the relative movements? Wouldn’t it be as AmillarySphere said - “As far as the receiver is concerned, the sender is moving along with the emitted pulse” in one case but “As far as the receiver is concerned, the sender is moving away from the emitted pulse” in the other case?

The Doppler effect is not "part of" or caused by time dilation. The cause is the motion of the emitter toward or away from the detector as described by Christian Doppler in 1842.
You can however include relativistic effects of the speed: relativistic Doppler effect.

Time dilation (which is never caused by a Doppler effect) is caused by relative velocities. Thus the amount of time dilation is dependent on the directions of the relative movements. See the transverse Doppler effect in the above link.

AmillarySphere is correct - if the physical situation is that the sender is moving along with the emitted pulse toward the receiver then (oddly enough) the sender is moving along with the emitted pulse toward the receiver !

 

[ynot]

I have never said a Doppler effect is part of time dilation but it seemed to me that others were and I have been trying to find out why they were. If they weren’t and they were merely saying that a light Doppler effect is additional to time dilation then I understand. Same thing would have to apply to changing time delay observations. I don’t understand however how light can be Doppler effected in any way however. If it can please explain (non-math) how.

I imagine a beam of laser light as being a solid steel bar that is mysteriously always emitted and received at a constant speed regardless of relative speeds of senders and receivers. If a stationary sender emits a bar then moves in the direction of the bar being emitted then the leading end of the bar would have to speed up accordingly. The bar couldn’t compress because that would mean the leading end would have slowed to less than c relative to the sender.

 

[Reality Check]

I have never said a Doppler effect is part of time dilation but it seemed to me that others were and I have been trying to find out why they were. If they weren’t and they were merely saying that a light Doppler effect is additional to time dilation then I understand. Same thing would have to apply to changing time delay observations. I don’t understand however how light can be Doppler effected in any way however. If it can please explain (non-math) how.

I did not say that you said a Doppler effect is part of time dilation. You definiely had a conditional clause in your post ("If this is so, and a Doppler effect is part of time dilation"). I merely pointed out that it is not.

I would have through that the classical Doppler effect is simple enough. But I cannot think of any simpler way to explain it other than what you see in textbooks or Wikipedia (e.g. the analogy with sound waves). And the relativistic Doppler effect is just using SR instead of classical mechanics (which really needs math).

Perhaps you can tell us what part of the Wikipedia article you do not understand.

 

[ynot]

I did not say that you said a Doppler effect is part of time dilation. You definiely had a conditional clause in your post ("If this is so, and a Doppler effect is part of time dilation"). I merely pointed out that it is not.

I would have through that the classical Doppler effect is simple enough. But I cannot think of any simpler way to explain it other than what you see in textbooks or Wikipedia (e.g. the analogy with sound waves). And the relativistic Doppler effect is just using SR instead of classical mechanics (which really needs math).

Perhaps you can tell us what part of the Wikipedia article you do not understand.

I believe I have a reasonably good understanding of the Doppler effect and have no problem with it being applied to anything but light. My misunderstanding had nothing to do with Doppler effects but with how some others seemed to me to be applying it to light. If the communication error was completely mine then I apologise to all concerned.

 

[sol invictus]

I don’t understand however how light can be Doppler effected in any way however. If it can please explain (non-math) how.

Ignore time dilation and length contraction for now.

Emitter is moving towards a stationary receiver at speed v. Emitter emits a light pulse once per second, which moves towards the receiver at speed c. Receiver receives pulses more often than once per second, because the emitter moves towards the receiver between each pulse emission. It receives them with frequency (1/second)(1+v/c).

Receiver is moving with speed v towards a stationary emitter. Emitter emits a light pulse once per second, which moves towards the receiver at speed c. Receiver receives pulses more often than once per second, because the receiver moves towards the emitter between each pulse reception. It receives them with frequency (1/second)(1+v/c).

That is the standard Doppler effect up to terms of size (v/c)^2. You'd get exactly the same result for sound, except with c replaced with s (the speed of sound), again up to terms of size (v/s)^2.

Light behaves almost exactly like any other wave (with speed c) unless the relative velocity of the emitter and receiver is close to c - in which case you must take time dilation etc. into account.