Everybody knows about the twin paradox. If a twin takes a trip in a spaceship around the galaxy while the other twin remains on earth, the twin who travelled will be younger than the twin who stayed home when he comes back.

The paradox is why the twin who travelled is the one to gets younger? Why not the one that stays at home? The answer is that the twin in the spaceship suffers the acceleration, so he is the one who gets younger.

Ok then. Now let's see another problem. Let's take two spaceships. Each twin is in one spaceship. They are approaching in a constant speed (close to the speed of light), with no acceleration. According to special relativity, twin A will se twin B getting youger, because in respect to twin A, twin B is moving. But, for twin B, twin A is the one getting younger, sice there can be no preffered referential. Hum, isn't that weird?

Now the problem itself: let's say that they are both smoking. They smoke at the same speed. Twin A smokes two cigarretes and sees twin B smoking one, due to time compression. Twin B smokes two cigarretes and sees twin A smoking only one, no preffered referential. Let's say now that when they cross each other in space, twin A throws his ash tray inside twin B spaceship. What will twin B see when he compares his ashtray with his brothers ash tray?
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Commented:
Or, if spaceship C signals the start, then it might look like:
From Twin A'a frame of reference:
11:50 Twin B starts 1st cigarette.
11:55 Twin A starts 1st cigarette.
12:00 Both twins finish 1st cigarette
spaceships pass, exchange ash trays.
Twins start second cigarette
12:05 Twin A finishes 2nd cigarette
12:10 Twin B finishes 2nd cigarette

and from Twin B's frame of reference:
11:50 Twin A starts 1st cigarette.
11:55 Twin B starts 1st cigarette.
12:00 Both twins finish 1st cigarette
spaceships pass, exchange ash trays.
Twins start second cigarette
12:05 Twin B finishes 2nd cigarette
12:10 Twin A finishes 2nd cigarette
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Commented:
Who starts/stops smoking when?  When do the two spaceships cross?
The two twins only agree on "now" at the moment they meet.
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Author Commented:
They start smoking when they are at a distance x from each other. They are at a relative velocity v, so they will cross when t=x/2*v. The values don't matter as long as v is big enought to make relativistic effects strong.

Let's see each twin point of view.

Twin A:

"I had smoked two cigarretes and my twin smoke just one by the time we cross and I trew the ash tray. My ashtray (A) has two cigarretes and his (B) has only one."

Twin B:

"I had smoked two cigarretes and my twin smoke just one by the time we cross and he trew the ash tray. My ashtray (B) has two cigarretes and his (A) has only one."

You could add a third spaceship (C) that remais always in the middle point between spaceships A and B. Due to symmetry, spaceship C would see the two twins smoke the same amount of cigarretes by the time they cross.

This is not a simple problem. If you guys need more explanation just ask.
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Author Commented:
You could also have spaceship C flash a light to give the start for both twins to start smoking. Light would travel at the same speed in both directions (of course) and spaceship C is in the middle point between the spaceships.
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Commented:
If, in twin A's frame of reference,
11:50 Both twins start smoking
11:55 Twin A done with first cigarette, starts second
12:00 Twin A done with second cigarette, twin B done with first
spaceships pass, exchange ashtrays.
12:10 Twin B done with second cigarette.

Then in twin B's frame of reference the events would be:
11:40 Twin A starts smoking first cigarette
11:50 Twin A done with first cigarette, starts second.
11:55 Twin B starts smoking first cigarette,
12:00 Twin A done with second cigarette, twin B done with first
spaceships pass, exchange ashtrays.
12:05 Twin B done with second cigarette
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Author Commented:
Ok, let's take the second situation, where spaceship C signals the start.

From Twin A'a frame of reference:
11:50 Twin B starts 1st cigarette.
11:55 Twin A starts 1st cigarette
12:00 Both twins finish 1st cigarette

Ok. let's put the ships a little further apart, so that they have time to smoke more cigarretes before the ships cross. It will be:

From Twin A'a frame of reference:
11:50 Twin B starts 1st cigarette.
11:55 Twin A starts 1st cigarette
12:00 Both twins finish 1st cigarette and start second.
12:05 Twin A finishes 2nd cigarrete. Starts 3rd.
12:10 Twin B finishes 2nd cigarrete. Starts 3rd.
Twin A finishes 3rd cigarrete. Starts 4th.
Ships cross. Ashtray A has 3 cigarretes and Ashtray B has 2 cigarretes.

and from Twin B's frame of reference:
11:50 Twin A starts 1st cigarette.
11:55 Twin B starts 1st cigarette.
12:00 Both twins finish 1st cigarette
Twins start second cigarette
12:05 Twin B finishes 2nd cigarette. starts 3rd.
12:10 Twin A finishes 2nd cigarette. starts 3rd.
Twin B finishes 3rd cigarette. starts 4th.
spaceships pass, exchange ash trays.
ashtray A has 2 and B has 3.

Notice that I just copy/paste your explanation. The only modifications were that I moved the ships further apart, so that they have more time to smoke and they dont stop smoking after the second cigarrete.
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Commented:
From Twin A'a frame of reference:
11:40 Twin B starts 1st cigarette
11:50 Twin B starts 2nd cigarette.
11:50 Twin A starts 1st cigarette.
11:55 Twin A starts 2nd cigarette.
12:00 spaceships pass, exchange ash trays.
12:00 Twin A starts 3rd cigarette
12:00 Twin B starts 3rd cigarette
12:05 Twin A finishes 3rd cigarette
12:10 Twin B finishes 3rd cigarette

From Twin B'a frame of reference:
11:40 Twin A starts 1st cigarette
11:50 Twin A starts 2nd cigarette.
11:50 Twin B starts 1st cigarette.
11:55 Twin B starts 2nd cigarette.
12:00 spaceships pass, exchange ash trays.
12:00 Twin B starts 3rd cigarette
12:00 Twin A starts 3rd cigarette
12:05 Twin B finishes 3rd cigarette
12:10 Twin A finishes 3rd cigarette

note that they only agree on the time of events at the moment the ships pass.
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Author Commented:
You are putting the ship cross event in the point where they have the same amount of cigarretes smoken. What if the ships cross at 12:10 instead of 12:00?

From Twin A'a frame of reference:
...
12:05 Twin A finishes 3rd cigarette
12:10 Twin B finishes 3rd cigarette
12:10 Twin A finishes 4th cigarette
12:10 ships cross. A:4, B:3

From Twin B'a frame of reference:
12:05 Twin B finishes 3rd cigarette
12:10 Twin A finishes 3rd cigarette
12:10 Twin B finishes 4th cigarette
12:10 ships cross. A:3, B:4

Notice that the time of crossing is arbitrary. You just have to move the ships further apart, keeping ship C in the middle.
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Commented:
I'm just adjusting the clock so they cross at 12:00
It could be, from A's frame of reference
30 minutes before crossing      Twin B starts 1st cigarette
20 minutes before crossing      Twin B starts 2nd cigarette
15 minutes before crossing      Twin A starts 1st cigarette
10 minutes before crossing      Twin B starts 3rd cigarette
10 minutes before crossing      Twin A starts 2nd cigarette
5 minutes before crossing      Twin A starts 3rd cigarette
0 minutes before crossing      Twin A finishes 3rd cigarette
0 minutes before crossing      Twin B finishes 3rd cigarette
ships pass, exchange ash trays
0 minutes after crossing      Twin A starts 4th cigarette
0 minutes after crossing      Twin B starts 4th cigarette
5 minutes after crossing      Twin A finishes 4th cigarette
10 minutes after crossing      Twin B finishes 4th cigarette

and reciprocally from B's frame of reference.
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Commented:
The error you're making, acerola, is that time itself is dilated, but this doesnt allow more actions to be taken in that time!
i.e. if A sees B time dilated (by a factor of 2 let's say), then he doesnt see B smoking two cigaretess instead of one, but he sees him smoking the same cigarette in twice the time!
Same reciprocal.
And you will have the same amount of ashes produced when they meet.

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Commented:
ditto

(i think. this has the type of content I am want to oppose, but i think scrontch has the popular response)
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Commented:
A fly in the rear window of a car travelling at 60 MPH (or for the metric crowd, about 90 KPH) flies to the windshield at a relative speed of 4 MPH. Is the fly flying at 64MPH or 4MPH.

Does the light reflected by an object traveling at or above the speed of light change because of the speed of the object it is reflected off of? Is the speed of the light reflected off of the back side of the object less than the speed on the front side?
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Author Commented:
ozo, your answer is probably correct. I just still don't understand it completely. I am kind of busy lately, so it is going to be a while before I can sit down and think about it.
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Author Commented:
"but he sees him smoking the same cigarette in twice the time"

I don't know, when we talk about "seeing" we must consider the time light takes to travel.

Anyway, if A sees B in "slow motion" shouldn't B see A in "fast forward"? I don't understand how both of them see each other in "slow motion".

Also, why in the twin paradox a twin gets younger? I've always been told that it was because of acceleration. And I've been also told that you can't apply special relativity in accelerated systems.
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Author Commented:
Now a different problem to help me understand it.

Ship A is stopped. Ships B and C are moving in opposite directions with the same steady velocity in relation to A. They are all in the same line and ship B is closer to ship A. Like this:

B-->   A                           <--C

First, ships A and B cross. When they do, they both start smoking. Ship B gets far away, crosses ship C. When B and C cross, B throws the ashtray into C and C continues smoking. C approaches A and when they cross, C throws the ashtray into A. Like this:

------------------------------------------------
A
B-->                <--C
------------------------------------------------
A             B-->
<--C
------------------------------------------------
A
C                            B-->
------------------------------------------------

Ok, A sees:

12:00 - A and B cross
- A and B start 1st cigarrete
12:05 - A starts 2
12:10 - A starts 3
- B starts 2
12:15 - A 4
12:20 - B finishes 2nd. 2 cigarretes in ashtray.
- B and C cross, thrwos ashtray.
- A starts 5
- C starts 3rd (got ashtray with 2 cigarretes)
12:25 - A 6
12:30 - A 7
- C 4
12:35 - A 8
12:40 - A 9 (8 cigarretes in ashtray A)
- C 5 (4 cigarretes in ashtray B)
- A and C cross. C throws ashtray into A

Is that correct ozo? What does A sees when he compares the ashtrays?
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Commented:
When they do, they both start smoking.
From who's point of view do we measure "when"?
Events that are simultaneous in A's frame of reference are
not simyltaneous in B or C's frame.
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Commented:
B sees:
10:50 - C starts first
11:25 - C starts second
12:00 - A and B cross
- A and B start 1st cigarette
12:05 - B starts 2
12:10 - B finishes 2nd.
- B and C cross, throws ashtray.
12:10 - A starts 2
12:20 - A starts 3
12:30 - A 4
12:40 - A 5
12:45 - C 3
12:50 - A 6
13:00 - A 7
13:10 - A 8
13:20 - A 9
- C 4
- A and C cross. C throws ashtray into A
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Commented:
Sorry, I think I lost count that should be:
B sees:
11:00 - C starts first
11:35 - C starts second
12:00 - A and B cross
- A and B start 1st cigarette
12:05 - B starts 2
12:10 - B finishes 2nd.
- B and C cross, throws ashtray.
- C starts 3rd
12:10 - A starts 2
12:20 - A starts 3
12:30 - A 4
12:40 - A 5
12:45 - C 4
12:50 - A 6
13:00 - A 7
13:10 - A 8
13:20 - A 9
- C 5
- A and C cross. C throws ashtray into A

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Commented:
C sees (adjusting clocks to be synchronized with A when they meet):

11:20 - A 1, B 1
11:30 - A 2
11:40 - A 3
11:50 - A 4
11:55 - B 2
12:00 - A 5
12:10 - A 6
12:20 - C 1
- A 7
12:25 - C 2
12:30 - C 3
- B finishes 2nd
- B and C cross, thrwos ashtray.
- A 8
12:35 - C 4
12:40 - A and C cross. C throws ashtray into A
- C 5
- A 9
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Commented:
No one sees anyone "getting younger", they see the other age at a different rate. That is not the same thing.

Another point is that to "exchange" the ashtrays is not so easy, remember, you will have accelerate each ashtray from it's velocity in one direction to an equal and opposite direction. To calculate a result you need to take this into account.

Regards
Gordon
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Commented:
this whole thing of twins, concept of one aging faster, or more, eludes me again.  I study, read, am told, believe, and then some time passes... and it eludes me again (some elasticity to return to doubter?).

One does not get younger than the other
(so there! were it true, we'd all have bought into the concept for life)
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Commented:
Symmetry does not mean that you simply reverse the parameters - so some of the above arguments are a bit misguided.
Don't forget, it depends in what you are interested to measure.  Time and space are equivalent in relativity (under transformation)
Time dilation in one frame will be experienced as length compression in the other.

When cosmic rays are produced in the galactic core they come screaming toward the earth's upper atmosphere at high energy, and smash into the upper atmosphere.  This produces mu-mesons that have mass, but are also travelling at a good fraction of the speed of light.

The best part is, that we know all about mu-mesons, and we know exactly what half-life they should have under normal circumstances.  This means we can calculate exactly how far they should get after being created in the upper atmosphere.  They shouldn't get far at all.  If you multiply their speed by the half life, it is pretty obvious that they shouldn't get anywhere near the ground before they decay.

Trouble is, they do.

So what is happening?  Relativity explains it perfectly.
The observer on the ground, that is us, sees the mu-meson as having more time - that is time dilation.  They exist longer in our time to do exactly the same thing they always do, live and decay.

But from the perspective of the mu-meson, it has NOTHING to do with time or clocks.  Quite simply, the distance between the upper atmosphere and the ground has contracted so they don't have so far to go as before.  Hence they make it to the ground with ease.

Space and time are equivalent under transformation.
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Commented:
The more contrived view was that we can SAY that we observed the  mu-meson path to be strangely stretched out, and we ca SAY that our clocks would be read as strangely too fast.  Except that this inverse transformation is only meaningful to the state of knowledge of a human being, it is NOT the actual physical transformation that occurs in the real world.  The real world has only length contractions and time dilations.

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Commented:
> "Also, why in the twin paradox a twin gets younger? I've always been told that it was because of acceleration. And I've been also told that you can't apply special relativity in accelerated systems."

Exactly. thats's why the twin paradox is more of the resort of general relativity.

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Commented:

Yes you can calculate the age of the moving twin.
Yes you get a definite result.
Yes one is younger.
Yes, that is what would actually happen.
No, there is nothing wrong with SR in that respect.
No, it has nothing to do with accelerations.
And Yes Einstein was unhappy with that.

So what is the problem?
Well Einstein wasn't happy about assuming "this guy is stationary" and then being able to derive a consequence.
So he invented GR to try and find a way to make it harder to be able to work with those kinds of "absolutes".

SR works fine, it is correct, but it just doesn't explain things enough.

You don't need silly big long trips in space and nonsense to see that.  Even stupider is the idea of sending two ships in opposite directions.  They both come back younger, not than eachother, duh, but younger than both would have been if they didn't go.

Just put your space-stations into orbit around a planet with a massive gravity so that they can orbit at speed approaching the speed of light, that will do it.  But put one into a circular orbit and one more elliptical.  Then they are both technically in "free fall" and both experience exactly the same effect - weightlessness.
Suppose you blackout radio communications and shut the portholes etc.  If you confine yourself to measurements on the ship itself, no peeking out the portholes, you will not be able to tell which ship you are. So much for all that acceleration mumbo-jumbo.

You can even arrange things so that you can observe eachother briefly, by almost crossing the orbits, and then if you like you can exchange clock information and love letters etc.

Hey presto! The average orbital velocities will be different, so the effects of special relativity will produce an aging difference.

So there you have it.  No way for the crew to know that their ship was any different in itself, when they exchange notes, except that the clock numbers are definitely going out of whack.

The very nature of the layout, not the forces on the ships, is causing preferences to what should be purely relative motion.

So it must be something to do with the geometry of the setup.  That is why Einsten started to look at how the geometry of the environment could connect to the reality of the local frame, and that lead to GR.

Non-linarities all over the place. And no solution to the GUT (Grand Unified Theory) just yet.
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Commented:
Oh and BTW, as I pointed out before, the thing about clocks is part of a mind-game.  Since we are discussing physics again, and not information theory about clocks, I can let you look out of the portholes now, because what actually happens is that when you go super fast, you see the whole universe ahead of you shrunked.  Less distance to go, just like the muon.
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Commented:
Well that was all the "how", but the "why" question is tougher.  Nobel prize material again, maybe.

SR special relativity is the idea that the space we think we understand and the time we think we understand are the way that our primitive brains are conditioned to see them, and that our natural ideas about these being seperate are basically crap.

Einstein figured this out finally when he was riding on a train, and the reality of it so over-whelmed him that he had to get off the train and chuck-up.
(It all goes back to some problems he was having, imagining what it would be like to sit on a light beam and travel with it.)

The maths had already been done, by people like Maxwell, and Lorentz, but nobody realised the significance.

The idea that time is a kind of direction, or that directions are a kind of time, is pretty shlonky, so nature plays a pretty joke on us.  Nowadays we just call them "space-time" because we suspect they are actually aspects of something deeper.

They are not completely equivalent either, but you can make a bit of one into a bit of the other.  And that seems to connect to how fast you go.  Its as if your reality gets put out of alignment when you  move.  Kind of like drinking to much and then trying to walk.  The faster you go, the more pronounced the effects.

Theses distortions are predictable, but there are even more elaborate kinds of distortions waiting in "general relativity".

As a simple rule, remember that "Moving clocks run slow" and "lengths are foreshortened".  As an object whizzes past us, we can see that a bit of space is borrowed to become time instead.  The motion of the object has had a real effect on our universe - it has got rid of some space, but it has added to time, a kind of cosmic book-keeping.

It appears to us to be projected in "slo-mo", so it can take up a lot more of our time to do some standard business, in our universe it has a slow clock.
In its universe it has lost out in the space real-estate game - it actually loses space - it compresses the entire universe in its direction of motion. Wierd but true.

So the twin paradox is when the moving twin gets to go on a compressed journey, whilst we watch him in slo motion replay.  Space converting into time between two frames in relative motion.

Such grand conversions are real.  All of spacetime is  plastic like that, and at that level of description there is no concept of process, it just "is" like that.

Other grand conversions are possible.  The space-time metric is only one view of the 4D gizmo.  From QT Quantum theory we know that space is the inverse of momentum, and energy is the inverse of time.  That really gets things into an almighty tangle.  Energy/time has the units on momentum (p), so we can show x1, x2, x3, t cordinates as
Whoop-de-doo.  Now as well as converting space into time, we should be able to see the conversion of mass into energy, just by moving something.  And that is exactly what happens when you go back and look at the moving object.

Simple rule:  Moving objects get heavier.

Some momentum has been lost from one perspective, but some energy (in the form of mass) has been gained from the other perspective.

Actually its a bummer.  Not only does it lead to E=mc2 kaboom, but it menas that the more you accelerate a rocket the heavier it gets until you can't get it to go any faster.  At the speed of light in vacuo it gets infinitely heavy.

That is something else, the speed of light is a limit on the structure of spacetime.  Its the fastest anything can go, provided that it hasn't got any mass.  The most common thing like that is light of course, but its not the only thing, so its NOT a thing about light, its a thing about space/time.  Light is just one of those various things that try to go just as hard out as its little legs will carry it, without limits of its own, but sadly the universe gets in the way.
Or maybe thats not such a bad thing, or we would never get to see any light before it accelerated to infinity, and all energy would soon be lost.

Just a final note, light does have energy, so it does have mass, but it has no rest mass, meaning light can never be "stopped".  It has "gone the whole way" if you like.  In other words it has distorted spacetime as much as it possibly can as far as the rotation thing goes.  That means that it has borrowed  and shrunken all of the space it can lay its hands on and converted it all to time for us to witness it in.

So now we can answer Einstein's question, what is it like to travel with light.  The strange answer can only be that spacetime does not exist in the frame of reference of a photon, everything is totally closed up together, the point of emission must be identical to the point of absorption, the time of travel must be zero and the distance to travel must be zero as seen by a photon.
But as seen by us we get a very different universe, with pretty rainbows, lah de dah ...

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Commented:
Do you understand yet, or do you want to go over another set of events from various frames of reference?
Do you see that the ash tray goes from one frame of reference, with one notion of "simultaneous", to another with a different notion of "simultaneous"?
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Commented:
The original paradox is due to speed, not acceleration.

As your velocity approaches c, the speed of light in a vacuum, time appears (from your point of view) to pass slower.  Hence you age less, causing the original paradox.

To start from a situation where A is in a ship, and B stays on a planet, A would only have time to smoke one cigarette, and B would have time to smoke two.  If B could somehow see A throughout this time (which would be impossible due to the light-bending properties of near-light-speed travel, but let's suspend disbelief) he would just see A smoking one cigarette REALLY slowly.  So no paradox.

Now speed B up to near-light-speed too, and time seems to slow for him as well.  He now sees A acting at a normal speed (for him) and they both have time to smoke one cigarette.  Again, no paradox.

Put C on a planet, and run the same experiment, and C would see A and B smoking slowly, and smoke one cigarette, A and B would see each other acting at normal speeds (as their time dilation effects would be equal) but would see C smoking really fast, completing two cigarrettes.

Now, if you want to really fuse brain cells, speed them up to faster than light speeds, and you'll have issues.

For example.

A stationary (10 light minutes from B)
B starts stationary, smokes one cigarrette. (takes 10 minutes)
When B finishes the cig, A sees him start.
B starts cig2, and 5 minutes later, starts towards A at light speed.
10 minutes later, when B is halfway through cig 3, he arrives at A at the same time as the view of him halfway through cig 2 (because he travelled at the same speed as the light)
At the same time, a whole lot of light that's been reflected from B while he travelled arrives, let's assume it gets missed in the confusion.
B arrives halfway through a cig.
A has seen him smoke 1.5 cigs
but there are two buts in the ashtray.

B, travelling at light speed, suffers 100% time dilation, and hence has no time pass while he travels, so his cig doesn't burn, and he has actually smoked the number of cigs that A has seen him smoke.

Alternative:

B travels at 50% c, giving him 50% time dilation, and he experiences 10 minutes in the 20 it takes him to travel to A.  A just sees him smoke the second half of cig2, and the first half of cig3, in slo-mo, leaving everything as it should be when they meet.

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Commented:
Hey I think it's more simple than all of these answers ... they both travel at the same speed...they smoke the same cigarets ... B would see the same cigarets smoked in the asstray of A as in his own :P
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