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tommac
2010-Apr-12, 05:54 PM
I was wondering if all forms of red shift are equivalent? If so how are they equivalent?

I thought that the redshift would show how much time dilation a light source is going through compared to another? Is this true?

Cougar
2010-Apr-13, 03:22 AM
I was wondering if all forms of red shift are equivalent? If so how are they equivalent?
I thought that the redshift would show how much time dilation a light source is going through compared to another? Is this true?

These questions are monstrously ill-framed. The equivalence principle (http://en.wikipedia.org/wiki/Equivalence_principle) is not simply about equivalence in general. The red shift that is measured can have contributions from relative velocity, the gravity of a very massive source, and cosmic expansion. At very large distances, the first two become practically negligible.

I wouldn't say a light source "is going through time dilation." Time dilation is what we perceive because we're in a very different frame of reference from the light source.

tommac
2010-Apr-13, 03:35 AM
These questions are monstrously ill-framed. The equivalence principle (http://en.wikipedia.org/wiki/Equivalence_principle) is not simply about equivalence in general. The red shift that is measured can have contributions from relative velocity, the gravity of a very massive source, and cosmic expansion. At very large distances, the first two become practically negligible.

I wouldn't say a light source "is going through time dilation." Time dilation is what we perceive because we're in a very different frame of reference from the light source.

Yes ... so the difference between the two frames is represented by redshift, right?

WayneFrancis
2010-Apr-13, 05:36 AM
Tommac, we've been through this.

I've gone through the thought experiment to show yourself that there is NO real time dilation with cosmic expansion.

If you bring 2 or more objects separated by cosmic inflation back together the only time dilation present will come from the "return trip". That can be calculated and the clocks will otherwise agree on the time so there fore there is no actual time dilation despite it appearing like there is. The actual separation does not cause any real time dilation.

Ken G
2010-Apr-13, 06:31 AM
I was wondering if all forms of red shift are equivalent? If so how are they equivalent?
I think one good answer to what I think you are asking is that we must be very cautious about "marrying our explanations" involving causes. Physical theories often have a character that "process A is the cause of phenomenon B", but this kind of statement is best seen as a pedagogy associated with that theory, rather than a physical truth required by that theory. By "pedagogy", I mean a way of explaining something, or way of seeing something, that works for us but is by no means unique. A physical truth would need to be unique, and that is much harder to come by.

All too often, common language suggests physical truth when in fact all it really is is a pedagogy. "Causes of redshift" are a classic example-- they are pedagogies, a redshift is a redshift and that's all. Some pedagogies are elegant and popular, some are awkward and disfavored, and some are so widespread that you almost have to use them just to be understood. But they are all just ways of looking at it, often closely allied with a particular choice of coordinatization, or a particular set of observers. Above all, they are related to the language we use, not the reality that is somehow independent of that language. That's a general answer-- if you wanted something more specific, you would need a more specific question.

And "time dilation" is another classic example of a pedagogical or language-based description-- I would never look to time dilation as a physical truth, and I personally dislike language that suggests it is something more than a coordinate choice.

Tensor
2010-Apr-13, 01:00 PM
And "time dilation" is another classic example of a pedagogical or language-based description-- I would never look to time dilation as a physical truth, and I personally dislike language that suggests it is something more than a coordinate choice.

While I agree with you Ken, the problem is that most people don't have the necessary understanding or math to break it down to a coordinate choice. Most people only understand it as a language based description. Which is what keeps the ATM section so busy. ;)

tommac
2010-Apr-13, 02:56 PM
Tommac, we've been through this.

I've gone through the thought experiment to show yourself that there is NO real time dilation with cosmic expansion.

What is the difference between real time dilation and not-real time dilation?

Also how does c stay constant if there is no "real" time dilation?

tommac
2010-Apr-13, 02:57 PM
So you are claiming twins paradox?

Tommac, we've been through this.

I've gone through the thought experiment to show yourself that there is NO real time dilation with cosmic expansion.

If you bring 2 or more objects separated by cosmic inflation back together the only time dilation present will come from the "return trip". That can be calculated and the clocks will otherwise agree on the time so there fore there is no actual time dilation despite it appearing like there is. The actual separation does not cause any real time dilation.

DrRocket
2010-Apr-13, 03:51 PM
I was wondering if all forms of red shift are equivalent? If so how are they equivalent?

Of course not. Anyone who thinks that all forms of red are equivalent has never observed a woman choosing a shade of lipstick.

Ken G
2010-Apr-13, 07:49 PM
While I agree with you Ken, the problem is that most people don't have the necessary understanding or math to break it down to a coordinate choice. Most people only understand it as a language based description. Which is what keeps the ATM section so busy. ;)Yes, there really is no good solution-- when someone asks a subtle question, if we give the subtle answer, we can't win if they don't understand the subtle answer. But if we give the dogmatic answer, it is actually not responsive to the subtlety of the question, and the questioner then becomes right in rejecting the dogmatic answer. The problem may be when people are more adept at asking subtle questions than they are at digesting subtle answers, but still, I feel a deeper kind of question calls for a deeper kind of answer!

mugaliens
2010-Apr-13, 11:38 PM
And "time dilation" is another classic example of a pedagogical or language-based description-- I would never look to time dilation as a physical truth, and I personally dislike language that suggests it is something more than a coordinate choice.

I feel a deeper kind of question calls for a deeper kind of answer!

An object moving away from us will be redshifted, correct?

An object with no relative velocity, but deeper in a gravity well will be redshifted, correct?

Given two synchronized clocks, A stays in GEO, B is sent to the Moon and back. Upon its return, B will be slightly behind A, correct?

Given two synchronized clocks, both on Earth, with A at sea level and B on a mountaintop. A will lag behind B, correct?

Ken G
2010-Apr-14, 12:26 AM

An object moving away from us will be redshifted, correct?How do you know the object is moving away from us? In other words, you define your terms first, and then the consequences of those definitions follow. There's no way to take you out of your language. For example, a perfectly good language involves saying that objects that are redshifted are moving away from us, but we may choose to prefer a different language, involving different definitions. My point is merely that if we forget the role we are playing in choosing those definitions, we come under the false impression that our words are somehow an absolute accounting of what is actually happening.

An object with no relative velocity, but deeper in a gravity well will be redshifted, correct?How do you know if an object, deep in a gravity well, has a "relative velocity"? The precise way to define relative velocity is with clocks and rulers, but then the object can't be far away, it must be passing the clocks and rulers.

Given two synchronized clocks, A stays in GEO, B is sent to the Moon and back. Upon its return, B will be slightly behind A, correct?
Correct-- at last an experimental result.

Given two synchronized clocks, both on Earth, with A at sea level and B on a mountaintop. A will lag behind B, correct?When you later bring them down and compare them, yes. But how do you know what bringing it down did? Or you can use light to look at it-- but what is the lag there? In physics, there are local measurements, and there are inferences we make from those measurements. The former are observable invariants, the latter involve coordinate choices. The first involves a minimum of our imposing our language onto reality, the latter involves a lot of that. (What I'm saying is that reality is in some ways more than our coordinate choices, because there are things going on we are not describing, and in other ways is less than our coordinate choices, because other choices would generate equally correct predictions, so reality expresses a certain ambivalence about our coordinate choices.)

Andrew D
2010-Apr-14, 05:38 AM

A wise man is one who dwells upon what he already knows as he learns what he doesn't yet understand. If he spends all his time thinking about what he doesn't understand, how can he possibly understand anything he thinks?

tommac
2010-Apr-15, 03:05 AM

An object moving away from us will be redshifted, correct?

An object with no relative velocity, but deeper in a gravity well will be redshifted, correct?

Given two synchronized clocks, A stays in GEO, B is sent to the Moon and back. Upon its return, B will be slightly behind A, correct?

Given two synchronized clocks, both on Earth, with A at sea level and B on a mountaintop. A will lag behind B, correct?

And one more, does an equal amount of redshift observed between statements 1 + 2 correlate to an equal amount of time dilation as stated in 3 + 4?

Ken G
2010-Apr-15, 03:19 AM
And one more, does an equal amount of redshift observed between statements 1 + 2 correlate to an equal amount of time dilation as stated in 3 + 4?Yes, those are related because when you use the concept of "time dilation", you are choosing to make that same association.

tommac
2010-Apr-15, 03:57 AM
Yes, those are related because when you use the concept of "time dilation", you are choosing to make that same association.
So if I choose to make that "same association" can I apply the same time dilation to the redshift from universal expansion? I understand that we have two co-moving frames, but can I make the same association?

WayneFrancis
2010-Apr-15, 04:07 AM
I'm going to be a broken record here.

Object A, B & C are in a line and spaced 10km apart.
There clocks are synchronised
Cosmic expansion starts
Each object appears to be receding from the other objects at a rate of 10m/s/km
After 100seconds cosmic expansion stops
Objects A&C travel at accelerate near instantly to .8c and return to point B.

Object A, B & C are in a line and spaced 10km apart.
There clocks are synchronised
Object A & C accelerate away from B in opposite directions at a rate of 10m/s/km
After 100seconds they stop
Objects A&C travel at accelerate near instantly to .8c and return to point B.

What are clocks readings at the end of each scenario?
Will the 2 scenarios produce the same results?
Why or why not?

Ken G
2010-Apr-15, 04:26 AM
So if I choose to make that "same association" can I apply the same time dilation to the redshift from universal expansion? I understand that we have two co-moving frames, but can I make the same association?Of course, time dilation is just a coordinate choice, you can make it anything you want when the events are widely separated. You're just matching up the "nows" in some arbitrary way, to fit the redshift you see. That works fine, but it's not really saying very much.

tommac
2010-Apr-23, 03:39 PM
Of course, time dilation is just a coordinate choice, you can make it anything you want when the events are widely separated. You're just matching up the "nows" in some arbitrary way, to fit the redshift you see. That works fine, but it's not really saying very much.

Great ... but the redshift we see can tell us something about the state of the source of the emmitor at the time of emmission right?

Hornblower
2010-Apr-23, 04:48 PM
Great ... but the redshift we see can tell us something about the state of the source of the emmitor at the time of emmission right?

A redshift could be the result of:
1. Local Doppler effect
2. Gravitational effect
3. Cosmological expansion
4. Any two of the above
5. All of the above

With no other information about an isolated object, we may not be able to disentangle the components.

For example, Sirius B's gravitational redshift can be ascertained because the primary's spectrum enables us to pin down the radial velocity of the system. For an isolated white dwarf, it would be more difficult to tell how much is due to gravitation and how much is due to radial velocity.

Ken G
2010-Apr-23, 05:00 PM
Great ... but the redshift we see can tell us something about the state of the source of the emmitor at the time of emmission right?Subject to a given coordinate choice, yes. In "absolute reality", no, a redshift does not have a decomposable meaning the way many imagine.

Ken G
2010-Apr-23, 05:08 PM
A redshift could be the result of:
1. Local Doppler effect
2. Gravitational effect
3. Cosmological expansion
4. Any two of the above
5. All of the above
It's even worse than that-- "reality itself" does not even distinguish these various "causes". We decide the breakdown between the causes when we choose the coordinatization, which is saying that we choose how we will describe the causes when we choose the overall language we are applying in general. Relativity gives us, among other things, the power to recognize what reality is saying, and what we are saying-- what we are choosing to add to the reality when we select our favored language about the reality.

With no other information about an isolated object, we may not be able to disentangle the components.Yes, and one of the bits of "information" we will need is what coordinates are being chosen. If I choose coordinates where the object is always at the same distance, then I will conclude it is all gravitational redshift and none of it is a Doppler shift. It would be a bizarre coordinate choice, but I could still use it and predict every observable correctly-- that's the "general" in general relativity.

For example, Sirius B's gravitational redshift can be ascertained because the primary's spectrum enables us to pin down the radial velocity of the system. For an isolated white dwarf, it would be more difficult to tell how much is due to gravitation and how much is due to radial velocity.There is certainly a standard meaning of a "gravitational redshift" that corresponds to what tidal gravity is doing, rather than what fictitious or "coordinate" gravity is doing. My point is merely that this is a choice of language we have made, related to our choice of coordinates. It is a perfectly logical and clear choice of language, but "reality itself" couldn't care less-- a redshfit is a redshfit no matter how our language chooses to decompose it.

To clarify what I'm saying with an example we all know, if you see a star that appears to be redshifted by its radial velocity, you can still say that "it is redshifted because it is moving away from me" or you can say "it is redshifted because I am moving away from it", or you could even say "it was blueshifted by moving toward an observer that I perceive as moving away from me very fast, and then redshifted even more by my motion away from that observer." Reality itself would just view all that as a mishmash of human language.

tommac
2010-Apr-23, 07:35 PM
I am not looking to disentangle ... I am looking for a knowledge of state.

For example, lets take 3 scenerios, 1) pure GR, 2) pure SR and 3 a mix between GR and SR.

if we keep the redshift constant relative to us ( as the observer ), can we agree that in all 3 cases we observe the emmiter as having the same time dilation?

A redshift could be the result of:
1. Local Doppler effect
2. Gravitational effect
3. Cosmological expansion
4. Any two of the above
5. All of the above

With no other information about an isolated object, we may not be able to disentangle the components.

For example, Sirius B's gravitational redshift can be ascertained because the primary's spectrum enables us to pin down the radial velocity of the system. For an isolated white dwarf, it would be more difficult to tell how much is due to gravitation and how much is due to radial velocity.

Ken G
2010-Apr-23, 08:40 PM
I am not looking to disentangle ... I am looking for a knowledge of state.

For example, lets take 3 scenerios, 1) pure GR, 2) pure SR and 3 a mix between GR and SR.

if we keep the redshift constant relative to us ( as the observer ), can we agree that in all 3 cases we observe the emmiter as having the same time dilation?"Pure" SR means inertial observers and no gravity. That is the only situation where you can take the coordinates seriously enough to assert the "existence" of time dilation, but even then it is just the language of having a standard coordinate system. All other situations recognize time dilation for what it is-- an awkward comparison between two separate ways to coordinatize time, that have no particular reason to be compared that way. The invariant is that some number of wavefronts, say 10, were emitted between event A and event B on source S, and those same 10 were absorbed between event C and event D at observer O. If the 10 wavefronts were emitted in a proper time of 10 seconds at the source S, then the emission rate was 1/second, which we might expect from the mechanism doing the emitting. If the time between C and D at the observer is 20 seconds of proper time, then the observer will say the signal was redshifted to half its original frequency. What more can be said? Not much, it depends on the coordinates used to connect those 10 seconds at the emitter to the 20 seconds at the observer. We certainly cannot say with any absolute certainty what fraction of that factor of 2 reduction was due to "time dilation by the source", but if there's no gravity and the observer O is inertial, there is a standard coordinate system to use to talk about how much of it was time dilation by the source.

tommac
2010-Apr-23, 09:26 PM
Lets take the pulses of a supernova for example. How could we prove that a supernova was going through time dilation because of local gravity, or because of the speed it is moving away from us. or one of the other factors.

From what I understand we cant. But we should see that regardless of how it got time dilated, the redshift should reflect a different frequency of the pulses.

However why dont quasars show timedilation?

"Pure" SR means inertial observers and no gravity. That is the only situation where you can take the coordinates seriously enough to assert the "existence" of time dilation, but even then it is just the language of having a standard coordinate system. All other situations recognize time dilation for what it is-- an awkward comparison between two separate ways to coordinatize time, that have no particular reason to be compared that way. The invariant is that some number of wavefronts, say 10, were emitted between event A and event B on source S, and those same 10 were absorbed between event C and event D at observer O. If the 10 wavefronts were emitted in a proper time of 10 seconds at the source S, then the emission rate was 1/second, which we might expect from the mechanism doing the emitting. If the time between C and D at the observer is 20 seconds of proper time, then the observer will say the signal was redshifted to half its original frequency. What more can be said? Not much, it depends on the coordinates used to connect those 10 seconds at the emitter to the 20 seconds at the observer. We certainly cannot say with any absolute certainty what fraction of that factor of 2 reduction was due to "time dilation by the source", but if there's no gravity and the observer O is inertial, there is a standard coordinate system to use to talk about how much of it was time dilation by the source.

Ken G
2010-Apr-23, 11:43 PM
Lets take the pulses of a supernova for example. How could we prove that a supernova was going through time dilation because of local gravity, or because of the speed it is moving away from us. or one of the other factors. What I'm saying is you can't answer any of those questions until you choose a coordinate system, because those are not elements of reality, they are how reality is interpreted through the lens of a particular way of coordinatizing it. But there is a standard coordinatization you can use, which generates the standard language you will hear. For distant supernovae, that's a cosmological coordinatization, and the standard is "comoving coordinates". That means you connect your own local vicinity to the supernova through a chain of observers all moving with the average motion of the mass in their piece of the universal expansion. Those coordinates generate a picture of what is happening that is exactly the same as if the light was little ants crawling at ant-speed across a rubber chess board that is being continuously stretched in all directions. That picture completely accounts for the redshifting you see, and it also accounts for the fact that if you see redshift of a factor of 1/2 in the frequency, then the time the supernova explosion lasts will be multiplied by a factor of 2 relative to what people at the supernova would have seen as the time it took. The exact same thing happens to ants on a stretching chessboard-- if two ants set out 1 second apart, and arrive at the same destination after the board is stretched by a factor of 2, they will arrive 2 seconds apart.

Note that framed in those coordinates, there is no time dilation, all the increase from 1 second to 2 seconds is entirely due to the stretching of the board during transit. On the other hand, if the redshift in the arrival frequency is attributed to SR-like movement on a stationary chess board, then some of that redshift will be due to the increasing distance to the source, and some of it will be due to "time dilation" at the source (you can calculate the necessary breakdown, it will be roughly half and half with these numbers).

There is yet a third language that can be used with that supernova, the language of gravitational redshift. One can say, as we do near black holes in our neck of the woods, that the supernova occured in a deeper universal gravitational well that we are now in, so "time was running more slowly" back then. Then all of the redshift is time dilation, and nothing is happening to the distance between us and the supernova at all (instead, our rulers have gotten shorter since the supernova happened).

Three coordinates, three languages, three answers to your question. All get used, depending on context and purpose.

However why dont quasars show timedilation?They do-- in the language in which they do. But in the standard such language for talking about quasars, comoving coordinates, little of the redshift is due to time dilation (there is some local gravitational time dilation in the quasar itself).

tommac
2010-Apr-23, 11:49 PM
By coordinate system can I use the observers? Or are you saying that all we can really tell is what we observe, everything else has issues of interpretation? So we could say that all redshifts represent the same level of time dilation ... however this doesnt really tell us much? Or am I as usual totally missing the point.

What I'm saying is you can't answer any of those questions until you choose a coordinate system, because those are not elements of reality, they are how reality is interpreted through the lens of a particular way of coordinatizing it. But there is a standard coordinatization you can use, which generates the standard language you will hear. For distant supernovae, that's a cosmological coordinatization, and the standard is "comoving coordinates". That means you connect your own local vicinity to the supernova through a chain of observers all moving with the average motion of the mass in their piece of the universal expansion. Those coordinates generate a picture of what is happening that is exactly the same as if the light was little ants crawling at ant-speed across a rubber chess board that is being continuously stretched in all directions. That picture completely accounts for the redshifting you see, and it also accounts for the fact that if you see redshift of a factor of 1/2 in the frequency, then the time the supernova explosion lasts will be multiplied by a factor of 2 relative to what people at the supernova would have seen as the time it took. The exact same thing happens to ants on a stretching chessboard-- if two ants set out 1 second apart, and arrive at the same destination after the board is stretched by a factor of 2, they will arrive 2 seconds apart.

Note that framed in those coordinates, there is no time dilation, all the increase from 1 second to 2 seconds is entirely due to the stretching of the board during transit. On the other hand, if the redshift in the arrival frequency is attributed to SR-like movement on a stationary chess board, then some of that redshift will be due to the increasing distance to the source, and some of it will be due to "time dilation" at the source (you can calculate the necessary breakdown, it will be roughly half and half with these numbers).

There is yet a third language that can be used with that supernova, the language of gravitational redshift. One can say, as we do near black holes in our neck of the woods, that the supernova occured in a deeper universal gravitational well that we are now in, so "time was running more slowly" back then. Then all of the redshift is time dilation, and nothing is happening to the distance between us and the supernova at all (instead, our rulers have gotten shorter since the supernova happened).

Three coordinates, three languages, three answers to your question. All get used, depending on context and purpose.
They do-- in the language in which they do.

tommac
2010-Apr-23, 11:49 PM
They do-- in the language in which they do.

Can you go into detail on this? Or is that another thread?

Ken G
2010-Apr-23, 11:56 PM
By coordinate system can I use the observers?Observers can be used to define the coordinates locally, but there's really so such thing as a global reference frame, so you need to specify a chain of observers all the way from the source to the detector to have coordinatize its path. Other than being a chain, the motion of the observers (motion and acceleration) are arbitrary, and the language is different with every choice. This is often overlooked in cosmological language, because comoving coordinates are so often used, but for things like nearby black holes it can be very unclear what coordinates are in use.

Or are you saying that all we can really tell is what we observe, everything else has issues of interpretation? Right.

So we could say that all redshifts represent the same level of time dilation ... however this doesnt really tell us much?Not quite-- in some language, you have lots of time dilation, but the same phenomenon in another language might have very little. To avoid confusion, it is necessary to either state the coordinates in use, or adopt a standard that is clear enough, but don't ask about which type is the "real cause" of the redshift-- that must be expressed in coordinate-free language and is rather abstract.

tommac
2010-Apr-24, 12:09 AM
got it ... thanks

Observers can be used to define the coordinates locally, but there's really so such thing as a global reference frame, so you need to specify a chain of observers all the way from the source to the detector to have coordinatize its path. Other than being a chain, the motion of the observers (motion and acceleration) are arbitrary, and the language is different with every choice. This is often overlooked in cosmological language, because comoving coordinates are so often used, but for things like nearby black holes it can be very unclear what coordinates are in use.
Right.
Not quite-- in some language, you have lots of time dilation, but the same phenomenon in another language might have very little. To avoid confusion, it is necessary to either state the coordinates in use, or adopt a standard that is clear enough, but don't ask about which type is the "real cause" of the redshift-- that must be expressed in coordinate-free language and is rather abstract.

Ken G
2010-Apr-24, 12:11 AM
Can you go into detail on this? Or is that another thread?I'll just give an example in a much simpler situation, where we have no universal expansion. We have a laser that emits a beam at a specific frequency. Then we have an observer who, in the frame of the laser, is moving toward the laser when the pulse was emitted, but en route the detector accelerates and ends up moving away from the laser, just as the pulse is detected at a redshifted frequency. Then we ask, "what caused the redshift, and when did it happen?" The natural Einstein coordinates that the laser would use generates a different answer than if we use the Einstein coordinates of observers instantaneously moving with the detector. The laser would say that the light was never redshifted until the last instant that it was absorbed by the detector, and none of the prior motion of the detector had anything to do with it. But the detector, using instantaneous Einstein coordinates, would say that the pulse was originally blueshifted by the motion of the laser toward the detector, but gravitational redshifting appeared as the detector accelerated. In this case, everything the detector did while the pulse was in transit is relevant to the cause of the final redshift. It's all just language, and clarity of coordinates is all you can ask for.

tommac
2010-Apr-24, 02:36 AM
Wow ... pretty cool! Thanks again.

I'll just give an example in a much simpler situation, where we have no universal expansion. We have a laser that emits a beam at a specific frequency. Then we have an observer who, in the frame of the laser, is moving toward the laser when the pulse was emitted, but en route the detector accelerates and ends up moving away from the laser, just as the pulse is detected at a redshifted frequency. Then we ask, "what caused the redshift, and when did it happen?" The natural Einstein coordinates that the laser would use generates a different answer than if we use the Einstein coordinates of observers instantaneously moving with the detector. The laser would say that the light was never redshifted until the last instant that it was absorbed by the detector, and none of the prior motion of the detector had anything to do with it. But the detector, using instantaneous Einstein coordinates, would say that the pulse was originally blueshifted by the motion of the laser toward the detector, but gravitational redshifting appeared as the detector accelerated. In this case, everything the detector did while the pulse was in transit is relevant to the cause of the final redshift. It's all just language, and clarity of coordinates is all you can ask for.