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Today's Physics Question....?

Lonesomedave

Lonesomedave

May 13, 2011
783
30
Nashville, Cats
#1
ok...so today i am asking about the red shift of light

suppose you have two objects in space, right next to each other (although, i suppose, it really doesn't matter what the initial state is)

suppose they start moving directly away from each other at 3/4 (75%) of light speed. that is, each one is moving at 3/4 light speed

suppose one emits a beam of light that ultimately catches up with the other

how much would the light be red shifted and what would determine the red shift?

i believe it would be determined by both their speeds. here is my thinking: since, as i understand it, red shift is caused by the fact that light emitted from a moving object will have the peaks and troughs of it waves emitted at a slightly greater distance from each other than a stationary object

therefore, shouldn't the receiving object's speed cause the light waves to be received at a slightly greater distance from each other than if the object were stationary?

Bill, Mohawk, Titus, any physics or astronomy guys out there...put on your thinking caps

davesignatureII-1.png
 
#3
You can't really consider either object as being stationary. There is no such thing as "stationary" except in a relative sense. The only thing that matters is their speed relative to each other (thank you, Albert Einstein).

The actual working of the Doppler effect given on this page is pretty straightforward and linear, but it seems intuitively wrong to me. According to this formula, for two objects moving apart at the same speed as the waves' travel, the observed frequency would be halved. But intuitively no wave would be "observed" at all as the waves could never reach the receding object. This matches my understanding that for two objects travelling apart at the speed of light, the frequency effect would be infinite and the light would be redshifted out of existence. But according to this formula, that wouldn't happen. Maybe Titus can clarify.

Link Removed

The equation or formula for the observed frequency of a waveform for a moving source is:

fo​ = fv/(v ± vs​)

where

fo​ is the observed frequency
v is the velocity of the waveform
vs​ is the velocity of the source
f is the emitted frequency
± is plus or minus; plus (+) is used when motion is away from you and minus (−) is used when motion is toward you
Click to expand...

EDIT - this seems to be based on an approximation that works where vs​ is small relative to v. For larger values of vs​, the calculations become a bit more complicated:

(source frequency/observed frequency) = square root<(1+beta)/(1-beta)>

where beta is the relative velocity as a fraction of the speed of wave travel. This makes sense to me now as this will give the infinite redshift referred to above.
 
#5
Yes, it's only the relative velocity that matters. The obects don't each have their "own velocity", only a single value for their velocity relative to each other. But give me a couple of minutes as I'm editing my earlier post.
 
#8
That is an interesting question (I won't ask why you want to know). My gut feeling says that they would become invisible to each other as the total velocity would be greater than the speed of light. It would be infinite red shift as Bill states above.
 
#9
Lonesomedave said:
suppose you have two objects in space, right next to each other

suppose they start moving directly away from each other at 3/4 (75%) of light speed. that is, each one is moving at 3/4 light speed

suppose one emits a beam of light that ultimately catches up with the other
Click to expand...


You are describing a situation that can't happen. Their combined velocity causes then to separate at a speed greater than the speed of light, (1.5 x C) and therefore any light beam emitted by either will never reach the other.
 
#12
hbarcat said:
You are describing a situation that can't happen. Their combined velocity causes then to separate at a speed greater than the speed of light, (1.5 x C) and therefore any light beam emitted by either will never reach the other.
Click to expand...

yeah, i used to think that too...but unless these guys have taught me wrong, it is not true.

the speed of light is c (@ 186,000 miles per second) and it does not care what the speed of it's emitter is

thus, when the emitting object emits the light, it goes out at c and it is chasing an object that is only moving at 3/4 c, so it WILL catch up

davesignatureII-1.png
 
#13
Lonesomedave said:
yeah, i used to think that too...but unless these guys have taught me wrong, it is not true.

the speed of light is c (@ 186,000 miles per second) and it does not care what the speed of it's emitter is

thus, when the emitting object emits the light, it goes out at c and it is chasing an object that is only moving at 3/4 c, so it WILL catch up

davesignatureII-1.png
Click to expand...

Speed of light is expressed as a Capital C- lower case c is used for expressing the speed of sound.
 
#16
Lonesomedave said:
yeah, i used to think that too...but unless these guys have taught me wrong, it is not true.

the speed of light is c (@ 186,000 miles per second) and it does not care what the speed of it's emitter is

thus, when the emitting object emits the light, it goes out at c and it is chasing an object that is only moving at 3/4 c, so it WILL catch up

davesignatureII-1.png
Click to expand...
You still haven't grasped the idea of relativity, Dave. That's unsurprising as it's a tricky concept.

It's meaningless to think of the light going one way and the emitter moving the other. As soon as a pulse of light is emitted, the photons of light and the emitter get further apart at the rate of c. That's it. That's all you can say. It's doesn't mean anything to talk of the emitter moving in the opposite direction as there's no such thing as absolute motion.
 
#17
bassybill said:
You still haven't grasped the idea of relativity, Dave. That's unsurprising as it's a tricky concept.

It's meaningless to think of the light going one way and the emitter moving the other. As soon as a pulse of light is emitted, the photons of light and the emitter get further apart at the rate of c. That's it. That's all you can say. It's doesn't mean anything to talk of the emitter moving in the opposite direction as there's no such thing as absolute motion.
Click to expand...

while it's quite true to say i have not grasped the concept of relativity, i think you missed my point.

some of these guys were saying that the light emitted by the emitter would never reach the receiver because the combined speeds were, in effect, 6/4 the speed of light.

i was trying to say that is not true. the speed of light is fixed, and as soon as it is emitted, it starts chasing (at c) an object whose velocity is 3/4 c....so it will catch up

davesignatureII-1.png
 
#18
So, I think it goes something like this - 1. The flaw in the perception implied by the original argument is that the speeds add but it's not that simple. The two objects are moving away from each other at 3/4 c only as perceived by a third observer.

2. The observation of light emitted by one object towards the other is subject to the Lorentz contraction in time so observers on either of the two "moving" objects won't perceive they are moving away from one another at 1.5 c, but something less than c because time on each moving object runs more slowly compared to the third observer mentioned in #1.

Time running slower on significantly faster moving objects was demonstrated by experiment and leads to the curious twins paradox.

All IIRC, it's been a while since I touched relativity to any depth.
 
#20
hbarcat said:
You are describing a situation that can't happen. Their combined velocity causes then to separate at a speed greater than the speed of light, (1.5 x C) and therefore any light beam emitted by either will never reach the other.
Click to expand...

Yup. The light will never reach it.

Light travels at 1X the speed of light.

The objects are moving 1.5X the speed of light away.

"each one is moving at 3/4 light speed"
 

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