Direction of time

[phyti]

Why should time have a direction if it's a scalar?

A clock accumulates 'time'. A complete clock has registers for sec, min, hrs, etc, like an odometer. In practice the larger units day,  month, yr. etc, are posted as a calendar, but still a record. So where's the direction? It's 3:21 pm, 9-6-2019, which way do I go?

[Mordred]

The direction becomes evident when you describe time on a number line. Positive direction implying an increase in the set of real numbers. Ie 1,2,3... Seconds yes the values are scalar but the set can be given a vector quantity under graph.

Which becomes essential under relativity by assigning time units of length via the interval ct.

Edited September 6, 2019 by Mordred

[jajrussel]

On 8/30/2019 at 4:29 AM, michel123456 said:

Since it is physically impossible to "get out of time", we should always add inherently 1 dimension (the T dimension) to anything observed or described. And not add time as a 4th dimension, as if geometry could exist "out of time". It gives the false impression that space could somehow exist without time.

So, basically time is the one dimension  that all others need be based on?

 What happens when time stops? I don’t know the certainty but my understanding is that the math says time can stop, yet when watching a video of the said moment on a train that Einstein came to the realization of relativity it made sense that at the realization obvious for the observer that time continued on based on his personal observation that time for him at the observation seemed no different for him. I have forgotten the word for time being the same in all frames, but if it has been shown to be true that causality is the same in all frames then time never stops. I would think that reality of an observation trumps the math, so certain predictions of the math remain just that, predictions, until observed in the observed frame referenced. If time is the reference that defines all other dimensions, and time is Always measured the same Then all other dimensions should be assumed unchanging just as casually. If I’m thinking wrongly please tell me how? 
 

An attempt at clarification of my present understanding. Time dilation only occurs for the observer with regard to the observed not physically to the one being observed. 
 

the second hand in the clock is observed to stop by the observer, but in reality the second hand does not stop.

[jajrussel]

On 9/6/2019 at 3:24 PM, phyti said:

Why should time have a direction if it's a scalar?

A clock accumulates 'time'. A complete clock has registers for sec, min, hrs, etc, like an odometer. In practice the larger units day,  month, yr. etc, are posted as a calendar, but still a record. So where's the direction? It's 3:21 pm, 9-6-2019, which way do I go?

In my opinion time occurs in the direction of change. Only because that is the direction we track it. The direction is always dependent on the direction we track it. The direction we track change is usually with regard to gravity in some way. Which should mean something... The result is always? Related? Hmm?

 You can go in what ever direction you please.

Edited October 2, 2019 by jajrussel

[swansont]

3 minutes ago, jajrussel said:

In my opinion time occurs in the direction of change.

What does that mean?

Change has a direction? That lines up with time? What happens with a system that isn't changing?

 

2 hours ago, jajrussel said:

  What happens when time stops? I don’t know the certainty but my understanding is that the math says time can stop

That's kind of a vague statement. What math? I am aware of only one circumstance where one could argue that time stops, and that's in a reference frame that is not the observer's.

 

2 hours ago, jajrussel said:

yet when watching a video of the said moment on a train that Einstein came to the realization of relativity it made sense that at the realization obvious for the observer that time continued on based on his personal observation that time for him at the observation seemed no different for him. I have forgotten the word for time being the same in all frames, but if it has been shown to be true that causality is the same in all frames then time never stops. I would think that reality of an observation trumps the math, so certain predictions of the math remain just that, predictions, until observed in the observed frame referenced. If time is the reference that defines all other dimensions, and time is Always measured the same Then all other dimensions should be assumed unchanging just as casually. If I’m thinking wrongly please tell me how? 

We know that time is not always measured the same, and we know that length is not measured the same. We also know that these differences compensate for each other, such that c is always the same.

 

 

[jajrussel]

1 minute ago, swansont said:

What does that mean?

Change has a direction? That lines up with time? What happens with a system that isn't changing?

 

Sorry I was editing maybe I cleared up what I meant? Is there such a system? Beyond speculation? The singularity maybe? At its center? You can track time from there but where can you go?

My assumption is that nothing changes dimensionally for the one being observed.

[swansont]

12 minutes ago, jajrussel said:

Sorry I was editing maybe I cleared up what I meant? Is there such a system? Beyond speculation? The singularity maybe? At its center? You can track time from there but where can you go?

My assumption is that nothing changes dimensionally for the one being observed.

Something falling into a black hole will have the time "stop" as far as a distant observer is concerned, but that's only according to the distant observer.

What does "nothing changes dimensionally" mean? 

[Janus]

2 hours ago, jajrussel said:

So, basically time is the one dimension  that all others need be based on?

 What happens when time stops? I don’t know the certainty but my understanding is that the math says time can stop, yet when watching a video of the said moment on a train that Einstein came to the realization of relativity it made sense that at the realization obvious for the observer that time continued on based on his personal observation that time for him at the observation seemed no different for him. I have forgotten the word for time being the same in all frames, but if it has been shown to be true that causality is the same in all frames then time never stops. I would think that reality of an observation trumps the math, so certain predictions of the math remain just that, predictions, until observed in the observed frame referenced. If time is the reference that defines all other dimensions, and time is Always measured the same Then all other dimensions should be assumed unchanging just as casually. If I’m thinking wrongly please tell me how? 
 

An attempt at clarification of my present understanding. Time dilation only occurs for the observer with regard to the observed not physically to the one being observed. 
 

the second hand in the clock is observed to stop by the observer, but in reality the second hand does not stop.

You can never observe the other clock as completely stopping as that would require it to travel at c*, which is impossible. It can get closer and closer to c, but never actually reach it.

Let's use an analogy to illustrate what is happening.

imagine two people who start off walking from the same point but at an angle to each other. They have equal length strides.  After so many steps, they check their progress. Each person will measure that after x number of steps they will have traveled a distance of y from the starting point in the direction they are walking. However, if they check the other person's progress against their own, they will note that the other person has traveled a shorter distance in this same direction ( the direction he, himself, is walking). So each of them measures his own progress as being perfectly normal while the other person falls further and further "behind".

This is equivalently what happens with time dilation. Each of us measures time according to our frames "time axis", and frame in motion with respect measure along different time axis. This is the basic difference between the concept of space-time and the old concept of space and time.  With space-time, time and space are combined and there is no absolute "time axis", but rather the time axis is frame dependent. ( a separation between two events that one frame measures as only being separated in space, could be measured as being separated in both space and time by another frame.)

* Actually, this isn't really true either,  If you plug c into the time dilation equation, you end up with T = t`/0 and division by 0 is undefined.

[jajrussel]

13 minutes ago, swansont said:

Something falling into a black hole will have the time "stop" as far as a distant observer is concerned, but that's only according to the distant observer.

What does "nothing changes dimensionally" mean? 

The simplest answer to the first part is just “yes,”

 for the second part I mean nothing as in nothing changes for the one observed to include all of the standard 4 accepted dimensions the clock towers second hand keeps ticking with regard to his observation of the second hand. the observer sees the second  hand as stopped. Not so for the one being observed. Not so for the one being observed. Dimensionally everything is the same. In this analogy the second hand. how does  the song go? time keeps  on ticking, ticking, ticking into the future. 🤔 it’s an old song so maybe we can substitute the past, but generally the future is assumed as the direction we are moving into, and the song is much better that way. Then maybe I have the words wrong. I’ve always had that problem with songs maybe it is slipping, slipping, slipping. Don’t know if it makes a difference? 😊 I should know better than to try and come up with my own analogy. I just get confused.

42 minutes ago, Janus said:

You can never observe the other clock as completely stopping as that would require it to travel at c*, which is impossible. It can get closer and closer to c, but never actually reach it.

Let's use an analogy to illustrate what is happening.

imagine two people who start off walking from the same point but at an angle to each other. They have equal length strides.  After so many steps, they check their progress. Each person will measure that after x number of steps they will have traveled a distance of y from the starting point in the direction they are walking. However, if they check the other person's progress against their own, they will note that the other person has traveled a shorter distance in this same direction ( the direction he, himself, is walking). So each of them measures his own progress as being perfectly normal while the other person falls further and further "behind".

This is equivalently what happens with time dilation. Each of us measures time according to our frames "time axis", and frame in motion with respect measure along different time axis. This is the basic difference between the concept of space-time and the old concept of space and time.  With space-time, time and space are combined and there is no absolute "time axis", but rather the time axis is frame dependent. ( a separation between two events that one frame measures as only being separated in space, could be measured as being separated in both space and time by another frame.)

* Actually, this isn't really true either,  If you plug c into the time dilation equation, you end up with T = t`/0 and division by 0 is undefined.

Einstein already  supplied  the analogy. It required a lot less thought. I read that the only thing required was the acceptance that c was invariant. Most lawyers  trip the one being questioned up by asking the same question over and over we suspect there must be a purpose so the answer will very slightly each time to the effect it becomes confusing. What Einstein said is not confusing until you start to analyze the statement as if analysis  is needed at which point every analysis must also be invariant or you end up drowning in a sea of confusion😳 there I tried my own analogy. I should be in a heap of trouble now... My assumption is that if c is invariant then ultimately unless you live in a universe of very different dimensions which I believe requires a different geometry, all 4 of the standard dimensions will be the same, the units of measure may be different but the dimensions will be as invariant as c, for the one being observed.

[jajrussel]

1 hour ago, swansont said:

That's kind of a vague statement. What math? I am aware of only one circumstance where one could argue that time stops, and that's in a reference frame that is not the observer's.

I don’t know what math my understanding is that mathematically relativity predicts several seemingly impossible things one such being time stopping due to acceleration which as Janus said it is impossible for a clock to travel at c? It was not my analogy my understanding is that it was Einstein’s , and yes, but from the hip because I am already at the point of confusion that observation is because of the observers point of reference so it may be observed by the observer as being in another frame of reference but it is entirely related to the observers frame of reference. 
some would argue quid pro quo? Einstein said he imagined the train pulling away from the clock tower at c another would suggest that would require that the clock pull away from Einstein at c. Then suggest that, that is impossible and the answer to that is also simply, yes. It is impossible.

🤔 Hmm, my understanding of quid pro quo is apparently somewhat different than CNN’s cause I  kept wondering what in the hell where They talking about? Perhaps, I solicit the same response. If I do, I am sorry.

[michel123456]

21 hours ago, jajrussel said:

So, basically time is the one dimension  that all others need be based on?

 What happens when time stops? I don’t know the certainty but my understanding is that the math says time can stop, yet when watching a video of the said moment on a train that Einstein came to the realization of relativity it made sense that at the realization obvious for the observer that time continued on based on his personal observation that time for him at the observation seemed no different for him. I have forgotten the word for time being the same in all frames, but if it has been shown to be true that causality is the same in all frames then time never stops. I would think that reality of an observation trumps the math, so certain predictions of the math remain just that, predictions, until observed in the observed frame referenced. If time is the reference that defines all other dimensions, and time is Always measured the same Then all other dimensions should be assumed unchanging just as casually. If I’m thinking wrongly please tell me how? 
 

An attempt at clarification of my present understanding. Time dilation only occurs for the observer with regard to the observed not physically to the one being observed. 
 

the second hand in the clock is observed to stop by the observer, but in reality the second hand does not stop.

I don't understand clearly what you are trying to say.

What I try to say is:

To me Time is very fundamental. More fundamental than space.

From my understanding, time is "inside" the spatial dimensions, it is not something you add after "creating" Space.

The distance that separates you from the stars can be estimated with 2 values: the number of rods (or kilometers or yards) that you must put in between, or the time you need to get there (in practice the time light needs to get to you). The 2 measures are equivalent.

IOW one could consider that time is the equivalent of distance, expressed in a different manner. Literally that time & distance are the same thing: that would explain naturally why space expands when time shortens, keeping c at the same value.

However it is unconventional because time is defined by "what the clock measures" and not "what the tape-measurers measure". And one is used to observe a distant object as "far away" and not "time away".

Edited October 3, 2019 by michel123456

[Strange]

2 minutes ago, michel123456 said:

The distance that separates you from the stars can be estimated with 2 values: the number of rods (or kilometers or yards) that you must put in between, or the time you need to get there (in practice the time light needs to get to you). The 2 measures are equivalent.

That is correct for nearby stars. It doesn't work on larger distance because expansion means that the stars have moved away while the light was travelling. So the time the light took is not equal to either the distance when it was emitted or the distance when it arrived.

4 minutes ago, michel123456 said:

Literally that time & distance are the same thing: that would explain naturally why space expands when time shortens, keeping c at the same value.

Exactly. It is actually a rotation of the coordinate system between the time and distance axes.

[jajrussel]

On 10/2/2019 at 12:39 PM, Janus said:

You can never observe the other clock as completely stopping as that would require it to travel at c*, which is impossible. It can get closer and closer to c, but never actually reach it.

Is this a common and accepted thought?

 If the observer is moving away at near c and sees the second hand as nearly stopped does it mean that it would  require the clock to to be traveling at near c also?

 It seems important? It creates the mirror image. It also creates the same time zone for both observer and the clock tower. Well, it is the velocity that creates the time zone. Wouldn’t the math agree that if both the clock tower and the observer were seen as traveling at the same velocity then the time zone for both would have to be equal so time for the observer and time for the observed clock tower would have to be equal, or nearly equal so reality does not change for the observer nor the observed. The mirror effect places them both in equal time zones created by their equal velocities.

Invariant  c is the same for both areas so an observer in either location would see the other’s time as having slowed down due to the invariance of c, but the reality for neither has changed because the inverse, or mirror effect has them both sharing equal velocities?

 Which seems to suggest that there isn’t exactly a twin paradox.

[Janus]

1 minute ago, jajrussel said:

Is this a common and accepted thought?

 If the observer is moving away at near c and sees the second hand as nearly stopped does it mean that it would  require the clock to to be traveling at near c also?

 It seems important? It creates the mirror image. It also creates the same time zone for both observer and the clock tower. Well, it is the velocity that creates the time zone. Wouldn’t the math agree that if both the clock tower and the observer were seen as traveling at the same velocity then the time zone for both would have to be equal so time for the observer and time for the observed clock tower would have to be equal, or nearly equal so reality does not change for the observer nor the observed. The mirror effect places them both in equal time zones created by their equal velocities.

Invariant  c is the same for both areas so an observer in either location would see the other’s time as having slowed down due to the invariance of c, but the reality for neither has changed because the inverse, or mirror effect has them both sharing equal velocities?

 Which seems to suggest that there isn’t exactly a twin paradox.

They don't have "equal velocities".  Velocity combines both speed and direction.   If you say that one in moving at 0.9999c in one direction relative to a given frame and the other is moving at 0.9999c in the other direction relative to that frame, it is the same as saying one has a velocity of 0.9999c and the other one has  a velocity of -0.9999c.  To be traveling at the same velocity, they would have to be at rest with respect to each other.

And  in this case, each of them would have a speed of 0.999999995... c relative to each other as measured by either.

And while someone in that frame which measures both as moving at 0.9999c would say that the clock would tick at the same rate, each clock would say that the other is ticking slow ( about 0.0001 times as fast as their clock.

[jajrussel]

On 10/3/2019 at 10:00 PM, Janus said:

They don't have "equal velocities".  Velocity combines both speed and direction.

Okay. Didn’t mean to mislead by using the wrong word. The word I meant was speed.

 

On 10/3/2019 at 10:00 PM, Janus said:

To be traveling at the same velocity, they would have to be at rest with respect to each other.

If they are traveling at the same speed, in respect to each other what would they be? Does the time dilation equation require a vector?

This is a website I found they use the word speed in the descriptive.

 I am looking at the equation I don’t t see a vector indication? It is a somewhat lengthy read.

http://www.emc2-explained.info/Time-Dilation/#.XZbJaS8pCf0

It is the mirror effect I was wondering about. If the observer is moving at near c does it require that the observed must also be seen as moving at near c? I have seen this said before. There was a good video about it, but if I remember correctly the idea was dismissed with a shrug. My short rendition goes ( well yeh, well yeh, okay, true, but, well, not really, dismissed with a shrug). The way my mind works There is a possibility I misunderstood the video...

My question would be after thinking about it... as per the equation if two people are moving at the same speed are they n effect in equal time zones?

Edited October 9, 2019 by Phi for All
requested by poster

[jajrussel]

23 hours ago, Strange said:

That is correct for nearby stars. It doesn't work on larger distance because expansion means that the stars have moved away while the light was travelling. So the time the light took is not equal to either the distance when it was emitted or the distance when it arrived.

I don’t remember anyone ever pointing this out  for why light years doesn’t  work for distance. So thank you. It’s really rather simple when someone just out and out says it🙂. Thank you...

7 hours ago, jajrussel said:

The way my mind works There is a possibility I misunderstood the video...

Actually I did misunderstand the video what he said was that relativity creates the paradox by having both brother see each other as leaving at near c. One ages faster than the other. I’m submitting  that since it is an analogy that as both brothers are seen as leaving at near c, lets say 99.9% a more reasonable percent of c thenThen both brothers should be considered from both views. Write the dilation equation down twice enter the speed for brother 1 in one equation enter brother 2s speed in the other equation it should show that time effects each at the same rate. If relativity creates the paradox then using relativity fairly in the thought problem should eliminate the paradox. It’s relativity that says both brothers see each other moving away at near c. There is no paradox.

Edited October 4, 2019 by jajrussel

[Janus]

12 hours ago, jajrussel said:

Okay. Didn’t mean to mislead by using the wrong word. The word I meant was speed.

 

If they are traveling at the same speed, in respect to each other what would they be? Does the time dilation equation require a vector?

This is a website I found they use the word speed in the descriptive.

 I am looking at the equation I don’t t see a vector indication? It is a somewhat lengthy read.

http://www.emc2-explained.info/Time-Dilation/#.XZbJaS8pCf0

It is the mirror effect I was wondering about. If the observer is moving at near c does it require that the observed must also be seen as moving at near c? I have seen this said before. There was a good video about it, but if I remember correctly the idea was dismissed with a shrug. My short rendition goes ( well yeh, well yeh, okay, true, but, well, not really, dismissed with a shrug). The way my mind works There is a possibility I misunderstood the video...

 

This is a website I found they use the word speed in the descriptive.

 I am looking at the equation I don’t t see a vector indication? It is a somewhat lengthy read.

http://www.emc2-explained.info/Time-Dilation/#.XZbJaS8pCf0

It is the mirror effect I was wondering about. If the observer is moving at near c does it require that the observed must also be seen as moving at near c? I have seen this said before. There was a good video about it, but if I remember correctly the idea was dismissed with a shrug. My short rendition goes ( well yeh, well yeh, okay, true, but, well, not really, dismissed with a shrug). The way my mind works There is a possibility I misunderstood the video...

My question would be after thinking about it... as per the equation if two people are moving at the same speed are they n effect in equal time zones?

The time dilation equation requires a relative velocity, which is what the v stand for.  In this case, it doesn't matter if you consider it negative or positive, because you are squaring it in the equation so the result is always positive.  So in this case, it is the same as their having  a relative speed with respect to each other.  But the key point is that the time dilation is determined by the relative speed to the frame doing the measurement, not to some other third frame.  If I have a bunch of clocks moving away from a center point, they all have the same speed relative to that point, but have varying relative speeds with respect to each other, and thus each will measure the other clocks as ticking slow by various amounts.

Just because relative to that central point all the clocks have the same speed and thus tick at the same rate according to someone at that central point does not mean that they all tick at the same rate according to the individual clocks.

When you say two clocks have the same speed, you have to  say what frame they have the same speed relative to.  And to determine what either of these clocks will measure as happening to the other clock, you would have to know the relative directions of the travel of each clock in our initial frame, so that you can work out the relative speed between the clocks as measured by the clocks.  If they are traveling in the same direction in that frame, then they have 0 relative speed.( according to both the clocks and the initial measurement frame)

If they are moving in opposite directions at v, then each clock will measure the relative speed of the other as being:

2v/(1+v^2/c^2)

And this value is what you would plug into the time dilation equation to determine what rate each clock would measure the other as running.

Again, there is no absolute value you can apply to "speed", nor is there an absolute frame from which it can be measured.

If you say something has a speed of x, you have to supply the reference frame that speed is measured from.  And saying that "two clocks have the same speed" is meaningless by itself.

[jajrussel]

3 hours ago, Janus said:

The time dilation equation requires a relative velocity, which is what the v stand for.  In this case, it doesn't matter if you consider it negative or positive, because you are squaring it in the equation so the result is always positive.  So in this case, it is the same as their having  a relative speed with respect to each other.  But the key point is that the time dilation is determined by the relative speed to the frame doing the measurement, not to some other third frame.  If I have a bunch of clocks moving away from a center point, they all have the same speed relative to that point, but have varying relative speeds with respect to each other, and thus each will measure the other clocks as ticking slow by various amounts.

Just because relative to that central point all the clocks have the same speed and thus tick at the same rate according to someone at that central point does not mean that they all tick at the same rate according to the individual clocks.

When you say two clocks have the same speed, you have to  say what frame they have the same speed relative to.  And to determine what either of these clocks will measure as happening to the other clock, you would have to know the relative directions of the travel of each clock in our initial frame, so that you can work out the relative speed between the clocks as measured by the clocks.  If they are traveling in the same direction in that frame, then they have 0 relative speed.( according to both the clocks and the initial measurement frame)

If they are moving in opposite directions at v, then each clock will measure the relative speed of the other as being:

2v/(1+v^2/c^2)

And this value is what you would plug into the time dilation equation to determine what rate each clock would measure the other as running.

Again, there is no absolute value you can apply to "speed", nor is there an absolute frame from which it can be measured.

If you say something has a speed of x, you have to supply the reference frame that speed is measured from.  And saying that "two clocks have the same speed" is meaningless by itself.

Okay. Thank you...

[jajrussel]

So why doesn’t my image in the mirror look about half my age. I assume it’s moving fairly fast?🤔🙂

[Janus]

5 minutes ago, jajrussel said:

So why doesn’t my image in the mirror look about half my age. I assume it’s moving fairly fast?🤔🙂

Not relative to you.

[jajrussel]

2 minutes ago, Janus said:

Not relative to you.

Hmm, kinda looks like he could be my twin? Oh, my bad, not that kind of relative... sorry.

[md65536]

On 10/6/2019 at 4:30 PM, jajrussel said:

So why doesn’t my image in the mirror look about half my age. I assume it’s moving fairly fast?🤔🙂

It you had a mirror that left you at birth and traveled at a speed of c/3 away from you, you would always look half your age in the mirror.

Your reflected image would appear to be n/2 light years away when you see it at age n.

Pop quiz! This mirror's moving at a relativistic speed. Why am I not using gamma or relativistic composition of velocities? What's the Doppler shift of your image, and why isn't it the relativistic Doppler shift?

Edited October 8, 2019 by md65536

[jajrussel]

Ah, so the mirror Has to travel away from me at speed. Here I was jokingly thinking that my image photons should be sufficient😊. 
 

perhaps this means that if someone  has a mirror set up far enough away, I might see a reflection  half my age? Though maybe somewhat grainy?

 About those test😒. I’m at the age where if I arrive at the checkout counter in the grocery store then realize I forgot something I just let it go for 2 reasons. 1. Hurry up, is no longer achievable, 2. I am liable to find myself wondering around the store trying to remember where I left my shopping cart...So, I don’t do well with test which is why I tend to approach them as puzzles no one expects an old man to even remember he is doing a puzzled, let alone correctly finish it🙂. But, I can spend hours reading and thinking about the questions, so I do look forward to the puzzle, and getting it wrong, then starting over again... over, and over... again, etc.  😴 

Let me c. Hmm, the mirror can’t move at c, yet the photon can, so the photon has a slight advantage. 🤔 This might be where I have to stop reasoning and start using science... I might be in trouble already. Time to reflection...I mean time to reflect/research.

[jajrussel]

Okay, like the kids in school I started making jokes because I am clueless, so switching back to reason I would guess red shifted, because I can’t think of a reason why a mirror moving away from me reflecting photons would act any differently than anything else. Guessing, the waves stretch out as the mirror moves away?

 Now I have to go look up Relativistic Doppler shift, since I am in the “say what?” range with that question as in didn’t know there was one.

Okay I found a website but I am still puzzled.

http://astronomyonline.org/Science/RelativisticRedshift.asp

 it seems to suggest that if I am sitting in a train at near c looking at my reflection in a mirror held in my hand the top equation or the non-relativistic equation would suffice. However if the mirror is moving away from me at near c then the bottom equation becomes necessary. Could be that I am completely misunderstanding what it is saying, so I’ll switch to a bigger device (easier to read) and read it again.

Edited October 9, 2019 by jajrussel

[Janus]

2 hours ago, jajrussel said:

Okay, like the kids in school I started making jokes because I am clueless, so switching back to reason I would guess red shifted, because I can’t think of a reason why a mirror moving away from me reflecting photons would act any differently than anything else. Guessing, the waves stretch out as the mirror moves away?

 Now I have to go look up Relativistic Doppler shift, since I am in the “say what?” range with that question as in didn’t know there was one.

Okay I found a website but I am still puzzled.

http://astronomyonline.org/Science/RelativisticRedshift.asp

 it seems to suggest that if I am sitting in a train at near c looking at my reflection in a mirror held in my hand the top equation or the non-relativistic equation would suffice. However if the mirror is moving away from me at near c then the bottom equation becomes necessary. Could be that I am completely misunderstanding what it is saying, so I’ll switch to a bigger device (easier to read) and read it again.

The second equation is always the correct one, it is just as v become smaller, the answer it gives converges towards the answer given by the first equation.

v is always the relative velocity between source and observer*.  What the observer/source velocity "as a pair" is with respect to some other frame of reference makes no difference.

 

*technically, the difference in velocities between the source at the moment of emission and the observer at the moment of reception.  So for example, if the source and observer are at rest with respect to each other when the light is emitted, and then after that, the source accelerates to a new velocity with respect to to the observer, the observer will see no red-shift when the light emitted before that acceleration occurred gets to him.  However, if the observer changes his velocity between emission and reception, he will see a frequency shift as a result of his velocity change.