1 The correct explanation for the twin paradox

This is JUST NOT TRUE. Assuming they are identical clocks, A's clock runs at EXACTLY THE SAME RATE as B's clock.

This is as much an error in English phrasing as it is in the physics. It is wrong at both levels.

In YOUR phrasing above there is an inconsistency. When you say "A's clock runs slower than B", your words compare the INTRINSIC RATES of their clocks, and since the clocks are identical, so are their intrinsic rates. In order to make a correct statement, you MUST mention who is doing the measuring.

Yes, many elementary books on SR, and most ancient texts also get it wrong. If a book says "moving clocks run slow", discard it and get a better book. I recommend:
Taylor and Wheeler, _Spacetime_Physics_. Misner, Thorne, and Wheeler, _Gravitation_.

2 The correct explanation for the twin paradox

Not among physicists, who UNDERSTAND relativity. Only among fools and idiots who DON'T understand it but insist in attempting to write about it nevertheless.

But it is true that many popular writers, and most ancient writers, use verbal shortcuts to get the main point across while being technically wrong. Such as "moving clocks run slow" -- this is WRONG, but if you have seen how many words I have to use to set the record straight, you can appreciate why popular authors take the shortcut (even though it is wrong).

Tom Roberts

3 The correct explanation for the twin paradox

It is about the lengths of the paths through spacetime that the two twins follow between their meetings. For timelike paths the path length is the total elapsed proper time. The traveling twin's clock does NOT "tick slower" than the home twin's clock, but rather the length of the path the traveling twin followed has less elapsed proper time.

"Time dilation" is ALSO not about "clocks ticking slower", it is a different geometrical property related to the projection of the moving clock's tick rate onto the inertial frame that is measuring it.

Tom Roberts

4 The correct explanation for the twin paradox

The twin paradox (wrong name) involves the explanation of the outome of a certain experiment: Consider two obsevers A and B who each have an identical clock. Observer A is considered to stay at home. Observer B travels for some time and returns back "home" When they meet and compare clocks the clock of A shows 20 ticks and the clock of B shows 15 ticks. How come?

The real question to answer first is: what is considered a "valid" explanation.

Can you use as part of the explanation complex numbers?

IMO the explanation is physical in the sense that the behaviour of clocks is affected by how fast you move a clock (and gravity). This is also the case for clocks who use light signals. The behaviour of such a clock depents on the speed of light and the speed of the clock relatif to the speed of light.

>	"Time dilation" is ALSO not about "clocks ticking slower", it is a different geometrical property related to the projection of the moving clock's tick rate onto the inertial frame that is measuring it.

The issue in the twin paradox is to explain why the clock of the moving twin runs behind. (of course you can rephrase this question and putting it a different coat) The real question to answer is: is it possible that the clock of the moving observer runs faster than the stay at home. (has more elapsed proper time, if you like)

Nicolaas Vroom

5 The correct explanation for the twin paradox

>	The twin paradox (wrong name) involves the explanation of the outome of a certain experiment:... When they meet and compare clocks the clock of A shows 20 ticks and the clock of B shows 15 ticks. How come?

"How come" as in "cause" is not part of physics but of metaphysics. No matter the "cause", it wont change the prediction of the model; it wont change the math of SR.

>	The real question to answer first is: what is considered a "valid" explanation.

And physicist answered that a long time ago: Physics has no explanation; such a concept does not apply; its the prediction of the model, to "pop out value" that matters.

>	IMO the explanation is physical in the sense that the behaviour of clocks is affected by how fast you move a clock (and gravity).

Perhaps. But such metaphysical concepts are not necessary, so why carry them around? Thats why the modern philosophy is to remove such concepts from physics, since it wont change the models (the equations, the predicted results).

>	The issue in the twin paradox is to explain why the clock of the moving twin runs behind.

NO. Perhaps *you* would like such a dynamical view or understanding, but physicist moved past that and realized that such views become obsolete and unnecessary.

>	The real question to answer is: is it possible that the clock of the moving observer runs faster than the stay at home. (has more elapsed proper time, if you like)

SR-compute. Conclusion: As the twins reunite, its the non inertial twin's value that is less than the other twin (& by the gamma factor).

6 The correct explanation for the twin paradox

No matter how many times this is explained to people like you in this group, you do not understand.

Let again try the car odometer analogy. Two identical cars make a trip from Chicago to New York, but they use different routes. While the odometers (ie the clocks) are both measuring miles (ie seconds), due to the different routes (ie spacetime path) the trip accumulated distance in miles of each odometer (ie clock) is different.

>

The real question to answer first is: what is considered a "valid" explanation. Can you use as part of the explanation complex numbers? IMO the explanation is physical in the sense that the behaviour of clocks is affected by how fast you move a clock (and gravity). This is also the case for clocks who use light signals. The behaviour of such a clock depents on the speed of light and the speed of the clock relatif to the speed of light.

nonsense.

7 The correct explanation for the twin paradox

What is your golden rule to decide that I do not understand? In general what I understand are the outcomes from experiments. Some people start with postulates and using these postulates to predict the future. Finally they need experiments to prove these postulates. For me the most important are the outcomes of these experiments. With the aid of different experiments I try to understand.

What is wrong with that?

>

Let again try the car odometer analogy. Two identical cars make a trip from Chicago to New York, but they use different routes. While the odometers (ie the clocks) are both measuring miles (ie seconds), due to the different routes (ie spacetime path) the trip accumulated distance in miles of each odometer (ie clock) is different.

8 The correct explanation for the twin paradox

At what point in time does the clock run faster? Is it one second after the traveling twin moves?

Is it one minute after the traveling twin moves?
Is it one hour after the traveling twin moves?
Is it one day after the traveling twin moves?

At what point in time does the clock run faster?

9 The correct explanation for the twin paradox

>

What is your golden rule to decide that I do not understand? In general what I understand are the outcomes from experiments. Some people start with postulates and using these postulates to predict the future. Finally they need experiments to prove these postulates. For me the most important are the outcomes of these experiments. With the aid of different experiments I try to understand. What is wrong with that?

Which one. You didn't say anything at all.

10 The correct explanation for the twin paradox

I will put the explanation without "odometers", but for sure you will not understand.

a)Both clocks (of the stay at home (point A) and the traveller twins) are accurate clocks (may be atomic clocks).
b)When the traveller departs and travels at a speed v c)the traveller twin clock follows a path through spacetime, which it turns out is shorter than the path through spacetime the stay at home twin followed. Yes, even if the stay at home twin did not move or travel, its time coordinate changed. Yes, the traveller twin path through spacetime changed all of the coordinates (x,y,z and t).
d)From the above, the accumulated time(the sum of ticks) of the traveling clock is then LESS than the accumulated time of the stay at home twin.

Why is traveller’s proper time shorter than that of the stay at home twin? the answer is the particular structure of the relativistic spacetime that is responsible for the difference of accumulated or proper times. Let us see why.
In classical mechanics and ordinary space, the Pythagorean theorem indicates that z^2 = x^2 + y^2, as in any right-angled triangle, which implies that z < x + y.
But Special Relativity requires the introduction of a four-dimensional geometrical structure, the Poincaré-Minkowski space-time, which couples space and time through the speed of light.
The Pythagorean theorem becomes s^2 = x^2 – c^2t^2, and a straightforward algebraic manipulation allows us to deduce that s is always longer than x + ct. As said previously, s measures the proper time. In Poincaré-Minkowski geometry, the worldlines of inertially moving bodies maximize the proper time elapsed between two events.

11 The correct explanation for the twin paradox

The point is that odometers measure distance, while clocks measure elapsed (proper) time. This is an ANALOGY. The usual twin paradox with instantaneous accelerations is a triangle, and the clocks measure the elapsed (proper) time along each path. As the geometry is hyperbolic, the one that traversed two sides of the triangle experienced less elapsed (proper) time than the one who traversed one.

Each odometer measured 1 meter for every meter traversed. Each clock measured 1 second for every second traversed.

Tom Roberts

12 The correct explanation for the twin paradox

Because the car analogy serves to explain why, in the twin gedanken, identical clocks which follow different paths when reunited show different readings.

> >	I will put the explanation without "odometers", but for sure you will not understand.

>	If your explanation is solely based on experiments you have a high chance that I will understand. If your explanation is solely based on mathematics you have a low chance that I will understand except the logic inherent in mathematics.

Actually, first the explanation is geometrical and secondly a multitude of physical experiments and observations confirm the geometry of the spacetime.

> >

c)the traveller twin clock follows a path through spacetime, which it turns out is shorter than the path through spacetime the stay at home twin followed. Yes, even if the stay at home twin did not move or travel, its time coordinate changed. Yes, the traveller twin path through spacetime changed all of the coordinates (x,y,z and t).

>	IMO when I travel then I travel through space in time. You use a concept spacetime but that is someting that physical does not exist. i.e it is a mathematical concept based on complex numbers. s = x + ivt or s = l + ivt with v = c and constant. l = a vector

For sure spacetime is a model created by our thougths. Nature itself appears to use not mathematics nor geometry. We do not really know how and why Nature does this and that.

Copernicus thought of a model in which the Sun is at the center of a circle where the Earth is orbiting the Sun. This is a geometrical 2D model which you can say it appears to agree with our senses of the situation (also thoughts).

Spacetime is another geometrical model extending the previous one by using the time coordinate. The orbit would be now a 3D geometrical model, where the Earth orbit now follows an Helix path through spacetime, while the Sun follows a straight line. For sure you would agree this is a model as physical as the Copernican one. Note that no mathematics (real or complex) are needed up until now.

For sure also you can add coordinates (dimensions) to your models and that does not make them less physical the the Copernican one.

> >	d)From the above, the accumulated time(the sum of ticks) of the traveling clock is then LESS than the accumulated time of the stay at home twin.

>	All of that is mathematical correct but how do you demonstrate that this is true.

You can't demonstrate the true or the wrongness of a model. What you can do is to perform experiments which can verify or falsify the model. Verifying a model does not proof the model is correct. Falsifying a model implies the model has to be revised. So since SR and GR models were proposed, thousands of experiments have been and are being carried out to verify or falsify the validity of SR and GR.

13 The correct explanation for the twin paradox

In other words, 'when' does the clock run faster? Are both clocks the same time two days later after the traveling twin?
How about a week later? Are the clocks still the same?? Or, are the clocks differnt times the moment the traveling twin ...travels?
When does it speed up or slow down??? A year later? A second later?
Or, ....whenever it feels like it.
No one can answer this question cause...no one knows.
I guess you gotta stop making 'thought experements' and measure it in the real world.

14 The correct explanation for the twin paradox

That's not the real problem. The real problem is that time does NOT "flow at different rates" [#], and yet when the twins rejoin they are different ages.

[#] That is, for a traveling twin who experiences gentle accelerations that she survives, within her spaceship time always flows as she is accustomed to -- she can measure any time-dependent physical process inside her spaceship and MEASURE that time flows as usual (e.g. measuring the frequencies of atomic lines; the lifetimes of metastable states, etc.). Indeed, after accounting for the acceleration from her spaceship's thrust, she can use ALL of the physics textbooks and reference materials we use today, WITHOUT CHANGE (except for the difference in gravity).

With the analogy:

clock -> odometer time -> distance

Tom Roberts

15 The correct explanation for the twin paradox

On Thursday, 20 July 2017 17:08:45 UTC+2, Paparios wrote:

>	Let again try the car odometer analogy. Two identical cars make a trip from Chicago to New York, but they use different routes.

Consider the following 2 options: One car travels straight from Chicago to New York. The odometer will show 600 miles. Car two travels from Chicago to Houston and then straight to New York. The odo meter will show 600 + 600 = 1200 miles. Both car will start at the same moment and arrive at the same moment. This implies that the second car drives the fastest. Both cars have a clock. Both clocks are reset at the start of the experiment. Question: when both cars are in New York will both clocks show the same reading?

>	The usual twin paradox with instantaneous accelerations is a triangle, and the clocks measure the elapsed (proper) time along each path. As the geometry is hyperbolic, the one that traversed two sides of the triangle experienced less elapsed (proper) time than the one who traversed one.

This implies (if my understanding is correct) that the second clock should show less elapsed proper time. In simple terminology; the second clocks runs behind

>	Each odometer measured 1 meter for every meter traversed.

Okay

>	Each clock measured 1 second for every second traversed.

Here we have a problem. What do you mean?

To solve the issue "how clocks perform" we have to made two (4) assumptions:
1) We agree that every where, the universe, at this moment has the same time after the Big Bang. This implies that the Universe has everywhere the same age.
2) We agree that every where in the universe at this moment, all events that can be be indentified, are simultaneous events. 3) As such we also agree that a self centered view of the Universe (of what I see and observe) is irrelevent.
4) As such it is our responsible to define a clock which shows the age of the Universe.

The problem is that an odometer is not very helpfull in this exercise, which as far as I understand can only be used to measure distances here on earth (?) and not in space.
When you want to study the twin "paradox" different identical clocks with different speeds are used. Different speeds require accelerations and these accelerations change the performs of the clocks. At the pages 26 and 27 in the book GRAVITATION the concept "good" and "bad" clocks is introduced. "Bad" clocks undergo accelerations. Accelerations imply different speeds. IMO when you change the speed it is the inner workings of the clock that changes. This is important for a clock which uses lightsignals to function, because the speed of light does not change. The result is that the usual clock rate changes. The most important lesson is "not" to use clocks with different speeds when you want to unravel the laws of nature.

16 The correct explanation for the twin paradox

That is not the point of the analogy at all. The point is that you probably would agree in that the different lectures on the odometers, after the two different trips, are not due to any physical change to the odometers themselves but to the different travelled distances.

The analogy is that, in the twin scenario, the different lectures of the twin clocks, are not due to any physical change to the clocks themselves but to the different paths through spacetime.

17 The correct explanation for the twin paradox

With clocks: clock one will accumulate more clock seconds than clock two. This means that the odometer analogy is useless.

18 The correct explanation for the twin paradox

19 The correct explanation for the twin paradox

20 The correct explanation for the twin paradox

21 The correct explanation for the twin paradox

Get conscious, man. Have you ever seen 2 clocks with identical readings? The question is not whether clocks have identical indications or not. What matters is: is difference between them "proper" or "erroneous".

22 The correct explanation for the twin paradox

23 The correct explanation for the twin paradox

but if you combine a light-clock with a space-time odometer..

24 The correct explanation for the twin paradox

The change in the odometers come because of the different physical distances travelled.

>	The analogy is that, in the twin scenario, the different lectures of the twin clocks, are not due to any physical change to the clocks themselves but to the different paths through spacetime.

I do not think you need the concept of spacetime to explain this behavior. If you have a clock at "rest" (#) this clock will tick at a constant rate, that means the time between each tick is constant. If after a tick you move the clock the next tick will be later. If you move the clock back the next tick again will be later. From there on the clock will again tick at his original constant rate. (all compared with an identical clock)

The reason is because the speed of light can be considered locally a physical constant. The innerworkings of certain clocks are based on lightsignals. When you move such a clock its behaviour will change.

When you move the clock in fact there are different speeds and accelerations involved. In fact these accelerations are the cause that the moving clock (compared with the clock at rest) runs behind or ticks slower.

A whole different issue is to predict in advance how much the clock runs behind or ticks slower. In order to do that you need more measurements and this requires mathematics, but the mathematics sec does not explain the behaviour of the clocks.

(#) To call a clock at rest is a physical simplification. The whole issue is that if a clock is at rest or not, has no influence physical on the speed of light. The assumption is in order to calculate the speed of light (from A to B) you should use clocks which don't move. All of this becomes simpler if only one reference frame is involved.

See also recent discussion in thread at 26 July: Why there must be an absolute frame - New Book

Nicolaas Vroom

25 The correct explanation for the twin paradox

First, every clock is at rest with respect to itself and with respect to co-moving clocks (relativity is always local, meaning in the vicinity of a spacetime location). That implies that comparison with clocks that are not near is impossible. Say you want to compare your at rest in the Moon clock with your at rest at Earth clock. For that you need to exchange signals, which will take 1.3 seconds (and changing) to reach the other clock. So you will be comparing one current clock reading with the reading of the other clock but from 1.3 seconds before.

What it is usually presented in twin paradox scenarios is the following:

26 The correct explanation for the twin paradox

[First, as I keep saying, this is NOT ABOUT ONE CLOCK "RUNNING FASTER" THAN THE OTHER -- identical clocks ALWAYS run at identical rates. This is about the total elapsed proper time for each twin between their separation and reunion.]

Given that the home twin remains at rest in an inertial frame the answer is clear: NO.

Proof: Use the usual coordinates in the inertial frame of the home twin, denote the separation as happening at time T0, and the reunion at T1. The home twin's clock displays

Tom Roberts

27 The correct explanation for the twin paradox

The ANALOGY is strictly in Euclidean geometry in which there is no time. You are to look ONLY at the values on the odometers. Driving speed is irrelevant.

Tom Roberts

28 The correct explanation for the twin paradox

>	What it is usually presented in twin paradox scenarios is the following: 1) You start with two synchronized identical clocks before the twin departs. 2) The Traveling twin etc. (See the second figure in http://www.einsteins-theory-of-relativity-4engineers.com/twin-paradox-2.html

29 The correct explanation for the twin paradox

Well, it is clear you do not understand this. Let us take baby steps:

1)The flying distance is d = 3 light-years.
2)The plane speed is v = 0.6c. Then, from the point of view of the Earth twin, the plane takes d/c = 5 years to complete the travel from event1 to event2 (and, of course 5 years to return to Earth).
3)The interval (distance through spacetime) is ds^2 = c^2 dt^2 - dx^2. This is an invariant value for both twins.
4)Replacing numbers ds^2 = 5^2 - 3^2 = 25 - 9 = 16 square light-years.
5)For the traveling twin ds'^2 = ds^2 = dt'^2 - dx'^2 = 16 square light-years.
6)The traveling twin is present at both event1 and event2, so his dx'^2 = 0.
This implies (from 5)) that dt'^ = 16. So from the traveling twin point of view, the travel lasted only 4 years.
7)When the twins reunite, the Earth twin will say the trip took 10 years to complete, while the traveling twin will say the trip took 8 years to complete.

> >	Atomic clocks do not rely in lightsignal at all.

>	Please study: https://en.wikipedia.org/wiki/Atomic_clock#Optical_clocks

These optical clock are on research studies and they are not related at all to your misconceptions.

> >	First, accelerations do not affect atomic clocks working at all Secondly, you can use a constant acceleration of one g etc.

>	In the above experiment they used an ideal setup. In reality always accelerations are involved. You start from 0c, 0.1c 0.2c, 0.3c, 0.2c, 0.1c, 0c -0.1c -0.2c -0.3c -0.2c, -0.1c and finally 0c. Now your spacecraft is back to base and you can compare clock readings.

That does not make any sense unless you specify the time coordinate.

30 The correct explanation for the twin paradox

>	1)The flying distance is d = 3 light-years. 2)The plane speed is v = 0.6c. Then, from the point of view of the Earth twin,

And from a point of a walking on a street twin, trees and buildings are running around. An idiot said!! So, there is no possibility of a mistake.

Paparios 27 JUl El jueves, 27 de julio de 2017, 11:04:59 (UTC-5), mlwo...@wp.pl escribió:

>	W dniu czwartek, 27 lipca 2017 17:19:03 UTC+2 uzytkownik Paparios napisal:

> >	1)The flying distance is d = 3 light-years. 2)The plane speed is v = 0.6c. Then, from the point of view of the Earth twin,

>	And from a point of a walking on a street twin, trees and buildings are running around. An idiot said!! So, there is no possibility of a mistake.

But, according to the Merriam-Webster dictionary, you are wrong!

31 The correct explanation for the twin paradox

I do not think the problem is on my side. The reason is the text is not clear

>

1)The flying distance is d = 3 light-years. 2)The plane speed is v = 0.6c. Then, from the point of view of the Earth twin, the plane takes d/c = 5 years to complete the travel from event1 to event2 (and, of course 5 years to return to Earth). 3)The interval (distance through spacetime) is ds^2 = c^2 dt^2 - dx^2. This is an invariant value for both twins.

Now compare this with the equation in reflection 1.
Starting point is the equation:
c^2*t^2 - v^2*t^2 = L^2 which L^2 = c^2*t0^2
t0 = time with clock at rest t = time with moving clock Now you get: c^2*t^2 - v^2*t^2 = c^2*t0^2
or: c^2*t^2 - 0.6^2*c^2*t^2 = c^2*t0^2
or t^2 - 0.6^2*t^2 = t0^2 0r 0.64*t^2 = t0^2 0r 0.8*t = t0 0r 4t = 5t0
That means that 5 ticks (years) for the clock at rest corresponds with 4 ticks (years) of the moving clock.

>

4)Replacing numbers ds^2 = 5^2 - 3^2 = 25 - 9 = 16 square light-years. 5)For the traveling twin ds'^2 = ds^2 = dt'^2 - dx'^2 = 16 square light-years. 6)The traveling twin is present at both event1 and event2, so his dx'^2 = 0. This implies (from 5)) that dt'^ = 16. So from the traveling twin point of view, the travel lasted only 4 years. 7)When the twins reunite, the Earth twin will say the trip took 10 years to complete, while the traveling twin will say the trip took 8 years to complete.

And what is the correct answer?

> > >

Atomic clocks do not rely in lightsignal at all.

> >	Please study: https://en.wikipedia.org/wiki/Atomic_clock#Optical_clocks

>	These optical clock are on research studies and they are not related at all to your misconceptions.

The issue is what happens when you use such a clock to test its behaviour.

> > >

First, accelerations do not affect atomic clocks working at all Secondly, you can use a constant acceleration of one g etc.

> >	In the above experiment they used an ideal setup. In reality always accelerations are involved. You start from 0c, 0.1c 0.2c, 0.3c, 0.2c, 0.1c, 0c -0.1c -0.2c -0.3c -0.2c, -0.1c and finally 0c. Now your spacecraft is back to base and you can compare clock readings.

>	That does not make any sense unless you specify the time coordinate.

What I want to say in principle when you want to test a moving clock always accelerations and deaccelerations are involved. During such an acceleration slowly the behaviour of a clock changes. The same with deaccelerations to stop the spacecraft which brings the behaviour back to normal (Considered from one frame)

The result of the experiment as mentioned under (7) above demonstrates this change in behaviour of the two clocks.

Nicolaas Vroom

32 The correct explanation for the twin paradox

33 The correct explanation for the twin paradox

Comparing clock ticks is not the answer to the twin scenario (that would be equivalent to say the different odometer lectures are due to odometers reading at different distance rates in km/km).
What the interval measures is the total distance along a spacetime world line, which does not depend on the clock ticking (actually we know accurate clocks ticking is not affected by gravitation, ie they tick always at 1 sec/sec).

> >

4)Replacing numbers ds^2 = 5^2 - 3^2 = 25 - 9 = 16 square light-years. 5)For the traveling twin ds'^2 = ds^2 = dt'^2 - dx'^2 = 16 square light-years. 6)The traveling twin is present at both event1 and event2, so his dx'^2 = 0. This implies (from 5)) that dt'^ = 16. So from the traveling twin point of view, the travel lasted only 4 years. 7)When the twins reunite, the Earth twin will say the trip took 10 years to complete, while the traveling twin will say the trip took 8 years to complete.

>	And what is the correct answer?

The correct answer is that the traveling twin path through spacetime is shorter than the Earth twin path through spacetime.

> > >

In the above experiment they used an ideal setup. In reality always accelerations are involved. You start from 0c, 0.1c 0.2c, 0.3c, 0.2c, 0.1c, 0c -0.1c -0.2c -0.3c -0.2c, -0.1c and finally 0c. Now your spacecraft is back to base and you can compare clock readings.

> >	That does not make any sense unless you specify the time coordinate.

>	What I want to say in principle when you want to test a moving clock always accelerations and deaccelerations are involved. During such an acceleration slowly the behaviour of a clock changes.

This is your assertion and experiments have proven it is false.

>	The same with deaccelerations to stop the spacecraft which brings the behaviour back to normal (Considered from one frame) The result of the experiment as mentioned under (7) above demonstrates this change in behaviour of the two clocks. Nicolaas Vroom

No it does not demonstrate anything of the sort.

34 The correct explanation for the twin paradox

okay, you don't want to pick a clock, pick a "technical detail".. - show quoted text -

35 The correct explanation for the twin paradox

36 The correct explanation for the twin paradox

> >	Comparing clock ticks is not the answer to the twin scenario (that would be equivalent to say the different odometer lectures are due to odometers reading at different distance rates in km/km).

>

The twin scenario (horrible description, it is more about clock comparison under different conditions) is all about clock ticks. See: http://www.einsteins-theory-of-relativity-4engineers.com/twin-paradox-2.html The stay at home clock measures 10 ticks or 10 years. The moving clock measures 8 ticks or 8 years.

You are so much confused about what a comparison means:

1) One clock (the traveling clock) travels far away at a high speed and after a while it returns to Earth to reunite with its staying at Earth twin clock.
2) The clock comparison is not at all related to the ticking of each clock. If that were the case, the result would be this clock is ticking faster or slower than the other. Actually, such comparison will show both clocks are ticking at exactly the same rate they were before the starting of the gedanken.
3) The clock comparison is related to the reading shown on each clock, where the Earth clock shows 10 years have passed by, while the traveling clock shows
8 years have passed by. This is the accumulated time on each of the clocks (similarly to the accumulated distance shown by the odometers) followed through each clock path through spacetime.

> > > >

7)When the twins reunite, the Earth twin will say the trip took 10 years to complete, while the traveling twin will say the trip took 8 years to complete.

> > >

And what is the correct answer?

> >	The correct answer is that the traveling twin path through spacetime is shorter than the Earth twin path through spacetime.

>	You invented a new answer. The correct answer should reflect the idea which of the two clocks shows the correct time. It is either 10 years, 8 years or maybe neither one.

Again, each clock (in a similar way to an odometer) shows at the end of the gedanken the accumulated time of each clock path through spacetime. So your conclusion above is total nonsense. When the clock reunite, they world line through spacetime continue together, following the Earth world line but with the traveled clock showing the time of two years ago.

37 The correct explanation for the twin paradox

>	1) One clock (the traveling clock) travels far away at a high speed and after a while it returns to Earth to reunite with its staying at Earth twin clock. 2) The clock comparison is not at all related to the ticking of each clock.

Of course. We can check it practically at GPS. One of the clocks ticks faster, but they keep the same time - againt the moronic prophecies of your idiot guru.

38 The correct explanation for the twin paradox

Sorry, I try to understand.

>	2) The clock comparison is not at all related to the ticking of each clock. If that were the case, the result would be this clock is ticking faster or slower than the other.

Correct. That describes what I understand.

>	Actually, such comparison will show both clocks are ticking at exactly the same rate they were before the starting of the gedanken.

That is only correct when the spacecraft is back at base and has a speed of zero. From here on the ticking rate is as usual (as being at rest), but not while travelling.

>	3) The clock comparison is related etc

See at the end.

> > > > >

7)When the twins reunite, the Earth twin will say the trip took 10 years to complete, while the traveling twin will say the trip took 8 years to complete.

> > > >

And what is the correct answer?

> > >

The correct answer is that the traveling twin path through spacetime is shorter than the Earth twin path through spacetime.

> >	You invented a new answer. The correct answer should reflect the idea which of the two clocks shows the correct time. It is either 10 years, 8 years or maybe neither one.

>	Again, each clock (in a similar way to an odometer) shows at the end of the gedanken the accumulated time of each clock path through spacetime.

Each clock at the end of the experiment shows the (accumulated) time in seconds, in ticks or counts.

>	So your conclusion above is total nonsense.

?

>	When the clock reunite, they world line through spacetime continue together, following the Earth world line but with the traveled clock showing the time of two years ago.

That means the moving clocks runs behind? The true question is how do you explain that. IMO the explanation is physical and depends how the clock is build and how the clock functions.

The problem with what people call the twin paradox IMO is not a paradox if you consider that it is related to the behaviour of clocks. (That certain processes are time dependent)

39 The correct explanation for the twin paradox

Again the ticking rate of a clock is completely different to the accumulated ticks of a clock through a spacetime path. If you do not understand this you will not understand what relativity is.

Similarly, if a car odometer reads 100km for a path joining two cities 50km apart, it does not mean the odometer is "ticking" at 2km/km! It only means the path followed to reach the other city was actually 100km long.

> >	Again, each clock (in a similar way to an odometer) shows at the end of the gedanken the accumulated time of each clock path through spacetime.

>	Each clock at the end of the experiment shows the (accumulated) time in seconds, in ticks or counts.

Correct, but that reading has nothing to do with the ticking rate (sec/sec).

> >	When the clock reunite, they world line through spacetime continue together, following the Earth world line but with the traveled clock showing the time of two years ago.

>	That means the moving clocks runs behind?

It is not running behind in the sense of being slow.

>	The true question is how do you explain that. IMO the explanation is physical and depends how the clock is build and how the clock functions.

No, neither the building of the clock or how the clock functions has anything to do with the difference. Of course, certain clocks are not appropiate to perform the gedanken (sand clocks or pendulum clocks).

The explanation is indeed physical: Nature appears to function according to a 4D manifold geometry, where space and time are intertwined.

>	The problem with what people call the twin paradox IMO is not a paradox if you consider that it is related to the behaviour of clocks. (That certain processes are time dependent)

Of course, this "paradox" is not a paradox at all. It is easily explained by SR.

>	The problem start when you introduce a human aspect in this physical/mechanical problem. The question becomes than more: how is it possible that humans on earth have aged 100 years while the pilot in the spacecraft has aged only 20 years?

The same as how two odometers show different readings in the traveling between two cities following different paths.

40 The correct explanation for the twin paradox

The first is physical and the second (spacetime) is mathematical.

>	Similarly, if a car odometer reads 100km for a path joining two cities 50km apart, it does not mean the odometer is "ticking" at 2km/km! It only means the path followed to reach the other city was actually 100km long.

What an odometer measure is only physical.

> > >

Again, each clock (in a similar way to an odometer) shows at the end of the gedanken the accumulated time of each clock path through spacetime.

> >	Each clock at the end of the experiment shows the (accumulated) time in seconds, in ticks or counts.

>	Correct, but that reading has nothing to do with the ticking rate (sec/sec).

> > >

When the clock reunite, they world line through spacetime continue together, following the Earth world line but with the traveled clock showing the time of two years ago.

> >	That means the moving clocks runs behind?

>	It is not running behind in the sense of being slow.

Then what is it? Any way you have to adjust that clock if you want to measure the age of the universe

> >	The true question is how do you explain that. IMO the explanation is physical and depends how the clock is build and how the clock functions.

>

No, neither the building of the clock or how the clock functions has anything to do with the difference. Of course, certain clocks are not appropiate to perform the gedanken (sand clocks or pendulum clocks). The explanation is indeed physical: Nature appears to function according to a 4D manifold geometry, where space and time are intertwined.

41 The correct explanation for the twin paradox

Wrong again. Our human senses detect x,y,z and t. Before we used to think x,y,z were separated from t. Now we know x,y,z,t are all intertwined and spacetime is every bit as physical as space and time are.

> >	Similarly, if a car odometer reads 100km for a path joining two cities 50km apart, it does not mean the odometer is "ticking" at 2km/km! It only means the path followed to reach the other city was actually 100km long.

>	What an odometer measure is only physical.

As physical as what a clock measures.

> > > >

Again, each clock (in a similar way to an odometer) shows at the end of the gedanken the accumulated time of each clock path through spacetime.

> > >

Each clock at the end of the experiment shows the (accumulated) time in seconds, in ticks or counts.

> >	Correct, but that reading has nothing to do with the ticking rate (sec/sec).

> > > >

When the clock reunite, they world line through spacetime continue together, following the Earth world line but with the traveled clock showing the time of two years ago.

> > >

That means the moving clocks runs behind?

> >	It is not running behind in the sense of being slow.

>	Then what is it? Any way you have to adjust that clock if you want to measure the age of the universe

What are you trying to say with that?

> > >

The true question is how do you explain that. IMO the explanation is physical and depends how the clock is build and how the clock functions.

> >

No, neither the building of the clock or how the clock functions has anything to do with the difference. Of course, certain clocks are not appropiate to perform the gedanken (sand clocks or pendulum clocks). The explanation is indeed physical: Nature appears to function according to a 4D manifold geometry, where space and time are intertwined.

>	IMO when you study the link: https://www.nicvroom.be/wik_Time_dilation.htm#ref1 the explanation is much simpler. (At least if a clock is considered)

All human created theories have to be a) accurate in predicting experimental measured values and b) be simple but as complete as possible.

Regarding relativity, both SR and GR are accurate and as complete as possible within their domain of applicability.

42 The correct explanation for the twin paradox

>	Our human senses detect x,y,z and t. Before we used to think x,y,z were separated from t. Now we know x,y,z,t are all intertwined and spacetime is every bit as physical as space and time are.

Physics has nothing to do with what we think or sense. The problem is what is the exact definition of physical. You can also call spacetime, space and time dimensions but than you are stuck with the definition: what is a dimension.

> > >

Similarly, if a car odometer reads 100km for a path joining two cities 50km apart, it does not mean the odometer is "ticking" at 2km/km! It only means the path followed to reach the other city was actually 100km long.

> >	What an odometer measure is only physical.

>	As physical as what a clock measures.

A clock is a physical object and what a clock displays is movement-in-general (time) in a circular fashion. Each "rotation" we call a tick a second or a minute. As such a clock displays time. But that does not immediate mean that time is a physical object the same as a clock.
We can also display time as a line in the direction t. The length of the line increases as a function v*t with v an arbitrary constant speed. When v = c we can define a line s with s^2 = (x + ict) * (x + ict)
As such we get s^2 = x^2 - (ct)^2.
Is this s (spacetime) something physical?

> > > >

That means the moving clocks runs behind?

> > >

It is not running behind in the sense of being slow.

> >	Then what is it? Any way you have to adjust that clock if you want to measure the age of the universe

>	What are you trying to say with that?

What I'm trying to say that if you want to measure the duration of something and you use two clocks and both show a different time than only one can be used to indicate the duration. Of course you could also use the average reading, but if you know what caused this difference (for example relatif movement) than I think it is better to call one inacurate and use the other one.

> > >

The explanation is indeed physical: Nature appears to function according to a 4D manifold geometry, where space and time are intertwined.

> >	IMO when you study the link: https://www.nicvroom.be/wik_Time_dilation.htm#ref1 the explanation is much simpler. (At least if a clock is considered)

>	All human created theories have to be a) accurate in predicting experimental measured values

43 The correct explanation for the twin paradox

>	You can also call spacetime, space and time dimensions but than you are stuck with the definition: what is a dimension.

degree of freedom, idiot.

44 The correct explanation for the twin paradox

No, poor idiot, our senses don't detect any coordinates. That's because coordinates are abstract.

Before we used to think

>	x,y,z were separated from t. Now we know x,y,z,t are all intertwined and spacetime is every bit as physical as space and time are.

Since your moronic physics stopped requiring their constructs to be measurable...

>	All human created theories have to be a) accurate in predicting experimental measured values and b) be simple but as complete as possible.

No - your idiot guru has proven they don't have.

>	Regarding relativity, both SR and GR are accurate and as complete as possible within their domain of applicability.

A lie, as expected from fanatic trash.

45 The correct explanation for the twin paradox

>	Physics has nothing to do with what we think or sense. The problem is what is the exact definition of physical. You can also call spacetime, space and time dimensions but than you are stuck with the definition: what is a dimension.

It appears that you do not know what physics is all about and what physical means. You should read about the history of physics, going back as to why we care about these things.

A physical dimension is a characteristic of Nature that can be observed and measured. A line has a dimension of one because only one coordinate (say x) is needed to specify a point on it In physics we use rulers (to measure x,y and z) and clocks (to measure t).

> > >

What an odometer measure is only physical.

> >	As physical as what a clock measures.

>	A clock is a physical object and what a clock displays is movement-in-general (time) in a circular fashion. Each "rotation" we call a tick a second or a minute. As such a clock displays time. But that does not immediate mean that time is a physical object the same as a clock.

t it is as physical as x. t has a value as x has. You can draw a x-t diagram which represents a physical event (the movement of a particle).

>	We can also display time as a line in the direction t. The length of the line increases as a function v*t with v an arbitrary constant speed. When v = c we can define a line s with s^2 = (x + ict) * (x + ict) As such we get s^2 = x^2 - (ct)^2. Is this s (spacetime) something physical?

First, your above derivation is nonsense. Secondly spacetime is physical. You appear to not know from where s comes. Here it goes in baby-steps:

1) There are two reference frames K and K', where K' is moving with speed v with respect to the origin of K, say to the right of line x.
2) A signal is send from a point x1 at time t1 in frame K. That signal propagates at speed c and arrives to a point x2 at time t2 in frame K.
3) The distance between the two events (sending and arrival) is obviously c(t2-t1).
4) That same distance is also given by sqrt[(x2-x1)^2].
5) We can then write the following relationship:
(x2-x1)^2=c^2(t2-t1)^2 ==> (x2-x1)^2 - c^2(t2-t1)^2 = 0
6) The same two events are observed from the K' reference frame, where the coordinates are (x'1,t'1) and (x'2,t'2).
7) The relationship is then (and considering the speed of light is the same in both frames):
(x'2-x'1)^2 - c^2(t'2-t'1)^2 = 0
8) Generalizing, the INTERVAL between the occurrence of any two events (x1,t1) and (x2,t2) is:
(s_12)^2 = (x2-x1)^2 - c^2(t2-t1)^2 9) From the principle of invariance of the speed of light, if the interval between any two events is zero in one inertial frame of reference, then it is also zero in any other inertial frame of reference.
10) If the two events are infinitely close to each other then the interval reduces to:

ds^2 = dx^2 - c^2dt^2

Nowhere complex numbers were used or needed.

> >	What are you trying to say with that?

>

What I'm trying to say that if you want to measure the duration of something and you use two clocks and both show a different time than only one can be used to indicate the duration. Of course you could also use the average reading, but if you know what caused this difference (for example relatif movement) than I think it is better to call one inacurate and use the other one.

Again, this is a COMPARISON of the readings of two clocks. Nowhere is anybody trying to determine a sort of absolute time, which by the way it does not exist.

> > > >

The explanation is indeed physical: Nature appears to function according to a 4D manifold geometry, where space and time are intertwined.

> > >

IMO when you study the link: https://www.nicvroom.be/wik_Time_dilation.htm#ref1 the explanation is much simpler. (At least if a clock is considered)

> >	All human created theories have to be a) accurate in predicting experimental measured values

>	This sentence is in conflict with the uncertainty principle which claims that you cannot measure both position and speed (momentum) of an elementary particle. See https://en.wikipedia.org/wiki/Uncertainty_principle

That has nothing to do with what I wrote. We can accurately predict and measure the speed. For instance we can predict and measure the perihelion precession of Mercury.

46 The correct explanation for the twin paradox

Tell me, poor idiot, how long are the longest rulers you have to measure x,y and z?

>	First, your above derivation is nonsense. Secondly spacetime is physical.

In the meaning: physics imagined it.

>	That has nothing to do with what I wrote. We can accurately predict and measure the speed. For instance we can predict and measure the perihelion precession of Mercury.

:) you would never do it if you treated your Shit seriously.

47 The correct explanation for the twin paradox

A much better name is parameter. A dimension is related to the physical length of a rod.

>	A line has a dimension of one because only one coordinate (say x) is needed to specify a point on it In physics we use rulers (to measure x,y and z)

Yes correct with a standard ruler you can measure the length of a rod. As such I have no problem with an odometer.

>	and clocks (to measure t).

A clock can be used to measure time but it is important to study the inner workings of such a clock i.e. its accuracy

> > > >

What an odometer measure is only physical.

> > >

As physical as what a clock measures.

> >	A clock is a physical object and what a clock displays is movement-in-general (time) in a circular fashion. Each "rotation" we call a tick a second or a minute. As such a clock displays time. But that does not immediate mean that time is a physical object the same as a clock.

>	t it is as physical as x. t has a value as x has.

As I said above the accuracy of the clock is important

>	You can draw a x-t diagram which represents a physical event (the movement of a particle).

That is correct.

> >	We can also display time as a line in the direction t. The length of the line increases as a function v*t with v an arbitrary constant speed. When v = c we can define a line s with s^2 = (x + ict) * (x + ict) As such we get s^2 = x^2 - (ct)^2. Is this s (spacetime) something physical?

>	First, your above derivation is nonsense. Secondly spacetime is physical. You appear to not know from where s comes. SNIP ds^2 = dx^2 - c^2dt^2 Nowhere complex numbers were used or needed.

I agree with this final sentence.

Still Spacetime is not a measured value but a calculated value. IMO it is possible to predict the performance of a clock without the concept of spacetime. The outcome also depents how the clock is build.

> >

What I'm trying to say that if you want to measure the duration of something and you use two clocks and both show a different time than only one can be used to indicate the duration. Of course you could also use the average reading, but if you know what caused this difference (for example relatif movement) than I think it is better to call one inacurate and use the other one.

>	Again, this is a COMPARISON of the readings of two clocks. Nowhere is anybody trying to determine a sort of absolute time, which by the way it does not exist.

I'm not speaking about absolute time but about the age of the universe. If all people involved use different clocks with different speeds you will never find a usefull answer.

48 The correct explanation for the twin paradox

> >	Again, this is a COMPARISON of the readings of two clocks. Nowhere is anybody trying to determine a sort of absolute time, which by the way it does not exist.

>	I'm not speaking about absolute time but about the age of the universe. If all people involved use different clocks with different speeds you will never find a usefull answer.

No clocks have been used to determine the Big Bang. The time that has passed since that event — otherwise known as the "age of the universe" — is 13.799 ± 0.021 billion years.

>	In fact when I wrote above about average reading that is not very "clever". What I should have written when two clocks show different readings (after they reunite) you should take the fastest moving clock (higest number as ticks) as your reference clock.

When you move from New York to London, it is obvious you adjust your clock to the London time. This has nothing to do with time or relativity.

>

In the original article they used an plane with a speed of v=0.6c (That means the staying at home twin aged 10 years and the moving twin aged 8 years) It is not that clock that you should use, but the observer at rest here on earth. The question is: is that trully the fastest moving clock? I doubt it.

What they are doing is compare the time period elapsed in each clock. The two year difference is not due to any clock error and the traveling twin is indeed two years younger.

49 The correct explanation for the twin paradox

>	No clocks have been used to determine the Big Bang. The time that has passed since that event — otherwise known as the "age of the universe" — is 13.799 ± 0.021 billion years.

Have you heard your idiot guru has "discovered" time is relative?

50 The correct explanation for the twin paradox

>	No clocks have been used to determine the Big Bang. The time that has passed since that event — otherwise known as the "age of the universe" — is 13.799 ± 0.021 billion years.

You neglect the periods when a day was like a week, like a month, like a year and like a century.

51 The correct explanation for the twin paradox

>	W dniu piatek, 4 sierpnia 2017 19:55:03 UTC+2 uzytkownik Paparios napisal:

>>	No clocks have been used to determine the Big Bang. The time that has passed since that event — otherwise known as the "age of the universe" — is 13.799 ± 0.021 billion years.

>	Have you heard your idiot guru has "discovered" time is relative?

Does not matter. In average the Universe, with all in it, is not moving very fast. Actually you are right by mistake. Relativity effects are not present at very large scale. This since there are LARGE distances among mass bodies, hence the curvature may safely be considered close to ZERO.

One more proof, for Upside-Down Evolution. In the past planets etc were closer to each other. Lots of fun. Yes, they DID land on Moon, but that must have been FAR in the PAST.

me (Nicolaas Vroom change) 16:44 (9 minutes ago)

> >	In fact when I wrote above about average reading that is not very "clever". What I should have written when two clocks show different readings (after they reunite) you should take the fastest moving clock (higest number as ticks) as your reference clock.

>	When you move from New York to London, it is obvious you adjust your clock to the London time. This has nothing to do with time or relativity.

And when you travel from London to the planet Pluto you adjust your clock to Pluto time. That solves the twin paradox.

> >

In the original article they used an plane with a speed of v=0.6c (That means the staying at home twin aged 10 years and the moving twin aged 8 years) It is not that clock that you should use, but the observer at rest here on earth. The question is: is that trully the fastest moving clock? I doubt it.

>	What they are doing is compare the time period elapsed in each clock. The two year difference is not due to any clock error

but caused by?

>	and the traveling twin is indeed two years younger.

and the moving clock runs behind. (and I do not understand why)

Thanks

Nicolaas Vroom