I think I solved the twin paradox

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I'm just a layman and I don't know what I'm talking about! (Just thought I'd clear the air on that point In any case, I think I've solved the twin paradox. However, being someone who doesn't know what he's talking about, I'm sure there's something wrong with my conclusions. I hope someone will gently point out where the mistake is.

Here's my conclusion...when the traveling twin arrives back on Earth he will be the same age as the twin that stayed behind. And how did I arrive that this conclusion? By applying the two relativistic effects that seem to be ignored in all versions of this thought experiment that I've read...Lorentz contraction of the traveling twin, and time dilation of the Earth.

I'll quickly reiterate the experiment just so everyone knows the version I'm working from. This is the Wikipedia version and I've read it in other places as well. Only special relativity is considered.

Twins on Earth; star 4.45 light years away; one twin travels at 0.8666c towards star then comes back; acceleration/deceleration, as well as turnaround, assumed to be instantaneous.

So the story goes...

From the point of view of the twin on Earth, a trip to the star and back at .8666c takes 10.28 years. So the twin in the space ship is away for 10.28 years. However, time dilation comes into play and we see his time slow down by a factor of .5 so he only ages 5.14 years.

Meanwhile, from the point of view of the twin in the ship, another relativistic effect, Lorentz contraction, comes into play. He sees the distance to the star as being only 2.23 light-years. Being at rest in his frame of reference, he sees the star zoom up in 2.57 years and then zoom away for 2.57 years. Total trip time...5.14 years, and we have consistency!

It's a nice sounding story, but methinks it's wrong. Why? Well, from the Earth-twin's PoV, what of Lorentz contraction of the traveling twin? And from the space-twin's PoV, what of time dilation of Earth.

As best as I can tell, the contraction of the space-twin is completely ignored in all solutions. This is the critical mistake. Likewise, dilation of time on Earth is mentioned, sometimes, but also seems to be ignored. But dilation of time on earth is critical for bringing consistency to my new view, which considers the contraction of the space-twin. So here we go!

The ground rules (or... it's all for naught if I don't have the basics right!)

When we say that time slows down for an object in motion relative to an observer at rest, we mean that time really does slow down...it's not an optical illusion. So what does that mean for Lorentz contraction? It means the same thing...that the object doesn't simply look contracted. It really is shorter in the direction of motion.

Nothing new there. How about this...what times are we comparing when we say an object is time dilated? We are comparing the actual time of the observer at rest vs. the actual time of the object in motion, as perceived by the observer at rest. So what about Lorentz contraction? What are we comparing? The actual length of the observer at rest vs. the actual length of the object in motion, in the direction of motion, as perceived by the observer at rest.

Again nothing new there. This thought experiment isn't about coming up with anything new. I'm simply properly applying what we already know.

So lets apply these relativistic effects properly. First up is the point of view from the twin on Earth, who we will call Earth-twin. Earth-twin is at rest, and his twin, who we'll call space-twin, is the twin in motion. Earth-twin sees space-twin flying off at 0.8666c. From Earth-twin's point of view, space-twin's time rate is cut in half...their clocks are truly ticking at different rates. This everyone knows. But something else has also changed. Space-twin is Lorentz contracted. From Earth-twin's pov, space-twin is truly shorter in the direction of travel.

Why is this important? Because it changes space-twin's distance to the star in the same exact way that his clock rate is changed. According to Earth-twin, space-twin's distance to the star is not 4.45 light-years, but 9.9 light years! This is perfectly consistent. In the same way that we easily accept two clocks in different frames ticking at different rates, we should also be willing to accept that two observers in different frames will perceive the same space differently. In fact, in what I call the classical solution, the analysis of the space-twin starts off with the distance between Earth and star cut in half! So we shouldn't have a problem with space-twin's distance being different. The question is...why 9.9 light-years? Just as time has slowed for space-twin (because space-twin's slow clock is being compared to earth-twins faster clock,) distances have increased for space-twin (because space-twin's yardstick is shorter than Earth-twin's yardstick.) Space-twin, who still thinks his yardstick is one yard long (because it really is…to him ) has to measure two yards for every Earth-twin yard! (Remember, we're comparing the contracted yardstick to Earth-twin's at-rest yardstick, just as we compare space-twin's dilated time to Earth-twin's at-rest time. It's all about Earth-twin's reference frame.)

NOW we have all that we need to properly determine space-twin's experience. The space that Earth-twin sees as 4.45 light-years is experienced by Space-twin as 9.9 light years due to his yardstick being half as long as Earth-twin's yardstick. Space twin is traveling at 0.8666c, so the trip to the star takes 5.14 light-years from Earth-twin's pov, while Earth-twin sees space-twin experience a trip distance of 9.9 light-years to the star and a trip time of 10.28 years. The trip back is exactly the same. And...since time dilation and Lorentz contraction go hand-in-hand, space-twin's clock only ticked half as many times throughout the trip. Space-twin experienced 10.28 years of time, as determined by Earth-twin (who is at rest.) Also, Since Earth-twin saw space-twin fly to a star 4.45 light-years away at 0.8666c and back again...he experienced 10.28 years as well.

Stated another way, in the same way that Earth-twin feels normal time passing (a tick is a tick), but also sees that space-twin is experiencing dilated time (a space-twin tick is two Earth-twin ticks,) Earth-twin sees his normal space (a yard is a yard) but also sees that space-twin is experiencing contracted space (a space-twin yard is half an Earth-twin yard.) Since twice as many space-twin yardsticks are need to measure Earth-twin's distance to the star, it follows that space-twin must travel twice as far.

This makes sense because in the examination of space-twin we will contract not only the Earth and star, but the space in between. From Earth-twin's view It would seem inconsistent to contract the moving space ship and nothing else. For consistency, we must contract the distance the ship travels as well.

Now it's space-twin's turn to take a rest and see how all objects move in relation to him.

A resting space-twin sees the earth moving away at 0.8666c and the star moving toward him at 0.8666c. From space-twin's frame, the distance between the Earth and the star is 2.23 light-years, right? Wrong. It's 4.45 light years.

The root of this long-standing mistake is that the value of 2.23 light-years is derived from 4.45...which was taken from outside the reference frame. That is, the value, 4.45 light-years, came from the Earth-twin's resting frame. But as soon as Earth starts moving, space-twin is outside of that frame and he experiences the same space and time differently. So why would space-twin use, in his calculations, a value from Earth-twin's frame? The space that equals 4.45 light-years in Earth-twin's frame must have a different value in space-twin's frame. And I don't mean the Lorentz contacted space... I mean the space used to later calculate the Lorentz contracted space. As soon as space-twin started moving, the value of 4.45 light-year distance becomes meaningless because it's from a different frame. There must be a complementary value in space-twin's frame that represents the same space in Earth-twin's frame. In fact, we've already calculated the complementary value. When discussing the point of view of Earth-twin, we calculated that space-twin experiences Earth-twin's space of 4.45 light years as 9.9 light years. So when we switch to space-twin's frame, the Lorentz contracted distance should be calculated from 9.9 light-years., giving a contracted distance between the Earth and star of 4.45 light years.

From this point the rest is academic because the situation is now fully symmetrical. From space-twin's pov, Earth-twin experiences the same time dilation, contraction, and lengthening of distance that space-twin experienced previously. The result is as before...both space-twin and the Earth-twin experience 10.28 years of time passing.

Now, not only are we consistent, but sensible as well! (one twin aging more than another...I mean really, who's ever heard such nonsense?! )

At the very least, it's different. Remember, be gentle

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Well, first of all, you are wrong, because the twin "paradox" has been experimentally confirmed many times over. So you shouldn't frame it in terms of "I think this is correct," but rather "why is this incorrect?"

Anyway, I'm a layman myself and I've only scanned your post, but it looks like you're mixing frames incorrectly at a crucial point. You're saying the space twin actually has farther to travel because he's contracted. But again, he's only contracted in the Earth frame, which is irrelevant to his own experience of time and space. Also, you say "According to Earth-twin, space-twin's distance to the star is not 4.45 light-years, but 9.9 light years!" This is incorrect. According to Earth twin, space twin is flattened, but still traveling 4.45 light years at .866C. If the Earth twin, for some reason, was going to measure the distance in "space-twin lengths" while unaware that the space twin was contracted, only then would he consider the distance to be 9.9 light years. But if that were the case, he would also measure the space twin as traveling at 1.7C!

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...Lorentz contraction of the traveling twin, and time dilation of the Earth...

Not sure what you mean by "time dilation of the Earth".

The space twin accelerates out of Earth's frame and because of that his clock will run slower.

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Well, first of all, you are wrong, because the twin "paradox" has been experimentally confirmed many times over. So you shouldn't frame it in terms of "I think this is correct," but rather "why is this incorrect?"

Thanks for responding! Yes, I agree. I’m just trying to understand what’s wrong with it. That said, I think the points you raised can be addressed with more clarity on my view, without having to change my view. Especially on the issue you raise first…

You're saying the space twin actually has farther to travel because he's contracted. But again, he's only contracted in the Earth frame, which is irrelevant to his own experience of time and space.

Absolutely correct, of course. The issue I raise, though, is why do we use 4.45 light-years, a measure from a different frame of reference, to determine space-twin’s distance to the star. Space-twin is in a different frame. Time is different...why should distance (or more appropriately, space) be the same?

Also, you say "According to Earth-twin, space-twin's distance to the star is not 4.45 light-years, but 9.9 light years!" This is incorrect. According to Earth twin, space twin is flattened, but still traveling 4.45 light years at .866C.

The situation that I’m explaining is that of noting a difference in another frame, while maintaining your own frame. We already accept this with time. The clock in our frame ticks at one rate, but we note that the clock in another frame ticks at a different rate. What I’m saying is that this same exact view must also apply to contraction. Earth-twin sees the distance to the star as 4.45 LY, and, within his frame, will see the ship travel 4.45 LY. But just as Earth-twin notes that time is ticking slower for space-twin (although Earth-twin cannot experience that,) Earth-twin also notes that space-twin is traveling 9.9 LY (although Earth-twin cannot experience that.)

If the Earth twin, for some reason, was going to measure the distance in "space-twin lengths"...

Doh! Didn’t say that!

…while unaware that the space twin was contracted, only then would he consider the distance to be 9.9 light years. But if that were the case, he would also measure the space twin as traveling at 1.7C!

Earth-twin simply notes that space-twin’s yardstick is shorter. In the accepted solution, Earth-twin experiences 10.28 years while space-twin experiences 5.14 years. Why? Because there’s a ratio between the two frames...two Earth ticks for every tick on the ship. All I’m saying is that the same must apply to contraction. There’s a ratio between the two frames...one Earth yard for every two yards on the ship. What I’m also saying is that this contraction must also be applied to space-twin’s entire universe (in the direction of travel, of course.) Space-twin see his trip to the star as 4.45 LY, not 9.9LY, just as a tick of his clock feels like a normal tick to him. Meanwhile, Earth-twin sees a slow tick occurring (as related to himself) as well as a longer distance (as related to himself.) That’s why Earth-twin would not determine space-twin’s speed to be 1.7c...space twin is going further, but his clock is going slower as well. From Earth-twin’s point of view, space-twin would measure speed to be 0.8666c (in his own frame) and distance to be 4.45 LY (in his own frame.)

From Earth-twin’s point of view, space-twin experiences half as many ticks, and twice as many yards.

Anyways, I thought it was an interesting and different way to look at the situation. Thanks for your comments!

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Not sure what you mean by "time dilation of the Earth".

The space twin accelerates out of Earth's frame and because of that his clock will run slower.

I was referring to the accepted solution when the frame is switched and the traveling twin is now the twin at rest. The distance between Earth and star is contracted, and that's the reason for the trip time to be 5.14 years. But if Earth is in motion, then Earth-time must also be dilated. Earth's time dilation is like the uncle is prison...everyone knows about it but no one talks about it.

The traveling twin's contraction is like a night of heavy drinking...no one remembers it at all!

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The time dilation is symmetrical when there is a constant velocity between them. As they are moving apart, each does indeed see the other's time rate slow by the same degree. The reason it's different is in the shifting of frames on the part of only the space twin, by means of acceleration.

And measuring in "space twin lengths" is indeed equivalent to what you're trying to do, i.e. claiming his metric in his own rest frame is somehow affected by his dilation in the Earth rest frame.

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The time dilation is symmetrical when there is a constant velocity between them. As they are moving apart, each does indeed see the other's time rate slow by the same degree. The reason it's different is in the shifting of frames on the part of only the space twin, by means of acceleration.

Well, the symmetry of my explanation would apply acceleration effects symmetrically, but I believe that takes us out of the realm of special relativity, and I didn’t want to go there. That’s why, when I laid out the original parameters, I said acceleration is considered instantaneous. But I know sometimes you just have no choice but to go in a certain direction to get the right answer, and that seems to be the case here. So I know that, ultimately, I may be left having to understand more that I can about the scenario.

And measuring in "space twin lengths" is indeed equivalent to what you're trying to do, i.e.

But we do this anyway. Don’t we? We say that if space-twin’s ship is 100 meters long when at rest with Earth-twin, then Earth-twin sees the ship contract to 50 meters long when moving at 0.8666c. But we don’t change how space-twin sees his ship. Space-twin still sees his ship as 100 meters long.

That view is fully accepted. All I’ve done is simply extend that view beyond the ship. If a distance, viewed by Earth-twin as 50 meters, is measured by space-twin to be 100 meters, doesn’t it follow that a distance measured by Earth-twin to be 4.45 LY would be measured by space-twin to be 9.9 LY?

Another way of posing this question...why would we limit contraction to the limited space of space-twin’s ship? What about the 100 meters in front of the ship? How does space-twin see that? And just as important a question, how does Earth-twin view the 100 meters that space-twin views? Shouldn’t the space in front of the ship (and behind the ship) follow the relativistic views applied to the space that the ship itself occupies? Shouldn’t all space in the direction of space-twin’s motion be contracted?

claiming his metric in his own rest frame is somehow affected by his dilation in the Earth rest frame.

Ah, that’s exactly what I said doesn’t happen. Space-twin doesn’t see himself traveling 9.9LY, anymore than he sees his clock ticking slower or his ship being 50 meters long. Space-twin sees himself traveling to a star 4.45 LY away, in normal time, in a normal ship, at 0.866c. It is Earth-twin who sees, when compared to his own space, a space-twin clock ticking slower, a space-twin ship getting shorter, and a space-twin distance to the star getting longer.

And thanks for trying to explain (I did notice that the hand-smacking-the-head smile is first on the list! )

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Well, the symmetry of my explanation would apply acceleration effects symmetrically, but I believe that takes us out of the realm of special relativity, and I didn’t want to go there. That’s why, when I laid out the original parameters, I said acceleration is considered instantaneous. But I know sometimes you just have no choice but to go in a certain direction to get the right answer, and that seems to be the case here. So I know that, ultimately, I may be left having to understand more that I can about the scenario.

It doesn't matter if the acceleration is instantaneous, actually.

That view is fully accepted. All I’ve done is simply extend that view beyond the ship. If a distance, viewed by Earth-twin as 50 meters, is measured by space-twin to be 100 meters, doesn’t it follow that a distance measured by Earth-twin to be 4.45 LY would be measured by space-twin to be 9.9 LY?

No, it does not follow. That's the key. The ratios between different lengths does not hold between reference frames. They are symmetrically and oppositely modifed. For example, each twin sees himself as twice the height of the other. Treat the Earth and destination star, at rest relative to one another, as a single object, with a dimension of 4.45ly. To the same degree that the space twin sees his brother contract, earth-star contracts as well. Earth twin sees the ratio between earth-star and space twin double, while space twin sees that same ratio cut in half.

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No, it does not follow. That's the key.

“The ratios between different lengths does not hold between reference frames.”

If you’re saying that you don’t take a property from one frame (like a half-ticking clock) and apply it in another frame...yes, ratios don’t hold between frames.

“They are symmetrically and oppositely modifed.”

Yes.

“For example, each twin sees himself as twice the height of the other.”

When standing along the direction of travel...yes.

“Treat the Earth and destination star, at rest relative to one another, as a single object, with a dimension of 4.45ly. To the same degree that the space twin sees his brother contract, earth-star contracts as well.”

Yes.

“Earth twin sees the ratio between earth-star and space twin double”

One ET meter to two ST meters...yes.

“while space twin sees that same ratio cut in half.”

One ST meter to two ET meters...yes.

But lets go back to the first thing you said...

“The ratios between different lengths does not hold between reference frames.”

When the frame at rest notes time dilation in the frame in motion, rest-frame doesn’t start considering moving-frame’s time in its own activities, does it? Rest-frame doesn’t say, “hey my trip was 5 seconds, not 10, because I like using moving-frame’s clock to measure my time.” We don’t apply dilation to the resting frame.

Why then would we apply moving-frame's contraction to the resting frame? Why, upon seeing Earth-star contract, are we so willing to say, “hey my trip was 2.23LY, not 4.45, because I like using moving-frame’s contraction to measure my space.” That seem inconsistent to me. As you said, ratios don’t hold across frames.

Well, I think at this point we’re approaching “going in circles”, so I will leave it to your last response (if you desire to make one.) But thanks for providing challenges to my view (which is always for a person to provide to himself.) It was a good exercise for me to apply my theory to the situations suggested.

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But lets go back to the first thing you said...

“The ratios between different lengths does not hold between reference frames.”

When the frame at rest notes time dilation in the frame in motion, rest-frame doesn’t start considering moving-frame’s time in its own activities, does it? Rest-frame doesn’t say, “hey my trip was 5 seconds, not 10, because I like using moving-frame’s clock to measure my time.” We don’t apply dilation to the resting frame.

Why then would we apply moving-frame's contraction to the resting frame? Why, upon seeing Earth-star contract, are we so willing to say, “hey my trip was 2.23LY, not 4.45, because I like using moving-frame’s contraction to measure my space.” That seem inconsistent to me. As you said, ratios don’t hold across frames.

We're not applying the moving-frame's contraction to the resting frame. We're applying the moving-frame's contraction to the moving frame. In the moving frame, earth-star has contracted to 2.23LY. Space twin thus measures his own trip as 2.23LY. Earth twin measures space twin's trip as 4.45LY. What is the problem?

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Okay, one more

We're not applying the moving-frame's contraction to the resting frame. We're applying the moving-frame's contraction to the moving frame. In the moving frame, earth-star has contracted to 2.23LY. Space twin thus measures his own trip as 2.23LY.

This is the error that I believe has been made for so long. Yes, space-twin measures the Earth-star contraction as 2.23LY. But that doesn’t make his trip 2.23LY.

This is as simply as I can put it. If we, at rest, want to measure one second of contracted time, our resting clock needs to tick for one-half seconds. If we want to measure 2.23LYs of contracted distance, our resting distance must be 4.45LYs.

When the moving star arrives at space-twin, we say that, during the trip, Earth-star experienced one second for every two seconds experienced by space-twin. In the same exact way, we must also say that, during the trip, for every yard experienced by Earth-star, space-twin experienced 2 yards. When the star arrives at space-twin, the tape measure that space-twin hooked on the Earth before it left will read 4.45 LY.

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...This is the error that I believe has been made for so long. Yes, space-twin measures the Earth-star contraction as 2.23LY. But that doesn’t make his trip 2.23LY...

It was put this way in a different thread.

"Earth says it is because he aged slower, and he says it is because the distance was shorter. Either explanation is equally valid (There is no one right explanation.)"

I found it easier to understand the twin paradox when I started with how acceleration affected the clock speed. Then I could add other components of the story and it made more sense.

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Okay, one more

This is the error that I believe has been made for so long. Yes, space-twin measures the Earth-star contraction as 2.23LY. But that doesn’t make his trip 2.23LY.

Yes it does. There is no difference between what he measures and what is. His trip is 2.23 ly long in his frame. Which, at 0.886 c takes 5.14 years.

This is as simply as I can put it. If we, at rest, want to measure one second of contracted time, our resting clock needs to tick for one-half seconds. If we want to measure 2.23LYs of contracted distance, our resting distance must be 4.45LYs.

When the moving star arrives at space-twin, we say that, during the trip, Earth-star experienced one second for every two seconds experienced by space-twin. In the same exact way, we must also say that, during the trip, for every yard experienced by Earth-star, space-twin experienced 2 yards. When the star arrives at space-twin, the tape measure that space-twin hooked on the Earth before it left will read 4.45 LY.

In the Earth frame, a tape measure is stretched between Earth and star and is marked off in 1 meter lengths. Thus it has 42,100,560,000,000,000 marks and is that many meters long.

Space twin carries a meter stick which he lays alongside the measuring tape as he travels. He notes that that the marks on the tape are spaced at a distance that is 1/2 the length of his meter stick. Thus he travels 1 meter for every two marks he passes. He counts the same number of marks during the trip, and thus by his reckoning, the distance between the ends of the tape is 21,050,280,000,000,000 meters, or 2.225 ly.

You are just confusing yourself with all this jumping between frames.

The twin Paradox is "solved", simply by taking into account

1. Time Dilation

3. Length contraction

3. The Relativity of Simultaneity.

The third one you haven't even touched on.

Basically it states that if you have two clocks in the same frame and separated in the x axis and synchronized to each other in their own frame, they will not be synchronized according to a frame that has a relative motion along the x axis relative to the clocks. The difference between the clocks increases with increased separation in the x axis.

Taking it one frame at a time:

Earth Frame:[/i]

The space twin leaves on Jan 1 3000, which is the date both on Earth and at the distant star. It takes 5.14 years for the space twin to make it to the star, making the date both on Earth and the star upon arrival Feb 19 3005. During which time, the space twin aged 2.57 years due to time dilation.

The space twin then takes another 5.14 years to return to Earth on a date of April 10 3010, while aging another 2.57 years, aging a total of 5.14 years while 10.28 years pass on Earth and the distant star.

Space twin frame:

Now while in the Earth frame, it is Jan 1, 3000 both on Earth and at the distant star when the twin leaves, The instant the space twin starts moving at .866 c, it remains Jan 1, 3000 on Earth but jumps forward to Nov 8 3003 at the distant star due to the Relativity of Simultaneity .

On the outward trip, the space twin ages 2.57 yrs, while the Earth and the distant planet ages 1.285 yrs. So that on arrival, it is Mar 14, 3001 on Earth and Feb 19, 3005 at the distant planet.

The space twin heads back to Earth, in doing so, he changes his relative velocity with respect to the Earth frame, and so the Earth clock and star clock switch roles, the Earth clock become the one that is ahead, so that now while the date at the Star (which the space twin is still next to) remains at Feb 19, 3005, the date on the Earth jumps forward to Feb 26 3009.

The space twin ages 2.57 yrs on the return trip while the Earth and star age 1.285 years, making it April 10 3010 on Earth and Jun 3, 3006 at the star.

When the Space twin stops back at Earth the date at the star jumps forward to April 10 3010

The space twin ages 5.14 years while 10.28 years have passed on Earth

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It was put this way in a different thread.

"Earth says it is because he aged slower, and he says it is because the distance was shorter. Either explanation is equally valid (There is no one right explanation.)"

I found it easier to understand the twin paradox when I started with how acceleration affected the clock speed. Then I could add other components of the story and it made more sense.

According to the clock postulate acceleration has no effect.

“The clock hypothesis states that the tick rate of a clock when measured in an inertial frame depends only upon its velocity relative to that frame, and is independent of its acceleration or higher derivatives.”

Here are some links to it.

http://math.ucr.edu/home/baez/physics/Relativity/SR/clock.html

http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html

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There is no difference between what he measures and what is.

That’s right.

His trip is 2.23 ly long in his frame.

That’s wrong.

Say that space-twin is at rest with Earth-twin on Earth. The star is 4.45 LY away. Space-twin now gets into his ship, which, coincidently, is 4.45 LY long (it’s a big ship.) Now space-twin speeds up to .8666c. How long does space-twin measure his ship to be? Is it 2.23LY long or 4.45 LY long? If what you say is true...

“There is no difference between what he measures and what is.”

...then he will measure 4.45LY, and that’s what is. In his frame, traveling to the star, the distance is still 4.45LY (the front of his ship is already there!)

Space-twin does not experience contraction, just like he doesn't experience time dilation. Those phenomena are merely observed from a different frame. His ship appears to be 2.23LY from the other frame. But to space-twin, his ship appears to be 4.45LY long, and his clock appears to be running normally, and his speed appears to be .8666c, and he will experience a trip time to the star of 5.14 years.

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“There is no difference between what he measures and what is.”

...then he will measure 4.45LY, and that’s what is. In his frame, traveling to the star, the distance is still 4.45LY (the front of his ship is already there!)

No, the distance between the Earth and the star is 2.23LY, and his ship is 4.45LY long. Length contraction is reciprocal.

Space-twin does not experience contraction,

Yes, he does. Earth-star is contracted in space-twin's rest frame.

just like he doesn't experience time dilation.

Yes, he does. Earth-star's clocks run slower in space-twin's rest frame.

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No, the distance between the Earth and the star is 2.23LY, and his ship is 4.45LY long.

So he gets into his ship and instantly accelerates to .8666c. Earth is behind him, so the star is now at (or slightly past) the middle of his ship? That would mean that the star moved from the front end of his ship to the middle of his ship instantaneously and that a passenger sitting in the middle of the ship would now be at the star.

I wish people would stop saying “you’re wrong, this is how it is,” and simply apply my view to some other situations and demonstrate that it comes up with the wrong answer.

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I wish people would stop saying “you’re wrong, this is how it is,” and simply apply my view to some other situations and demonstrate that it comes up with the wrong answer.

But it has already been demonstrated to be wrong by actual observation.

Your view leads to the conclusion that the Earth twin and space twin each age the same amount while the space twin makes his trip.

There is an observation of muons created in the upper atmosphere by cosmic rays reaching the surface of the Earth that refute this view. Muons are very short-lived particles, even traveling at nearly the speed of light, they would travel only a few hundred meters before decaying into other particles.

But these upper atmosphere created muons are measured at the surface of the Earth, 20 kilometers from where they were created. This can only be true if the muons underwent time dilation due to their high velocity and aged at a much reduced rate, which allowed them to exist long enough to reach the surface. IOW, While a muon created at rest on the Earth's surface will decay in an average of 2.2 ms, his twin created 20 km up and moving at near light speed lives for at least 60.6 ms (Earth time), it aged 1/30 as fast as the Earth muon (it still decayed in 2.2 ms by its own internal clock).

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But it has already been demonstrated to be wrong by actual observation.

There is an observation of muons...

Yes, but the muons, as well as the clocks flown around the world, where also subject to gravity and its effects. The version of the Twin Paradox that I am questioning refers to SR only.

In any case, I think I have found the explanations I was looking for on the follow web page (pages)

http://www.glafreniere.com/matter.htm

So I'm going to study those pages for a while to get a better understanding of the theories proposed.

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I'm just a layman and I don't know what I'm talking about! (Just thought I'd clear the air on that point In any case, I think I've solved the twin paradox.
The twin paradox doesn't actually need to be solved. The reason it's called a paradox is because it defies intuition, i.e. it is merely an apparent contradiction. It's not really something that is not understood by relativists. In fact it's one of those things that's understood very well.
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Yes, but the muons, as well as the clocks flown around the world, where also subject to gravity and its effects. The version of the Twin Paradox that I am questioning refers to SR only.

The effects due to gravity are irrelevant to this observation.

1.Time differences due to gravity are due to differences in potential, and the differnce in potential between sea level and an altitude of 20 km, is just too small by many orders of magnitude. Not only as predicted by theory but also as observed. If a 20 km difference can produce a time dialtion factor of 30, then people in Denver should be constantly reseting their watches to keep the right time with everyone else, and the Astronauts in the Shuttle in orbit at 300km should experience even a greater time dialtion factor.

2. Gravitational time dilation works the other way. Clocks run faster at higher altitudes. Since the cosmic ray created muon spends the majority o fts time at altitudes greater than sea level, it would age faster not slower[/i] due to the effects of gravity. Since we see the opposite the effects of gravity cannot appreciable, and we are left with SR time dialtion to explain the extended lifetime.

In any case, I think I have found the explanations I was looking for on the follow web page (pages)

http://www.glafreniere.com/matter.htm

So I'm going to study those pages for a while to get a better understanding of the theories proposed.

Don't waste your time. From the little I scanned, it is written by a crackpot who has no idea of what he is talking about.

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The effects due to gravity are irrelevant to this observation.

No they’re not. If you had reviewed the data from the flight of the atomic clocks you would have known that the clock was running faster at the end of its trip (the expected outcome.)

But I suspect you simply scanned the results. I’ve noticed a lot of scanning around here. Maybe if you fully read things you’d be better equipped to understand the theories proposed, and be able to properly articulate why the theory is wrong. That would be a little more helpful than “I scanned it...he’s a crackpot and you’re wrong.”

I wouldn’t call the guy a crackpot since his formulas give the same exact answers that Einsteinian relativity does. You can use his formulas to design the GPS system and you’d get the same exact system that’s in place now. The only difference between the two theories is the reason why all this happens (wave theory of matter and the existence of aether vs. shrugged shoulders.)

Personally, I think he’s likely right, but Einstein’s way is easier for me to work with so that’s what I’m sticking to. And Einsteinian relativity tells me the twins are the same age.

Oh...it also tells me that the passenger on the moving train sees the lightning bolts strike the ends of the train at the same time, just like the observer on the platform. But that’s another story.

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No they’re not. If you had reviewed the data from the flight of the atomic clocks you would have known that the clock was running faster at the end of its trip (the expected outcome.)

What you just did is very, very bad in three ways. First off, Janus was talking about muons traveling at nearly the speed of light, not airplanes moving at nearly the speed of sound. You moved the goalposts to suit your argument. In this case of muons produced in the upper atmosphere, gravitational time dilation is negligible.

Secondly, the Hafele-Keating experiment had planes flying in two directions. While the westbound plane's clock did run faster over the course of the experiment, the eastbound plane's clock ran slower. Selectively quoting only the part of some experiment that supports your evidence and ignoring the remainder is false attribution.

Thirdly, general relativity alone does not explain even the behavior of the westbound plane's clock in the Hafele-Keating experiment. Both general and special relativity are needed to explain the behavior of both clocks.

Use of fallacies is strongly discouraged at this site.

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Maybe if you fully read things you’d be better equipped to understand the theories proposed, and be able to properly articulate why the theory is wrong. That would be a little more helpful than “I scanned it...he’s a crackpot and you’re wrong.”

When I got to the point where he says:
For example, one should answer this simple question: how does a photon work, from a mechanical point of view? Surely, nobody ever proposed an acceptable explanation. The point is that, as long as this question remains unanswered, nobody is entitled to believe that photons really exist. Up to now, it was just a convenient word hiding one's ignorance. Additionally, there is absolutely no evidence of photons inside radio waves.

I knew that there was no sense in reading any further, since it is obvious that the author doesn't even have any idea what the definition of "photon" is. He isn't hiding his own ignorance very well.

This lack of understanding of a fundamental concept, and the very style of the writing just scream, "crackpot".

Oh...it also tells me that the passenger on the moving train sees the lightning bolts strike the ends of the train at the same time, just like the observer on the platform. But that’s another story.

Not if the lightning strikes occur simultaneously to the platform observer at the instant the passenger passes him.

OTOH, If you have a situation where the light from the lightning flashes reaches the platform observer at the same instant the passenger passes him, then yes, they both see the flashes at the same time.

Like thus:

However, this still means that the lightning strikes didn't occur at the same time according to the passenger, as seen in this animation which shows the same events as determined by the passenger.

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What you just did is very, very bad in three ways. First off, Janus was talking about muons traveling at nearly the speed of light, not airplanes moving at nearly the speed of sound.

Janus’s response...

“The effects due to gravity are irrelevant to this observation.”

...was in response to my comment which started...

“Yes, but the muons, as well as the clocks flown around the world...”

So if Janus’s response was referring to muons only then that would have been clarified in the post. But it wasn’t. So my presumption is that Janus was referring to the airplanes as well. If that’s wrong, Janus is perfectly capable of clarifying that point for me.

Secondly, the Hafele-Keating experiment had planes flying in two directions. While the westbound plane's clock did run faster over the course of the experiment, the eastbound plane's clock ran slower. Selectively quoting only the part of some experiment that supports your evidence and ignoring the remainder is false attribution.

Well if you really want to get into the details, the test was done with 4 clocks, all of which were flown in one direction and then the other. In each flight, at least one clock changed in the opposite direction of what was predicted, and this was after the clocks measured drift rates were accounted for (interestingly, the clock that was closest to the predicted eastward dilation, also dilated westward.) Hafele & Keating performed two rounds of corrections to get the clock data to agree with the predicted results.

A. G. Kelly didn’t agree with the results...but there are always detractors. What concerns me more is that the guy who created the clocks, Louis Essen, didn’t think they were accurate enough to perform the experiment. Considering that 138ns was the closest any clock got to the predicted 275ns westward drift, and that the spread between the actual slowest and fastest westward results was 457ns, I’d say the expert is probably right.

The clock mentioned above, which was closest to the predicted eastward value, was off the most from the westward value by 319ns. So if you’d like to discuss the selective ignorance of evidence, I’d be happy to discuss the fact that the true clock results were anywhere but on target.

The NPL recreated the experiment and said it works. However, I haven’t been able to find the actual data. There doesn’t seem to be a link to it on their website.

Thirdly, general relativity alone does not explain even the behavior of the westbound plane's clock in the Hafele-Keating experiment. Both general and special relativity are needed to explain the behavior of both clocks.

Correct. That was my point. That comparing an experiment based on both SR and GR, to a thought experiment based on SR only, makes no sense. So when I bring up an issue in an SR experiment, it makes no sense to counter with points from an SR+GR experiment.

That’s what I meant when I said, “Yes, but the muons, as well as the clocks flown around the world, where also subject to gravity and its effects. The version of the Twin Paradox that I am questioning refers to SR only.” Apparently, that wasn’t clear enough.

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Consecutive posts merged
When I got to the point where he says:

Well, lets forget about the “crackpot”.

If you would care to continue this discussion, I would rather spend time trying to get you to sense that something is wrong with the way the twin paradox is laid out. It makes no sense for me to explain any sort of corrected result from a slightly different viewpoint if you’re not yet willing to consider that viewpoint.

I’d like to refer back to space-twin’s spaceship, which I made 4.45 LY long. Lets say that Earth-twin has an identical spaceship. This ship doesn’t go anywhere in the experiment...it just sits there. So space-twin starts on his trip. Space-twin’s time, as observed, slows. Also, space-twin’s ship, as observed, is half its resting length, or 2.23LY long.

If space-twin needs 1/2 a tick of his clock to move forward in time one tick of Earth-twin’s clock (regular ol’ accepted time dilation) wouldn’t we also say that he has to travel two lengths of his ship to move forward one length of earth-twin’s ship?

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I’d like to refer back to space-twin’s spaceship, which I made 4.45 LY long. Lets say that Earth-twin has an identical spaceship. This ship doesn’t go anywhere in the experiment...it just sits there. So space-twin starts on his trip. Space-twin’s time, as observed, slows. Also, space-twin’s ship, as observed, is half its resting length, or 2.23LY long.

How does the spacecraft accelerate instantaneously along its entire length?

The answer is: It can't. Doing so would require the compression or tension, depending on whether the thrust comes from the aft or forward end of the vehicle to propagate instantaneously. The best you can do is to place thrusters along the entire length of the vehicle. To bring this elongated vehicle to 0.8666c, the thrusters at the front of the vehicle will need to start firing years in advance of those in the back. The timing needs to be exact so that the wave of tensile force never occurs. Now comes the time for our adventurer to enter the back end of the vehicle. When the thrusters at the aft end of the vehicle finally ignite, the front end of the vehicle is well beyond has been Alpha Centauri. As far as the spacecraft is concerned, the distance between the Earth and Alpha Centauri has shrunk.

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