Relativists: Enlighten me.

[Terry Sampson]

Hafele–Keating experiment - Wikipedia

Kinematic time dilation
According to special relativity, the rate of a clock is greatest according to an observer who is at rest with respect to the clock. In a frame of reference in which the clock is not at rest, the clock runs more slowly, as expressed by the Lorentz factor. This effect, called time dilation, has been confirmed in many tests of special relativity, such as the Ives–Stilwell experiment and experimental testing of time dilation.[1] Considering the Hafele–Keating experiment in a frame of reference at rest with respect to the center of the earth, a clock aboard the plane moving eastward, in the direction of the Earth's rotation, had a greater velocity (resulting in a relative time loss) than one that remained on the ground, while a clock aboard the plane moving westward, against the Earth's rotation, had a lower velocity than one on the ground

 

[Subduction Zone]

Your model appears to be overly complex and you are abusing the term "reference frames". Usually one wants to work with inertial frames of reference, and that means that they cannot accelerate by definition.

 

[Aupmanyav]

I think, Jim and Polymath discussed reference frames earlier also. Something yet not clear, Jim?

 

[Terry Sampson]

Something yet not clear, Jim?

Yep, but it looks like I may have to wait till Polymath wakes up to get my enlightenment. I just thought I'd give others a chance to straighten me out before he gets here.

 

[Terry Sampson]

Your model appears to be overly complex and you are abusing the term "reference frames".

Really? Well, darn, ...

 

[Twilight Hue]

Time is a constant. It only seems slower or faster from a point of reference.

 

[Terry Sampson]

Time is a constant. It only seems slower or faster from a point of reference.

Thanks for that pearl. Guess that must be why none of the worldlines are vertical in the figure with the most diagonal lines.

 

[Subduction Zone]

Really? Well, darn, ...

Rather than using a confusing sample why not work on a simpler one if you want to understand this. For example you could take a spaceship flying past you. Inside it there are two mirrors and a beam of light repeatedly bouncing back and forth between them. It is very bright so you can see the few air particles that it interacts with as it flies by. From your perspective the light is not moving in a straight line. It is moving at an angle back and forth, but since it is light you observe it moving at the speed of light. The people inside the spacecraft only see it bounding back and forth. It travels a much shorter distance for them and it is also moving at the speed of light. You can use this to calculate the apparent slowing of the clocks in the passing spaceship.

 

[Terry Sampson]

Rather than using a confusing sample why not work on a simpler one if you want to understand this.

I suppose I could, but to do it your way I'd have to get rid of most of my straight lines and all of my circles; and I think they look so pretty.

 

[Subduction Zone]

I suppose I could, but to do it your way I'd have to get rid of most of my straight lines and all of my circles; and I think they look so pretty.

You could have fewer straight lines. Just two straight lines representing the mirrors position on the spaceship and the diagonal line of the light bouncing back and forth between them.

 

[Polymath257]

None of your frames is an inertial reference frame. If you want to have acceleration (including circular motion), you have to deal with a non-inertial frame. Given your difficulty with inertial frames, trying to explain how non-inertial frames work is going to be near-impossible.

In particular, you will need a bit of math.

More specifically, how do you determine, in 8, that both are the same distance from some 'center'?

 

[Terry Sampson]

In particular, you will need a bit of math.

Ackkk! Over my dead body!!!

More specifically, how do you determine, in 8, that both are the same distance from some 'center'?

What if I hire Hafele and Keating to help me? They seem to have been pretty clever guys. After all, they figured out where the center of the earth was, didn't they?

None of your frames is an inertial reference frame.

Can't slip anything by you, can I?

If you want to have acceleration (including circular motion), you have to deal with a non-inertial frame. Given your difficulty with inertial frames, trying to explain how non-inertial frames work is going to be near-impossible.

Poly, Poly, ... you're breakin' my heart.
When Hafele and Keating performed their now famous experiment, they flew a plane east and flew a plane west. Now, I won't swear to it, but I think that even if a person is a flat-earther, he or she will concede that, to do that, somebody had to accelerate and fly circular paths.

And, if memory serves me, the Hafele-Keating Experiment is one of the more popular early tests and confirmations of Einstein's theory of Special Relativity. It got that status in spite of the accelerations involved.

Way back, ... probably around 2003 or 2004, an easy-going, competent relativist told me and some wanna-be relativists this, in a now-defunct, on-line Physics forum:

• “The younger Twin is the one with the shortest worldline, regardless of how that is accomplished.
  • Acceleration in the Twins' scenario accomplishes two related purposes:
    1. It makes it possible for Twin B to travel somewhere. Without this the whole idea of the experiment is moot.
    2. It is one way of making it possible for Twin B to return home instead of receding indefinitely into the distance. Arguably, without this the experiment is also moot.”

Since then, I've become acquainted with Don Lincoln [of Fermilab fame], who has put up a goodly number of Youtube videos, including these two:

(See, in particular, the no-math video. Whether you're into videos or not, give me a little time and I'll post transcripts of both videos.)

 

[Terry Sampson]

@exchemist @ratiocinator

"I get by with a little help from my friends." Help!?

(Come quick, before Rational Experiences gets here. )

 

[exchemist]

@exchemist @ratiocinator

"I get by with a little help from my friends." Help!?

(Come quick, before Rational Experiences gets here. )

Sorry Terry, I can do atomic and molecular QM, but we chemists did not spend any time on relativity. About the only time we use it is to explain the colour of gold.

(I've had RE on Ignore for a while now - it was getting painful.)

 

[Terry Sampson]

Sidebar stuff: Attached are nine transcripts of a Fermilab employee's Youtube videos [Dr. Don Lincoln] in which he discusses a number of topics encountered in Einstein's theory of Special Relativity. [Attachment 006 is a paper, not a transcript, for which there is no video.] Three more transcripts are attached in my next post.

(Continued in my next post)

 

[Terry Sampson]

(Continued from my last post.) Final three Youtube video transcripts.

 

[Terry Sampson]

it was getting painful.

Wise move, then.

 

[ratiocinator]

@exchemist @ratiocinator

"I get by with a little help from my friends." Help!?

(Come quick, before Rational Experiences gets here. )

What's your question? I just looked through one of the transcripts and he's right, the twins "paradox" isn't about acceleration.

You can actually work it out in several different ways. You can use relativity of relativity of simultaneity (what's simultaneous on Earth with the turnaround point in the travelling trajectory changes suddenly in going from the receding to the approaching frame) or just consider length contraction of the route taken by the travelling twin (in her frame of reference) or you can calculate the invariant intervals in the "stationary" frame.

 

[Terry Sampson]

What's your question?

False alarm. I think I've figured out the answer to my question, to my satisfaction.
My question was:

• In my scenario, there is: Non-motion, Motion, and Non-motion.
• The Hafele-Keating Experiment can be evaluated similarly, in STR: Non-Motion, Motion, and Non-motion.
• The notion that a Loedel Diagram can be used to accurately describe all or some portion of the "Motion" in my scenario, IMO, is based on the assumption that all motions are relative.
  • And I defy anyone to tell me which worldline in my Loedel Diagram is the shortest.
• However, in the H-K Experiment, there really is such a thing as "the shortest worldline".
  
• Question: So, why does my "analogy" fail?

Historically, anti-relativists and uninformed relativists have tried to attribute the H-K Experiment results and the Twin Paradox's Gedanken results to acceleration. However, as you noted, Don Lincoln correctly points out that "acceleration" is a "red herring". He attributes the actual and hypothetical results to the fact that "the youngest twin" occupies two frames, while "the older twin" only occupies one. [Attachment 011 above: Twin Paradox: The real explanation (no math).]

I know what Lincoln is saying, I just don't like the way he says it. I prefer another way.

Thanks for taking the time to respond.