# The Derivation of Relativity Theory from Twins Paradox

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The twin paradox, a theory of relativity must cross experiment, let us begin to analyse it correctly.

The Derivation of Relativity Theory from Twins Paradox.pdf

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28 minutes ago, YuanShenhao said:

let us begin to analyse it correctly

Go on then...

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What is space-time? Distance / Velocity = Time

First there is distance and speed, and then there is time.

You can read the attached file "The Derivation of Relativity Theory from Twins Paradox.pdf" carefully, then you can understand what is space-time, can understand the twin paradox

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I am going to assume you have posted your paper for comment and critique and that English is not your first language.

So at least some of my comments may bue due to a language problem.

Quote

No, the scientists have been done various

measurements on the speed of light, whether it's relatively static or moving, the ultimately measured results are turned out to be a constant speed of light, although they appear to be in

contradiction with classical Newton's law, but from what we measured, the result is turned out to

be a constant speed of light, the conclusions from the practices should be respected, so the

theory “constant speed of light” has become an axiomatic existence.

**You need to explain exactly what you mean by constant speed of light because just stating it is constant or observed to be constant could mean several different things.

Quote

Try to observe the spring, we put the spring on the car with uniform

movement and put it still on the table, their frequency of vibration will be the same? The answer

is it will be the same,

**I beg to differ. Even in Newtonian theory the frequency of the spring will vary with position in the gravitational field. This simple (http://hyperphysics.phy-astr.gsu.edu/hbase/shm2.html) form of solution takes g as independent of x and therefore constant (note yet another use of the word constant).  But strictly g is not the same on the floor and on the table.

Quote

The first thing is to explain a term: inertial coordinate system, any reference system

established by Newton's law of motion, known as the inertial reference system, with the short

name inertial system. In a word, it refers to those which are in line with the classic Newtonian

mechanics.

**This is too wide a definition of inertial. Newtons laws still apply to in non inertial frames, just differently.

Quote

However, this space-time point will often be ignored by us, which is the third-party reference

for the comparison between two inertia systems, without it, there is no above conclusion.

**Einstein introduced the third frame to define an unknown function (and show that it is equal to unity) he introduced for the sake of mathematical completeness. You have omitted this step, so the third frame is unnecessary.

Quote

deduction of special theory of relativity, time is related to speed v

**not speed, but relative speed. Speed by itself requires reference to a particular frame. The point is that relative speed is the same in both frames.

Quote

but for general relativity time is

also related to the degree of distortions in time and space (called as gravitational field in Newton

way). Whose space-time distortion is greater (greater gravitational field), whose time will run

more slowly, for a material that will be reflected in the acceleration, whose acceleration is bigger,

who will run the time more slowly. How can this be related to the time and speed of special

relativity? I am wandering that if you have noticed, the so-called acceleration, in the calculus state

will appear as speed.

**The rest of this paragraph has the seed of a correct point but is garbled and needs rewording. In particular speed is not acceleration.

Quote

Let us return to reality, for example, we drive a car on Earth, the faster we drive the more

fuel-efficient it will be

**Really? So driving my car at 100mph is more fuel efficient than driving it at 50 mph?

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I haven't read the entire text of the link, but this passage quote by Studiot caused me to take note.

but for general relativity time is also related to the degree of distortions in time and space (called as gravitational field in Newton way). Whose space-time distortion is greater (greater gravitational field), whose time will run more slowly, for a material that will be reflected in the acceleration, whose acceleration is bigger, who will run the time more slowly.

It may just be your wording here, but it seems to indicate that you are operating under a common misconception here,  that gravitational time dilation is related to the local strength of the gravity field, and that by extension, differing values of acceleration will cause different rates of time dilation.  This is not the case.  Gravitational time dilation is due to a difference in gravitational potential.  The clock at the higher potential runs faster.  This is an important difference in that it is theoretically possible to have two clocks which experience exactly the same force of gravity and yet be at different potentials and run at different rates.

As far as acceleration goes there is the "Clock postulate" which state that acceleration does not add any extra element to time dilation. (outside of the fact that it can increase relative velocity.)   The proof of this come from the fact that you can have acceleration without a change of speed, such as in the case of circular motion.

An object traveling in a circle at a constant speed in under a constant centripetal acceleration.     The value of the centripetal acceleration depends on both the radius and tangential speed of the object.  Thus, by varying the radius, you can subject an object to various combinations of speed and acceleration.  You could, for example, vary the speed while keeping the acceleration constant or keeping the speed constant and vary the acceleration.

Such experiment have been done by putting radio-isotope samples on very high speed centrifuges capable of creating accelerations of 1,000's of gs.  They have all shown the clock postulate to be valid.  The time dilation measured for the samples only depended on the sample's speed relative to the lab and was independent of the acceleration values.

This is not to say that acceleration cannot play a role in time dilation, but only that its role is more in line with that of gravitational time dilation.   One can imagine two clocks one behind the other and accelerating such that in the frame of the clocks, their distances remain constant.   They are both experiencing the same acceleration, however, the clock in the direction of the acceleration will run faster than the trailing clock.  Being in different positions relative to the acceleration is the equivalent of being at different gravitational potentials and causes a like time dilation between the clocks.

If I misinterpreted your meaning, then please excuse my interruption.

Edited by Janus

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On 2018/1/24 at 7:17 PM, studiot said:

You need to explain exactly what you mean by ‘constant’ speed of light because just stating it is constant or observed to be constant could mean several different things.
My viewpoint:
The velocity of the light we measure is a constant

I beg to differ. Even in Newtonian theory the frequency of the spring will vary with position in the gravitational field. This simple (http://hyperphysics.phy-astr.gsu.edu/hbase/shm2.html) form of solution takes g as independent of x and therefore constant (note yet another use of the word constant).  But strictly g is not the same on the floor and on the table.
My viewpoint:
I totally agree with you, and I mean that the spring is compared in two cases of static and uniform motion, which implies that the other conditions are the same.

This is too wide a definition of inertial. Newton’s laws still apply to in non inertial frames, just differently.
My viewpoint:
Yes, I finally set out that Newton's law and relativity are unified.

Einstein introduced the third frame to define an unknown function (and show that it is equal to unity) he introduced for the sake of mathematical completeness. You have omitted this step, so the third frame is unnecessary.
My viewpoint:
I don't do the evaluation for the third frame Einstein, if Einstein understood the physical meaning of Lorenz transformation, I believe he would agree with me

not speed, but relative speed. Speed by itself requires reference to a particular frame. The point is that relative speed is the same in both frames.
My viewpoint:
I think that your explanation is just a conjecture, or a mathematical model, a hypothesis introduced in order to explain a phenomenon.

The rest of this paragraph has the seed of a correct point but is garbled and needs rewording. In particular speed is not acceleration.
My viewpoint:
I've already said that in the differential case, the acceleration is the velocity. V=delta t*a

Really? So driving my car at 100mph is more fuel efficient than driving it at 50 mph?
My viewpoint:
This is only an image of the explanation, to explain the truth: the greater the speed, the greater the resistance to be overcome

I want to know how you explain the twin paradox.

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On 2018/1/25 at 1:31 AM, Janus said:

It may just be your wording here, but it seems to indicate that you are operating under a common misconception here,  that gravitational time dilation is related to the local strength of the gravity field, and that by extension, differing values of acceleration will cause different rates of time dilation.  This is not the case.  Gravitational time dilation is due to a difference in gravitational potential.  The clock at the higher potential runs faster.  This is an important difference in that it is theoretically possible to have two clocks which experience exactly the same force of gravity and yet be at different potentials and run at different rates.

My viewpoint:

Yes, if acceleration affects the size of the speed in a certain period of time, then the acceleration will affect the time. Speed is the impact of the key time, from Lorenz transformation can be seen.

As far as acceleration goes there is the "Clock postulate" which state that acceleration does not add any extra element to time dilation. (outside of the fact that it can increase relative velocity.)   The proof of this come from the fact that you can have acceleration without a change of speed, such as in the case of circular motion.

My viewpoint:

No mistake, if the acceleration does not change the speed and only changes the direction of the velocity, it does not affect the time expansion. That is to say, the two clocks of the same velocity, their time expansion is the same. This is also an example of the size of the velocity that affects the time. If the acceleration does not increase the speed, the acceleration will not affect the time. The same is true of the acceleration caused by the gravitational field.

An object traveling in a circle at a constant speed in under a constant centripetal acceleration.     The value of the centripetal acceleration depends on both the radius and tangential speed of the object.  Thus, by varying the radius, you can subject an object to various combinations of speed and acceleration.  You could, for example, vary the speed while keeping the acceleration constant or keeping the speed constant and vary the acceleration.

My viewpoint:

Yes, we have learned this content in high school. The satellite needs to stay at its orbit, and it needs the speed of response. If there is a clock on the satellite, the time of this clock will only be related to the speed of the satellite, and the gravity is not directly related to the time of the earth. The effect of gravity is already reflected in the speed of the satellite.

Such experiment have been done by putting radio-isotope samples on very high speed centrifuges capable of creating accelerations of 1,000's of gs.  They have all shown the clock postulate to be valid.  The time dilation measured for the samples only depended on the sample's speed relative to the lab and was independent of the acceleration values.

My viewpoint:

It is true that speed is the key to influence time.  Acceleration can reflect the effect of time if acceleration  affects the size of the speed. This effect is calculated by calculus.

This is not to say that acceleration cannot play a role in time dilation, but only that its role is more in line with that of gravitational time dilation.   One can imagine two clocks one behind the other and accelerating such that in the frame of the clocks, their distances remain constant.   They are both experiencing the same acceleration, however, the clock in the direction of the acceleration will run faster than the trailing clock.  Being in different positions relative to the acceleration is the equivalent of being at different gravitational potentials and causes a like time dilation between the clocks.

If I misinterpreted your meaning, then please excuse my interruption.

So I think my view is exactly the same as yours. Your speech is more affirmative of the correctness of my theory.

Thank you very much. Let's continue our discussion.

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Edited by YuanShenhao

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Abstract: Relativity has been put forward in many scientific experiments, and has been
applied in many fields. All these are enough to explain the correctness and greatness of relativity.
However, the twin paradox of this hypothesis by experiment, the special theory of relativity to
explain is caught in a dilemma, but the experiment itself is not so complicated, why? Is there a
loophole in relativity? Is the theory of relativity so deep that ordinary people can't understand it?
The answer is negative. Relativity can explain this experiment very easily, because the reason why
we get into trouble is that we have not been able to understand the theory of relativity in a
narrow sense.

Keywords: twin paradox; light; relativity; Lorenz transform

To study the theory of relativity, we begin with the Lorenz transformation.
The theory of relativity is Einstein's greatest theory, including the special theory of relativity
and general relativity, so how to correctly understand this great theory? First of all, we have to
understand a very important mathematical deduction, Lorenz transformation, which is intended
to prove the existence of the ether.

1. Lorenz transform
First of all, the introduction premise of Lorentz transformation is the constant speed of light.
Then why can we set this premise? Is it a hypothesis? No, the scientists have been done various
measurements on the speed of light, whether it's relatively static or moving, the ultimately
measured results are turned out to be a constant speed of light, although they appear to be in
contradiction with classical Newton's law, but from what we measured, the result is turned out to
be a constant speed of light, the conclusions from the practices should be respected, so the
theory “constant speed of light” has become an axiomatic existence.

For the constant speed of light, we can also observe from the spread of electromagnetic
waves. When the signal source is away from the observer, the observer can observe the
phenomenon of redshift, the so-called redshift, that is, the wavelength of the electromagnetic
wave is elongated, and the speed of electromagnetic waves has not changed. This is already a
basic common sense of modern communication, light also belongs to an electromagnetic wave,
also with its features, so we should unswervingly believe that constant speed of light, do not
doubt. But note that there is a very important concept, we are talking about is the constant speed
of light, we are not saying that the light speed is the fastest, in the future we will know that the
speed of information delivery can be far greater than the speed of light, and may even exist
matters which are beyond the speed of light. But, these are not important. What we want is the
constant speed of light. We do not want the one which is fastest. This is the real reason for the
speed of light entering into our field of vision. If the sound can achieve a constant speed, then we
can introduce the sound into the derivation of Lorentz transformation. Why? The following
derivation process can be easily understood by high school students.

The constant speed of light, we can regard it as the characteristics of light. So, what are the
objects around us, which also do not change their own characteristics of exercise performance
with the outside world? Try to observe the spring, we put the spring on the car with uniform
movement and put it still on the table, their frequency of vibration will be the same? The answer
is it will be the same, this is only an example to illustrate that there are always some things that
they do not interfere with certain external factors, there is no relationship with light, just to show
that the light has the feature of constant speed, and the spring has the characteristics of constant
frequency, these are only the unique properties of the materials.

Well, with this big premise, we can do mathematical derivation.

The first thing is to explain a term: inertial coordinate system, any reference system
established by Newton's law of motion, known as the inertial reference system, with the short
name inertial system. In a word, it refers to those which are in line with the classic Newtonian
mechanics.

It is conceived that there are two inertial coordinates S system and S'system, the origin O' of
the S'system is relative to the origin O of the S system, which moves along the X axis in the
positive direction of the rate v. The space-time coordinates of any event in the S and S'systems
are (x, y, z, t), and (x', y', z', t'). t and t'are the time of S system and S' system, respectively. When
the two inertial coordinate system is reconnected, the timing starts respectively.
If x= 0, then x'+vt'=0. This is a necessary condition for the transformation to be satisfied, so the
transformation of the coordinates of any event from the S'system to the S system is conjecture.
x=γ（x'+vt'） (1)
The constant γ is introduced in the formula, named Lorenz factor.
The principle of relativity is introduced, that is, the form of physical equations in different inertial
systems should be the same. So the transformation of the above event coordinates from the S
system to the S'system
x'=γ（x－vt） (2)
The transformation of y with y', z and z' can be directly obtained, that is,
y'=y (3)
z'=z (4)
Replace (2) into (1) and solve t'
t'=γt +(1－γ2) x/γv (5)
On the basis of the above derivation, the principle of the constant speed of light is introduced to
seek the value of γ.
The coincident origin O (O') sends out a beam of light along the direction of the X axis, and the
wavefront coordinates of the beam are (X, Y, Z, T), (X', Y', Z', T'). According to the principle of the
constant speed of light, there is
X=cT (6)
X'=cT' (7)
The principle of the relativistic light constant is that the coordinate value X is equal to the speed
of light C multiplying time T, and the coordinate value X'is equal to the speed of light C
multiplying time T'. (1) (2) multiplied
xx'=γ2(xx'－x'vt+xvt'－v2tt') (8)
With the event of the wave front as an object, (8)
XX'=γ2(XX'－X'VT+XVT'－V2TT') (9)
(6) (7) substitution (9), reduced Lorenz factor
γ= (1－（v/c）2)－1/2 (10)
(10) substituting (5), simplifying
t'=γ(t－vx/c2) (11)
Put (2), (3), (4), (11) together, that is, the Lorenz transformation of the S system to the S'system
x'=γ(x－vt)，
y'=y，
z'=z，
t'=γ(t－vx/c2) (12)
According to the principle of relativity, From (12) we can get the Lorenz transformation from the
S'system to the S system
x=γ(x'+vt')，
y=y'，
z=z'，
t=γ(t'+vx'/c2) (13)

The above shows the entire process of Lorentz transformation, from which we can see, A, B
two objects refer to each other, the time of moving objects slowed down. This is the conclusion
that many scholars recognize, but is it true? Is it enough for A, B two objects refer to each other
enough? Let us do an experiment: in the absence of any reference object, A, B two objects stay
away from each other, the question is, who is moving, who is still, or both are in motion? Is it clear?
It's not clear for anyone. Obviously, the two things refer to each other will just make more
complicated. This is also a very important reason why many researchers have troubles over the
research of the twin paradox.

However, our deduction obviously points to a clear conclusion. The frame of reference for
motion slowed down. Yes, nothing wrong. Let us start the analysis. The whole derivation is based
on the speed of light, the constant speed of light, except that we must also pay attention to a very
important point, which is (O, O ') point. Since the S coordinate system is not moving, when
referring to O point, the time on S does not become faster nor slower. That is to say, the speed of
time has not changed. While S' is in motion, observing S' from S time has slowed down. So here is
the question, the time getting slower is compared with which one. Of course, it is compared with
the time on S, and the time on S does not change, which is for the reference to decide? It is the O
point, so we say that the time on S' become slower and which O point is also for the reference.
What is O point? It is space-time, space-time point which is located on S. With the same principle,
this could also be applied for the observation of S from S'.

However, this space-time point will often be ignored by us, which is the third-party reference
for the comparison between two inertia systems, without it, there is no above conclusion. I
believe after the above analysis, you will have a sudden understanding about the twin paradox,
we will describe in detail later. We can boldly put forward the conclusion that the speed of time
requires space-time for reference. Without a third party, there is no way to compare A, B two
subjects.

2. Theory of relativity
Well, let's go to the theory of relativity. First let us derive special relativity from the twins
paradox: that is the story of one of the twins on earth travels to space, and when he comes back,
he finds out that his brother has become an old man. The special theory of relativity explains this
phenomenon. It has been many years after the spacecraft was returned to earth, due to the
slowdown of time on the spacecraft.

So, I believe many people will have such questions, since it is a relative movement, why it
must be that the time on the spacecraft slow down? Why it can't be that is the time on earth get
slower? Obviously, such a question has stepped into the difficult situation, in which there are only
A, B two things to compare each other. Let us first come back to reality, there are two women on
earth are competing which one is more beautiful, either of them won't step back (completely
controversial to clear out), in the end what we should do? The introduction of a third-party
referee, by the third party to determine who in the end is more beautiful. Then who will be older
for our twins? We also need a third party, it is space-time, whose relative space-time is faster,
whose time will be the slower one, and who will be younger, apparently the relative space-time
movement of spacecraft is faster, so time of which will be slower. (The time runs slowly, and
human body functions naturally work slowly, but as a client he does not feel the time slowdown.)
We take a fish as an example, when the time comes to a complete stop, just as the fish are frozen,
and we observe it, its time stopped at that time. And when it's thawed, its time starts again, and
as the fish, it does not even know that time has stopped, and when it's thawed, it does not think
that the time ever stopped. In its thoughts, yesterday was the day before today). The conclusion
derived from the Lorentz transformation is completely consistent with the conclusion of the twins
paradox. We must note this that the third party except A, B: time and space is a competent time
judge.

We have been talking about inertial movement all the time, then how about we get rid of
this inertial system? This is also the question Einstein focused on at that time, so he put up with
general relativity, so what is general relativity? Is there any contradiction with the special theory
of relativity? In a word, the general theory of relativity is the existence of the quality of the object
which leads to a distortion of time and space, this distorted space-time is fully in line with the
surface geometry. This must had been starting a conjecture, but later scientists validated this
geometric effect through experimental observations. Since it was verified, then things get simpler,
our space is no longer a flat carpet, the time and space are distorted, the straightforward
calculation is no longer adequate, and the motion of an object requires calculus to calculate.
Under the calculus, the general relativity appears as a special theory of relativity. At a low
speed, the special theory of relativity shows in a very Newton way. We have unified these theories?
I think so. However, we must note that the descriptions of the special theory of relativity and the
general theory of relativity over the slowdown of time are not the same. According to the
deduction of special theory of relativity, time is related to speed v, but for general relativity time is
also related to the degree of distortions in time and space (called as gravitational field in Newton
way). Whose space-time distortion is greater (greater gravitational field), whose time will run
more slowly, for a material that will be reflected in the acceleration, whose acceleration is bigger,
who will run the time more slowly. How can this be related to the time and speed of special
relativity? I am wandering that if you have noticed, the so-called acceleration, in the calculus state
will appear as speed. (The acceleration affects the time only when the acceleration affects the size of the speed.)

Let us return to reality, for example, we drive a car on Earth, the faster we drive the more
fuel-efficient it will be; the faster the speed boost the more fuel will be cost (all reflected in
resistance), that is, who encountered a bigger resistance from distortion of time, who will run
slower, the faster the relative space-time the greater the resistance will be, the greater the
acceleration the greater resistance will be. The laws of nature are always so similar, why not our
universe?

The special theory of relativity generally explains common small physical phenomena, for
the interpretation of celestial bodies we usually adopt general relativity. Since the bigger the
mass is, the more distortions will occur to space and time, these two are unified. We have used a
lot of scientific experiments and engineering cases to prove the correctness of the special theory
of relativity and general theory of relativity. Science is always based on the experiments, from the
experimental phenomena we can deduce the science behind and derive the hidden truth behind,
which is the theories have been experimentally proved, they are worthy our trust.

The following are two typical experiments and applications:
The cancellation of GPS's slow-bell effect is a good example of the application of special
theory of relativity and we would not be able to use GPS without considering the special
relativistic slow-bell effect of high-speed satellites.

The observations of the solar eclipse of the solar ecliptic star also well prove the validity of
general relativity. This experiment can in further verify the speed of light, believing that light will
be merely deflected and its speed will not change (I do not know if this observation has been
done or not).

3. Conclusion
Based on the above, we can put forward the following points:
1. No third parties can not be compared, and no way to explain the twins.
2. There's space, speed, and then time. L/V=T
3. The resistance of space-time distortion and speed is the root of time slow.
4. The effect of space-time distortion is the geometric effect (general relativity conclusion)
5. The special theory of relativity and general relativity are unified.
6. Newton's law is relativism under specific conditions, Newton's law + light speed constant
+ space-time distortion = relativity theory
When we want to compare two things, we must find a reference of third parties, otherwise
we will lose the meaning of comparison. Maybe this reference is so obvious, maybe it's hidden
behind your back and waiting for your discovery silently.

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4 hours ago, YuanShenhao said:

Yes, we have learned this content in high school. The satellite needs to stay at its orbit, and it needs the speed of response. If there is a clock on the satellite, the time of this clock will only be related to the speed of the satellite, and the gravity is not directly related to the time of the earth. The effect of gravity is already reflected in the speed of the satellite.

This is not true. GPS systems, for example, have to take into account both the relative velocity of the satellite and the receiver AND the different in gravitational potential. Ignoring either of these would give the wrong results.

7 hours ago, YuanShenhao said:

I want to know how you explain the twin paradox.

It is explained by applying the rules of special relativity. You can find many explanations on line (there are some excellent ones by "Janus" on this and other forums).

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1 hour ago, Strange said:

This is not true. GPS systems, for example, have to take into account both the relative velocity of the satellite and the receiver AND the different in gravitational potential. Ignoring either of these would give the wrong results.

It is explained by applying the rules of special relativity. You can find many explanations on line (there are some excellent ones by "Janus" on this and other forums).

Yes, these are the factors that we can generally consider, but in addition to these, it is necessary to consider the time slow effect caused by the satellite movement.

My paper has a clear description of how to interpret the twin paradox by Lorenz transformation.Wiki also has a twin paradox explanation, I think it is very funny.
Can you simply explain Janus's point of view?

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2 minutes ago, YuanShenhao said:

Yes, these are the factors that we can generally consider, but in addition to these, it is necessary to consider the time slow effect caused by the satellite movement.

That is not an additional fact, it is the first one I mentioned: "have to take into account both the relative velocity of the satellite and the receiver "

4 minutes ago, YuanShenhao said:

Can you simply explain Janus's point of view?

Special relativity.

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4 minutes ago, YuanShenhao said:

Yes, these are the factors that we can generally consider, but in addition to these, it is necessary to consider the time slow effect caused by the satellite movement.

My paper has a clear description of how to interpret the twin paradox by Lorenz transformation.Wiki also has a twin paradox explanation, I think it is very funny.
Can you simply explain Janus's point of view?

The twin paradox is easily explained, Lorenz transformation is clearly illustrate this point

......

The above shows the entire process of Lorentz transformation, from which we can see, A, B
two objects refer to each other, the time of moving objects slowed down. This is the conclusion
that many scholars recognize, but is it true? Is it enough for A, B two objects refer to each other
enough? Let us do an experiment: in the absence of any reference object, A, B two objects stay
away from each other, the question is, who is moving, who is still, or both are in motion? Is it clear?
It's not clear for anyone. Obviously, the two things refer to each other will just make more
complicated. This is also a very important reason why many researchers have troubles over the
research of the twin paradox.

However, our deduction obviously points to a clear conclusion. The frame of reference for
motion slowed down. Yes, nothing wrong. Let us start the analysis. The whole derivation is based
on the speed of light, the constant speed of light, except that we must also pay attention to a very
important point, which is (O, O ') point. Since the S coordinate system is not moving, when
referring to O point, the time on S does not become faster nor slower. That is to say, the speed of
time has not changed. While S' is in motion, observing S' from S time has slowed down. So here is
the question, the time getting slower is compared with which one. Of course, it is compared with
the time on S, and the time on S does not change, which is for the reference to decide? It is the O
point, so we say that the time on S' become slower and which O point is also for the reference.
What is O point? It is space-time, space-time point which is located on S. With the same principle,
this could also be applied for the observation of S from S'.

However, this space-time point will often be ignored by us, which is the third-party reference
for the comparison between two inertia systems, without it, there is no above conclusion. I
believe after the above analysis, you will have a sudden understanding about the twin paradox,
we will describe in detail later. We can boldly put forward the conclusion that the speed of time
requires space-time for reference. Without a third party, there is no way to compare A, B two
subjects.

2 minutes ago, Strange said:

That is not an additional fact, it is the first one I mentioned: "have to take into account both the relative velocity of the satellite and the receiver "

Special relativity.

Special relativity !  Well, if I can say so: twin paradox can be explained by science.

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Good morning, Yuan.

I'm glad to see you are now fully participating in the forum process.

As regards my comments, they were not contradictions of your work.

They were, just as I said, comments on the text.
This means that I think something was not properly explained or defined at the point in the text I highlighted.

Or that it seemed at odds with something you wrote at another part of the text.

In fact at one point I think you have said the opposite of what you really mean.

It does not mean convey my opinion on the subject, that would come later.

I am trying to help you put your work into a coherent piece of English for presentation.

Then we can consider the truth or otherwise of it.

This is a normal process when someone writes a paper, as you have done.

So let us put something straight to begin with.

your title reads

"The derivation of relativity from the twins paradox."

But unless you accept relativity, the twins paradox does not arise.

You have it the wrong way round.

The twins paradox arise because we have observed relativity.

So the twins paradox is derived from relativity.

Edited by studiot

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28 minutes ago, studiot said:

Good morning, Yuan.

I'm glad to see you are now fully participating in the forum process.

As regards my comments, they were not contradictions of your work.

They were, just as I said, comments on the text.
This means that I think something was not properly explained or defined at the point in the text I highlighted.

Or that it seemed at odds with something you wrote at another part of the text.

In fact at one point I think you have said the opposite of what you really mean.

It does not mean convey my opinion on the subject, that would come later.

I am trying to help you put your work into a coherent piece of English for presentation.

Then we can consider the truth or otherwise of it.

This is a normal process when someone writes a paper, as you have done.

So let us put something straight to begin with.

your title reads

"The derivation of relativity from the twins paradox."

But unless you accept relativity, the twins paradox does not arise.

You have it the wrong way round.

The twins paradox arise because we have observed relativity.

So the twins paradox is derived from relativity.

Hi, studiot

I'd like to hear how you use the relative theory to explain the twin paradox.

Let's focus on twin paradox.

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30 minutes ago, YuanShenhao said:

I'd like to hear how you use the relative theory to explain the twin paradox.

Let's focus on twin paradox.

Maybe it would help if you said which part of the existing explanation you don't understand.

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Here is a start.

The coordinates of a single event point are {x,y,z,t} in one observational coordinate frame and {x',y',z',t'} in another.

The values of x',y' z' and t' in terms of x, y z and t are given in a linear transformation.

Concentrating on time and considering that the t' frame is moving with velocity v parallel to the x (of the t frame) axis so we can drop the y and z

t' = At + Bx; where A and B are constants

So t' may be greater than, less than t or even negative depending on these constants.

Constant B allows for the fact that observers in t and t' may start counting time from different zero event points.

Introducing the relative velocity of the t and t' frames and doing some algebra leads us to

A=1(1v2c2)=γ

and

B=γvc2

So we have exchanged constants A and B for two others, gamma and c.

Gamma is the Lorenz factor and is only valid for the combination of the two frames in question
c is the speed of light and is valid for all frames.

This is useful as these constants apply to the transformation of all four coordinates, not only time.

None of these linear transformations lead to a 'dilation' of the coordinates.

Noting that t and t' refer to the same event point we can answer the question what does dilate then?

I said you need two (event) points for this.

If we consider the difference between two points that is (x2 - x1) and (t2 - t1) in the first frame and (x'2 - x'1) and (t'2 - t'1) in the second frame
We have a length and a time difference.

Many physical quantities come in two flavours like this.

Electric potential and potential difference both measured in volts
Temperature and temperature difference both measured in degrees

Each of the two flavours have the same units but somewhat different characteristics and are used for different purposes in physics.

So back to relativity, these differences are taken between the same two event points (before we had one, now we have two points) but viewed in the different frames.

So we are talking about the same length and the the same time difference in both cases.

If you perform the Lorentz transformations on coordinates from one frame to yield the coordinates for both points in the other and take the length and time differences in each frame you will get different numbers.

So observers in each frame will evaluate these differences as being different numbers.

Alternatively if we substitute in the Lorenz transformations into my difference formula above (x2 - x1) and (t2 - t1) in the first frame and (x'2 - x'1) and (t'2 - t'1) in the second frame

we will obtain formulae for what happens when we consider the same time difference or distance difference (length) from the standpoint of difference frames.

In other words we will obtain the formulae called time dilation and length contraction.

One final note

These formulae are developed using linear or 'first order' analysis.

This is OK when the event points are close to each other and in particular the differences can become infinitesimals.

So ΔtandΔx become δtandδx

This allows us to define, or assign meaning to, calculus operations involving relativity formulae.
Edited by studiot

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!

Moderator Note

Similar topics merged. One thread per subject, please

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3 minutes ago, swansont said:
!

Moderator Note

Similar topics merged. One thread per subject, please

I wish this topic can merged to sciences-->physics--->relativit. NOT HERE.Of course here is your place, you have the right to decide.

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16 minutes ago, YuanShenhao said:

I wish this topic can merged to sciences-->physics--->relativit. NOT HERE.

!

Moderator Note

So long as you are advancing an explanation that is at odds with mainstream physics, that will not happen.

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12 hours ago, YuanShenhao said:

Let us first come back to reality, there are two women on
earth are competing which one is more beautiful, either of them won't step back (completely
controversial to clear out), in the end what we should do? The introduction of a third-party
referee, by the third party to determine who in the end is more beautiful.

But all you've done here is introduce a Third subjective opinion.  You have not established any absolute standard of "beauty". A different third party might conclude differently or that there is no difference in the level of beauty of the two woman.   There are are, in fact, any number of Third parties to choose from, each with their own standard of "beauty".

The point behind space-time is not that it supplies an absolute reference, but that it is entirely relative, even to the point that what part of it constitutes time and what part space.

The constant speed of light, we can regard it as the characteristics of light. So, what are the

objects around us, which also do not change their own characteristics of exercise performance
with the outside world? Try to observe the spring, we put the spring on the car with uniform
movement and put it still on the table, their frequency of vibration will be the same? The answer
is it will be the same, this is only an example to illustrate that there are always some things that
they do not interfere with certain external factors, there is no relationship with light, just to show
that the light has the feature of constant speed, and the spring has the characteristics of constant
frequency, these are only the unique properties of the materials.

Here you go down a common Rabbit hole,  The idea that it is the properties of light that "determines" Relativistic effects.  In truth, what is happening is that the behavior of light is exposing an underlying fundamental principle in the rule governing the universe,  In this case the nature of "time" and "space" and their interrelationship.  The invariant speed  for light is a "symptom" and not a cause.   Thus the spring in you example above is equally subject to this principle, and in fact the spring in the car and on the table would when compared from a proper frame of reference vibrate at different rates. (There is one reference frame in which they would vibrate at the same rate, the one which both springs have an equal relative velocity with respect to.)

I'd like to hear how you use the relative theory to explain the twin paradox.

By taking into account all three Relativistic effects: Time dilation, length contraction, and the Relativity of simultaneity.  Too, many times People who struggle with the Twin Paradox do so because they just focus on time dilation and neglect the other two.

The Twin paradox, in its standard form involves three inertial frames:  That of the "stay at home" twin, that of the outbound leg of the "traveling" twin and that of the return leg of the "traveling " twin.   I put "stay at home" and "traveling" in quotes, because they don't applying in an absolute sense.  The one real distinction between the two is that one remains at rest with respect to a single inertial frame of reference the whole time, and the other changes which reference frame he is at rest relative to during the course of the scenario.  So, for now on, I'll refer to the " stay at home" twin as A and the "traveling twin" as B ( it also saves on typing).

Dealing with the Twin paradox in SR involves examining it from the perspective of both our twins.

We will start with A.  As far as A is concerned,  B simply travels out some distance at a set speed and then returns at that same speed.  For our example, we'll use a distance of 8 light years and a speed of 80% of the speed of light.   Thus for A it will take 10 yrs to make each leg of the trip and 20 years for the round trip.  During which time, he will measure B as undergoing time dilation, and aging 60% as fast as he is, and as a result aging a total of 12 years during the trip. For A, time dilation is enough to explain the age difference.

For B, things are a bit more more complex.   First off, he has to consider Length contraction.  This was not a concern for A, because the only length contraction involved as far as he was concerned, was that which effected B, and this had no effect on either the time needed for the Trip nor B's aging during the trip.  B has to consider it because the 8 light distance between A and the point where B turns around, is the distance measured by A.  B will measure this distance as being length contracted to 60% of 8 light years or 4.8 light years.  At 80% of the speed of light, it takes B 6 yrs by his clock for the distance between A and himself to reach 4.8 light years. at which point he makes an instant acceleration so that A and he are approaching again.  Note that the 6 years he has measured as passing between his separation from A is the same as what A measured for him due to time dilation.

But what is happening to A time-wise, according to B? A is undergoing time dilation.  Thus A is aging at 60% the rate B measures himself as aging and has aged 3.6 years in the time it takes for their separation to grow to 4.8 light years.  Thus just before making his turn around,  According to B, A has aged 2.4 years less than he has.  But then A makes his acceleration and changes the frame of reference he is at rest with respect to.  In doing so, he has to take Relativity of Simultaneity into account.

Relativity of Simultaneity is the fact that observers in different inertial frame do not agree on the Simultaneity of events.   Thus if we have two clocks at rest with respect to inertial Frame  which are synchronized to each other in this frame and separated by some distance in the x direction.  Then according to inertial frame s' which has a relative motion with respect to s in the x direction, the two clocks in s will not be in sync with each other, one of the clocks will read later than the other.(though they will still both tick at the same rate)

With our twin example, we can illustrate this by assuming that in A's inertial frame, there is a clock placed 8 light years distant (at B's turn around point) which is synchronized to A's clock. Thus, according to A, when B reaches it Both it and A's clock reads 10 yrs.

According to B however in an inertial frame with a relative velocity of 80% of c to A's frame, the clocks at these two points are not in sync, but instead the clock at the turnaround point reads 6.4 years ahead of A clock. A's clock read 0 when B and A separate, and the turn around clock already reads 6.4 years.  By the time he reaches this clock, both it and A's clock will have advanced 3.6 years and the turn around clock will read 10 yrs, while A's clock reads 3.6 years.

Then B makes its acceleration, and transitions to a new inertial frame of reference which has a velocity in the opposite direction of his initial one.  Now, due to the Relativity of Simultaneity, the roles of the clocks of the clocks at A and the turn around point are reversed,  A's clock is now the one that is ahead.  While the turn-around clock (the one he is still right next to) still reads 10 yrs,  A's clock (according to B's new inertial frame), reads 16.4 years.   A's clock advance another 3.6 years during the 6 years according to B for them to meet up again and reads a total of 20 yrs upon their meeting up again.

The upshot is that while both A and B both agree in the end that A accumulated a total of 20 years and B accumulated a total of 12 years during their separation, they have totally different perspectives as to what led to this result.

This is the gist of SR: That inertial frames in relative motion with respect to each other measure time and space differently and that the very concepts of "time" and "space" are not absolute but frame dependent.

To illustrate how this differs from the Newtonian model of time and space, we'll use the following images.

We'll plot space and time as a grid and a figure like this.

This represents the view from a particular inertial frame. The vertical lines are are time and the horizontal space.

Viewing this from another frame of reference is the equivalent of rotating the above image.

In Newtonian physics, this would be represented like this.

the figure has rotated, but so have the grid lines, and thus the figure's relation to the grid lines remains the same. The grid lines, and thus time and space are absolute relative to the figure.

But in Relativity the view from another frame of reference would look like this.

The figure has rotated, the grid lines remain vertical and horizontal, they are not absolutely fixed to the figure but are dependent on the inertial frame in which it is viewed from.

In the first image, a horizontal line represents a "moment in time", and the Vertical line points in space.  If you look at the ends of oval,  you see that they have the same relative position with repsect to the  time lines but different positions relative to space.  They are like two events that happen at the same moment but are separated by some distance.

In the second image, representing the Newtonian view, changing the inertial frame from which we view this make no difference, these events maintain their relative positions relative to the Time and space lines and the two event still occur at the same time.

But in the third view, that of Relativity, the ends don't maintain the same relationship to the time and space lines when we view it from a new inertial frame.  One end is "above" the other relative to the Grid and the two events that the ends represent do not occur at the same time in this view.

It is this difference between how space and time "behave" that separates the Newtonian and Relativistic models.

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12 hours ago, Janus said:

1.We will start with AA.  As far as AA is concerned,  B simply travels out some distance at a set speed and then returns at that
same speed.  For our example, we'll use a distance of 8 light years and a speed of 80% of the speed of light.
Thus for AA it will take 10 yrs to make each leg of the trip and 20 years for the round trip.  During which time, he will
measure B as undergoing time dilation, and aging 60% as fast as he is, and as a result aging a total of 12 years during the
trip. For AA, time dilation is enough to explain the age difference.

ME:

I agree with this view.

2.For B, things are a bit more more complex.   First off, he has to consider Length contraction.  This was not a concern for AA,
because the only length contraction involved as far as he was concerned, was that which effected B, and this had no effect on
either the time needed for the Trip nor B's aging during the trip.  B has to consider it because the 8 light distance between AA
and the point where B turns around, is the distance measured by AA.  B will measure this distance as being length contracted to
60% of 8 light years or 4.8 light years.  At 80% of the speed of light, it takes B 6 yrs by his clock for the distance between
AA and himself to reach 4.8 light years. at which point he makes an instant acceleration so that AA and he are approaching
again.  Note that the 6 years he has measured as passing between his separation from AA is the same as what AA measured for him
due to time dilation.

ME:

This paragraph and the above description are an meaning, and I didn't see anything else.

3.But what is happening to AA time-wise, according to B? AA is undergoing time dilation.  Thus AA is aging at 60% the rate B
measures himself as aging and has aged 3.6 years in the time it takes for their separation to grow to 4.8 light years.  Thus
just before making his turn around,  According to B, AA has aged 2.4 years less than he has.  But then AA makes his acceleration
and changes the frame of reference he is at rest with respect to.  In doing so, he has to take Relativity of Simultaneity into
account.

ME:

This is to say that if B is a reference, then AA will also expand. You said, "when B arrives, AA's time has passed for 3.6
years, and B has been over for 4.8 years."
A mistake has been made here: 4.8 light years are calculated distances based on AA, and now you use B as a reference to
calculate A, and the data used 4.8 light years come from the data obtained by A for reference, so you will enter the dead circle
completely. Please think about it carefully.

4.Relativity of Simultaneity is the fact that observers in different inertial frame do not agree on the Simultaneity of events.
Thus if we have two clocks at rest with respect to inertial Frame  which are synchronized to each other in this frame and
separated by some distance in the x direction.  Then according to inertial frame s' which has a relative motion with respect to
s in the x direction, the two clocks in s will not be in sync with each other, one of the clocks will read later than the
other.(though they will still both tick at the same rate)

ME:

You say:”This is to say that for S', the time of the two clocks on the S is different“. I think the speed of light transmission
requires time, not the relativistic effect.

5.With our twin example, we can illustrate this by assuming that in AA's inertial frame, there is a clock placed 8 light years
distant (at B's turn around point) which is synchronized to AA's clock. Thus, according to AA, when B reaches it Both it and
AA's clock reads 10 yrs.

ME:

I agree with this view.

6.According to B however in an inertial frame with a relative velocity of 80% of c to AA's frame, the clocks at these two points
are not in sync, but instead the clock at the turnaround point reads 6.4 years ahead of AA clock. AA's clock read 0 when B and
AA separate, and the turn around clock already reads 6.4 years.  By the time he reaches this clock, both it and AA's clock will
have advanced 3.6 years and the turn around clock will read 10 yrs, while AA's clock reads 3.6 years.

ME:

You say: "the turning point clock is 6.4 years ahead of the AA clock". This is very unreasonable. I have already explained
it.
You say, "the turning point clock is 10 years, and the AA clock is 3.6 years". You are wrong, AA is 10 years, and it can't be
3.6 years. Because the turning point clock does not follow the B movement

7.Then B makes its acceleration, and transitions to a new inertial frame of reference which has a velocity in the opposite
direction of his initial one.  Now, due to the Relativity of Simultaneity, the roles of the clocks of the clocks at AA and the
turn around point are reversed,  AA's clock is now the one that is ahead.  While the turn-around clock (the one he is still
right next to) still reads 10 yrs,  AA's clock (according to B's new inertial frame), reads 16.4 years.   AA's clock advance
another 3.6 years during the 6 years according to B for them to meet up again and reads a total of 20 yrs upon their meeting up
again.

ME:

Logical confusion.

In fact, Lorentz transformation has been clearly described space-time as the third party reference exists, why do we still
struggle with only A, B to compare?

In the absence of any reference object, A, B two objects stay away from each other, the question is, who is moving, who is
still, or both are in motion? If there is an alarm clock on A and B, who can say which alarm clock is slow? Is it clear?
It's not clear for anyone. Obviously, the two things refer to each other will just make more complicated. This is also a very
important reason why many researchers have troubles over the research of the twin paradox.

12 hours ago, Janus said:

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I’m sorry to say that I proved your first premise wrong not that long ago.

There is a logical explaination for the deviation in time between the twins:

Starting with the paradox of symmetry vs time deviation:

Ok, so we can agree that the TP says that the twins respective views of their brothers time are symmetrical for the entire trip, so how do they each experience different amounts of time.

There are several valid mathematical solutions that all claim something a little different as to the sources that cause the time deviation, such as relativistic redshift, or gravity or frame jumping, or the turn around, but none of which really explain how the paradox is physically resolved.

So they are valid in proving that there is no pardox, but not definitive in explaining why there is no paradox.

For this you need to use a logical model. To understand why, I will first provide the logical model that definitively explains the solution. Then I will provide the logical reasoning why math is not a reliable model for explaining a
problem.

The Definitive Solution:
To find the solution using logic, we must find the assymetry to the problem keeping in mind that the solution wont be intuitive because its still in the relativistic domain. So if time is symmetrical, and velocity is invariant, then that leaves only distance.

Now, if we look at the two inertial reference frames:
in the traveling twins inertial reference frame we only have the ship
In the Earth twins inertial reference frame, we have the Earth, the destination system, and the distance inbetween.

Therein lies the assymetry! The Earth twin only sees the ship contract, the traveling twin sees the distance to the destination contract. Note that its only the dimension in front of the moving object that gets length contracted in the effectively static frame.

So, because the traveling twin is only traveling 60% of the distance, the trip only takes 60% of the time.

It seems amaazingly trivial in hind site right?

But that’s what logic does, It simplifies the problem through convergence, which goes hand in hand with why it clarifies a problem.

Quote
“If you cant explain it simply, you don't understand it well enough.”
-Albert Einstein

But the logical explanation isn’t the complete answer either! Thats because we can’t prove anything using logic, we can only explain things. To prove there is no paradox we need to do the math which has already been done... repeatedly.

Which is why math is not the best at providing an explaination of the problem. Thats because if there is no paradox, then all mathematical models will balance out by virtue of their being deterministic regardless of what source your testing.  They will all be seen as being the source, because the gap in time is always in the math..
Quod erat demonstrandum

To sum up:
By defining math as being deterministic, we can prove that their is no paradox. If it were a paradox the math shouldnt balance out, ergo, showing the math balances out proves their is no paradox.

Then by defining the logic to being all valid thinking that’s not math, we may solve the intuitive falacy in order to find the logical explanation.

Or as I’ve said many times before math quantifies, and logic clarifies.
or more importantly, logic and math are complimentary opposites.

But the consequences of how we define math and logic are even more profound than solving physics.What makes them opposites, is basically that math is deterministic and logic is not, for example:
1. we can only invalidate the logical models.
2. we can only validate the mathematical models.
•
1. we can use the mathematical models to Quantify the problem
2. we can use the logical models to clarify the problem
•
1. The fact math is deterministically defined is why we can apply mathematical methodology to disprove the paradox.
2. The fact logic is not deterministically defined means we must use logic to find a logical model for the problem, which in this case involves deductive logic.
•
1. Why logic is prone to falicy of intuitive premise
2. Why math is prone to falicy of intuitive conclusions
...... and I could go on, with more examples of how they’re complimentary opposites.

Therefore, since logic and math are opposites, that’s a very good reason why we should not define logic as a type of math.

So would the two down votes that appeared at the instant of the post care to explain your preminitions of an angruement?

Edited by TakenItSeriously

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And by the way, since I wrote that reply on a local editor and cut and pasted that reply without typeing it in the editor, there was no way you could have read it in the two seconds it took from both downvotes.

What are you guys trolls from Russia or something?

Edited by TakenItSeriously

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24 minutes ago, TakenItSeriously said:

And by the way, since I wrote that reply on a local editor and cut and pasted that reply without typeing it in the editor, there was no way you could have read it in the two seconds it took from both downvotes.

What are you guys trolls from Russia or something?

Well I have no idea about the downvotes, but I can spot several inconsistencies in your explanation which stand out.

I do rather tend to read the prospectus rather than rushing to the voting booth.

2 hours ago, TakenItSeriously said:

Or as I’ve said many times before math quantifies, and logic clarifies.

Yes I think there is a lot of truth in that.

2 hours ago, TakenItSeriously said:

or more importantly, logic and math are complimentary opposites

But I don't see how this follows since there is much logic used in the development of any mathematical analysis. (By development I don't mean the initial creation of the mathematical theory, I am referring to it's use in the case concerned.)

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