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Originally Posted by Celestial Mechanic
Please look at my earlier posting in this thread for the resolution of the twin "paradox". The proper formulae for the redshift and blueshift are still not being used which is why you are arguing about a non-existent "jump". Please read my two "When Harry Meets Sally" posts in the "Einstein's Theories ..." thread where the K-calculus is used to derive the proper formulae.
The "jump" exists when trying to define "Now" for distant events in different reference frames. Certainly if you look at things from a redshift/blueshift perspective, and just keep track of what time you see when looking through a telescope you don't have any of these problems. Maybe your approach is the better one--it leaves off a lot of the fiddly bits.

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I'm inclined to agree. I think whatever Sam5 is misunderstanding is pretty fundamental, so a simple solution to this non-paradox has got to be a help.

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Originally Posted by freddo
I'm inclined to agree. I think whatever Sam5 is misunderstanding is pretty fundamental, so a simple solution to this non-paradox has got to be a help.
I don't think Sam5 is ever going to agree with any of you, no matter how patiently you explain it to him.

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Here's the answer using simple equations:

(tau)^2 = (time)^2 - (distance)^2

Bob travels at 3/5c. Therefore in 10 years (as measured by Anne's clock) he moves a total distance of 6 light years (as measured by Anne). But Bob does not move at all in his own frame of reference!

So Bob's wristwatch time is tau.

(tau)^2 = (10)^2 - 6^2 = 100-36 = 64 (years)^2

Therefore Bob's time elapsed is 8 years but Anne measures 10 years. QED.

I'm also of the opinion that Sam5 will take no notice of clear explanations.

5. Originally Posted by Sam5
Why don’t you apply that here? Bob is “stationary” while Ann “moves”.
Originally Posted by Sam5
It’s not the kids’ fault that they don’t understand this.
It's not an adult's fault either, this is not an easy subject.

It's not their fault, unless they just don't want to understand it.

6. Okay, Sam, I've realized that your misunderstanding of SR is much more basic than I previously thought. So, let's start at the very beginning. Much of the next couple of paragraphs is real basic stuff, and I am not implying that you don't understand it. I just want to plainly set out what we're talking about.

First of all, take a plain piece of paper (not graph paper this time) and mark a point on it. Now, how can we define that point? We can use cartesian coordinates, and say it is (x,y). No two points on the paper will have the same x,y values, so those values uniquely identify that particular point . . . except: those numbers, by definition, only define that point relative to another point, (0,0). On a sheet of paper, we can easily identify a corner as (0,0), with the edges as the axes. However, if the paper were infinite in size, we would have to simply arbitrarily define an origin point (0,0) and arbitrarily define our x- and y-axes, and then we can define all other points relative to that point.

Now, to move into three-dimensional space, we need to add a third coordinate, z, with its own arbitrary axis. To locate an event, in space-time, we add a fourth coordinate, t, with its own axis. So, once we define our arbitrary origin point at (0,0,0,0), any other point can be defined relative to that origin by it's own coordinates (x,y,z,t).

Let's say you've got a light bulb sitting next to you. You turn the light bulb on. That's our first event, so we'll designate that as the origin and call it (0,0,0,0). Five minutes later, you turn off the light. That event occurs at (0,0,0,5) - our spatial coordinates stay the same. Five minutes after that, you smash the bulb. That event, then, is at (0,0,0,10).

Now, here's where SR gets a little complicated. Consider that under SR there is no absolute motion, only relative motion. That means that from a reference frame that is in relative motion to that light bulb, the spatial events would change for those events. For this discussion, we'll limit the movement to being along the x-axis. So, if our reference frame says the light bulb is moving to the left at 0.6c, then the light-bulb can't even be at (0,0,0,5) for that second event. At best, it would have to be at (-3,0,0,5). Now, keep in mind that we are not physically changing anything. All we are doing is changing the designation of that point in space-time. With me so far?

Now, here's where SR get's really complicated. The speed of light, c, must remain a constant. If we consider two events - a pulse of light being emitted at an emitter, and that light being received at a receiver - then, we can conclude that the values of x (in light-minutes) and t (in minutes) must be the same. So, if relative motion causes us to conclude that the value of x changes, then so too must the value of t change.

Now, again, we are not physically changing anything. All we're doing is saying that a point in space-time corresponding to (0,0,0,5) relative to the origin in one reference frame would correspond to (-3.75,0,0,6.25) relative to the same origin point but in the other reference frame. [NOTE: I had the numbers wrong in this last sentence and have corrected them]

Now, I think I'm just going to leave it at that for now and we'll make sure this is clear before we move on any further.

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Originally Posted by Diamond
Bob travels at 3/5c. Therefore in 10 years (as measured by Anne's clock) he moves a total distance of 6 light years (as measured by Anne). But Bob does not move at all in his own frame of reference!
You can’t mix distances like that. You have Ann seeing Bob move 6 light years in distance at the velocity of .6 c, while you have Bob seeing Ann move only 4.8 light years distance at the velocity of .6 c, so you’ve got two different experiments, two different “trips” mixed into one.

In one trip, you’ve got Ann seeing Bob moving 6 light years, and in the next trip you’ve got Bob seeing Ann moving 4.8 light years. Then you are comparing Ann’s clock time at the end of the first thought experiment to Bob’s time at the end of the second thought experiment.

Of course if Ann sees Bob move 6 light years at .6 c that will take 10 years by her clock. And if Bob sees Ann move 4.8 light years at .6 c, that will take 8 years by his clock.

Your thought experiment has Bob turning around too soon, at 4 years on his clock, which is the same dilated 4 years that Ann sees on his clock while she sees 5 years on her clock. But Bob doesn’t “see” that same dilation on his own clock because he is in his own inertial frame and he sees Ann, not himself, as moving and time dilating.

By having Bob turn around based on what Ann “sees” on his clock, the guy who invented this thought experiment is not following SR theory and he is purposely making the distances and times traveled asymmetrical.

Einstein didn’t do this, the guy who wrote the thought experiment did this.

Einstein created the clock paradox by reporting only what one observer saw on all the clocks, and he left out any mention of what the other observer saw. That was a small error on his part.

In the Ann and Bob thought experiment, the inventor of it has Ann and Bob moving different distances just so they can both “see” different times for the other to travel those distances. That is not an “error”, it is something else.

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You are playing with early 20th Century mathematical diagrams and you aren’t even paying attention to what happens in reality. This kid has a good grasp of what happens in reality:

“The light from a distant star passing right near the surface of the Sun on the way to the observer takes the form of a plane wave. The rays of the plane wave of light traveling closer to the Sun (source of gravitation) are in essence slowed due to the effect of time dilation only. If the light of the rays closer to the Sun travel slower over a reference time increment than the rays farther away, then using Huyghens’ principle, the plane wave is deflected toward the source of gravity (see figure 25)........ The light pulse moves with a velocity less than "c" along the curve relative to reference observers far away......”

SOURCE

If in reality, your reference frame is a galaxy moving at .6 c relative to the earth, which is just about the only thing that actually does move at .6 c relative to the earth, then the speed of light inside that galaxy is “c” relative to the stars in the galaxy, but photons of light inside that galaxy that are aimed in the direction of the earth and that will eventually reach the earth are moving at less than c relative to the earth, while they are inside that galaxy.

Originally Posted by SeanF
Now, I think I'm just going to leave it at that for now and we'll make sure this is clear before we move on any further.

Before we move on any further, you need to understand what is happening in physics and cosmology today.

On the large astronomical scale, “c” is no longer a “limiting speed”, and “c” is no longer the only speed of light relative to all observers.

Things have changes during just the past 10 years.

“in these cosmological variables the speed of light is c with respect to local comoving observers.

The time and distance used in the Hubble law are not the same as the x and t used in special relativity, and this often leads to confusion. In particular, galaxies that are far enough away from us necessarily have velocities greater than the speed of light:

(diagram)

The light cones for distant galaxies in the diagram above are tipped over past the vertical, indicating v > c.

SOURCE

I’ve mentioned to you before that modern cosmology theory is no longer bogged down in the old transitory Edwardian era of electrodynamics and kinematics theoretics, and it has now entered the 21st Century.

9. Originally Posted by Sam5
Originally Posted by SeanF
Now, I think I'm just going to leave it at that for now and we'll make sure this is clear before we move on any further.
Before we move on any further, you need to understand what is happening in physics and cosmology today.

On the large astronomical scale, “c” is no longer a “limiting speed”, and “c” is no longer the only speed of light relative to all observers.

Things have changes during just the past 10 years.

“in these cosmological variables the speed of light is c with respect to local comoving observers.

The time and distance used in the Hubble law are not the same as the x and t used in special relativity, and this often leads to confusion. In particular, galaxies that are far enough away from us necessarily have velocities greater than the speed of light:

(diagram)

The light cones for distant galaxies in the diagram above are tipped over past the vertical, indicating v > c.

SOURCE

I’ve mentioned to you before that modern cosmology theory is no longer bogged down in the old transitory Edwardian era of electrodynamics and kinematics theoretics, and it has now entered the 21st Century.
You still don't understand what you're talking about. "[L]ocal comoving observers" in your quote above refers to observers close enough to the emitter that the expansion of space has no effect, whether those observers are at rest relative to the emitter or not. They're saying exactly what I said, that the expansion of space contributes to the recession values of distant galaxies (and the light coming from them), but it does not invalidate Special Relativity.

However, I am now forced to conclude that you no longer insist that SR is flawed in and of itself, but only consider it flawed in that it doesn't deal with the expansion of space. If you did consider SR to be internally inconsistent, then you would be willing to discuss it under those terms.

10. Hey, Sam5, did you read that whole page before you posted it?

"But there is no contradiction with the special relativistic principle that objects do not travel faster than the speed of light, because if we plot exactly the same space-time in the special relativistic x and t coordinates we get: (diagram)"

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Originally Posted by Jobe
Originally Posted by freddo
I'm inclined to agree. I think whatever Sam5 is misunderstanding is pretty fundamental, so a simple solution to this non-paradox has got to be a help.
I don't think Sam5 is ever going to agree with any of you, no matter how patiently you explain it to him.
Agreed. His misunderstandings are SO fundamental that he simply won't even acknowledge them when pointed out. He won't discuss the basics, only the more complicated impications. Until he's willing to step back and start from the beginning and ACCEPT the facts (there are many factual errors in his posts, not just errors in the application of the theory), he won't be able to learn why he is wrong.

All of the math you guys are doing is pointless until he learns what the theory SAYS. Then he can learn how to calculate what it says.

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Eroica, I just read this entire thread and wow did you open up a can of worms however, I am learning more every day. I love this board. 8)

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Originally Posted by crazy4space
Eroica, I just read this entire thread and wow did you open up a can of worms however, I am learning more every day. I love this board. 8)
Well, it's not so much that Eroica opened up a can of worms as the can of worms leaped from another thread to this one (leaping worms. I assume they manage that something like a pogo stick).

I think the worms first started in the Einstein's Theory of Relativity thread before hopping here. If I may, I'd like to suggest that we make some attempt to isolate the worms to this thread--if they show signs of spreading to yet another thread, just refuse to reply. Even better, perhaps they can be shovelled into the Against the Mainstream section.

14. Originally Posted by Sam5
....This kid has a good grasp of what happens in reality: ...The rays of the plane wave of light traveling closer to the Sun (source of gravitation) are in essence slowed due to the effect of time dilation only.... The light pulse moves with a velocity less than "c" along the curve relative to reference observers far away......” SOURCE
Though some of the contributing authors to the "Physics Post" website you linked to are respected and quite well known (Paul Davies, Michio Kaku), there are other contributors who are students and amateurs. Now, certainly students and amateurs have the potential to be correct, but I don't think it is at all effective or compelling to cite such Physics Post contributors as authorities on topics as well investigated as general relativity. Erich Schoedl, the author of the post you cited, includes nothing in his biographical thumbnail about who he is, what his background or qualifications are, and he appears nowhere else on the internet.... For me, this does not instill much confidence in his particular interpretation of the reality behind geodesics.

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Originally Posted by Sam5

I also say that “relative motion” can not have any possible effect on any kind of clock, since the clock feels no kind of “force” applied to it through “relative motion” alone.
Sam, you've said this over an over. What you need to understand is that it's not the clock that's affected by time dialation, it TIME that's affected by time dialation. The clock is merely part of that reference frame, and is used to represent this difference in the passage of time. There doesn't need to be any kind of "force" involved

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Originally Posted by Sam5
For example, the earth is moving “relative” to billions of other bodies, and we can’t possibly have any kind of real “time dilation” effect caused by our “relative motion” relative to those other bodies.
Sure we can experience time dilation! We ARE experiencing time dilation, when observed from a another reference frame moving at relativistic speeds compared to our frame. We, just as they, say "all is normal here, while time is slow over there". This is what makes SR such an interesting topic!

17. Originally Posted by daver
... (leaping worms. I assume they manage that something like a pogo stick.)
Worms? Probably some form of quantum tunneling.

18. Originally Posted by Jim
Originally Posted by daver
... (leaping worms. I assume they manage that something like a pogo stick.)
Worms? Probably some form of quantum tunneling.
Wow! Is the BABB the location of the first stable wormhole in the Internet Quadrant? Should we start calling this place BAjor?

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Originally Posted by Eroica
Originally Posted by Eta C
The problem is that from B's point of view there has to be a time where he sees A's clock as running fast compared to his. That can't happen during the coasting periods. We've all agreed that during those periods he sees A's clock as running slow, as predicted by SR. The time when he sees A's clock running fast has to come during the non-inertial accelerations. To determine that, from B's non-inertial reference frame, requires GR.
This seems to be the nub of the problem. I for one do not agree that B sees A's clock as running slow during all the coasting periods, and fast during the accelerations. On his way out, B sees A's clock running slow and A sees B's clock running slow. Then B turns for home and immediately B sees A's clock running fast. A's clock continues to run fast from B's perspective all the way home. But A does not see B's clock running fast until some time after B's has turned for home. (Let's say B turns for home when he is 10 uncontracted light-years away: A won't see B's clock running fast until 10 years after B has turned around.)
Sorry yet again for lagging a couple day's behind. . .

Eroica, as stated in the other thread, the above is not correct. SR time dilation has nothing to do with direction. A's clock appears to run slow to B both going away and heading back home.

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Originally Posted by Wally
Eroica, as stated in the other thread, the above is not correct. SR time dilation has nothing to do with direction. A's clock appears to run slow to B both going away and heading back home.
I don't remember the post of Eroica's that you're quoting, but if B is observing A's clock through a telescope, B will see A's clock as running slow on the way out and fast on the way back (Doppler effect). If B is trying to compensate for Doppler by using the classical equation, or looks at A's clock while passing, then Yes, A's clock will appear to be running slowly.

21. Originally Posted by Wally
Originally Posted by Eroica
Originally Posted by Eta C
The problem is that from B's point of view there has to be a time where he sees A's clock as running fast compared to his. That can't happen during the coasting periods. We've all agreed that during those periods he sees A's clock as running slow, as predicted by SR. The time when he sees A's clock running fast has to come during the non-inertial accelerations. To determine that, from B's non-inertial reference frame, requires GR.
This seems to be the nub of the problem. I for one do not agree that B sees A's clock as running slow during all the coasting periods, and fast during the accelerations. On his way out, B sees A's clock running slow and A sees B's clock running slow. Then B turns for home and immediately B sees A's clock running fast. A's clock continues to run fast from B's perspective all the way home. But A does not see B's clock running fast until some time after B's has turned for home. (Let's say B turns for home when he is 10 uncontracted light-years away: A won't see B's clock running fast until 10 years after B has turned around.)
Sorry yet again for lagging a couple day's behind. . .

Eroica, as stated in the other thread, the above is not correct. SR time dilation has nothing to do with direction. A's clock appears to run slow to B both going away and heading back home.
The time dilation (if a clock is running fast or slow) is direction independent. However the simultaneity difference (if a clock is ahead or behind) is direction-dependent.

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Hi Cougar,

I never said that the kid was an “authority”. In fact, I started to post his comments a few days ago, but I decided not to because he is not an authority.

What I said was, “This kid has a good grasp of what happens in reality:”

But this does not make him any kind of “cosmology authority”.

There is another kid on that board that has one of the worst “twins paradox” stories I’ve ever seen, and last night I started typing up a response to him to let him know what all he is doing wrong. But my response got up to be several paragraphs in length, and it pointed out so many things he said that are incorrect, I decided that I didn’t want to hurt the kids feelings by criticizing his paper so much, so I just didn’t say anything to him.

Originally Posted by Cougar
Erich Schoedl, the author of the post you cited, includes nothing in his biographical thumbnail about who he is, what his background or qualifications are, and he appears nowhere else on the internet....
I could tell by what he wrote that this particular kid is very smart. He has the light beam slowing down at the sun, as "seen" from the earth, but not slowing down at the sun, as "seen" from the sun, and that is correct. However, he didn't mention that at the sun, the beam in deep space will be "seen" as moving faster than c. It slows down to "c" at the sun only in reference to local sun atomic clocks. That is because the beam at the sun is in the same local "comoving space" as the sun and its local atomic clocks.

23. Originally Posted by daver
[Snip!]... but if B is observing A's clock through a telescope, B will see A's clock as running slow on the way out and fast on the way back (Doppler effect). If B is trying to compensate for Doppler by using the classical equation, or looks at A's clock while passing, then Yes, A's clock will appear to be running slowly.
Someone else here gets it. You cannot use the dilation factor gamma all by itself, nor the classical Doppler formula (1+beta for redshift of wavelength, 1-beta for blueshift of wavelength), but both together. In the example of Anne and Bob cited earlier, with the velocity of 0.6c, this means that both see the other's clock run half as fast during the redshift phase, and twice as fast during the blueshift phase.

Bob sees redshift for 4 years and blueshift for 4 years. During the redshift phase he receives 4*0.5 = 2 years of Anne's signals, and during the blueshift phase he receives 4*2.0 = 8 years more of Anne's signals, for a total of 10 years of Anne's signals received in 8 years.

Anne sees redshift for 8 years and blueshift for 2 years. During the redshift phase she receives 8*0.5 = 4 years of Bob's signals, and during the blueshift phase she receives 2*2.0 = 4 years more of Bob's signals for a total of 8 years of Bob's signals received in 10 years.

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Originally Posted by SeanF
The time dilation (if a clock is running fast or slow) is direction independent. However the simultaneity difference (if a clock is ahead or behind) is direction-dependent.
Yes, what he said. I had interpreted "running slow" as time dilated.

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Originally Posted by Eroica
Originally Posted by daver
Of course, if you're watching the earth clock via telescope you don't see the jump even when switching reference frames, you only get the jump when you try to compensate for distance (when you try to figure out "What time is it NOW on Earth").
The truth comes out at last! So I was right all along. Bob "sees" no jump in Ann's clock. Nor does he "infer" a jump when he tries to figure out what time it is NOW on Earth. Why? Because Bob is not an idiot. He understands relativity and is familiar with thing like time dilation, Fitzgerald-Lorentz contraction and the relative nature of simultaneity. He does the math and is not surprised to discover that 5 years have passed on Ann's clock when he turns around, even though only four have passed on his clock.
But, the point remains, Bob does NOT "see" ann's clock running faster than his on the return trip. It continues to run slower, just like it did during his outbound trip.

26. Originally Posted by Sam5
I could tell by what he wrote that this particular kid is very smart. He has the light beam slowing down at the sun, as "seen" from the earth, but not slowing down at the sun, as "seen" from the sun, and that is correct. However, he didn't mention that at the sun, the beam in deep space will be "seen" as moving faster than c. It slows down to "c" at the sun only in reference to local sun atomic clocks. That is because the beam at the sun is in the same local "comoving space" as the sun and its local atomic clocks.
Are you using "comoving" in the same context that Wright does on the pages you linked to? He uses it to mean "motionless relative to the Hubble flow":

Originally Posted by Edward L. Wright
The Hubble law defines a special frame of reference at any point in the Universe. An observer with a large motion with respect to the Hubble flow would measure blueshifts in front and large redshifts behind, instead of the same redshifts proportional to distance in all directions. Thus we can measure our motion relative to the Hubble flow, which is also our motion relative to the observable Universe. A comoving observer is at rest in this special frame of reference. Our Solar System is not quite comoving: we have a velocity of 370 km/sec relative to the observable Universe. The Local Group of galaxies, which includes the Milky Way, appears to be moving at 600 km/sec relative to the observable Universe.
(Bolding in the above is mine, italics are in the original)

That's not what you mean, though, is it?

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Originally Posted by daver
Originally Posted by Wally
Eroica, as stated in the other thread, the above is not correct. SR time dilation has nothing to do with direction. A's clock appears to run slow to B both going away and heading back home.
I don't remember the post of Eroica's that you're quoting, but if B is observing A's clock through a telescope, B will see A's clock as running slow on the way out and fast on the way back (Doppler effect). If B is trying to compensate for Doppler by using the classical equation, or looks at A's clock while passing, then Yes, A's clock will appear to be running slowly.
This thought experiment doesn't take actual doppler effects into account. The "seeing" bob does of Ann's clock is merely an illustration that Bob still perceives time going slower for Ann than he does for himself at relativistic speeds, regardless of direction. I think Eroica wanted (wants???) to have Bob perceive time as going faster for Ann on the trip home, in order to account for her being older when he gets back. This is what I'm trying to clarify.

28. Originally Posted by Wally
A's clock appears to run slow to B [when B is] both going away and heading back home.
I still disagree. If Bob keeps his telescope trained on Ann during the whole of his trip, he will see events on Earth taking place at slower than the normal rate during the outgoing phase of his trip. It would be like watching a movie in slow motion.

Once he turns around, events on Earth will appear to pass at an accelerated rate. Now it's as though Bob is watching one of those old Charlie Chaplin movies.

If this is not what Bob perceives, then how can he possibly observe all 10 years of Ann's life in just 8 years of his life? Perhaps we're still confusing two different meanings of the expression running slow?

29. Originally Posted by Eroica
Originally Posted by Wally
A's clock appears to run slow to B [when B is] both going away and heading back home.
I still disagree. If Bob keeps his telescope trained on Ann during the whole of his trip, he will see events on Earth taking place at slower than the normal rate during the outgoing phase of his trip. It would be like watching a movie in slow motion.

Once he turns around, events on Earth will appear to pass at an accelerated rate. Now it's as though Bob is watching one of those old Charlie Chaplin movies.

If this is not what Bob perceives, then how can he possibly observe all 10 years of Ann's life in just 8 years of his life? Perhaps we're still confusing two different meanings of the expression running slow?
I think we may be. If Ann is sending out "pulses" every second, Bob will receive all 10 years worth of pulses. Some of them he will receive faster than one per second, some slower. It is only when he tries to reconcile the observed Doppler effect with the predicted Lorentz contraction that he will notice something wrong.

As I said before (maybe in the other thread), I think it will appear to Bob as if there were two Anns for a period of time sending overlapping signals - they just don't arrive overlapping because some of them are coming from "farther away."

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Originally Posted by SeanF
As I said before (maybe in the other thread), I think it will appear to Bob as if there were two Anns for a period of time sending overlapping signals - they just don't arrive overlapping because some of them are coming from "farther away."
No, Bob should only see one Ann. She will be red-shifted when he's moving away, and blue shifted when he returns. If we're doing the 4 years out, 4 years back at .6 c (from Bob's point of view), he
sees (through his telescope) that two years for Ann will have passed during his outbound trip, and 8 years during his return trip (he sees her clock run at half speed on the way out and double time on the way back).

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