I knew you didn't mean to imply there were gaps.

I don't think the alternative analogy is an improvement.
If the two observers are reading different stories, we have
no way to compare their experiences, so the analogy doesn't
reveal anything.

I disagree that the confusion you wish to avoid is actually
significant, and disagree that your way of considering time
relationships is superior. On the contrary, as it has been
expressed so far, it introduces greater confusion than it
possibly eliminates. A better analogy might fix that, or
it might not.

In any case, as you said originally, and as you say next, the
two stories begin identically and end identically, so if pages
are not ripped out from the middle, how can they be different?
Makes no sense to me.

I don't believe that I'm hanging on to any concept of absolute
time. It is not obvious to me that people who ask about time
running faster or slower are hanging on to a concept of absolute
time, either. But I'm not sure if we disagree on how to describe
time relationships or if we merely disagree on the efficacy of
the analogy you introduced.

I think your original analogy was really nifty-- different people
reading the same narrative at different rates, yet interpreting
the time flow in the narrative as being equivalent. But I'm not
at all sure that nifty analogy is appropriate, useful, or clear
in explaining time relationships in relativity.

We have three different times: The amount of virtual time in
the narrative being read, the amount of time it takes the Earth
person to read that narrative, and the amount of time it takes
the Jupiter person to read the narrative. It is the fact that
the narrative is identical for the two readers which allows a
comparison to be made. Without that identity, the analogy says
nothing at all: The Earth reader has time to read 'War of the
Worlds', but the Jupiter reader doesn't have time to finish
'War and Peace'. Okay, so what? It doesn't tell us anything
about the time relationship between the two readers.

There is only one movie.
The distance from the movie screen to Earth is virtually the same
as the distance from the movie screen to Jupiter, such that there
are no differences in light time-of-flight from the screen to the
two observers.

They each see every frame of the movie, from beginning to end.
They are together when they see the first frame, and again when
they see the last frame. In between, since I manage to finagle
the trajectory of the visitor to Jupiter such that there are no
differences in the light time-of-flight, you might say that the
two observe the same frames simultaneously. Yet the one who goes
to Jupiter sees the movie in less time than the one who stays on
Earth. He likes the movie better because it was faster-paced
than the movie the Earthbound observer saw.

Yes-- they did see two different movies, even though they were
watching the same projection on the same screen, what you might
consider to be "simultaneously".

I'm not convinced that there is such a thing as "simultanaity"
for distant observers, though. For observers who are together,
yes. Start moving them apart and it becomes less and less clear
what "simultaneous" means. When they are far enough apart that
they can no longer communicate, it may mean nothing.

In my analogy, the two observers watch the same movie, but the
Jupiter viewer sees a shorter, faster-paced movie than the Earth
viewer. In your analogy, the two read two slightly different
stories, with some of the action left out of the Jupiter story
in order to make it fit his available reading time. What action
is left out? Where in the story is it left out? How is it left
out? These questions are difficult or impossible to answer.
It may be the fault of your analogy, or it may be the fault of
the concept you intend the analogy to convey. I don't know
which. The analogy is too confusing.

If they are watching two different movies, or reading two different
books, there are no simultaneous events, no comparison between the
two different narrative timelines, and there is no point to the
non-analogy.

Was anyone saying that? Anyone?

Given my scenario, that they both watch the same movie, how would
you explain why the movie is shorter and faster-paced for one than
for the other?

-- Jeff, in Minneapolis

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"I find astronomy very interesting, but I wouldn't if I thought we
were just going to sit here and look." -- "Van Rijn"

"The other planets? Well, they just happen to be there, but the
point of rockets is to explore them!" -- Kai Yeves

Perhaps a simpler example would be the observation of a very distant surpernova? Assume the supernova is 5 billion light years away and we on Earth measure the duration of the supernova as 500 hours. If we had previously sent a clock to Jupiter, an observer on Jupiter would see that clock measure the very same supernova as having a shorter duration than 500 hours.

If we on Earth could observe that clock on Jupiter with a telescope we would see it ticking away the seconds slower than clocks here on Earth. The observer on Jupiter also watches that clock ticking away the seconds, and if they look in their telescope they see our clocks on Earth ticking at a faster rate. So we can say that clocks run faster on Earth than they do on Jupiter as we have seen both clocks running at constant, but different rates.

Does that mean that scientists who evolved in a different star system on a planet with higher gravity, using the exact same theories and clocks as our own, would have a different figure for the age and size of the observable universe?

On the contrary, relativity does give us a way to compare their experiences, that's part of the whole point of relativity! The analogy is quite precise in that regard. Of course, the stories may refer to similar events happening somewhere else-- and if so, that is merely bringing in yet a third observer (the one those other events are happening to)-- and yet a third story. The idea that there is just "one story" here is exactly what relativity is telling us we have to get away from thinking. There are many stories, and only when you put them all together do you get "objective reality", because reality is in the experiences of the observers and nothing else. We have no other way to even talk about reality, now do we?
And yet, this is precisely how reality works. This is an observed result.

Then we'll have to agree to disagree. I think the analogy is spot on.Correct-- these are called "proper times".
No, if you say the narrative is identical, then the narrative only includes what is happening to one observer. There is nothing to compare to-- the "comparison" you mention simply does not exist. The actual comparison that gets made is between two different narratives, the narrative of what happens to one observer, and the narrative of the completely different experiences of the other observer while considering what is happening to that first observer. Those are different narratives, and all differences in time stems from those differences in narratives. Otherwise, what "difference" are you referring to? You are talking about two clocks-- each clock is its own narrative, or there is no comparison to be made.
The analogy is not intended to tell the time relationship, one needs relativity for that. The analogy tells you why you need relativity, nothing more.
Again, that is incorrect. There are two movies, each is a movie of a clock. The reason the clocks read different times is not that the "rate of time" is different, it is simply that there are in fact two movies. If you say the "movie" is just the other clock, what comparison are you drawing? You need two clocks, and that's two movies, that's the deal.
You can set the light time of flight time to be anything you like, it makes no difference to me. Communication could be entirely at the vastly slower speed of sound, through all kinds of different media, and my understanding of the relativity will be no different.
All you are saying is that each clock sees two movies-- its own movie, and the movie of the other clock. That does not answer anything-- what matters is that one movie is longer than the other (say in the twin paradox). Thus the issue is, what interpretation do we give to the fact that one movie is longer than the other?

Some say it means one movie had "faster time", but I'm saying that perspective makes the implicit assumption that somehow the duration of the two movies had to be the same, so if more happens in one movie, itw as "sped up". No, I say, relativity is the relaxing of the requirement that two different movies that start and end at the same place and time but follow different courses have to be the same duration, that is very much the central concept of relativity-- the accumulation of differences in simultaneity can be permanently ingrained along closed paths in spacetime. So saying "time is sped up" is exactly missing much of the point of relativity, and I think is a leading cause of many of the questions we have on this forum from people who are misled into a false understanding of what relativity means.

I'm not sure what you are trying to construct here. In the twin paradox, the spaceborne twin can watch a movie of the stay-home twin, and in so doing see a movie in which a lot happens in a short time. Similarly, I can speed read "War and Peace" and achieve the same sensation. To me, all this does is support the value of the analogy.
I think you are starting to get at what I am saying, and the important difference between what is local and we can experienece, versus what is nonlocal that we conceptualize. Simultaneity is not a "thing", it is a convention, defined in relativity. That's all it is, it's a useful convention. What is invariant is the accumulation of simultaneity shifts that become real on closed paths in spacetime-- one has to include some way to handle that in the theory, because they are observed. Relativity has its way of treating simultaneity that accomplishes this.
Again, it is not at all unclear in relativity. But what you are really saying is, the concept takes on an arbitrariness. Exactly-- that's just what I mean about the arbitrariness of associating pages in two different books, read at two different speeds. Should we say the book that is read slowly has a slower rate of time, or shall we say that all characters in books experience time normally, the "problem" is with the person reading/watching them? The latter is my analogy.

You could take it a step further and imagine a reader who is nearsighted, and can read nearby books very quickly but blurry faraway books only slowly. Now the "twin paradox" is two books, one that stays in the reader's lap, while the other is moved to a larger distance and then moved back. We are not surprised the reader has made less progress in the "spaceborne" book-- do we then say that "time was slow" for the characters in the spaceborne book? So why would we say that in the twin paradox? It feeds the very misconceptions that relativity requires we escape.

The difference in these analogies has nothing to do with interpretations of time flows, it is merely in which movies you are talking about. My analogy explains why one twin gets to have more experiences than the other, while they are separated. Those are two different movies. You are talking about how one twin experiences their own life, versus how the other twin conceptualizes the rate of action in that same first twin's life. So your analogy is like a single book read by readers of two different speeds-- so one gets a fast-paced book and the other a slow-paced book, but it's the same book. So you see, it's still my analogy, just looking at a different aspect of the exact same situation. The analogy works fine for both situations-- the nearsighted reader of two books, or the fast and slow readers of the same book.

I just explained why none of these questions are hard to answer at all, and why the analogy works perfectly to answer them.

On the contrary, as I mentioned above, relativity is perfectly clear in its convention for matching up simultaneous events in the two movies/books.
I'd explain it by saying that if ten different readers read War and Peace, it will indeed be shorter and faster-paced for some than for others. No trouble there, the analogy is again spot on. What you need relativity for is to tell you which are the fast readers, not whose "time is sped up".

My friend and I have had this discussion without being able to figure it out.:

If we have a car and a bus that each can travel at 0.75 times speed of light. Then each of them starts travelling in exactly (180 degree) opposite direction to each other in a straight line from a given spot in space.

Now won't the car be travelling greater than the speed (1.5 times) of light as viewed by someone travelling in the bus ?.

Sorry, this may be a simple answer to some but not to me.. if you do know, what IS the answer ?.

One suggestion that came up was that for the traveller in the bus time is slowing down and distances as measured is shrinking with this slow down in time the traveller in the bus will still calculate the speed of the car as less than the speed of light. Is this suggestion plausible and is the answer ?.

No, that would violate relativity. With questions like this, it pays to note how different reference frames get different answers. If you choose the "stationary" reference frame in which the car and bus have the speeds you quote, then indeed the distance between the car and bus will increase at the rate 1.5 c. However, nothing is actually moving at that speed in that frame-- it is just a mathematical quantity, a rate of change of distance between two moving objects.

To interpret 1.5 c as an actual speed, you have to take the reference frame of the car or bus, but then a strange thing happens-- in that frame, the other vehicls is not moving at 1.5 c, it is moving at a speed < c. Relativity tells you how to switch from the stationary frame to the vehicle frame-- so it explains why the other vehicle's speed will not come out 1.5 c. In other words, relativity is not a theory about how things move, it is a theory about how to change reference frames and look at the same movement.
That's basically right, that's how the speeds can come out different from you'd naively expect. But be careful, the words you chose represent an implicit choice of a reference frame-- the stationary frame, not the frame of the bus. It is quite important to be explicit, not implicit, in your choice of reference frame for every statement you make. Time in the bus, on the other hand, is just time, functioning normally-- it is only when that time is viewed from a different frame that it seems like a different time. So times and lengths can be messed around, and the notion of what "now" means also gets messed around, in two different frames-- but that is because we have changed frames, not because time has changed.

If you look at events happening to the person actually experiencing them, time happens normally, that's what we mean by the laws of physics being the same for all observers. But when you look at what is happening to one observer from the "point of view" of a different observer at a different place to whom those events are not actually happening, then time can appear to be slowed down. It's not time that's slowed down, it is the way that other observer is matching up those events to the events that really are happening to them. That was what the analogy with the books was about-- each observer has their own book, with different things happening in them, but when they are at the same place and time the events in the books must be the same. The lengths of the books, however, do not have to be the same, it's all in how you match up the pages and call them simultaneous with each other.

Some more (maybe silly) random thoughts/questions ?..

Physics says: Speed of light is the maximum upper bound on the speed of travel in a straight line.

What is the maximum upper bound on the speed of rotation -- radians per second ?.

Is there a maximum speed and does it depend on the size/radius of the object.. lets just consider spherical objects for now.

Does the mass of the object grow bigger as it rotates faster ?.

Does the object becomes smaller as it rotates faster ?. So if the speed of rotation approaches the above maximum speed what is the radius of the object approach to ?.

If an object becomes smaller as it rotates faster.. then the rate at which it should shrink be faster for the same rate of increasing rotation speeds for bigger objects ?.

Actually; they sound like pretty good questions to me. I don't have an authoritative answer, but do have some thoughts to test my understanding of the topic...

The rotation is dependent on the angular momentum of the material that makes up the object. Tidal forces are another factor, but at those speeds, there's nothing that can possibly speed it up. Anything outside the surface would be slower than surface speed.

Any incoming material would not go SOL unless it would be a black hole. That's where the advanced physics come in. I would think that would be the maximum limit based on the framing of your questions.

As far as growing or shrinking. Again; it's the constituent material (at least in the Newtonian sense) so the remaining questions need to take that point of view rather than from the view of the object itself changing.

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If light cannot be observed at rest, then what happens when light is slowed, as in a supercool rubidium gas thingy?

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It depends on how you choose to model the light. If you take a classical electromagnetic description, then it is possible to slow the group velocity of the fields that you see propagating around, if you put the waves in a medium. Slowing light is how your eyes focus images, for example. But one can also say that the light itself is not slowed, only the interference pattern that controls the fields, and the fields tell the light where to go. The light itself can be treated as a particle that is flitting about in those fields, always at speed c, but not necessarily in a straight line.