Radioactive dating

[Colter]

Is this your escape answer to deny reality?

Which tells you your clocks slow from increased velocity whether you can detect that change or not.

Just as you don’t deny we are in motion despite not being able to tell. You can’t deny clocks slow due to changes in velocity even if we can’t tell.

To accept one truth and deny the other to save an incorrect belief would be termed hypocrisy.

You have a closed mind and are not interested in searching for truth. You deliberately ignore facts that don't fit your YEC agenda based an the exaggerated and scientifically inaccurate history of the Israelites.

Basically you project onto others what you yourself do.

 

[xianghua]

#2 If there were a rock subjected to enough heat to make it into plasma, it would not be a rock any more.

if i remember right a star formation start with a plasma temp.

 

[essentialsaltes]

if i remember right a star formation start with a plasma temp.

Yes, the sun is still at plasma temperature. The earth, however, is not.

In the formation of the solar system... "The various planets are thought to have formed from the solar nebula, the disc-shaped cloud of gas and dust left over from the Sun's formation.[28] The currently accepted method by which the planets formed is accretion, in which the planets began as dust grains in orbit around the central protostar. Through direct contact, these grains formed into clumps up to 200 metres in diameter, which in turn collided to form larger bodies (planetesimals) of ~10 kilometres (km) in size.[29] These gradually increased through further collisions, growing at the rate of centimetres per year over the course of the next few million years."

When we have clumps, it is clearly no longer plasma hot. So the formation of the Earth follows after the last time that material was plasma hot.

 

[dad]

I'm reading this and I feel like I'm being asked to "prove" that the world and everything in it wasn't created Last Thursday.

Actually you are just being asked to prove what you claim about the very nature of the world having been the same. You know this, because...? I guess it is hard to face the facts about your religion.

 

[dad]

Nice story.

Anything beyond the scope of physical, natural only science is a story to those of your religion. No problem.

 

[dad]

Science? It means pretty much what I’ve spent my life doing. And it means knowing your argument for what it is. (The last bit also requires logic)

Vague statement of faith that amounts to an admission of submersion in propaganda you thought was fact that you can't begin to defend here.

 

[dad]

Yes, the sun is still at plasma temperature. The earth, however, is not.

In the formation of the solar system... "The various planets are thought to have formed from the solar nebula, the disc-shaped cloud of gas and dust left over from the Sun's formation.[28] The currently accepted method by which the planets formed is accretion, in which the planets began as dust grains in orbit around the central protostar. Through direct contact, these grains formed into clumps up to 200 metres in diameter, which in turn collided to form larger bodies (planetesimals) of ~10 kilometres (km) in size.[29] These gradually increased through further collisions, growing at the rate of centimetres per year over the course of the next few million years."

When we have clumps, it is clearly no longer plasma hot. So the formation of the Earth follows after the last time that material was plasma hot.

Hard to believe anyone earth actually believes that godless and absurd fable.

 

[essentialsaltes]

Hard to believe anyone earth actually believes that godless and absurd fable.

Not so hard when we see clumps forming in orbits around other stars.

I know, I know, who ya gonna believe, your own eyes or a godded and absurd fable.

 

[FrumiousBandersnatch]

Anything beyond the scope of physical, natural only science is a story to those of your religion. No problem.

I'm a-religionist; i.e. non-religious. But, in general, yes, you're right - they're all stories, unsubstantiated anecdotes. They've remained unsubstantiated for around 2,000 years, so it seems unlikely to change.

 

[Justatruthseeker]

It made no difference to him until he compared himself to his twin who had remained in a non-accelerating frame.

You really need to grasp that motion is relative; saying that everything else is in motion is exactly equivalent to saying we are in motion with respect to everything else.

That's saying exactly the same thing, from a different reference frame - as above.

There is an infinite number of ways our rate of time can be seen to pass - depending on which of an infinite number of frames you measure it with respect to.

If you're not interested in other frames, then it makes no difference. If you accelerate so you're moving with respect to your starting frame, you can calculate the time dilation relative to your starting frame, but unless you're comparing your age after acceleration with something in your starting frame that didn't accelerate (and which would now be some distance away), why would you? In what circumstances, other than travelling away from and then back to Earth at relativistic velocities, would it be relevant?

The classic Hafele–Keating experiment that measured the kinematic time dilation on aircraft, did so with respect to an inertial frame at the centre of the Earth (because neither the surface nor the aircraft were inertial frames). Aircraft flew both east and west at roughly the same height and airspeed.

For the aircraft flying eastward, time slowed relative to the clock on the ground, i.e. it lost 184ns relative to that clock; for the plane flying westward, the clock on the ground ran slow relative to the aircraft, i.e. it gained 96ns relative to the ground clock - because the clock on the ground was rotating west to east with the Earth. So Hafele–Keating confirmed both time dilation and that it is relative to a given frame (the clock on Earth's surface).

You have to compare clocks in different frames to establish what the change is, if any, because it depends on the relative motion of the two frames.

But, as I said before, if you're not comparing with clocks in other frames, i.e. you're only dealing with events in your comoving frame, it's just irrelevant.

I am glad to see you recognize your error, even if you then try to play it off as if it isn't an error on your part....

"You have to compare clocks in different frames to establish what the change is, if any, because it depends on the relative motion of the two frames.

But, as I said before, if you're not comparing with clocks in other frames, i.e. you're only dealing with events in your comoving frame, it's just irrelevant."

But this is exactly what you are trying to do. Compare the moving twins clock in the here and now, with the frame he WAS in before he began his motion. You can not calculate into the past without invariably comparing the two frames in which clocks ticked at a different rate than in the frame you currently occupy. The twin's clock in the stationary frame, of which you were once part of, does not tick the same rate as the clock in your current frame. It ticks faster.....

We are not just dealing with events in our co-moving frame in the here and now. We are comparing this frame in the here and now, to another frame in the past in which clocks ran at a different rate than they do now due to changes in velocity.....

You can not compare the moving twins frame to the stationary twins frame without adjusting for time dilation.... And since you are not calculating for the rate of time now, but in the past when you were a part of that other frame..... you are left with no choice but to compare two different frames in which time runs at a different rate and adjustments MUST be made......

The twin CAN NOT use his current clock rate to calculate the rate in the other frame before he began acceleration. HIS PAST..... Likewise you can not use your current clock rate to calculate into YOUR PAST..... The clock rates are not the same.....

This is your error. You are invariably comparing two different frames, that run at different rates of time, but trying to use only your current rate of time when it in all actuality speeds up the further back in time you go. This makes your calculation of time passed based upon decay rates in error.

 

[Justatruthseeker]

Using your own argument have you adjusted your own biological age for time dilation since you are in the same accelerated frame?
The human body can be used as a biological clock as Galileo demonstrated using his pulse rate to time the period of a swinging pendulum.

So tell us your true age, thousands of years old, tens of thousands of years old...........

Older than my calendar years, since my decay rate would have been faster in the past.....

But this is the point I am trying to get across, see above post. You can't compare this frame in the here and now to a past frame in which time ran at a different rate without adjusting for time dilation.

Just as in one calendar year, I will have aged less than I did in one calendar year in the past.....

I simply will not notice this because I will continue to call slower ticks of time seconds, just as I once called faster ticks of time seconds, even if they are not of the same duration.....

 

[Justatruthseeker]

OT: The speed of light. I have heard from many sources, that a solid can never reach the speed of light. I have to assume they mean there, the speed of light relative to some point in spacetime.

I revere science and even respect scientists enough to suppose that there is some concept that I just don't get in all this, since scientists make so many claims that are hard to make sense of, so I ask the following questions, maybe to help me understand.

I have also heard that when an object reaches the speed of light, it becomes energy. (To me, that doesn't quite make sense if E=MCsquared, but anyway). If that is true, when object #1 is approaching the speed of light, compared to location A, and object #2 is traveling an opposite direction, say at nearly the speed of light, then they each to the other would seem to be energy. I wonder then, is all matter actually energy, since it is obviously receding from some point past the speed of light? You seem to imply that no perception of one to the other would be possible, so the question is moot. Yet it seems to me that perception is not the definition of reality. (I.e. the fact we don't see that object receding from us does not mean it is not). We see all objects as cohesive reality; in the less abstract mind, for that object to become energy, how can if remain cohesive, so that as it slows it becomes the same object again?

I ask all that to introduce the following question: Is all energy matter sped up, or the potential to be matter if slowed down? If so, would the waveform of that energy define the matter it becomes? and vice-versa?

I understand all this seems to assume that the whole object reaches the speed of light at the same time, which is not proven, nor does it reference any relation of the action of the atoms and their parts within the object to the speed of the object.


The sonic boom is relative to the speed of the air in which the soundwave is compressed and unable to escape forward. If one was able to travel the speed of light, I must assume that can only be relative to a point, since it seems there is no static medium to travel through.

If a "universe", then, is separating from this one faster than the speed of light, there must exist spacetime between the two, by which the difference can be actual, no? If the direction from the one could be known, could not a theoretical spaceship, traveling from the edge of this "universe" approaching the speed of light send information at the speed of light relative to that ship toward the departing "universe" faster than that departure? (I put "universe" in quotes, since these seem more like galaxies to me than universes, since I have heard that a universe is defined by spacetime --there being no reality (spacetime) outside of it).

Ahhh, the speed of light and all of its misunderstandings. I can clear that up for you, but only if you are willing to accept that it isn't "just because", or some mythical infinite energy or mass hocus pocus, about the best answer you will get from even the so-called experts.....

It is really quite simple conceptually, but as I am sure you have noticed peoples unwillingness to treat everything as relative despite their proclamations they believe this, and instead they treat this frame as an absolute frame..... So set are they in this mode of thinking they can not envision that clocks in slower frames - of which we were once part of - do not tick the same rate as our current clocks. Thinking they can continue to use the rate of clocks today to calculate into frames in the past when the velocity was less.....

But I digress, enough with the silliness of treating this frame as absolute....

So unlike anyone else you have asked, I am going to explain why light always remains c regardless of velocity.... and lo and behold, do it in simple to understand English instead of trying to hide ignorance behind big words meant only to confuse....

Look at the speedometer on your car. Imagine that 100 mph is the speed of light and the fastest it can give readings for. Accelerate to 50 mph. As you accelerate your division mark spacing (clocks and rulers) begin to change with your increase in energy on the quantum level from your change in velocity.

Now comes the most important part of all. You must now rotate the dial so that your zero point follows the needle.

Notice the consequences. 100 mph is still 100 mph and can never be reached. Also your velocity through space now reads as zero. Just as it does right now despite our spinning around the earth's surface at 1,000 mph, orbiting the sun at 67,000 mph, which is orbiting the galaxy at 514,000 mph, which is itself moving through space at an unknown velocity.

This is key to understanding. No matter how fast your actual velocity through space may be, all your devices will always say you are stationary because your zero points reset proportionally to energy gained as well. This change in our zero points compensates exactly for our change in velocity.

This is why you continue to see everything as normal, despite clock ticks changing duration and rulers changing length. Your zero points have shifted along with your clocks and rulers. this is also why every other frame seems to change as well. You no longer share the same starting points for your measurements. Your zero points are not the same as other frames.

This is how longer ticks of time and different length rulers can calculate the same result for light as shorter ticks of time. They are not using the same zero points on the energy scale. As soon as you start to understand that our zero points also shift along with our measuring devices (why we always appear as stationary to ourselves), you'll begin to understand why c is always c regardless of velocity and length of clock ticks.

So one can never reach c using your own clocks and rulers, the very nature of our measuring devices changing along with our zero points makes this impossible. There never will be any traveling at 1/2 of c or 99.9% of c, or any number for yourself. You will at all times regardless of your actual velocity through space read as stationary to your own devices.

Light always travels at c because with every change in velocity your zero points change along with your clocks and rulers. And you will never notice this because you will continue to call different duration ticks of time seconds, even as you understand they are changing and not the same as they were before.....

And this is why science has no real answer for why c always remains c despite the change in clocks and rulers. By not understanding (or accepting) that zero points shift, they treat this frame as an absolute frame without even realizing that they are doing so; while declaring fervently that everything is relative and no absolute frames exist........

 

[Justatruthseeker]

You have a closed mind and are not interested in searching for truth. You deliberately ignore facts that don't fit your YEC agenda based an the exaggerated and scientifically inaccurate history of the Israelites.

Basically you project onto others what you yourself do.

No, see above post to you. it is clear you recognize what must be done, but just refuse to then do what you know is right because it causes damage to your set system of beliefs..... I understand, people have a natural tendency to self rationalize and do whatever it takes to keep their world from crashing down before their eyes...

I too was once in your position, trying to pretend that this frame is the same frame as one in the past that was moving at a different velocity. i too tried to rationalize it away. You know your error, the question is will you overcome your reluctance to accept what is true or continue to indulge in fantasies that it is always the other person that never sees?????

 

[FrumiousBandersnatch]

I am glad to see you recognize your error, even if you then try to play it off as if it isn't an error on your part....

"You have to compare clocks in different frames to establish what the change is, if any, because it depends on the relative motion of the two frames.

But, as I said before, if you're not comparing with clocks in other frames, i.e. you're only dealing with events in your comoving frame, it's just irrelevant."

But this is exactly what you are trying to do. Compare the moving twins clock in the here and now, with the frame he WAS in before he began his motion. You can not calculate into the past without invariably comparing the two frames in which clocks ticked at a different rate than in the frame you currently occupy. The twin's clock in the stationary frame, of which you were once part of, does not tick the same rate as the clock in your current frame. It ticks faster.....

We are not just dealing with events in our co-moving frame in the here and now. We are comparing this frame in the here and now, to another frame in the past in which clocks ran at a different rate than they do now due to changes in velocity.....

You can not compare the moving twins frame to the stationary twins frame without adjusting for time dilation.... And since you are not calculating for the rate of time now, but in the past when you were a part of that other frame..... you are left with no choice but to compare two different frames in which time runs at a different rate and adjustments MUST be made......

The twin CAN NOT use his current clock rate to calculate the rate in the other frame before he began acceleration. HIS PAST..... Likewise you can not use your current clock rate to calculate into YOUR PAST..... The clock rates are not the same.....

This is your error. You are invariably comparing two different frames, that run at different rates of time, but trying to use only your current rate of time when it in all actuality speeds up the further back in time you go. This makes your calculation of time passed based upon decay rates in error.

But we're not comparing with other frames. All the events of interest happened in our comoving frame.

We have no twin with which we're meeting up to compare our age or the passage of time. If the solar system had zipped around the universe at relativistic speeds for a million years just after the Cambrian explosion, it would make no difference to our measures of the age of the Earth or anything else in the solar system. The Earth would still go around the sun once a year, the time it takes to orbit would still be the same fraction of a radioisotope half-life, all our clocks would still be in sync, mutations would still occur at the same rate, river valleys would erode over the same number of years, and life would still evolve at the same rate as if the solar system had stayed where it was. An observer on Alpha Centauri would probably disagree, as might someone who'd been left behind when the tour began, but we're not interested in what other observers might or might not agree on because we're not comparing our timeline with hypothetical observers elsewhere.

But (forgetting hypothetical relativistic tours) even if we had some means to compare our timeline with, for example, Alpha Centauri, we would not see any discrepancy, because the expansion of the universe affects all stars and galaxies similarly, and it will make no difference whether you think they're being accelerated through space (they're not) or being separated by the expansion of the metric of spacetime itself.

The key point is that there's no fixed absolute time against which you can measure the rate of your time passing. Whether you see it or not, your objections depend on there being some absolute standard for comparison - and there isn't one; that's what relativity is all about.

 

[dad]

Not so hard when we see clumps forming in orbits around other stars..

Tell us what these little clumps tell you about what the nature of time is in deep space? Hilarious.

 

[dad]

I'm a-religionist; i.e. non-religious. But, in general, yes, you're right - they're all stories, unsubstantiated anecdotes. They've remained unsubstantiated for around 2,000 years, so it seems unlikely to change.

Many if not most people in the origins fables religion are atheists. The stories of science cannot be substantiated as they are physical only, natural world based stories about a future and past that is more than just that.

As for the stories of the bible, I believe they are substantiated and verified true by the One who rose from the dead.

 

[Mark Quayle]

Ahhh, the speed of light and all of its misunderstandings. I can clear that up for you, but only if you are willing to accept that it isn't "just because", or some mythical infinite energy or mass hocus pocus, about the best answer you will get from even the so-called experts.....

It is really quite simple conceptually, but as I am sure you have noticed peoples unwillingness to treat everything as relative despite their proclamations they believe this, and instead they treat this frame as an absolute frame..... So set are they in this mode of thinking they can not envision that clocks in slower frames - of which we were once part of - do not tick the same rate as our current clocks. Thinking they can continue to use the rate of clocks today to calculate into frames in the past when the velocity was less.....

But I digress, enough with the silliness of treating this frame as absolute....

So unlike anyone else you have asked, I am going to explain why light always remains c regardless of velocity.... and lo and behold, do it in simple to understand English instead of trying to hide ignorance behind big words meant only to confuse....

Look at the speedometer on your car. Imagine that 100 mph is the speed of light and the fastest it can give readings for. Accelerate to 50 mph. As you accelerate your division mark spacing (clocks and rulers) begin to change with your increase in energy on the quantum level from your change in velocity.

Now comes the most important part of all. You must now rotate the dial so that your zero point follows the needle.

Notice the consequences. 100 mph is still 100 mph and can never be reached. Also your velocity through space now reads as zero. Just as it does right now despite our spinning around the earth's surface at 1,000 mph, orbiting the sun at 67,000 mph, which is orbiting the galaxy at 514,000 mph, which is itself moving through space at an unknown velocity.

This is key to understanding. No matter how fast your actual velocity through space may be, all your devices will always say you are stationary because your zero points reset proportionally to energy gained as well. This change in our zero points compensates exactly for our change in velocity.

This is why you continue to see everything as normal, despite clock ticks changing duration and rulers changing length. Your zero points have shifted along with your clocks and rulers. this is also why every other frame seems to change as well. You no longer share the same starting points for your measurements. Your zero points are not the same as other frames.

This is how longer ticks of time and different length rulers can calculate the same result for light as shorter ticks of time. They are not using the same zero points on the energy scale. As soon as you start to understand that our zero points also shift along with our measuring devices (why we always appear as stationary to ourselves), you'll begin to understand why c is always c regardless of velocity and length of clock ticks.

So one can never reach c using your own clocks and rulers, the very nature of our measuring devices changing along with our zero points makes this impossible. There never will be any traveling at 1/2 of c or 99.9% of c, or any number for yourself. You will at all times regardless of your actual velocity through space read as stationary to your own devices.

Light always travels at c because with every change in velocity your zero points change along with your clocks and rulers. And you will never notice this because you will continue to call different duration ticks of time seconds, even as you understand they are changing and not the same as they were before.....

And this is why science has no real answer for why c always remains c despite the change in clocks and rulers. By not understanding (or accepting) that zero points shift, they treat this frame as an absolute frame without even realizing that they are doing so; while declaring fervently that everything is relative and no absolute frames exist........

Forgive my ignorance for a moment if you will, but so far it seems to me you have told me what I always knew. What I want to know is not how my C looks to me, as my zero point moves with me, but what my C looks like to others. You glanced at the question once, with mentioning why other things look different compared to my moving zero point. But you didn't address what happens as, say, my zero point moves past a zero point going in the opposite direction --both of us at more than half the speed of light relative to the point at which we crossed each other.

 

[sjastro]

I am glad to see you recognize your error, even if you then try to play it off as if it isn't an error on your part....

"You have to compare clocks in different frames to establish what the change is, if any, because it depends on the relative motion of the two frames.

But, as I said before, if you're not comparing with clocks in other frames, i.e. you're only dealing with events in your comoving frame, it's just irrelevant."

But this is exactly what you are trying to do. Compare the moving twins clock in the here and now, with the frame he WAS in before he began his motion. You can not calculate into the past without invariably comparing the two frames in which clocks ticked at a different rate than in the frame you currently occupy. The twin's clock in the stationary frame, of which you were once part of, does not tick the same rate as the clock in your current frame. It ticks faster.....

We are not just dealing with events in our co-moving frame in the here and now. We are comparing this frame in the here and now, to another frame in the past in which clocks ran at a different rate than they do now due to changes in velocity.....

You can not compare the moving twins frame to the stationary twins frame without adjusting for time dilation.... And since you are not calculating for the rate of time now, but in the past when you were a part of that other frame..... you are left with no choice but to compare two different frames in which time runs at a different rate and adjustments MUST be made......

The twin CAN NOT use his current clock rate to calculate the rate in the other frame before he began acceleration. HIS PAST..... Likewise you can not use your current clock rate to calculate into YOUR PAST..... The clock rates are not the same.....

This is your error. You are invariably comparing two different frames, that run at different rates of time, but trying to use only your current rate of time when it in all actuality speeds up the further back in time you go. This makes your calculation of time passed based upon decay rates in error.

If only you comprehended the twin paradox…………...
The paradox is about measurement not calculation, the only concern the twins have is their clocks are synchronized before the journey.
The description of the paradox is straightforward.
(1) Twins synchronize their clocks.
(2) One twin makes a round trip.
(3) Twins compare the time elapsed for the journey on their clocks.

The twins find their clocks are no longer synchronized as the travelling twin’s clock has run slower.
This has absolutely nothing to do with adjustments, calculations, or worrying about past events as the clock comparison is made in the same location in space time, in other words in the present.

There are quite a few methods of solving the paradox; one method is using Minkowski spacetime diagrams.
Minkowski spacetime diagrams are used for flat inertial frames and are therefore an approximation for the travelling twin’s accelerated frame of reference.
The approximation is valid as most of the travel time is in an inertial frame; it only the brief period of time when the twin changes direction to return to the stationary twin where there is an accelerated frame.
A Minkowski spacetime diagram is a two dimensional representation of spacetime and is composed of a horizontal x axis for distance and a vertical time axis w = ct.

The world line is the pathway of a particle or photon in spacetime and is the displacement in both space and time.
For a photon travelling in spacetime the displacements in distance and time are equal and the worldline of a photon is a straight line and forms a 45 degree angle with the time and distance axes.
Since a particle can never travel at or exceed the speed of light, the angle of the tangent of a world line of a particle is less than 45 degrees with the time axis.

When the Lorentz transformations are applied to a Minkowski spacetime diagram, the axes are no longer orthogonal, and the scale distance and time scales change which correspond to length contraction and time dilation.
The degree of distortion depends on the velocity of the frame.

We can use spacetime diagrams to illustrate the twin paradox and why it is not a paradox……………
The twins are called Dave and Bob where Bob is the travelling twin.
Bob travels away from Dave at a speed of 0.8c for 3 years after which he changes direction and travels back towards Bob at a speed of 0.8c for another 3 years before reaching him.

The Minkowski spacetime diagram for the twins is illustrated.

Since Dave is the stationary twin he is only moving in time hence his world line is along the time axis.
Bob is travelling in both space and time but less than c and is composed of an outgoing world line for 3 years and an ingoing world line of 3 years before meeting up with Dave.
The dots along Dave’s and Bob’s worldline correspond to yearly intervals.
Note that Bob’s yearly intervals are stretched out due to time dilation relative to Dave as Bob is moving relative to Dave.
The dashed lines and arrows are signals sent by Dave and Bob to each other.
Since the signals travel at c they are parallel to the Light lines.
Both Bob and Dave send signals to each other at yearly intervals.
As the space diagram clearly shows Dave has sent out 10 signals before Bob returned but only received 6 signals from Bob (including one on his return).
Clearly Bob’s clock was running slower than Dave’s and the paradox of each twin ending up younger than the other is broken.

The symmetry is also broken by the use of the Doppler factor:
√(c-v)/(c+v).
When Bob moves away from Dave the Doppler factor is √(c-0.8)/(c+0.8) = 1/3.
When Bob moves towards Dave the Doppler factor is √(c+0.8)/(c-0.8) = 3.

When travelling away Bob receives only one signal from Dave but nine signals for the return journey.
Dave on the other hand receives 3 signals from Bob in the first nine years and the remaining three in one year.

All of this is accomplished without your convoluted and ridiculously wrong approach.

 

[sjastro]

Older than my calendar years, since my decay rate would have been faster in the past.....

But this is the point I am trying to get across, see above post. You can't compare this frame in the here and now to a past frame in which time ran at a different rate without adjusting for time dilation.

Just as in one calendar year, I will have aged less than I did in one calendar year in the past.....

I simply will not notice this because I will continue to call slower ticks of time seconds, just as I once called faster ticks of time seconds, even if they are not of the same duration.....

And as I have shown your approach is complete nonsense.
FB has also noted a fundamental flaw there is no inertial frame for comparison.

 

[dad]

Minkowski spacetime diagrams are used for flat inertial frames and are therefore an approximation for the travelling twin’s accelerated frame of reference.

I might point out that no twin has ever left the earth area. What anyone thinks would happen to physical twins in deep space is gueeswork.

The world line is the pathway of a particle or photon in spacetime and is the displacement in both space and time.

The space and time and spacetime we are familiar with likely does not represent time or space in the far universe.

The degree of distortion depends on the velocity of the frame.

And where the frame is depends on if we are in the fishbowl or outside of this area.

We can use spacetime diagrams to illustrate the twin paradox and why it is not a paradox……………
The twins are called Dave and Bob where Bob is the travelling twin.

No. You may not. Only in the known area of this solar system.

But even here you won't see twins doing all that stuff you use the dream math on.

Bob travels away from Dave at a speed of 0.8c for 3 years after which he changes direction and travels back towards Bob at a speed of 0.8c for another 3 years before reaching him.

No, Bob never did that.

The dots along Dave’s and Bob’s worldline correspond to yearly intervals.

Impossible actually. Since you had them travelling at what, 8/10ths the speed of light? No probe or object or man has even gone ONE light day away. Any line you draw out that far does not apply and is not known to be in our space or time.

Not only that, but the Voyager craft are not travelling very fast compared to your sci fi imaginary twins.

When travelling away Bob receives only one signal from Dave but nine signals for the return journey.

Does he get a few high fives from Mickey mouse on the journey too?

All of this is accomplished without your convoluted and ridiculously wrong approach.

That's great, except...NOTHING was actually accomplished!