Are relativistic effects directional?

[Strange]

49 minutes ago, TakenItSeriously said:

For example, I’ve been told that the time dilation calibrated for in GPS satellites is almost entirely due to gravity. I know, different elevations and speeds, but I just get the feeling that gravity still dominated time dilation in that experiment but IDK for sure.

The problem is that your ideas are entirely based on half-remembered stories and feelings. And ignoring the science. 

[studiot]

1 hour ago, TakenItSeriously said:

Another words the waves transmitted from their own transponders are all in each twins own respective inertial reference frame regardless of where they are in space.

Depends upon who is looking at them.
And all inertial frames extend throught all space. i.e. they cover the same region.

[TakenItSeriously]

1 hour ago, studiot said:

Depends upon who is looking at them.
And all inertial frames extend throught all space. i.e. they cover the same region.

I agree, it can become a confusing mess. That’s why I like to break problems down to their simplest forms possible while still considering all relevant variables and points of view.

 

2 hours ago, Janus said:

No. You are over-generalizing a particular conclusion about the role of acceleration beyond its meaning. 

The conclusion is based on the "clock postulate".  Basically it states that local acceleration has no effect on the operation of a clock.  In other words, if you take a clock and put it in a high speed centrifuge and spin it up, the fact that the clock is experiencing a high value of acceleration has no additional effect on the rate of the clock ticking as measured from the lab frame. The clock will tick slow, but only by an amount due to its velocity relative to the lab frame.

This is not the same as saying that acceleration plays no role in the resolution of the Twin paradox.  The clock postulate only deals with how an inertial frame measures the accelerating clock, and does not deal with what would be measured from the accelerating frame itself.   

So for example, assume we have clock sitting at the center of the centrifuge in the lab frame. In addition to the clock spinning in the centrifuge, and the central clock, we have a third clock and observer traveling in an inertial frame at the same speed as the centrifuge clock and at a tangent to it such that its path and the centrifuge clock just touch at one point, so that if the two clocks were at that point at the same moment, they would have identical instantaneous velocities.  The difference being that the centrifuge clock has an acceleration toward the center clock,a and the third clock doesn't.  

If we compare what these two clock conclude as to what is happening two the center clock at that moment, they would come to different conclusions. the inertially moving clock would say that the central clock is running slow, while the centrifuge clock, which is under acceleration, would say that the central clock runs fast.

If a physicist says that acceleration is not the reason for the time difference they mean that in a specific way, and you are trying to infer a much broader meaning beyond that which they meant.

 

 

I’m a little confused about what each clock is doing.

Is it that the central clock is spinning around at the center point of centrifuge A.

Another clock is revolving around the spinning clock at some radius on the perimeter of A

A third clock is revolving around a separate centrifuge B and the two circular paths meet up like two spinning gears?

Edited November 27, 2019 by TakenItSeriously

[Janus]

4 hours ago, TakenItSeriously said:

A synopses of the modified version includes three observers

1. Bob at rest on Earth.
2. Alice drifting past the Earth at 80%c on her way to the star 8 ly away.
3. Carole drifting in the opposite direction at 80%c passes the star at the same time Alice passes it.

Carole collects Alices information such as travel time, travel distance from the Earth, observations on Bobs time, etc. She then proceeds to Earth and passes all of Alices information as well as her own to Bob and the time experienced by both travelers only adds up to 60% of the time experienced by Bob.

As far as Carole is concerned it is 12.8 years later for Bob as she passes Alice than it for Alice.

For example if Alice left Bob when it was the year 2020 for Bob, when Alice and Carole meet, according to Alice it is a bit past the middle of 2023 for Bob, but for Carole it is already  almost halfway into 2036 for Bob.    According to Carole, Alice left Bob 27 1/3 years before Alice and Carole meet, and during that time advanced at a rate of 0.6 that of her own, and thus advanced from 2020 to 2036 in those years in the next 6 years, Bob's clock advances another 3.6 years to read 2040 when Carole arrives.   In other words, for Carole,  Bob ages 20 years between Alice leaving him and Carole arriving, while Carol herself ages 33 1/3 years.

For Alice, Bob ages 3.6 yrs between the time she leaves him and meets up with Carole, it will take another 27 1/3 years by her clock for Carol and Bob  to meet during which time Bob ages 16.4 years, and Carol 6 years ( the relative speed between Carole and Alice is 0.97561..  and Carole's clock ticks at 0.21951... her own clocks rate)

The whole transferring the Alice's info of distance and time to Carole is just a red-herring  and doesn't give you anything equivalent to a total accumulated time For Bob, as you are jumping from a frame where it is 2023 for Bob to one where it is already 2036.

2 hours ago, TakenItSeriously said:

I agree, it can become a confusing mess. That’s why I like to break problems down to their simplest forms possible while still considering all relevant variables and points of view.

 

 

I’m a little confused about what each clock is doing.

Is it that the central clock is spinning around at the center point of centrifuge A.

Another clock is revolving around the spinning clock at some radius on the perimeter of A

A third clock is revolving around a separate centrifuge B and the two circular paths meet up like two spinning gears?

Whether or not the central clock(A) is rotating is of no consequence.

The second clock(B) is traveling in circle around the central clock.

The third clock(C) is traveling in straight line that runs tangent to B's path at one point.

Edited November 28, 2019 by Janus

[TakenItSeriously]

2 hours ago, Janus said:

As far as Carole is concerned it is 12.8 years later for Bob as she passes Alice than it for Alice.

For example if Alice left Bob when it was the year 2020 for Bob, when Alice and Carole meet, according to Alice it is a bit past the middle of 2023 for Bob, but for Carole it is already  almost halfway into 2016 for Bob.    According to Carole, Alice left Bob 27 1/3 years before Alice and Carole meet, and during that time advanced at a rate of 0.6 that of her own, and thus advanced from 2020 to 2016 in those years in the next 6 years, Bob's clock advances another 3.6 years to read 2020 when Carole arrives.   In other words, for Carole,  Bob ages 20 years between Alice leaving him and Carole arriving, while Carol herself ages 33 1/3 years.

For Alice, Bob ages 3.6 yrs between the time she leaves him and meets up with Carole, it will take another 27 1/3 years by her clock for Carol and Bob  to meet during which time Bob ages 16.4 years, and Carol 6 years ( the relative speed between Carole and Alice is 0.97561..  and Carole's clock ticks at 0.21951... her own clocks rate)

The whole transferring the Alice's info of distance and time to Carole is just a red-herring  and doesn't give you anything equivalent to a total accumulated time For Bob, as you are jumping from a frame where it is 2023 for Bob to one where it is already 2016.

Whether or not the central clock(A) is rotating is of no consequence.

The second clock(B) is traveling in circle around the central clock.

The third clock(C) is traveling in straight line that runs tangent to B's path at one point.

Ok, I got it.

For sure acceleration adds a ton of complexity to this problem. BTW it’s not a stable model unless you add a balancing mass on the opposite side of B, say B’ but thats getting a little nit picky.

It reminds me of an even simpler model of two astronauts tethered together in flat space.

Someone gives them a push and they start spinning apart putting tension on the tether and ending up in a dual orbit kind of like a binary star system.

So what happens if you remove the surrounding universe from this model. They would have no reference frame to know that they’re even spinning and it would then seem as if they were just drifting in the void with a strange repulsive force that is pushing them apart.

Others would argue that their would no longer be a repulsive force and they would just be floating together in the void with the tether limp between them.

The point is that I agree that gravity or acceleration adds a ton of complexity to the problem. That’s why the three observer thought experiment (not mine BTW) was modified to only involve drift speeds taking acceleration out of the problem all together.

https://en.wikipedia.org/wiki/Twin_paradox?wprov=sfti1.

I will respond to your analysis of that problem next.

 

46 minutes ago, TakenItSeriously said:

As far as Carole is concerned it is 12.8 years later for Bob as she passes Alice than it for Alice.

For example if Alice left Bob when it was the year 2020 for Bob, when Alice and Carole meet, according to Alice it is a bit past the middle of 2023 for Bob, but for Carole it is already  almost halfway into 2016 for Bob.    According to Carole, Alice left Bob 27 1/3 years before Alice and Carole meet, and during that time advanced at a rate of 0.6 that of her own, and thus advanced from 2020 to 2016 in those years in the next 6 years, Bob's clock advances another 3.6 years to read 2020 when Carole arrives.   In other words, for Carole,  Bob ages 20 years between Alice leaving him and Carole arriving, while Carol herself ages 33 1/3 years.

For Alice, Bob ages 3.6 yrs between the time she leaves him and meets up with Carole, it will take another 27 1/3 years by her clock for Carol and Bob  to meet during which time Bob ages 16.4 years, and Carol 6 years ( the relative speed between Carole and Alice is 0.97561..  and Carole's clock ticks at 0.21951... her own clocks rate)

The whole transferring the Alice's info of distance and time to Carole is just a red-herring  and doesn't give you anything equivalent to a total accumulated time For Bob, as you are jumping from a frame where it is 2023 for Bob to one where it is already 2016.

I set the model up to be equivalent with the TP example you gave initially:

Bob’s time on Earth is still 20 years.

Essentially Alice’s travel time is 6 years, Carole’s travel time is a symmetrical 6 years so the total is12 years which is 60% of Bob’s time of 20 years.

I can’t see how you derived the numbers in your analysis. Can you please clarify?

Edited November 28, 2019 by TakenItSeriously

[Janus]

3 hours ago, TakenItSeriously said:

Bob’s time on Earth is still 20 years.

Essentially Alice’s travel time is 6 years, Carole’s travel time is a symmetrical 6 years so the total is12 years which is 60% of Bob’s time of 20 years.

I can’t see how you derived the numbers in your analysis. Can you please clarify?

I id go back a correct some of the years I used in my post. There were a couple places where I used the year 2000 as the starting year rather than 2020 (for example, I typed 2016 rather than 2036).

The number come from just applying SR to the scenario. If you want to avoid acceleration, you have to assume that Carole has been traveling at 0.8c relative to Bob the whole time and prior to when Alice and Bob were together.  She would conclude that Bob's clock ticked at a rate of 0.6 that of her own.  Thus between Bob's 2020 at Bob ( when Alice Leaves) and 2040 ( when Carole arrives, Alice must measure 20/0.6 yrs by her clock or 33 1/3 years.   We also knows that Shes measures 6 years between passing Alice and meeting Bob, so by her clock, Alice left Bob 27 1/3 years prior to her meeting with Alice.  Using the relativistic addition of velocities, we find Carole would measure Alice's velocity with respect to herself as being 0.97561.. c.  The time dilation factor would have her saying that Alice's clock ticked at a rate of 0.21951...  compared to her own . 021951 X 27 1/3 = 6 yrs which is how much time Carole expects that Alice's clock ticks off between passing between Bob and Meeting up with Alice. This is in agreement with what Bob and Alice would say.

In 27 1/3 years, Bob's clock would tick off 27 1/3 * 0.6 = 16.4 yrs between the time that Alice leaves Bob and Alice meets Carole. Meaning, according to Carole,  it is 2036 at Bob when see meets up with Alice.  We know that it is 2040 for Bob when Carole arrives, so Bob ages 3.6 years during the 6 yrs it take for Carole meet up with Bob after passing Alice, by her clock.

According to Alice, its is 2023 at Bob when she meets Carole because Bob's clock ticked at a rate of 0.6 and accumulated 3.6 years in the 6 yrs measured by her clock.

So when Alice and Carole meet, they will disagree as to what time it is for Bob at the time of their meeting.

[TakenItSeriously]

5 hours ago, Janus said:

Thus between Bob's 2020 at Bob ( when Alice Leaves) and 2040 ( when Carole arrives, Alice must measure 20/0.6 yrs by her clock or 33 1/3 years.

Sorry, I think you made a mistake here.

From Alices perspective:

Alices travel distance on the outbound leg due to length contraction should only be 8 Ly*0.6 = 4.8 Ly

therefore her travel time is 4.8/0.8 = 6 years.

[Janus]

3 hours ago, TakenItSeriously said:

Sorry, I think you made a mistake here.

From Alices perspective:

Alices travel distance on the outbound leg due to length contraction should only be 8 Ly*0.6 = 4.8 Ly

therefore her travel time is 4.8/0.8 = 6 years.

We are assuming no acceleration here, So Alice just keeps going after meeting with Carole. Alice's clock has already accumulated 6 yr by the time she meets Carole.

From her perspective, after that, Bob continues to recede at 0.8c, and Alice is catching up to him traveling at 0.97561.. c ,  For Alice, this take another 27 1/3 years for a total of 33 1/3 between the moment she leaves Bob until Carole Meets up with him, as measured by Alice. ( Bob starts with a 4.8 ly head start, moving at 0.8 c, with Carole leaving Alice at ~0.97551c. Thus the difference in velocity between Bob and Carole according to Alice is 0.97551c- 0.8c = 0.17551c,  This is the velocity at which Alice is saying that Carole is closing that 4.8 ly gap between herself and Bob 4.8ly/0.17551c = 27 1/3 years.   Or you just work out, as I did above, that according to Alice Carole's clock moving at 0.97551c is time dilated by a factor of ~ 0.21951 ( alice  according to Alice( Alice would say that her clock ticks some 4.56 times faster than Carole's), and Carole's clock advances 6 years between passing Alice and reaching Bob, that works out to being 6 x 4.56 = 27 1/3 yrs for Alice (accounting for rounding). Again added to the 6 yrs already experienced by Alice since she left Bob, giving, once again 33 1/3 yrs that pass for Alice between the start and end of the scenario. )

Again, you are missing the Big picture by just focusing on Alice before she meets Carole, and Carole after she meets Alice. These two isolated segments by themselves don't tell the whole story.

[TakenItSeriously]

1 hour ago, Janus said:

From her perspective, after that, Bob continues to recede at 0.8c, and Alice is catching up to him traveling at 0.97561.. c ,

I assume this contains some kind of typos.

I mean I think your saying that Alice’s perspective on Carole’s speed is 0.97561... c and vice versa which I understand without doing the math myself but the rest is nonsensical as written.

Edit to add, after reading it a few times more I think you’re trying to say the following:

From Alice’s perspective after passing Carole, Bob is receding at 0.8c and Carole is catching up to him at roughly 0.98c.

Is that correct?

Edited November 28, 2019 by TakenItSeriously

[Janus]

9 minutes ago, TakenItSeriously said:

I assume this contains some kind of typos.

I mean I think your saying that Alice’s perspective on Carole’s speed is 0.97561... c and vice versa which I understand without doing the math myself but the rest is nonsensical as written.

It make perfect sense by the rules of Relativity.

Here's the whole scenario in space-time diagrams.  For the sake of keeping things less cluttered, we'll have Bob start at Year 0 rather than 2020.

Alice also sets her clock to 0 When she is by Bob.  Carole. likewise sets her clock to zero when, according to her, Bob's and Alice's Clocks read zero.

Because of this, we will first consider Carole's frame:

The Blue line represents Bob, the Red Alice, and the Green Carole. the numbers on each line represent years ticking off for each.  Time for Carole is the vertical axis.  Horizontal lines are lines of simultaneity.  Draw a horizontal line and it will pass through events that are simultaneous for Carole, such as Bob's, Alice's, and Carole's clocks all reading 0

Go up to the gray horizontal line, and you see the when Bob's clock read 10 years according to Alice, Her own clock reads between 16 and 17 years and Alice's reads between 3 and 4 years.  where the Red and Green lines cross is when Alice and Carole meet. Carole's clock reads 27 1/3 years, Alice's 6, and Bob's 16.4 years.

6 years later, Carole meets Bob, Her clock reads 33 1/3 years, Bobs 20 years and Alice's somewhere after 7 yrs

If we transform to Bob's frame, we get this:

Bob's and Alice's clock still read 0 at the same time, however, Carole's clock already reads past 21 years. This is a consequence of the Relativity of simultaneity; events that are simultaneous for Carole( all three clocks reading 0) are not so for Bob ( or as we will see later, Alice)

When Bob's clock reads 10 yrs, Alice and Carole are meeting, Alice's clock reads 6 yrs and Carol's 27 1/3 yrs.  Bob agree with Carol as to what time Both Alice's and Carole's clocks read when they meet, but disagrees with Alice as what time is on his own clock when this happens.

Carole's meets Bob when his clock reads 20 and hers has added another 6 yrs and reads 33 1/3 years.

 

Now Alice:

Again Bob and Alice's clocks both start at 0 when they are together, but Carole's clock already read almost 26 yrs. In 6 yrs according to Alice, she meets up with Carole. Carole's clock has advanced to 27 1/3 yrs, and Bob's to 3.6 yrs.  it takes another 27 1/3 years By Alice's clock for Carol and Bob to meet, during which Bob's clock advances by 16.4 years and reads 20 years, and Carole's advances another 6 yrs to read 33 1/3 years. 

 

Everyone agrees as to what times passing clocks had, how much time ticked away Alice's clock between leaving Bob, and meeting Carole, and how much time passed on Carole's clock between passing Alice and meeting Bob.   They just don't always agree on when these events occurred by their own clock.

If this seems "nonsense" to you, that's on you.   It is more an indication of your lack of understanding Relativity than anything else.

Just because you personally don't understand something or find it difficult to wrap your mind around it doesn't, in of itself,  make it "nonsense".

While there are some things that, at first blush, seem nonsensical, and upon further examination do prove to be so, there are also things that, at first blush seem nonsensical,  but in the end turns out to not be so.

The second scenario is what one meaning for "Paradox" is:  "Something that seems like it shouldn't be true, but actually is".

And this is the usage of "paradox" in the term "the Twin Paradox".

[TakenItSeriously]

Edit to further add:

So in the corrected context, I think the point you may be trying to make is that all three points of view on the problem tells a very different story which I agree happens a lot in SR. Kind of like the simultaneity thought experiments. So how valid could any conclusion be unless they all meet at some point which is impossible without adding acceleration into the problem.

Is that about it?

1 minute ago, Janus said:

It make perfect sense by the rules of Relativity.

Here's the whole scenario in space-time diagrams.  For the sake of keeping things less cluttered, we'll have Bob start at Year 0 rather than 2020.

Alice also sets her clock to 0 When she is by Bob.  Carole. likewise sets her clock to zero when, according to her, Bob's and Alice's Clocks read zero.

Because of this, we will first consider Carole's frame:

The Blue line represents Bob, the Red Alice, and the Green Carole. the numbers on each line represent years ticking off for each.  Time for Carole is the vertical axis.  Horizontal lines are lines of simultaneity.  Draw a horizontal line and it will pass through events that are simultaneous for Carole, such as Bob's, Alice's, and Carole's clocks all reading 0

Go up to the gray horizontal line, and you see the when Bob's clock read 10 years according to Alice, Her own clock reads between 16 and 17 years and Alice's reads between 3 and 4 years.  where the Red and Green lines cross is when Alice and Carole meet. Carole's clock reads 27 1/3 years, Alice's 6, and Bob's 16.4 years.

6 years later, Carole meets Bob, Her clock reads 33 1/3 years, Bobs 20 years and Alice's somewhere after 7 yrs

If we transform to Bob's frame, we get this:

Bob's and Alice's clock still read 0 at the same time, however, Carole's clock already reads past 21 years. This is a consequence of the Relativity of simultaneity; events that are simultaneous for Carole( all three clocks reading 0) are not so for Bob ( or as we will see later, Alice)

When Bob's clock reads 10 yrs, Alice and Carole are meeting, Alice's clock reads 6 yrs and Carol's 27 1/3 yrs.  Bob agree with Carol as to what time Both Alice's and Carole's clocks read when they meet, but disagrees with Alice as what time is on his own clock when this happens.

Carole's meets Bob when his clock reads 20 and hers has added another 6 yrs and reads 33 1/3 years.

 

Now Alice:

Again Bob and Alice's clocks both start at 0 when they are together, but Carole's clock already read almost 26 yrs. In 6 yrs according to Alice, she meets up with Carole. Carole's clock has advanced to 27 1/3 yrs, and Bob's to 3.6 yrs.  it takes another 27 1/3 years By Alice's clock for Carol and Bob to meet, during which Bob's clock advances by 16.4 years and reads 20 years, and Carole's advances another 6 yrs to read 33 1/3 years. 

 

Everyone agrees as to what times passing clocks had, how much time ticked away Alice's clock between leaving Bob, and meeting Carole, and how much time passed on Carole's clock between passing Alice and meeting Bob.   They just don't always agree on when these events occurred by their own clock.

If this seems "nonsense" to you, that's on you.   It is more an indication of your lack of understanding Relativity than anything else.

Just because you personally don't understand something or find it difficult to wrap your mind around it doesn't, in of itself,  make it "nonsense".

While there are some things that, at first blush, seem nonsensical, and upon further examination do prove to be so, there are also things that, at first blush seem nonsensical,  but in the end turns out to not be so.

The second scenario is what one meaning for "Paradox" is:  "Something that seems like it shouldn't be true, but actually is".

And this is the usage of "paradox" in the term "the Twin Paradox".

Ugh, cross posted.

Sorry, I can take a while wile pondering the problem.

[TakenItSeriously]

Janus

Theres some confusion here on what was posted that I’d like to clarify before it gets out of hand.

First, please refer to this post:

When I was saying it was nonsensical I was referring to the particular sentence I quoted, not your entire post.

After I posted it, I realized what you must have meant to say....

You used an ambiguous reference of “her” which could have meant Carole or Alice. I assumed you meant Carole’s point of view when I saw you refer to Alice in the same sentence. The problem was compounded when you mistakenly referenced that Alice was catching up to Bob. It’s a minor error, but when speaking in the context of SR, it becomes very confusing and that’s why I said it was nonsensical as written.

I waited a while before replying trying to avoid a cross post. Unfortunately you were busy writing a long reply so my waiting only backfired.

After rethinking the problem with the corrected sentence I compounded the cross edit with a cross post before seeing your long reply and posted an encapsulation of what I thought you were trying to say.

So having said this, is that what you were trying to say, mor or less.

[Janus]

2 minutes ago, TakenItSeriously said:

Janus

Theres some confusion here on what was posted that I’d like to clarify before it gets out of hand.

First, please refer to this post:

When I was saying it was nonsensical I was referring to the particular sentence I quoted, not your entire post.

After I posted it, I realized what you must have meant to say....

You used an ambiguous reference of “her” which could have meant Carole or Alice. I assumed you meant Carole’s point of view when I saw you refer to Alice in the same sentence. The problem was compounded when you mistakenly referenced that Alice was catching up to Bob. It’s a minor error, but when speaking in the context of SR, it becomes very confusing and that’s why I said it was nonsensical as written.

I waited a while before replying trying to avoid a cross post. Unfortunately you were busy writing a long reply so my waiting only backfired.

After rethinking the problem with the corrected sentence I compounded the cross edit with a cross post before seeing your long reply and posted an encapsulation of what I thought you were trying to say.

So having said this, is that what you were trying to say, mor or less.

If you think that someone has made a slip, say, typing "Alice" when they likely meant "Carole" ( something very easy to do when writing a long explanation involving a number of actors), you can ask them to clarify, or point out that they might have slipped up there.  What you do not do is just throw out a blanket comment about it being "nonsensical", which can pretty much mean anything. 

 

[TakenItSeriously]

5 minutes ago, Janus said:

If you think that someone has made a slip, say, typing "Alice" when they likely meant "Carole" ( something very easy to do when writing a long explanation involving a number of actors), you can ask them to clarify, or point out that they might have slipped up there.  What you do not do is just throw out a blanket comment about it being "nonsensical", which can pretty much mean anything. 

 

That’s what I was trying to do.

As I said, I meant to say the sentence was nonsensical as written, not the entire post, and I did say that I assumed it must contain some typos.

Edit to add:

I apologize for any confusion.

Edited November 28, 2019 by TakenItSeriously