(Fig.1) Seen by clock-A (or clock-B ), the other clock-B (or clock-A ) appears to be moving and ticking slower. ← Which clock-A or B ticks slower is unknown, paradoxical.
According to the unphysical Einstein special relativity (= paradoxical Lorentz transformation ), a moving clock is said to tick slower than a stationary clock. ← illusory pseudo-science
In the upper figure ①, a clock-A is moving toward a clock-B at rest where a moving clock-A appears to run slower than the stationary clock-B.
But from the viewpoint of the clock-A , the clock-B appears to be moving toward the clock-A, hence, the clock-B appears to run slower than the clock-A (= figure ② ).
↑ This means which clock A (= ① ) or B (= ② ) is slower is paradoxical and unknown (= called twin paradox ), which shows Einstein relativistic theory is false.
On this page, we show this twin time paradox is a a real fatal paradox, and can Not be fixed even by using general relativity.
Contrary to hypes, the paradoxical Einstein relativistic theory is useless, Not applied to any phenomena such as GPS and illusory muon's lifetime.
(Fig.2) Clock-A on the ground runs slower than clock-B at a height of L under gravitational acceleration g according to general relativity.
According to general relativity, clock-A on the ground ticks slower than clock-B at a height of L under gravity of acceleration g.
This gravitational time dilation is related to the gravitational potential (= φ = -GM/r, this p.3,p.5 ) equal to acceleration g × the distance (= height ) L = -gL (= Δφ, this p.3, this 2nd-last-paragraph ).
The problem is that this general relativistic gravitational (= acceleration ) time dilation is also paradoxical (= so wrong ), causing unreal imaginary (or negative ) time like inside an unphysical black hole, when the distance L between these two clocks is very long.
As a result, twin paradox caused by a moving clock ticking slower in special relativity is a real fatal paradox that can Not be fixed by the (paradoxical) general relativity (= gravitational or acceleration time dilation )
(Fig.3) Clock-A starts to accelerate at g (= not gravity ) at the distance L from clock-B. ← This clock-A moving at a speed of v (= gt g is acceleration, t is time ) ticks slower ?
In the upper figure, a clock-A at rest starts to move or accelerate at a acceleration of g at distance L from a clock-B (= this force causing acceleration g is applied only to clock-A in this case, so No gravitational field nor no gravitational time dilation ).
The velocity v of this clock-A at a time t is v = gt, which gives the total special relativistic time dilation of the moving clock-A by integrating it with time (= figure.3-lower ).
↑ In this case, the moving (= accelerating ) clock-A runs slower than the clock-B at rest according to the special relativity (= no general relativity nor gravitational field is involved in this case ).
(Fig.4) From the viewpoint of the (accelerating) clock-A, clock-B appears to be accelerating toward the clock-A at fictitious gravitational acceleration of g, which causes time dilation ?
When the clock-A start to move and accelerate (= acceleration of g ) at distance of L from clock-B toward the clock-B at rest, from the viewpoint of the clock-A, the clock-B appears to be accelerating toward the clock-A by the fictitious gravitational acceleration of g, like rotating frame (= merry-go-round ) fictitious centrifugal potential ( this p.3-right ).
↑ From the viewpoint of the accelerating clock-A, all things including the clock-B appear to be accelerating at g in the opposite direction, which corresponds to the (fictitious) gravitational field influencing all things according to (unphysical) Einstein general relativistic equivalence principle.
First, from the viewpoint of the clock-A, the clock-B appearing to be moving (= accelerating ) at velocity v = gt (= t is time ) runs slower according to special relativistic time dilation (= upper figure ① ).
Second, from the viewpoint of the (accelerating) clock-A, all things appear to be accelerating at fictitious gravity (= acceleration of g ), which causes (fictitious) gravitational (= accelerating ) time dilation related to the fictitious gravitational potential = gL or gh (= L or h is distance between clocks A and B, this-(1)-lower, this p.5-upper, this p.3-lower~p.4 ) as shown in the upper figure ②.
So from the viewpoint of clock-A, the clock-A (= appears to be at lower fictitious gravitational potential or ground ) runs slower than clock-B by this fictitious gravitational time dilation.
By combining these special and general relativistic time dilation, the clock-A runs slower at the same rate as the clock-A moving frame (= compare the total time dilation of clock-A of the last of Fig.3 and Fig.4 which are the same. ← no twin time paradox ? ).
↑ There appears to be no (twin) paradox, because both in clock-A's moving and stationary frames, the clock-A runs slower by the same amount of time.
But this standard estimation seen in textbooks is false, because this gravitational time dilation seen in textbooks is just an approximate (= not real ) form (= applicable only to the case of very short distance L ), which cannot avoid true twin paradox when distance L is very long.
(Fig.5) From the viewpoint of the accelerating clock-A, the fictitious gravity causes paradoxical imaginary (= negative ) time dilation when distance L is very long.
From the viewpoint of the clock-A that starts to accelerate at acceleration of g at distance L from the stationary clock-B, all things including the clock-B appear to be accelerating in the opposite direction by the fictitious gravity g.
So the clock-A runs slower than clock-B from the viewpoint of the accelerating clock-A (= clock-A's rest frame ), because clock-A is at a lower fictitious gravitational potential like on the ground.
But when the distance L between the clock-A and B is very long (= L > c2/g ), the clock-A time (= dtA ) becomes unrealistically negative, which means as the clock-B is ticking, the clock-A is unrealistically going back in time toward the past (= due to negative dtA this-middle ) ?
↑ This is clearly paradox and unphysical, which proves Einstein relativistic theory is wrong.
Because in the moving clock-A's frame (= where clock-A is moving toward the stationary clock-B with No fictitious gravitational field ), both clock-A and B' times are positive (= not going back toward the past ), and only in the rest frame of clock-A (= from the viewpoint of clock-A ) the clock-A's time becomes negative (= dtA < 0 = to be precise, imaginary time of square root of negative ).
This fictional black hole like imaginary (= negative ) time in general relativity shows twin time paradox is real, irreparable., and relativistic theory is false.
(Fig.5') Clock-A time stops (= like on the fictional black hole surface ) or not depending on the existence of clock-C ? ← paradox !
In fact, gravitational (= or acceleration ) time dilation of general relativity is paradoxical and false from the beginning.
When the distance L between clock-A and clock-B under the gravity (= or fictitious gravity by acceleration ) is equal to c2/2g like in the upper figure, the clock-A's time dtA stops with respect to clock-B, like on the fictional black hole.
But if we consider the clock-C nearer to clock-A, the same clock-A's time does Not stop with respect to not only clock-C but also clock-B.
Because the distance L1, L2 between clock-A and clock-C (or clock-B ) is less than L = c2/2g, which makes the clock-A time dtA positive ( this figure-lower ).
This is clearly paradox, and general relativistic gravitational time dilation is also paradoxical and false.
(Fig.6) To avoid paradoxical imaginary time of black hole, true gravitational time dilation (= exponentially slower ) causes new real twin paradox, so Einstein is false.
From the viewpoint of the accelerating clock-A, the fictitious gravitational acceleration g causes the paradoxical imaginary (= negative ) time dilation like inside black hole, when the distance L between two clocks A and B is very long.
First of all, the present standard general relativistic (= gravitational ) time dilation expressed as the square root of 1-gL is paradoxical and wrong from the beginning.
Because the clock-A's time appears to stop (or become unreal imaginary rime ) with respect to very distant clock-B, and the same clock-A's time does not stop (nor become imaginary time ) with respect to the nearer clock-C in this paradoxical standard gravitational (= acceleration ) time dilation.
To remedy this paradoxical gravitational time dilation, we need to divide the distance L into infinite infinitesimally short distance ΔL (= L/n n → ∞ ) like the upper figure.
↑ This (new true) gravitational time dilation becomes exponentially slower ( this lower ), and never causes the stopped time or imaginary time like the unphysical black hole (= so black hole does Not exist in this new true gravitational time dilation equation ).
But even this new true gravitational time dilation (= lacking black hole ) can Not fix twin time paradox (= exponential gravitational time dilation cannot fix the ordinary square root or linear-type special relativistic time dilation ).
Standard (wrong) general relativistic gravitational time dilation causing black hole is just an approximate one applied only to extremely-short distance ( figure 6-lower )
(Fig.7) From the viewpoint of clock-A (or clock-B ), clock-B (or clock-A ) running far faster reaches the center point-O far earlier than clock-A (or clock-B ), which is clearly twin paradox about which clock-A or B is faster.
In the real twin paradox case shown in the upper figure, clock-A and clock-B start to accelerate at g for a short time dt (= 1/10 seconds ), and then, are moving at a constant speed v (= c/100 c is light speed ), arrive at the center point O at the same time ( this p.3-3.1 ).
But from the viewpoint of the (accelerating ) clock-A (= seen by clock-A ), the clock-B's time (= dtB ) appears to be run exponentially faster (= in true gravitational time dilation avoiding paradoxical black hole's imaginary time ).
As a result, when the distance L between clock-A and B is very long (= L = 1000c meter ), the clock-B running far (= exponentially ) faster reaches the center-O far earlier than clock-A (= clock-A is still in the initial accelerating state within dt ) from the viewpoint of clock-A.
↑ This clock-B's maximum velocity is v = c/100, so the special relativistic time dilation of clock-B is very small and negligible (= square root of 1-1/10000 is close to 1 ) compared to the exponentially faster general relativistic time effect. ← The clock-B seems to move far faster by the clock-B's time dtB ticking far faster (= clock-B or the stationary center-O's person getting far older ) than clock-A, Not by clock-B's speed itself becoming far faster.
From the viewpoint of the accelerating clock-B, the clock-A appears to run far faster (= clock-A gets far older than clock-B ) and reaches the center-O far earlier than the clock-B, which is the true twin paradox.
↑ So which clock-A or B reaches the center-O earlier is clearly paradox, and Einstein relativity is wrong.
Contrary to textbooks, relativistic twin paradox is proven to be real and irreparable.
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