Understanding Spacetime simultaneity in twin paradox scenarios

[ESponge2000]

TL;DR Summary

Lines of Simultaneity in alternative Twin Paradox scenarios (help me understand)

Context,
To start with? You all know the original twin paradox. Quick review so nobody is confused :
Original Twin Paradox:
Traveling twin travels at v=0.8c out 4 light years (5 earth years pass)and then he returns home. Earth twin ages 10 years and traveling twin ages 6 because the Lorentz factor at 0.8c is a nicely rounded 1/0.6
In this original , the trip is different for the traveling twin
Traveling twin outbound sees 3 years pass each way instead of 5, with distances contracted to 60% of normal size ,
sees earth twin age 1 year on outbound , and then the “calculated” lines of simultaneity for moving inertial frames

When traveling twin ages 3 years, reaches the turnaround point but immediately before de-accelerating, traveling twin’s line of simultaneity (x-axis) is on the line of Earth twin at age 1.8 years. If traveling twin stops and moves back to being in earth’s inertial frame then the traveling twin at age 3 is simultaneous with earth twin at age 5,
And as soon as traveling twin moves v=0.8c back towards earth , traveler is simultaneous with earth twin at age 8.2, This is how simultaneity works and I grasp it . If you could see the line of simultaneity without being restricted to the delay in the speed of light, you could see time travel in both directions every time you change your resting frame.

Now let’s move to my alternative confusion situation .
Using the original Twin paradox when the earth twin reaches age 1.8, the earth twin would not at all perceive being even close to simultaneous with a traveling twin who completed the outbound leg of the trip. However, we can say it when earth twin was 1.8 years old, earth twin decided now is a good time to copy my twin and begin the same journey v=0.8c in the same direction from earth , Then
At the moment before traveling twin makes the u-turn , We can say this
Earth twin now calculates after joining the same resting frame as traveling twin, that traveling twin is indeed 3 years old, simultaneous with the start of earth twin’s journey .,,. As they both are at rest with each other ? That 1.8 year old earth twin, seeing Doppler images of traveling twin 0.6 years old stems from light across a stationary gap of 2.4 light years hence the traveling twin calculated to be age 3.,,, so we can say as long as they both now stay in this outbound inertial frame relative to earth , each twin will calculate each other to be 2.4 light years apart from each other. Simply put, one can pretend it was the earth that was moving 0.8c not the traveler and that the earth twin at age 1.8 came to a full stop by becoming stationary with the traveling twin . They are 2.4 ly apart .
Thjs all still makes sense, until my Final Scenario

Final Scenario… where I’m stuck !!!!

When earth twin is 1.8 years old, earth twin was about to begin the v=0.8c journey . Instead, suppose a surprise thing happens. The traveling twin briefly comes to a full
Stop, but this time not after 3 years of travel, but rather on “earth’s” line of simultaneity, so way back when the traveling twin is 1.08 years old , has traveled according to earth (1.8 of the 5 years ) or 36% of outbound distance , at which time the 36% of 4 light years distance will be 1.44 light years of gap .
But now , suppose, simultaneously , with an imaginary train connecting the 2 travelers briefly back on earth’s reference frame , they then go back to 80% of c relative to earth, together , at the same time …
Well then , both twins will see length contraction in the universe , but both will not see any length contraction between the distance between each other , and this is because ONLY non-stationary objects undergo length contraction

So all is understood until I get here. If the traveling twin temporarily halts after he ages 1.08 yrs and then right after that they both build speed in lock step back to v=0.8C , then the traveling twins are 1.44 light years apart after they both are moving 0.8c because that length is invariant to the length they were apart when they were stopped

However, if at 1.8 years old, earth twin begins the journey to 0.8C to then on copy the traveling twin but where traveling twin does NOT make any full stop , then it looks like they are positioned 2.4 light years apart. What am I getting wrong here then ?

Is the gap between the 2 twins given earth twin takes off at age 1.8, 1.44 light years or is their gap 2.4 light years ?

 

[Ibix]

That is a lengthy post with a lot of minor variations to scenarios and I'm not clear I've understood your problem. Am I correct in thinking that you are asking about the case where two observers at rest with respect to each other but separated in space both accelerate simultaneously (according to the clocks of their rest frame) and instantaneously in the same direction? And what happens to the distance between them?

If so, this is a variant on Bell's spaceships paradox. It's usually done with non-instantaneous acceleration but the concept doesn't really change. The point is that the accelerations are not simultaneous in the initial rest frame but not the final one. So in the final inertial frame the distance between the twins changes because one twin started moving at a different time from the other.

 

[ESponge2000]

That is a lengthy post with a lot of minor variations to scenarios and I'm not clear I've understood your problem. Am I correct in thinking that you are asking about the case where two observers at rest with respect to each other but separated in space both accelerate simultaneously (according to the clocks of their rest frame) and instantaneously in the same direction? And what happens to the distance between them?

If so, this is a variant on Bell's spaceships paradox. It's usually done with non-instantaneous acceleration but the concept doesn't really change. The point is that the accelerations are not simultaneous in the initial rest frame but not the final one. So in the final inertial frame the distance between the twins changes because one twin started moving at a different time from the other.

That is correct what you said. But trying to simplify it. I’m finding that if the first traveler never pauses and the second traveler accelerates to the same velocity as the first traveler , the outcome is different from if the first traveler pauses briefly and then the second traveler accelerates WITH the first traveler, and that doesn’t make sense to me as the velocities and forces ultimately are the same

 

[ESponge2000]

That is correct what you said. But trying to simplify it. I’m finding that if the first traveler never pauses and the second traveler accelerates to the same velocity as the first traveler , the outcome is different from if the first traveler pauses briefly and then the second traveler accelerates WITH the first traveler, and that doesn’t make sense to me as the velocities and forces ultimately are the same

So scenario 1
Earth observer accelerates to meet traveling twin at the time the traveling twin perceives as simultaneous with himself , which results in earth twin coming into traveling twin’s reference frame . This leads to 2.4 light years between 2 ships …. Earth age 1.8 and 0 lightyears away , traveling twin age 3 and 2.4 light years away the full outbound distance

Scenario 2
Same as 1, except for a very brief moment , traveling twin pauses , and meets earth twin’s reference frame , Earth age 1.8 0 lightyears away , traveling twin pause age 1.08 and at pause 1.44 lightyears away (out of 4 light years journey), Then they accelerate together … But they are going to now be 1.44 light years away out of 2.4 light years journey. This is different from scenario 2 where they are 2.4 light years away out of 2.4 light years journey, and this should be not a different outcome

 

[Ibix]

So scenario 1
Earth observer accelerates to meet traveling twin at the time the traveling twin perceives as simultaneous with himself

You mean, the Earth twin accelerates at the same time (according to the teavelling twin's rest frame) as the traveller reaches some specified age?

Scenario 2
Same as 1, except for a very brief moment , traveling twin pauses , and meets earth twin’s reference frame , Earth age 1.8 0 lightyears away , traveling twin pause age 1.08 and at pause 1.44 lightyears away (out of 4 light years journey), Then they accelerate together …

You mean they both accelerate at the same time as the traveller reaches that same specified age, except this time according to the travelling twin's instantaneous rest frame, which is the same as the Earth's rest frame?

If I'm understanding you correctly, the root of your issue is that the two scenarios have a very different definition of when the Earth twin accelerates.

 

[ESponge2000]

You mean, the Earth twin accelerates at the same time (according to the teavelling twin's rest frame) as the traveller reaches some specified age?

You mean they both accelerate at the same time as the traveller reaches that same specified age, except this time according to the travelling twin's instantaneous rest frame, which is the same as the Earth's rest frame?

If I'm understanding you correctly, the root of your issue is that the two scenarios have a very different definition of when the Earth twin accelerates.

In both scenarios , the earth twin departs earth 1.8 earth yesrs after the traveling twin departed. In both scenarios the earth twin and the traveling twin both do exactly the same itinerary at the same time with just 1 small hiccup. Scenario 2 the traveling twin pauses course before resuming course for a negligible amount of time at such a time that would make traveling twin simultaneous with the 1.8 year old earth twin during the pause but not before the pause .

So do you understand the 2 scenarios now ? Based on them there shouldn’t be a difference after the pause from the first scenario but I’m getting one , why ?

 

[ESponge2000]

In both scenarios , the earth twin departs earth 1.8 earth yesrs after the traveling twin departed. In both scenarios the earth twin and the traveling twin both do exactly the same itinerary at the same time with just 1 small hiccup. Scenario 2 the traveling twin pauses course before resuming course for a negligible amount of time at such a time that would make traveling twin simultaneous with the 1.8 year old earth twin during the pause but not before the pause .

So do you understand the 2 scenarios now ? Based on them there shouldn’t be a difference after the pause from the first scenario but I’m getting one , why ?

And imagine the pause in scenario 2 is very short moment such that we can ignore any consequences of the time lost due to the pause , like 15 seconds of pause in years of travel but such that for that very brief interval they both get to be in earth’s inertial frame

 

[ESponge2000]

And imagine the pause in scenario 2 is very short moment such that we can ignore any consequences of the time lost due to the pause , like 15 seconds of pause in years of travel but such that for that very brief interval they both get to be in earth’s inertial frame

Something is off on either my Math or how I’m defining simultaneity let’s walk through my understanding . In my example we only have to deal with 2 inertial frames . Earth at rest, 0.8C velocity from earth at rest
The length contraction and time dilation between the 2 frames 0.6

In the moving frame, origin earth to destination is 2.4 light years : in earth frame it’s 4 light years . Simultaneity between frames is always .6 times the age ot the observer for each.

After 1.8 earth years pass, earth twin is simultaneous with 1.08 year old traveling twin when in the earth frame but simultaneous with 3 year old traveling twin in the traveler’s frame

That said, if the earth twin at 1.8 years enters the traveling frame it should be a 2.4 light year perceived gap and where both measure the origin to destination also as 2.4 light years in length

But when 1.08 year old traveler pauses say just barely before earth twin departs, they now are 1.44 light years apart and back to 4 light years from origin to destination … at this moment you can take a rope 1.44 light years long and it would connect the 2 ships. Then they both go Back to traveling frame together , the rope paradox rule is universe contracts but the rope does not …. So this rope remains 1.44 light years long explained of course by lack of simultaneity in the traveling frame … however , the distance apart scenario 2 i calculate to be 1.44 light years apart . In scenerio 1 in calculated their gap to be 2.4 light years apart ? Why is my math coming out different when the velocities are the same paths in both scenarios ?

 

[ESponge2000]

Something is off on either my Math or how I’m defining simultaneity let’s walk through my understanding . In my example we only have to deal with 2 inertial frames . Earth at rest, 0.8C velocity from earth at rest
The length contraction and time dilation between the 2 frames 0.6

In the moving frame, origin earth to destination is 2.4 light years : in earth frame it’s 4 light years . Simultaneity between frames is always .6 times the age ot the observer for each.

After 1.8 earth years pass, earth twin is simultaneous with 1.08 year old traveling twin when in the earth frame but simultaneous with 3 year old traveling twin in the traveler’s frame

That said, if the earth twin at 1.8 years enters the traveling frame it should be a 2.4 light year perceived gap and where both measure the origin to destination also as 2.4 light years in length

But when 1.08 year old traveler pauses say just barely before earth twin departs, they now are 1.44 light years apart and back to 4 light years from origin to destination … at this moment you can take a rope 1.44 light years long and it would connect the 2 ships. Then they both go Back to traveling frame together , the rope paradox rule is universe contracts but the rope does not …. So this rope remains 1.44 light years long explained of course by lack of simultaneity in the traveling frame … however , the distance apart scenario 2 i calculate to be 1.44 light years apart . In scenerio 1 in calculated their gap to be 2.4 light years apart ? Why is my math coming out different when the velocities are the same paths in both scenarios ?

Or in concept terms my math is showing :
Applying these rules :
-Rule 1: Lines of simultaneity don’t shift for an observer who stays in the same inertial frame

-Rule 2: 2 objects in the same inertial frame agree on measurements of distance and time within that reference frame

- Rule 3: 2 objects separated by a distance in one initial frame who agree on space and time and simultaneously move together into a new inertial frame that’s the same new inertial frame , now maintain the same measured distance apart but both observe the same length contraction to everything else that didn’t shift resting frames …

Applying these 3 rules , something doesn’t work math wise , which means 1 of these 3 rules is not correct

 

[jbriggs444]

Rule 3: 2 objects separated by a distance in one initial frame who agree on space and time and simultaneously move together into a new inertial frame that’s the same new inertial frame , now maintain the same measured distance apart but both observe the same length contraction to everything else that didn’t shift resting frames …

Do you understand what an inertial frame is? It is not something that you move into or move out from. All objects are in all inertial frames at all times.

The mental picture I use is that an "inertial frame" is a coordinate system. As such, it is conjured into existence using pencil and paper and imagination. It has no physical effects.

You can take coordinates for each object according to one inertial frame and transform them into coordinates relative to another frame. If you actually do this, you may find that things that were unclear and ambiguous become clear and obvious.

 

[Ibix]

Here are a few Minkowski diagrams detailing your scenario 2 and what I think is going wrong. If you haven't come across Minkowski diagrams before they are essentially displacement-time graphs, with x position recorded on the horizontal axis and time on the vertical axis. Conventionally units are picked so that the speed of light is 1.

Here's your scenario drawn in the Earth's rest frame:

The red line represents the Earth twin, staying at home until 1.8 years, at which point he accelerates to the right. The blue line represents the traveller, moving to the right at 0.6c with the exception of a brief stop about the same time (in this frame) as the Earth twin starts accelerating.

In relativity we take these graphs fairly literally as a map of spacetime. We can mark on it the region of spacetime that the traveller calls "during the first phase of the trip" and "during the last phase of the trip" - that is, excluding the brief stop. These regions are shaded in grey:

And we can draw the region of spacetime that the traveller calls "during the stop" - again, shaded in grey:

Just to hammer the point home, we can draw all of that on one graph:

Here you can clearly see the problem. According to this simultaneity scheme, the Earth twin starts moving twice! Once during the brief stop, and once during the final phase of the traveller's journey. This is, of course, nonsense. The problem is that bolting together three parts of inertial frames like this does not lead to a coherent picture of spacetime, any more than taking two random overlapping screenshots on Google Maps and pasting them side by side makes the contents of the maps appear twice in the real world. It's just a bad map.

You can use it, but in any calculations you do using this simultaneity scheme you need to manually correct for the fact that your map doesn't cover all of spacetime and does cover some bits of it twice. Most probably what you are doing wrong is assuming that because the Earth twin started moving "during" the traveller's stop he must be moving after the stop, which is not accounting for the mess this scheme makes of time ordering.

If you want to be able to tell a coherent story about how the traveller interprets distant events if he's not inertial then you need a non-inertial frame that doesn't have this mess. Unfortunately, the maths for this is rather more complicated than using inertial frames.

 

[PeroK]

And imagine the pause in scenario 2 is very short moment such that we can ignore any consequences of the time lost due to the pause , like 15 seconds of pause in years of travel but such that for that very brief interval they both get to be in earth’s inertial frame

The time that elapses on a clock or the amount you age by is directly the length of your path through spacetime. Acceleration doesn't come into the calculation.

 

[ESponge2000]

Do you understand what an inertial frame is? It is not something that you move into or move out from. All objects are in all inertial frames at all times.

The mental picture I use is that an "inertial frame" is a coordinate system. As such, it is conjured into existence using pencil and paper and imagination. It has no physical effects.

You can take coordinates for each object according to one inertial frame and transform them into coordinates relative to another frame. If you actually do this, you may find that things that were unclear and ambiguous become clear and obvious.

What I mean in my simplistic example is that suppose 2 objects not in motion with respect to each other, observe a clock that’s positioned half the distance between them? Can we agree here they are now going to actually view the same clock time when they look at that clock, and can rely on that clock to synchronize activity , set that clock halfway between them to the time it is where the clock is plus the light travel time from it to each object and there you go …. You now have a clock measuring Now , for BOTH objects to “see” what time is now

Now when that clock reads say 3:15pm it will be in simultaneity truly 3:15. At that time they will accelerate relative to their positions in the same direction to 80% of speed of light , They will actually do this by rapidly accelerating from 0 to 0.8c eventhough in my hypothetical example I make it simple by saying it’s an instant velocity change , Let’s just say it’s a very very fast acceleration for both objects .
While accelerating , my understanding is here’s what happens along the gap. The object in front of the line will be simultaneous with , relative to the preceding timeline (something that can’t be seen but only calculated) a backwards rewind flow of time in the rear view mirror, and a speeding up of time flow in the front view mirror …. This will accompany the acceleration until terminal velocity is reached, at which point the distribution of now in front and back will flow forwards at the same intervals , but be set differently due to the acceleration. This transformation my understanding is that it coincides with the length distance being nonvariant for both objects as long as they are applying equal force to the same directions… wait I might see the problem

Simultaneity changes along the course of the acceleration , so we have a difference we don’t have simultaneity … the length can’t remain st 1.44 light years in my example … it’s Rule 3 that’s off

 

[ESponge2000]

What I mean in my simplistic example is that suppose 2 objects not in motion with respect to each other, observe a clock that’s positioned half the distance between them? Can we agree here they are now going to actually view the same clock time when they look at that clock, and can rely on that clock to synchronize activity , set that clock halfway between them to the time it is where the clock is plus the light travel time from it to each object and there you go …. You now have a clock measuring Now , for BOTH objects to “see” what time is now

Now when that clock reads say 3:15pm it will be in simultaneity truly 3:15. At that time they will accelerate relative to their positions in the same direction to 80% of speed of light , They will actually do this by rapidly accelerating from 0 to 0.8c eventhough in my hypothetical example I make it simple by saying it’s an instant velocity change , Let’s just say it’s a very very fast acceleration for both objects .
While accelerating , my understanding is here’s what happens along the gap. The object in front of the line will be simultaneous with , relative to the preceding timeline (something that can’t be seen but only calculated) a backwards rewind flow of time in the rear view mirror, and a speeding up of time flow in the front view mirror …. This will accompany the acceleration until terminal velocity is reached, at which point the distribution of now in front and back will flow forwards at the same intervals , but be set differently due to the acceleration. This transformation my understanding is that it coincides with the length distance being nonvariant for both objects as long as they are applying equal force to the same directions… wait I might see the problem

Simultaneity changes along the course of the acceleration , so we have a difference we don’t have simultaneity … the length can’t remain st 1.44 light years in my example … it’s Rule 3 that’s off

When traveling twin is at terminal velocity and earth twin is at rest and then meets traveling twin, all of earth twin’s accelerations are with traveling twin at a terminal velocity ….

In scenario 2, there’s relative discrepancy on what does simultaneity actually mean because the “in between” v=0 and v=0.8c are all going to matter in how simultaneity of forces are calibrated , so it’s because I’m missing that piece that my math isn’t working. Am I right?

 

[ESponge2000]

When traveling twin is at terminal velocity and earth twin is at rest and then meets traveling twin, all of earth twin’s accelerations are with traveling twin at a terminal velocity ….

In scenario 2, there’s relative discrepancy on what does simultaneity actually mean because the “in between” v=0 and v=0.8c are all going to matter in how simultaneity of forces are calibrated , so it’s because I’m missing that piece that my math isn’t working. Am I right?

And these intervals of where forces align have massive flow of time consequences

 

[Ibix]

Do you understand that if he uses a naive "my current inertial frame" simultaneity convention then in scenario 2 the travelling twin will (erroneously) conclude that the Earth twin accelerates twice? Is that in your calculation?

None of this has consequences for the flow of time, by the way. It's just a bad representation of what happens.

 

[ESponge2000]

Do you understand that if he uses a naive "my current inertial frame" simultaneity convention then in scenario 2 the travelling twin will (erroneously) conclude that the Earth twin accelerates twice? Is that in your calculation?

None of this has consequences for the flow of time, by the way. It's just a bad representation of what happens.

if traveling twin pauses negligibly, then resumes course, and both the pause and unpause are as rapid as possible , I would think it should be as if the traveling twin didn’t pause at all, then earth twin accelerating to 0.8c should run the same math calculations as scenario 1. And 2.4 light years of a gap.

And here’s a way to have a rapid acceleration “this is a general relativity concept” Let’s have almost the entire acceleration take place by having both objects making big large circles around their start point like a carousel until they reach their terminal speed at which point they move off the circle following the line of travel … that would do it wouldn’t it ? Just a little teeny bit of absolute time dilation experienced during the perpetual motion

 

[Nugatory]

And these intervals of where forces align have massive flow of time consequences

No. That is not how forces and acceleration work in special relativity.

You are making an easy problem difficult by not using the math as it should be used.

Pick a single inertial frame - any frame will work but here it is best to start with the inertial frame in which the earth is at rest . Identify the interesting events (something starts or stops moving, something has traveled for time t according to a particular clock, ...), use the inertial frame you chose to assign x and t coordinates to each of these events. Add these to label points in the Minkowski diagram that @Ibix provided above.
Then use the Lorentz transformations (not the length contraction and time dilation formulas - they are applicable only in certain limited cases, and this problem is not one of them) to transform these coordinates to the coordinates that are assigned by the frame in which the earth twin is at rest after they and the earth gave separated (that is, the earth is moving away from the earth twin. Then redraw the Minkowski diagram using that frame - the earth and the earth twin's worldlines are slanting from lower right to upper left until the separation event, at which point the rwin's worldine will be vertical while the earth;s will contunue moving up and left).

Do that and the contradictions and confusion will go away. Until you do you're just thrashing around, trying to cut bread without a using a knife.

 

[Ibix]

if traveling twin pauses negligibly, then resumes course, and both the pause and unpause are as rapid as possible , I would think it should be as if the traveling twin didn’t pause at all

You think wrongly.

You are correct that it makes no difference to the actual physics of how long things take or whether something breaks. But it makes a huge difference to how the traveller interprets distant events - and it is that which is causing you trouble.

Do you see that the Earth twin appears to accelerate twice with your construction of inertial frames?

And here’s a way to have a rapid acceleration “this is a general relativity concept”

No, it's a special relativity concept. Anything in flat spacetime is SR. It's also irrelevant. The problem is with internal consistency issues with your model of simultaneity, not with how acceleration happens.

 

[ESponge2000]

No. That is not how forces and acceleration work in special relativity.

You are making an easy problem difficult by not using the math as it should be used.

Pick a single inertial frame - any frame will work but here it is best to start with the inertial frame in which the earth is at rest . Identify the interesting events (something starts or stops moving, something has traveled for time t according to a particular clock, ...), use the inertial frame you chose to assign x and t coordinates to each of these events. Add these to label points in the Minkowski diagram that @Ibix provided above.
Then use the Lorentz transformations (not the length contraction and time dilation formulas - they are applicable only in certain limited cases, and this problem is not one of them) to transform these coordinates to the coordinates that are assigned by the frame in which the earth twin is at rest after they and the earth gave separated (that is, the earth is moving away from the earth twin. Then redraw the Minkowski diagram using that frame - the earth and the earth twin's worldlines are slanting from lower right to upper left until the separation event, at which point the rwin's worldine will be vertical while the earth;s will contunue moving up and left).

Do that and the contradictions and confusion will go away. Until you do you're just thrashing around, trying to cut bread without a using a knife.

You think wrongly.

You are correct that it makes no difference to the actual physics of how long things take or whether something breaks. But it makes a huge difference to how the traveller interprets distant events - and it is that which is causing you trouble.

Do you see that the Earth twin appears to accelerate twice with your construction of inertial frames?

No, it's a special relativity concept. Anything in flat spacetime is SR. It's also irrelevant. The problem is with internal consistency issues with your model of simultaneity, not with how acceleration happens.

I think I am understanding this better. I am trying to make sense also of the Minkowski diagrams but I struggle with visual diagrams till I understand which one is which object’s x axis and I still need to study that more.

The accelerating twice is something I am getting though. Between the 0 and 0.8C motions the simultaneity is inconsistent and that makes the scenario complicated to calculate …. But am I right to say the closer to accurate effect of scenario 2 is closer to scenario 1 where the traveling twin didn’t make any brief stop ? Simply because like I said it was a very small % of the timeline no matter which reference frame we apply ?

 

[ESponge2000]

I think I am understanding this better. I am trying to make sense also of the Minkowski diagrams but I struggle with visual diagrams till I understand which one is which object’s x axis and I still need to study that more.

The accelerating twice is something I am getting though. Between the 0 and 0.8C motions the simultaneity is inconsistent and that makes the scenario complicated to calculate …. But am I right to say the closer to accurate effect of scenario 2 is closer to scenario 1 where the traveling twin didn’t make any brief stop ? Simply because like I said it was a very small % of the timeline no matter which reference frame we apply ?

Also explain to be what a Lorentz transformation calculation looks like that is not a time dilation / length contraction calculation.

At my basic level my understanding , aren’t these the same thing?. We Take the velocity/c 0.8, square that 0.64 , Take 1 minus that we have 0.36, Square-root this we have 0.6, Lorentz 1/0.6 is 1.66667

To get the Doppler with light delay …. If I take 1-v/c in this case 1-0.8 = 0.2, Multiply it by Lorentz 1.66667 = 1/3 = for both observers , A 3 year old will see the twin when age 1,

 

[jbriggs444]

Now when that clock reads say 3:15pm it will be in simultaneity truly 3:15.

In the case at hand we have two objects and a clock halfway between them. Let the distance between the objects be two light-minutes (as measured in their shared inertial rest frame)

When the clock reads 3:15 pm then it will be 3:15 at that event according to the inertial coordinate system shared by both objects and the clock.

When the right-hand object witnesses the clock turn 3:15 pm then it will be 3:16 pm at that event according to the inertial coordinate system shared by both objects and the clock.

When the left-hand object witnesses the clock turn 3:15 pm then it will be 3:16 pm at that event according to the inertial coordinate system shared by both objects and the clock.

There is no "truly" about it. Simultaneity is relative.

 

[ESponge2000]

In the case at hand we have two objects and a clock halfway between them. Let the distance between the objects be two light-minutes (as measured in their shared inertial rest frame)

When the clock reads 3:15 pm then it will be 3:15 at that event according to the inertial coordinate system shared by both objects and the clock.

When the right-hand object witnesses the clock turn 3:15 pm then it will be 3:16 pm at that event according to the inertial coordinate system shared by both objects and the clock.

When the left-hand object witnesses the clock turn 3:15 pm then it will be 3:16 pm at that event according to the inertial coordinate system shared by both objects and the clock.

There is no "truly" about it. Simultaneity is relative.

Simultaneity for non-accelerating objects that are also at rest relative to each other is constant. For instance, we could place a bunch of clocks in floating space that are close enough to stationary with earth, write “Stop to use this Earth- Use clock to read earth UTC time from this point only” on each clock , set the clock time fast to the time seen from earth plus the light travel time from earth to that clock …. If one day we colonize space we would then have synchronization of time

 

[ESponge2000]

In the case at hand we have two objects and a clock halfway between them. Let the distance between the objects be two light-minutes (as measured in their shared inertial rest frame)

When the clock reads 3:15 pm then it will be 3:15 at that event according to the inertial coordinate system shared by both objects and the clock.

When the right-hand object witnesses the clock turn 3:15 pm then it will be 3:16 pm at that event according to the inertial coordinate system shared by both objects and the clock.

When the left-hand object witnesses the clock turn 3:15 pm then it will be 3:16 pm at that event according to the inertial coordinate system shared by both objects and the clock.

There is no "truly" about it. Simultaneity is relative.

If the gap between objects is 2 light minutes , you put the clock in the middle halfway between the 2 objects and set the time on that clock to 3:16 when it would be 3:15 at that point and write on the clock “this clock matches the right time for objects A and B, but is 1 minute fast for observers at this location “

 

[PeroK]

If the gap between objects is 2 light minutes , you put the clock in the middle halfway between the 2 objects and set the time on that clock to 3:16 when it would be 3:15 at that point and write on the clock “this clock matches the right time for objects A and B, but is 1 minute fast for observers at this location “

In which reference frame do all these statements apply? They can't and don't apply in all reference frame, which I think is at the root of your confusion.

 

[PeterDonis]

Simultaneity for non-accelerating objects that are also at rest relative to each other is constant if you pick the appropriate simultaneity convention/choice of coordinates.

See the bolded addition in the quote above. It is crucial to a proper understanding of the topic.

 

[PeterDonis]

For instance, we could place a bunch of clocks in floating space that are close enough to stationary with earth

Unless they are at infinity, they will not be non-accelerating clocks. "Non-accelerating" means in free fall, and a clock "hovering" at a finite altitude above the Earth is not in free fall.

 

[ESponge2000]

In which reference frame do all these statements apply? They can't and don't apply in all reference frame, which I think is at the root of your confusion.

It needs to disclose only in positions where clock is at rest

 

[ESponge2000]

See the bolded addition in the quote above. It is crucial to a proper understanding of the topic.

 

[ESponge2000]

How can there be ambiguity on what choice of simultaneity coordinates to use for 2 objects at rest in the same resting frame? It would be the one for that resting frame not any other one ?

 

[ESponge2000]

How can there be ambiguity on what choice of simultaneity coordinates to use for 2 objects at rest in the same resting frame? It would be the one for that resting frame not any other one ?

I guess if we factor the distance apart we can disclose that there won’t be simultaneity in other reference frames if they are occupying different points in space

 

[jbriggs444]

How can there be ambiguity on what choice of simultaneity coordinates to use for 2 objects at rest in the same resting frame? It would be the one for that resting frame not any other one ?

Because there is no obligation to judge simultaneity according to the frame in which two objects happen to be at rest.

We are in a thread about [some modification of] the twin paradox. So there will normally be three reasonable choices of simultaneity convention. Infinitely many other choices are also possible.

 

[PeterDonis]

How can there be ambiguity on what choice of simultaneity coordinates to use for 2 objects at rest in the same resting frame?

Because "simultaneity" is a convention. It's not a law of physics. The "obvious" convention you are implicitly assuming is still a convention. There are an infinite number of other possible conventions, which simply don't occur to you, but they're still valid.

The real issue is not "ambiguity"; it is that "simultaneity" is not an invariant; it's not an actual physical thing; it's not an observable. It's an abstract property of your choice of coordinates. So it contains no actual physics. But you are trying to treat it as if it does. That doesn't work.

 

[ESponge2000]

Because there is no obligation to judge simultaneity according to the frame in which two objects happen to be at rest.

That’s a fair point , it is factually correct. We run a trip up with quantum particles entangled when we say
Entangled particle in location B is correlated to particle location A based on what property and angle particle A is measured … We measure particle A from angle X it has a spin of 45mm/s among other unknowns we couldn’t measure
Particle B is entangled to particle A and we now know among other unknowns , a detector of Particle B measuring particle B from angle X will determine it with 100% certainty has a spin of 45mm/s.
They 45 mm/s was not a discovery we learned from something the universe predecided by a code but was not made known to the universe till the measurement and choice of measurement was taken ! Particle B’s rotating speed, however, was determined by the measurement on particle A, “simultaneous” to the measurement on Particle A … well that is simultaneity we still have difficulty defining … superposition to collapse of a photon property we don’t know the way that plays on our concept of time

 

[Nugatory]

Particle B’s rotating speed, however, was determined by the measurement on particle A, “simultaneous” to the measurement on Particle A

We have known for decades now (start with a Google search for “Bell’s theorem experiments”) that that is incorrect.

Aside from the fact that none of these entanglement experiments have anything to do with speed of rotation (it’s the component of the spin in a particular direction that we’re talking about), we cannot conclude from the true statement that “if we measure B we will find….with 100 certainty” that any property of B has in fact been determined.

Even if it were correct, in most entanglement experiments the two measurements are spacelike-separated, meaning that whichever was done first is frame-dependent. Any description that starts with A being measured first is prima facie wrong.