Different Slices of Now Observable from Earth?

I don't get your problem here - as it says in the bit you quoted from Wiki: "...Gravitational redshift and blueshift frequency ratios are the inverse of each other, suggesting that the "seen" frequency-change corresponds to the actual difference in underlying clockrate."
It's just a matter of relative rates. The observer further out inteprets the clock further in as time dilated (running slow = redshifted). Conversely, an observer further in interprets the clock further out as time contracted (running fast = blue-shifted). Substitute light source = oscillator for 'clock', and there it all is.
Sorry, the problem is the use of the word "Doppler."
There are three types of true "Doppler" effects, Universe expansion source-observer velocity differentials, ordinary source-observer velocity differentials, and bending of EM by gravitational space-time distortions.

There is indeed a gravitational redshift, which is seen in things like white dwarfs.
It is certainly due to large distortions in space-time of some sort.

That is NOT a Doppler shift. That's my point.

But there is indeed a Doppler shift that can be caused by gravity, too.
That famous radio wave experiment showed that pulses take longer and longer to reflect back when the beam travels closer and closer to the sun.
Since the speed of light is constant in a vacuum, no matter what, that can only mean one thing - the path is longer, i.e. an apparent velocity differential.

That time delay causes a Doppler shift. The delay is longer than would be predicted by GR geometry alone, but that's irrelevant, it's still a Doppler shift caused by geometry. It is exceedingly tiny but not non-existent. That's because it appears as if there is relative movement, even though there isn't - the source and observer don't intrinsically "know" that the beam has passed through a portion of distorted space-time.

In fact, Einstein's first prediction of how much the sun would bend star light was off by a factor of two. His geometry was off. His geometry changed until if fit the facts. He threw in the "cosmological constant" for the same reason, by his own admission.

Gravitational lensing also causes a Doppler shift.
It's exceedingly tiny as well, but it's there.
Neither one of these two examples of gravitational Doppler shifts can possibly be blue-shifting because neither case can result in a shorter apparent path.

Einstein's thought experiments were interesting, but there haven't been too many more since GR that have resulted in advanced theories.
In fact, Einstein spent a lot of the rest of his life trying to think up experiments that disproved QM.

What does any of this have to do with "slices of now"?
A lot, IMO. What is the minimum possible Doppler shift?
Plank time? If so, that's your "slice of now."
But what if you add time dilation, then what?

Yes, I am being an ash. LOL
Heck, I could have brought up the quasar red-shift problem to become a double ash.

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Correct.Incorrect. Both aliens see the explosion at exactly the same time, but they disagree when it happened.
Ah, yes, the uncertainty principle. LOL

pervect
Staff Emeritus

No, it has nothing to do with the uncertanity principle

Let us imagine we have two different aliens, one with a huge telescope who is stationary, another with a huge telescope on a bicycle who is moving.

Furthermore, we'll assume that the stationary alien and the moving alien are very very very close to one another.

Then there are three events here: EVENTS are points on a space-time diagram.

1) The event at which the light from the explosion is emitted
2) The event at which the light is received by the stationary alien
3) The event at which the light is received by the moving alien.

It might be helpful to draw a space time diagram, and put the events on it.

There are also four non-zero coordinates of interest. While events are points on the space-time diagram, coordinates are labels that are used to describe the points. The moving alien and the stationary alien each have a coordinate system. But the coordinate systems are different.

The four coordinates of interest are

t1_moving and d1_moving, which are the time and distance coordinates (labels) that the moving observer assigns to event #1, the explosion.

t1_stationary and d1_stationary, which are the time and distance coordinates (labels) that the stationary observer assigns to event #1, the explosion.

Event #1 is the same event, but the labels assigned to it are different for the two observers.

Event's #2 and #3 are different events, but we'll assume that the aliens are "on top of one another" so that they can be considered to be essentially the same event.
Then we can say that event #2 and event #3 both have coordinates of t2_moving = t2_stationary = t3_moving = t3_stationary = 0. Similarly d2_moving = d2_starionary = d3_moving = d3_stationary = 0. So that's about 8 zero coordinates .

The coordinate's or labels that are given to event #1 are considerably different, for the moving observer and the stationary observer. Note that the event of seeing the light (event #2) has coordinates of (0,0) for both the moving and stationary observer. The coordinates assigned to the occurence of event #1 are not to be confused with the actual process of the reception of the light signal, but require some evaluation to turn the raw sensory data (seeing) into a consistent description of the universe (the coordinates assigned to the event).

What is being said , however, doesn't have anything to do with seeing, and bringing seeing into the picture is confusing things.

What is being said is that each alien, the moving and the stationary alien, have a concept of "now".

When an event occurs "now", you do not see it immediately, you see it after a lightspeed delay. It's wrong to think of "now" as the events that you SEE at the same time. "now" is the set of events that you assign as occuring "at the same time".

The point is that the set of events on the space-time diagram, which can be drawn as a line on the space-time diagram, that represents "now", is a different set of events ( a different line on the space-time diagram) for the moving alien and the stationary alien.

Sorry, the problem is the use of the word "Doppler."
There are three types of true "Doppler" effects, Universe expansion source-observer velocity differentials, ordinary source-observer velocity differentials, and bending of EM by gravitational space-time distortions.
There is indeed a gravitational redshift, which is seen in things like white dwarfs.
It is certainly due to large distortions in space-time of some sort.
That is NOT a Doppler shift. That's my point.
OK have no objection on that. Your mentioning of cosmic expansion is relevant for an accurate picture of how it would work out in the real universe: http://en.wikipedia.org/wiki/Metric_expansion_of_space, but we are just looking at distance and speed as factors here (in OP's query), or gravity as it has entered the discussion.
But there is indeed a Doppler shift that can be caused by gravity, too.
That famous radio wave experiment showed that pulses take longer and longer to reflect back when the beam travels closer and closer to the sun.
Since the speed of light is constant in a vacuum, no matter what, that can only mean one thing - the path is longer, i.e. an apparent velocity differential.
Light speed is only constant in vacuo as locally measured. Choosing SC's (standard Schwarzschild coordinates), the coordinate speed of light is less than the proper (locally measured) value c by a factor (1-GM/r) in the radial direction, and by a factor (1-GM/r)1/2 in the tangent direction to a central mass. The split between distance contraction and time dilation as contributions to reduced c is considered by many as somewhat arbitrary. Using ISC's (Isotropic SC's), coordinate c is less than proper c by a different, isotropic factor, and the split between length contraction and time dilation will also be taken as different. In both cases though, overall signal delay is due to both gravitationally effected distance and time, not just distance.
That time delay causes a Doppler shift. The delay is longer than would be predicted by GR geometry alone, but that's irrelevant, it's still a Doppler shift caused by geometry. It is exceedingly tiny but not non-existent. That's because it appears as if there is relative movement, even though there isn't - the source and observer don't intrinsically "know" that the beam has passed through a portion of distorted space-time.
There is both angular deflection and time delay, but no appreciable 'Doppler shift' (frequency change) provided light source and observation points are both far from the source of gravity. Only a significant difference in gravitational potential between source and receiver will give redshift/blueshift.
Gravitational lensing also causes a Doppler shift.
It's exceedingly tiny as well, but it's there.
Neither one of these two examples of gravitational Doppler shifts can possibly be blue-shifting because neither case can result in a shorter apparent path.
Covered by previous comment - Shapiro type time delay does not imply frequency change.

"So if a supernova exploded in the galaxy exactly 10 million years ago,the stationary alien would see it 10 million years later.
The alien cycling toward the galaxy would see it 9,999,999.8 years later."

Correct.
Originally Posted by Vanadium90: "The cycling alien would see it sooner."

Incorrect. Both aliens see the explosion at exactly the same time, but they disagree when it happened.
The assumption here being that stationary and cycling aliens are coincident when the light arrives. Is that any different to my alternate 'physical' explanation in #17, where the cycling alien observes a motional doppler shift, infers a slower time rate for events, and projects that rate for 10 million years in order to arrive at a different 'now' than the stationary alien? I try to give a handle on how the sense of a different now is arrived at by the actual observers. In #1, two different effects are presented. The first - Greene's scenario, implies a dominant ~ v/c factor (for v<<c) at work (motional Doppler -> spatial/temporal separation 'over time'), the latter one implies a far smaller ~ v2/c factor (transverse Doppler = time dilation) http://en.wikipedia.org/wiki/Relativistic_Doppler_effect. Both are generally always present, but the former is overwhelmingly greater for v << c. Disagree?

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OK have no objection on that.

Covered by previous comment - Shapiro type time delay does not imply frequency change.
Yes, of course, but it can cause an apparent velocity differential under the right conditions which gives a Doppler shift.
I could propose a thought experiment to show that, but it's getting a little too much off topic, probably.
It is under conditions where the source and the observer are at exactly the same gravity potential.
I think I was wrong about gravitational lensing possibly causing a Doppler shift, I'm still thinking that one out.

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Yes, of course, but it can cause an apparent velocity differential under the right conditions which gives a Doppler shift.
I could propose a thought experiment to show that, but it's getting a little too much off topic, probably.
It is under conditions where the source and the observer are at exactly the same gravity potential.
Ah - you may be right about a 'blip' type Doppler shift if this is referring to a dynamical aspect, where one is bouncing radar off say an orbiting planet as it passes behind the sun, or where a massive object passes across the line of sight between 'fixed' source and receiver. That should give a very small and brief kind of 'FM modulation' that symmetrically cancels as per a full sinusoidal cycle (modulation cycle that is - not one cycle of emitted radiation!). It would not exist though if source, receiver, and gravitating mass are in a fixed relation. So was that your idea?

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Ah - you may be right about a 'blip' type Doppler shift if this is referring to a dynamical aspect, where one is bouncing radar off say an orbiting planet as it passes behind the sun, or where a massive object passes across the line of sight between 'fixed' source and receiver. That should give a very small and brief kind of 'FM modulation' that symmetrically cancels as per a full sinusoidal cycle (modulation cycle that is - not one cycle of emitted radiation!). It would not exist though if source, receiver, and gravitating mass are in a fixed relation. So was that your idea?
OK, no one is yelling at me for being off topic so here goes:
Tell me if you can spot any logical errors in my thought experiment.

You have two spaceships traveling far apart form each other, but at the same velocity/direction.

They each use sophisticated celestial navigation to remain exactly the same distance from each other at all times (pretending they are in "flat" space at all times during the experiment).

Ship One continuously (no pulses) broadcasts an ordinary, spherically radiating microwave signal set at an extremely precise fixed frequency as monochromatic as possible.

Ship Two (the observer) receives the signal and measures the frequency with extreme precision.

They both pass by the sun perfectly tangentially, with the sun in between, so eventually the signal is blocked.

As the ships approach the sun, the apparent distance between the ships should increase at a rate which is mostly (but not a simple calculation as it is in "flat" space) proportional to the tangential velocity of the two ships with respect to the sun because the signal now has to pass through a region of space where the signal follows geodesic lines.

The two ships have to be far enough apart at all times from the sun to be in "flat" space and at exactly the same respective gravitation potential, to eliminate any "ordinary" gravitational red-shift.

If that rate of change of apparent distance is reasonably constant, there should be a Doppler shift in the received signal which remains about the same until the sun blocks the signal.

As they regain the signal after passing the sun, the Doppler shift should still be there exactly the same as before they passed the sun.

Once the two ships get far enough away for the sun to be in "flat" space again, the Doppler shift disappears.

The key is that the ships HAVE to use celestial navigation at all times to remain the exact same distance from each other, ignoring GR space-time distortion that the radar signal passes through.

If the apparent distance change includes an apparent acceleration, then the Doppler shift should also change as the ships approach and depart the area near the sun.

The experiment then can be repeated, with Ship Two now merely reflecting the signal back to Ship One. Now, Ship One is both the source and observer. The observed Doppler shift should be exactly twice as large, no matter if there is just an apparent constant velocity OR acceleration.

Of course, the Doppler shift will be tiny, probably unmeasurable even by the finest interferometer techniques available presently. I'm also assuming that any possible gravitational lensing will be far lower in intensity than the apparent Doppler effect and that the observer ship can completely eliminate the effect of any microwave signals coming from the Sun during the experiment. That could be the fly in the ointment.

As far as relating this experiment to the thread topic, I think it is safe to assume that both ships would experience the "same now" as an abstract construct, while their instruments are simultaneously telling them otherwise.

ha, ha, get it? simultaneously telling them they are not in the "same now." LOL

They both pass by the sun perfectly tangentially, with the sun in between, so eventually the signal is blocked.
This is equivalent to my second guess. If the radar beam is very narrow it will be blocked, otherwise diffraction ensures some 'gets by'.
If that rate of change of apparent distance is reasonably constant, there should be a Doppler shift in the received signal which remains about the same until the sun blocks the signal.
To the extent rate of change is constant, yes. But I would expect a rather peaky affair.
As they regain the signal after passing the sun, the Doppler shift should still be there exactly the same as before they passed the sun.
Not quite - sign of Doppler shift will reverse owing to reversed sense of rate of change of time delay. That's what was meant by 'full sinusoidal modulation cycle' - cancels overall. You will have to do your own searching on this, but in general it should be covered in theory of electro-optic phase modulation - in particular the transient modulation of the refractive index of an optical fiber element passing monochromatic light. Fascinating to consider the fine details. but yes, this is getting off topic.

This is equivalent to my second guess. If the radar beam is very narrow it will be blocked, otherwise diffraction ensures some 'gets by'.

To the extent rate of change is constant, yes. But I would expect a rather peaky affair.

Not quite - sign of Doppler shift will reverse owing to reversed sense of rate of change of time delay.
Yep, you're right. I was proposing a spherical wave propagating from the source like a radio station with only one antenna, not a beam, but sure a little bit would get by due to diffraction.

As the ships come out from behind the sun the apparent distance will appear to be decreasing with time, giving a blue shift, I missed that somehow. So, you CAN get a blue shift from gravitational bending, I was wrong about that. It would certainly be a very strange set of red, then blue shifts like you said.

It is fascinating and far from my expertise, which is polymer physics. Especially some of the newer results coming out using materials with negative RI's, which I don't understand at all.

I sent the thought experiment to my physics major college sophomore daughter. It will be interesting if she spots my error. If she does she'll be happy, she loves catching my mistakes!

Now, back to NOW! LOL

I sent the thought experiment to my physics major college sophomore daughter. It will be interesting if she spots my error. If she does she'll be happy, she loves catching my mistakes!
And maybe she's a good catch!:!!)
Now, back to NOW! LOL
Right on - there's no time like the present!

And maybe she's a good catch!:!!)

Right on - there's no time like the present!
Her boyfriend thinks so, and he's Russian from a rich family, so that's OK with me,
especially since they are both straight A physics majors this semester. <shameless bragging/>

And there is no better present than time!
I hope I get lots for Xmas.