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#1
02-27-2014, 07:30 AM
 KEED SPILLS..no, wait..PILL SKEEDS..SKILL PEEDS? Join Date: May 2011 Location: Nashville, Cats
Today's Physics Question....?

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

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Last edited by Lonesomedave : 02-27-2014 at 07:39 AM.
#2
02-27-2014, 07:39 AM
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#3
02-27-2014, 07:48 AM
 No need to ask, he's a smooth... Moderator Join Date: Mar 2005 Location: West Midlands UK
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.

http://www.school-for-champions.com/..._equations.htm

Quote:
 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
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.
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Last edited by bassybill : 02-27-2014 at 08:31 AM.
#4
02-27-2014, 07:52 AM
 KEED SPILLS..no, wait..PILL SKEEDS..SKILL PEEDS? Join Date: May 2011 Location: Nashville, Cats
ok...but bill, this formula says nothing about the velocity of the receiver....does this mean that it is irrelevant?

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#5
02-27-2014, 07:58 AM
 No need to ask, he's a smooth... Moderator Join Date: Mar 2005 Location: West Midlands UK
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.
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#6
02-27-2014, 08:01 AM
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#7
02-27-2014, 08:08 AM
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#8
02-27-2014, 08:51 AM
 keepin' the beat since the 60's Join Date: Dec 2007 Location: Studio City, SoCal, USA
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.
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#9
02-27-2014, 09:16 AM
 Registered User Join Date: Aug 2006 Location: Rochelle, Illinois
Quote:
 Originally Posted by Lonesomedave 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

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.
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#10
02-27-2014, 09:38 AM
 Registered User Join Date: Dec 2012
So the true question is wether or not the speed of light is relative (in which it's not) or am I missing the point... Yes probably the latter.
#11
02-27-2014, 10:00 AM
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#12
02-27-2014, 10:01 AM
 KEED SPILLS..no, wait..PILL SKEEDS..SKILL PEEDS? Join Date: May 2011 Location: Nashville, Cats
Quote:
 Originally Posted by hbarcat 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.
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

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Quote:
 "it is depressing to think that by the time he was my age, Mozart had been dead fifteen years" --Tom Lehrer
#13
02-27-2014, 10:15 AM
 Registered User Join Date: Oct 2007
Quote:
 Originally Posted by Lonesomedave 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
Speed of light is expressed as a Capital C- lower case c is used for expressing the speed of sound.
#14
02-27-2014, 10:18 AM
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#15
02-27-2014, 11:15 AM
 No need to ask, he's a smooth... Moderator Join Date: Mar 2005 Location: West Midlands UK
Quote:
 Originally Posted by 1958Bassman Speed of light is expressed as a Capital C- lower case c is used for expressing the speed of sound.
Interesting - I've never seen that convention. Is it an old, obsolete thing? The international symbol for the speed of light is lower case c.

http://physics.info/constants/
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#16
02-27-2014, 11:22 AM
 No need to ask, he's a smooth... Moderator Join Date: Mar 2005 Location: West Midlands UK
Quote:
 Originally Posted by Lonesomedave 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
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.
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Quote:
 Originally Posted by SBassman Man, I'd soil myself playing in a band like that.
#17
02-27-2014, 11:36 AM
 KEED SPILLS..no, wait..PILL SKEEDS..SKILL PEEDS? Join Date: May 2011 Location: Nashville, Cats
Quote:
 Originally Posted by bassybill 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.
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

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Quote:
 "it is depressing to think that by the time he was my age, Mozart had been dead fifteen years" --Tom Lehrer
#18
02-27-2014, 11:42 AM
 Registered User Join Date: Oct 2010 Location: Alexandria Virginia
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.
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#19
02-27-2014, 11:48 AM
 Hit Me With Your Rhythm Stick Join Date: Feb 2011 Location: NW England
Quote:
 Originally Posted by 1958Bassman Speed of light is expressed as a Capital C- lower case c is used for expressing the speed of sound.

Not sure about that. Lower-case c for speed of light.
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#20
02-27-2014, 11:48 AM
 Registered User Join Date: Nov 2013
Quote:
 Originally Posted by hbarcat 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.
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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