Refutation of Special Relativity for Dummies

[wogoga]

If my refutation (post #66) of Einstein's twin-paradox resolution was wrong then you would be able to show which point is wrong:

1. According to Einstein, reciprocal time dilation during inertial motion "is more than compensated by a faster pace" of resting twin U1 during direction-reversal of U2.
2. This "faster pace" of U1 is explained by a fictitious "homogenous gravitational field" acting on U1.
3. Gravitational attraction implies (stronger, lower) gravitational potential.
4. Gravitational potential leads to gravitational time dilation.
5. Thus, Einstein explains the "faster pace" with gravitational time-dilation.
6. Yet gravitational time dilation of U1 is the opposite of "faster pace of U1".

Apart from rather pointless nitpicking based on biased interpretation of my simplifying explanations, the brave defenders of Einstein's failed twin-paradox resolution come to contradicting conclusions:

Gravitational dilation is clocks ticking faster !
The gravitational time dilation of U1 is the same as the "faster pace of U1".

The gravitational potential is higher at point U2 than at point U1. So the clocks at U2 are faster than the clocks at U1.

Wikipedia on gravitational time dilation:

"The stronger the gravitational potential (the closer the clock is to the source of gravitation), the slower time passes."​

Reality Check is right insofar as Einstein's reasoning needs a "faster pace of U1". Darwin123 is right insofar as the (lower, stronger) gravitational potential of U1 leads to a slower pace of U1.

Cheers, Wolfgang
Symmetric Time Dilation Explained

 

[Darwin123]

Apart from rather pointless nitpicking based on biased interpretation of my simplifying explanations, the brave defenders of Einstein's failed twin-paradox resolution come to contradicting conclusions:




Wikipedia on gravitational time dilation:

"The stronger the gravitational potential (the closer the clock is to the source of gravitation), the slower time passes."​

Reality Check is right insofar as Einstein's reasoning needs a "faster pace of U1". Darwin123 is right insofar as the (lower, stronger) gravitational potential of U1 leads to a slower pace of U1.

Cheers, Wolfgang
Symmetric Time Dilation Explained

Apparently, RealityCheck and I are imagining reflected diagrams. In my diagram, U1 is the spaceship observer with a thrust that is pointing toward the earth which is U2. RealityCheck is imaging U1 as the observer on earth and U 2 as the spaceship that is turning around.

There may be a diagram earlier in the thread, or in Einstein's narrative, that specifies what U1 and U2 are. I don't remember one. Quite possibly I made the mistake.

RealityCheck and I are in full agreement as to the physics of what is going on. Wogoga is nit picking. The clock in the greater 'fictitious' gravitational potential is ticking slower, however one labels the clocks.

Wogoga is confused as to the difference between a field and a potential. Physicists would recognize these words outside of special relativity. The 'fictitious gravitational field' is the 'proper acceleration'. The 'gravitational potential' is an accumulated affect of the 'proper acceleration'.

Einstein referred to a 'fictitious gravitational field'. Or at least the English translation says 'fictitious gravitational field.' This is the phrase that I learned when I was in school long, long ago. The phrase 'proper acceleration' was coined long after I learned relativity. However, they are the same thing. 'Gravitational potential' is determined in the standard way from the 'fictitious gravitational field' which is the 'proper acceleration'.

I will use primed coordinates for any observer and unprimed coordinates specifically for an inertial observer. This way Wogoga won't be confused by who is U1 and U2.

Let the rocket man be at the point x=0. The earth man will be at a point x=X. When the rockets fire, the proper acceleration (i.e., fictitious gravitational field) is a constant (a) all over the universe. The potential of the rocket man is 0 in whatever units you wish to use. The potential of the earth man is 'aX' in whatever units you wish to use. Note that the 'proper acceleration' is 'F/m', where F is the total force on the rocket and m is the mass of the rocket.

As seen by the rocket man, the clock on the earth is simultaneously subject to both the Lorentz time dilation and to gravitational time expansion. Any expression that determines the rate of the clock on earth has to have one factor for the Lorentz time dilation and one factor for the gravitational time expansion.

The expression comes down to Wheeler's time-dilation formula as presented by Darwin in post #78:
dt' = dt (1-a*X/c^2) / sqrt(1-v^2/c^2)
where (according to Darwin123)
dt': small interval of time measured by the observer in the rocket.
dt: corresponding interval of time measured by observer on earth.
X: distance of rocket from earth.
a: the proper acceleration of the observer and,
a=F/m
where
F is the force on the rocket
m is the mass of the rocket.

So Wogoga should start again with the understanding that 'fictitious gravitational field' IS 'proper acceleration'.

 

[Darwin123]

As seen by the rocket man, the clock on the earth is simultaneously subject to both the Lorentz time dilation and to gravitational time expansion. Any expression that determines the rate of the clock on earth has to have one factor for the Lorentz time dilation and one factor for the gravitational time expansion.

The expression comes down to Wheeler's time-dilation formula as presented by Darwin in post #78:
dt' = dt (1-a*X/c^2) / sqrt(1-v^2/c^2)
where (according to Darwin123)
dt': small interval of time measured by the observer in the rocket.
dt: corresponding interval of time measured by observer on earth.
X: distance of rocket from earth.
a: the proper acceleration of the observer and,
a=F/m
where
F is the force on the rocket
m is the mass of the rocket.

So Wogoga should start again with the understanding that 'fictitious gravitational field' IS 'proper acceleration'.

I decided to be more specific so there is no ambiguity. The proper acceleration, a, as is determined by the inertial frame of the rocket. The earth observer is by definition any inertial frame. The proper acceleration for an inertial frame is zero.

The positive direction is in the direction of the earth. The displacement, X, can be positive or negative and the acceleration, a, can be positive or negative. The salient point is that in the example given, both a and X are positive.

The words earth and rocket can be interchanged as long as one properly assigns the force, F, of the noninertial frame. While the rocket isn't undergoing a force, the rocket frame is an inertial frame.

One can make up a problem where the rocket isn't accelerating but the earth is accelerating under the influence of a cosmic force.

The point Wogoga keeps missing is that the gravitational potential IS NOT homogeneous. It varies from place to place. The gravitational field IS homogeneous in this case. The gravitational field is the proper acceleration which is determined by the force on an observer. When the rocket fires, the proper acceleration is constant throughout the universe.

Here I will start complaining about the jargon. In some ways, I think the jargon is unnecessarily confusing. Because of the common usages of some of these words, one has to pay close attention to the text of relativity theory to understand relativity unambiguously.

There was a change in the jargon. Einstein used the phrase 'fictitious gravitational force' in 1905. Physicists today use the phrase 'proper acceleration'. Both terms can be confusing.

'Fictitious gravitational force' is not really fictitious. One can argue that it is physically real for both observers. A better word would have been 'subjective'. 'The subjective gravitational force' is locally measurable by the 'subject'. In this case, the subject is the observer in the rocket. It is not fiction to the subject.

'Proper acceleration' is another confusing phrase also because the quantity is subjective. The proper acceleration is not like the proper time, since not ever observer can measure it locally. A 'proper time interval' is the same measured quantity in each inertial frame. A 'proper acceleration' is locally measurable only by an observer which is subject to a force.

Since Wikipedia has a good article on 'proper time', I will use it. There has been too much nonsense attached to the word 'fictitious'. Some would argue that a subjective quantity is by definition 'fictitious'. However. I can see that can lead to confusion.

The analogy is made between 'acceleration' and 'justice'. Justice means something different to different observers. However, this does not mean that justice is 'fictitious'. Justice is not a fiction to the people who believe in it. However, 'true justice' is always 'proper'. Consistent with this analogy, I prefer 'proper acceleration' to 'fictitious acceleration'!

This is not nit picking. This is important to the logic of relativity.

Now back to the concrete error that Wogoga made. Wogoga misquoted Einstein. Wogoga has consistently replaced the word potential in Einstein's article. For instance, he replaced the word potential with attraction.

Wogoga was the only person to use the word 'attraction' as regards to relativity. I am sure that if anybody looks at the 1905 article, that will see the word 'potential' where Wogoga says 'attraction'.

The word 'attraction' is an ad hoc error. Wogoga chose it specifically to make an incorrect sentence. He wanted to prove Einstein wrong without understanding the word potential. So he substituted a word that he did not understand, 'potential', for a word that would make Einstein wrong. 'Attraction' is not 'potential' and never was!

So this is three concrete mistakes that Wogoga made.

1) Wogoga claimed that acceleration was negligible in special relativity.

2) Wogoga did not recognize that 'fictitious gravitational field' is the same as 'proper acceleration'.

3) Wogoga mistook a 'gravitational field' for 'gravitational potential'.


His claim that I am 'nit-picking' is not the same as pointing out where I am wrong. Does everyone agree?

 

[Reality Check]

Apart from rather pointless nitpicking based on biased interpretation of my simplifying explanations,

Pointing out your ignorant use of SR and GR is not nitpicking, wogoga.
We come to the same conclusion: Einstein (who created GR and so should know about it ) is correct in his resolution of the twin paradox by applying the equivalence principle and gravitational time dilation.
Dialog about Objections against the Theory of Relativity

It should be kept in mind that in the left and in the right section exactly the same proceedings are described, it is just that the description on the left relates to the coordinate system K, the description on the right relates to the coordinate system K'. According to both descriptions the clock U2 is running a certain amount behind clock U1 at the end of the observed process. When relating to the coordinate system K' the behaviour explains itself as follows: During the partial processes 2 and 4 the clock U1, going at a velocity v, runs indeed at a slower pace than the resting clock U2. However, this is more than compensated by a faster pace of U1 during partial process 3. According to the general theory of relativity, a clock will go faster the higher the gravitational potential of the location where it is located, and during partial process 3 U2 happens to be located at a higher gravitational potential than U1. The calculation shows that this speeding ahead constitutes exactly twice as much as the lagging behind during the partial processes 2 and 4. This consideration completely clears up the paradox that you brought up.

So without your quote mining, wogoga:
Reality Check is right as Einstein's reasoning leads to a "faster pace of U1 during partial process 3"
Darwin123 is right as Einstein's reasoning leads to "During the partial processes 2 and 4 the clock U1, going at a velocity v, runs indeed at a slower pace than the resting clock U2."
Einstein is right: "This consideration completely clears up the paradox that you brought up."

 

[Darwin123]

Apart from rather pointless nitpicking based on biased interpretation of my simplifying explanations, the brave defenders of Einstein's failed twin-paradox resolution come to contradicting conclusions:




Wikipedia on gravitational time dilation:

"The stronger the gravitational potential (the closer the clock is to the source of gravitation), the slower time passes."​

Reality Check is right insofar as Einstein's reasoning needs a "faster pace of U1". Darwin123 is right insofar as the (lower, stronger) gravitational potential of U1 leads to a slower pace of U1.

Cheers, Wolfgang
Symmetric Time Dilation Explained

Concrete error # 4 and 5:

4) The effective source of gravity is BEHIND the rocket, not in front like you assume.

4a) The gravitational potential is therefore HIGHER for the observer on earth, not lower as you assume.

When the astronaut decides to turn around, he turns on his rockets which create a force on the astronaut. This results in a 'homogeneous gravitational field' that is constant and pointed in the opposite direction as the force on the astronaut.

If there is a mass that is acting as a source, the gravitational force always points TOWARD the source. The gravitational field in this case is pointing away from the earth toward the astronaut. The gravitational field at the rocket is also pointed backwards.

Thus the earth is effectively above the rocket. The earth is actually falling toward the rocket as though there were a large mass behind the rocket. Anything on the earth has a greater potential energy relative to when it arrives at the rocket.

Because the earth is farther away from the gravitational force than the rocket, the potential at the earth is HIGHER than at the rocket. This is why the rate of clocks on earth are going SLOWER than at the rocket.

You apparently made the mistake of believing that the source of gravity is the rocket. In fact, the source is always found by following the gravitational field. The gravitational field is the negative of the proper acceleration. Since the proper acceleration is pointing toward the earth from the rocket, the source has to be behind the rocket.

I already pointed out that Wogoga switched gravitational field for gravitational potential. He hasn't shown me how he was correct. However, his repeated statement that the earth observer is at a lower potential has been repeated several times since then in a condescending manner. Hence, I have to count this as a separate error. Not only has he switched field for potential, he has misplaced the gravitational source.

One can easily illustrate this error but I believe a verbal description is sufficient. Since this is easy to illustrate, it is concrete. Wogoga asked us to find one concrete error that he has made. I have found four concrete errors.

Instead of addressing these concrete errors, he has accused me of 'nit picking'. It appears that any error clear enough to be concrete is going to also be nit picking. He always tries to change the subject. I predict that he won't be able to address even one of the four concrete errors that I pointed out.

I don't know whether to count these as two errors as one. I decided to count it as one. You apparently don't know what a gravitational source is.

I ask all lurkers to note that Wogoga assumed there was a source when he used the word attraction. The source in this case is as 'fictional' as the 'gravitational field'. However, the direction of a gravitational attraction is always toward the object doing the attracting.



Although it was pointed out to you, you kept on repeating it. So it is a very concrete error on your part.

I will expect you to either show me that I am wrong regarding the position of the source, or admit that you didn't know where the source was supposed to be.

You promised to correct all concrete errors. So far you have not addressed any of the concrete errors that I have pointed out. Instead, you always introduce a NEW concrete error.

Thank you for finding 'Wheelers' formula in Einstein's paper. Now I can just quote you quoting Einstein.

dt' = dt (1-[ax/c^2]^2)/sqrt(1-[v/c]^2)
where
a = F/m.

Here 'ax' is the 'fictitious gravitational potential' or 'proper potential'. If a>0, then the potential increases with 'x'. Not only did Eisntein write this equation down, but Wogoga has quoted from Einstein with regards to this equation.

I predict that Wogoga will continue to avoid talking about this equation, which resolves every paradox that he has been discussing. I also predict that he will NEVER address any of the numerous concrete errors that he has made. Further, I predict that he won't even acknowledge that anybody presented him with those concrete errors in the future.

 

[wogoga]

Instead of dealing with inconsistent objections, let us deal with the return trip of the journey of post #75.

We get the Lorentz transformation for the return trip from [1] to [4] of #75 by replacing v with -v:

[5] x' = 100 x + 99.995 t . . [7] x = 100 x' - 99.995 t'
[6] t' = 100 t + 99.995 x . . [8] t = 100 t' - 99.995 x'​

The linking event {x=0, t=0} transforming to {x'=0, t'=0} is the only event same location, same time. Because at the end of the journey, U1 and U2 meet again at the same location and the same time, we must rename the direction-reversal event from {0 LY, 1.00005 year} of frame F'(+v) to {0 LY, -1.00005 year} of a new frame F'(-v). Using the return-trip equations [7] and [8], the not-renamed event {t' = 0, x' = 1.00005} would transform to event {x = -100, t = 100.005}, where the x-coordinate -100 LY of twin U2 would have the wrong sign with respect to U1, as U2 remains at the relative position x = 100 LY during direction reversal.

The renamed event {x' = 0, t' = -1.00005 year} of F'(-v) transforms as needed to {100 LY, -100.005 year} of F. This result is reasonable, as with respect to resting twin U1, U2 will move during t = -100.005 year and t = 0 back from the direction-reversal position x = 100 LY to x = 0.

At direction-reversal, the moving twin U2 attributes x' = -1 LY to resting twin U1. The renaming of the direction-reversal time from t' = 1.00005 year of F'(+v) to t' = -1.00005 year of F'(-v) leads to this conclusion:

• Just before reversal, F'(+v) attributes the event {-1 LY, +1.00005 year} to U1, which transforms to F event {0, 0.01 year}.
• Just after reversal, F'(-v) attributes the event {-1 LY, -1.00005 year} to U1, which transforms to F event {0, -0.01 year}.

This again (see #75) shows that according to the Lorentz transformation also during the return trip, only 0.01 year of U1 correspond to the 1.00005 year of inertial motion of U2. The 1.00005 year of U2 range from event {0, -1.00005 year} to {0, 0}. The 0.01 year of U1 range from {0, -0.01 year} to {0, 0}.

In this calculation, the "speeding ahead" of 199.9 year of U1 with respect to U2 during direction-reversal does not show up explicitly.

Cheers, Wolfgang

Darwin123 in #88: "Section 4 of Einstein's 1905 article uses a formula for centripetal acceleration"
Darwin123 in #103: "Einstein used the phrase 'fictitious gravitational force' in 1905. Physicists today use the phrase 'proper acceleration'"
Reality Check in #99: "Gravitational dilation is clocks ticking faster"

 

[Reality Check]

Instead of dealing with inconsistent objections, let us deal with the return trip of the journey of post #75.

Repeating ignorance and an invalid analysis does not refute anything, wogoga.

The act of looking at only part of the journey is obviously dumb when Einstein resolved the paradox by looking at the entire journey: Dialog about Objections against the Theory of Relativity

You quote mined Einstein's paper

So without your quote mining, wogoga:
Reality Check is right as Einstein's reasoning leads to a "faster pace of U1 during partial process 3"
Darwin123 is right as Einstein's reasoning leads to "During the partial processes 2 and 4 the clock U1, going at a velocity v, runs indeed at a slower pace than the resting clock U2."
Einstein is right: "This consideration completely clears up the paradox that you brought up."

My post #95 was abut your quoted mines of the paper:

Your web page includes several errors. The only thing it gets right are the quotes from Dialog about Objections against the Theory of Relativity!. I suggest you take a step back, learn more about Special and General Relativity and rewrite the page using correct physics.

1. A quote.
2. A quote.
3. False.
   Gravitational attraction means that a gravitational potential exists.
   That gravitational potential gets lower as distance from the mass increases.
4. False.
   Differences in gravitational potential cause gravitational time dilation. The difference in the gravitational potential between the twins has to cause gravitational time dilation.
5. A quote.
6. False.
   Gravitational dilation is clocks ticking faster !
   The gravitational time dilation of U1 is the same as the "faster pace of U1".

 

[Darwin123]

Instead of dealing with inconsistent objections, let us deal with the return trip of the journey of post #75.

I had only one inconsistency. I switched U1 and U2 in one post. I accidentally agreed with one of you false and inconsistent conclusions.


You had repeatedly made the comment that the turning around twin (rocket) was at a higher potential than the inertial twin (earth). This is wrong.

You kept on claiming that the earth twin was at a lower potential than the rocket that is turning around. You coyly said that you were 'flabbergasted' by both the inconsistency and the reluctance of other posters to point this out. You claimed to have spent several days meditating on this obvious inconsistency. Yet, you never told us how you came to that hypothesis.

I pointed out several times that you didn't know the difference between field and potential. You responded with accusations against 'inconsistent Einsteinians'. You had plenty of time to tell us what a 'potential' really is.

You first quoted Einstein as saying that the rate decreased with potential. You also quoted Einstein as saying that the gravitational field is homogeneous.

Then, you printed the same quote with field replacing potential. Then, you said that the gravitational field was stronger near the source. Then you said that because the field was stronger near the source, the earth twin was at a higher potential than the rocket twin.

However, the gravitational field can't be stronger near the source because the field is 'homogenous'! Homogeneous means 'the same everywhere!

I made the mistake of briefly accepting your rather strident claim. That is how I switched U1 and U2.

The reader should note that Wogoga never addressed my original demand. I asked him to write out the full Lorentz transformation. I told him that his entire analysis was wrong because he used an incorrect version of the Lorentz transformation. He has never provided it.

The linking event {x=0, t=0} transforming to {x'=0, t'=0} is the only event same location, same time. Because at the end of the journey, U1 and U2 meet again at the same location and the same time, we must rename the direction-reversal event from {0 LY, 1.00005 year} of frame F'(+v) to {0 LY, -1.00005 year} of a new frame F'(-v).

There is no 'renaming' in the course of the journey. There is no synchronization during the journey other than at the birth of the twin brothers. Since this is now a discontinuous journey, there could be a discontinuous perception of time and distance.

So here is a fifth concrete mistake.


5) You are assuming that the perception of time and space has to be continuous even if the forces on the observer are discontinuous.

This is not true.

The time interval of the thrust can't be zero, really. The force of the thrust can't be infinite, really. Thus, the motion of the rocket can't be truly discontinuous in the strict mathematical sense of the word. This is as true in Newtonian physics as it is in relativity.

One can use an approximation where the force is an indefinitely large and the time interval is indefinitely short. Therefore, we can approximate the time in an noninertial frame as a discontinuous quantity.

This is basically a short cut in calculus. It has little to do with relativity. Analysis of discontinuous quantities is a common mathematical calculation. Assuming that the time interval of turn around is infinitesimal is just as valid as assuming that the time interval is infinite. If you don't like discontinuous quantities, just avoid posing problems in terms of them. If this approximation can't be made, then much of Newtonian mechanics is invalid.


If the rocket 'suddenly' turns around, then the force on the rocket has to be infinite for an infinitesimal amount of time. This can be handled with mathematically limits. Or maybe a physicist can use a Dirac delta function for the turn around. However, this special case can easily be handled using the FULL Lorentz transform that I asked for. There is a short cut through the analysis appropriate for this one special case.

I asked for the FULL Lorentz transform specifically to handle the special case of a 'sudden' turn around. You have changed the subject several times since then.

I won't write the whole thing. However, the main idea is simllar.

I will call the rocket ship twin U. I lost track of which number refers to which observer.


The rocket is turning around in the noninertial reference frame of the rocket at a time t and at a position x relative to the earth twin.

Just an infinitesimal amount of time BEFORE the rocket turns on the thrust on and off,
t_A' = t (1-[vx/c^2])/sqrt(1-[v/c]^2)

Note that I used the FULL Lorentz tranform here, which you never did.

The sign in this case designates direction. The rocket just before the thrust is turned on is moving with a velocity of +v.

where t_A' is the time at earth in the inertial frame of the rocket. However, the observer in the rocket is not going to stay in that inertial frame.

The rocket turns on and off for an infinitesimal time.

The sign in this case designates direction. The rocket just AFTER the thrust is turned on is moving with a velocity of -v. It is still at the position designated 'x'.

Just an infinitesmal amount of time AFTER the rocket turns on the thrust on and off,
t_B' = t (1+[vx/c^2])/sqrt(1-[v/c]^2)

Please note that I used the FULL Lorentz transform here, which you never did. I have merely replace +v with -v. The physical change in velocity is brought about by force of short duration on the rocket.

I haven't assumed anything about the force except for these two hypotheses.
I) The duration of the force in the rocket frame is infinitesimal.
II) The force is large enough so the velocity of the rocket as changed from +v to -v.

This is a very large force. However, it doesn't matter how large it is at any time during the turn around. As long as we can agree on both 1 and 2, we can agree on what happens within special relativity.


So let us look at the difference in ages caused by the sudden turn around which in turn was caused by the thrust, which is a force. The difference in ages at the end of the trip is merely the difference in times during this turn around.

I take it you know enough algebra to do the math. The difference in ages is:

t_B'-t_A' = -2tvx/c^2


Thus, the rocket twin at the end of the trip will be younger than the earth twin by 2vx/c^2.

The twin in the rocket will never know what happened to the twin on earth in the interval -2tvx/c^2. He may determine that the clock on earth simply jumped ahead. However, he won't be aware of this illusionary jump right away because no signal can go faster than the speed of light.

Note: the earth twin is not affected by the thrust during turn around. The thrust affect the twin in the rocket only. The thrust is 'perceived' by the twin in the rocket only.

You can add as many observers as you like, going at all velocities and all times. However, what each observer observes depends on the forces on that observer. If you don't tell anyone what forces are on an observers, then no one can predict what the observer will observe.


I predict that you won't really address this calculation. You have repeatedly avoided the full Lorentz transformation and will continue to ignore it.


Your FIVE concrete mistakes have let you to ignore the time jump, 2tvx/c^2, in your calculations. I have presented five concrete mistakes that you will never acknowledge. However, they are concrete mistakes on your part.

Concrete is not nit picking. I have shown you specific mistakes. You have not chosen to show how any of time is wrong. Every time I show you a concrete mistake, you present a new concrete mistake.

Your idea I guess is that it is a balance. If I present a number of concrete mistakes, then you think you can 'win' presenting the number plus one of contradictions made by Einsteinians.

It doesn't work that way. Unless you can provide a concrete reason that your statements are not concrete mistakes, no rational person can believe you.

Even if you find a real inconsistency in what Einstein says, you will have still made five concrete mistakes. Further inconsistencies can not make you correct. Accusations of nit picking can not make you correct. You owe explanations for your five concrete mistakes.

You have said that you will address any once concrete mistake. I have presented FIVE concrete mistakes that you made.


BTW: Thank you for entertaining us.

 

[wogoga]

If my refutation (post #66) of Einstein's twin-paradox resolution was wrong then you would be able to show which point is wrong:

1. According to Einstein, reciprocal time dilation during inertial motion "is more than compensated by a faster pace" of resting twin U1 during direction-reversal of U2.
2. This "faster pace" of U1 is explained by a fictitious "homogenous gravitational field" acting on U1.
3. Gravitational attraction implies (stronger, lower) gravitational potential.
4. Gravitational potential leads to gravitational time dilation.
5. Thus, Einstein explains the "faster pace" with gravitational time-dilation.
6. Yet gravitational time dilation of U1 is the opposite of "faster pace of U1".

The word, 'homogeneous,' means that it is everywhere the same. The gravitational FIELD is the same for both twins, U1 and U2, as well as all objects in between. The gravitational POTENTIAL which is caused by the FIELD , is different for U1 and U2.
Your error was in not understanding the word 'homogeneous'. The field acts on everything in the universe as observed by U1.

Concrete error # 4 and 5:

4) The effective source of gravity is BEHIND the rocket, not in front like you assume.

Ok. You are right. Insofar as Einstein uses a "homogeneous gravitational field", he uses an infinite mass attracting from x = x' = infinite. As the source is closer to direction-changing twin U2 than to U1, potential is stronger (lower) for U2 and time of U1 is less dilated, i.e. faster.

Thus, Einstein's resolution actually is (borderline) ingenious: He uses a gravitational field having a stronger effect (time dilation) on U2 in order to accelerate U1. Any concrete source having a stronger time-dilation effect on U2 also leads to a higher acceleration of U2.

In my honest attempt to simplify Einstein's argument and to make it more realistic, I unconsciously replaced a "homogeneous gravitational field" by a field caused by a concrete mass. By placing this concrete mass closer to U1, I could even drop as irrelevant Einstein's:

"An external force, acting upon U2 in the negative direction of the x-axis prevents U2 from being set in motion by the gravitational field."​

Thus the earth is effectively above the rocket. The earth is actually falling toward the rocket as though there were a large mass behind the rocket. Anything on the earth has a greater potential energy relative to when it arrives at the rocket.

Because the earth is farther away from the gravitational force than the rocket, the potential at the earth is HIGHER than at the rocket. This is why the rate of clocks on earth are going SLOWER than at the rocket.

This analogy makes the origin of Einstein's twin-paradox resolution, which I still consider untenable, easier to comprehend.

Sorry for having accused you of mistake where the mistake was mine.

Cheers, Wolfgang

 

[Reality Check]

Ok. You are right. Insofar as Einstein uses a "homogeneous gravitational field", he uses an infinite mass attracting from x = x' = infinite. ...

It looks like Darwin123 is right. You will continue to not understand the resolution of the twin paradox, confirm your existing concrete mistakes and make more concrete mistakes.

The full quote is

3. A homogenous gravitational field appears, that is directed towards the positive x-axis. Clock U1 is accelerated in the direction of the positive x-axis until it has reached the velocity v, then the gravitational field disappears again. An external force, acting upon U2 in the negative direction of the x-axis prevents U2 from being set in motion by the gravitational field.

A homogeneous gravitational field is a gravitational field that is homogeneous! This has nothing to do with infinite masses at infinity. The context suggests that the field is uniform (homogeneous) since it replaces a uniform acceleration.
Einstein takes acceleration and replaces it with an equivalent gravitational field. That field has nothing to do with mass. SIX concrete mistakes now?

An infinite (as in tending toward infinity) mass has an infinite gravitational field causing infinite accelerations. SEVEN concrete mistakes now?

I would say that is best to forget about the gravitational field of Earth since that will confuse you even further, wogoga.
Think of a twin paradox in on otherwise empty universe as stated in the paper. There is an "at home" clock at one point in space (U1). There is a travelling clock (U2) that accelerates, travels to another point in space, accelerates again, travels back to the first clock and accelerates a third time to come to rest.

 

[Darwin123]

Ok. You are right. Insofar as Einstein uses a "homogeneous gravitational field", he uses an infinite mass attracting from x = x' = infinite. As the source is closer to direction-changing twin U2 than to U1, potential is stronger (lower) for U2 and time of U1 is less dilated, i.e. faster.

Okay, I checked the full Lorentz transform. I copied it wrong. Allow me to fix the arguement.

Just an infinitesimal amount of time BEFORE the rocket turns on the thrust on and off,
t_A' = (t-[vx/c^2])/sqrt(1-[v/c]^2)
<corrected>

Note that I used the FULL Lorentz tranform here, which you never did.

The sign in this case designates direction. The rocket just before the thrust is turned on is moving with a velocity of +v.

where t_A' is the time at earth in the inertial frame of the rocket. However, the observer in the rocket is not going to stay in that inertial frame.

The rocket turns on and off for an infinitesimal time.

The sign in this case designates direction. The rocket just AFTER the thrust is turned on is moving with a velocity of -v. It is still at the position designated 'x'.

Just an infinitesmal amount of time AFTER the rocket turns on the thrust on and off,
t_B' = (t+[vx/c^2])/sqrt(1-[v/c]^2)
<corrected>

Please note that I used the FULL Lorentz transform here, which you never did. I have merely replace +v with -v. The physical change in velocity is brought about by force of short duration on the rocket.

I haven't assumed anything about the force except for these two hypotheses.
I) The duration of the force in the rocket frame is infinitesimal.
II) The force is large enough so the velocity of the rocket as changed from +v in A to -v in B.

This is a very large force. However, it doesn't matter how large it is at any time during the turn around. As long as we can agree on both 1 and 2, we can agree on what happens within special relativity.


So let us look at the difference in ages caused by the sudden turn around which in turn was caused by the thrust, which is a force. The difference in ages at the end of the trip is merely the difference in times during this turn around.

I take it you know enough algebra to do the math. The difference in ages is:

t_B'-t_A' = -2vx/c^2
<corrected>

Thus, the rocket twin at the end of the trip will be younger than the earth twin by 2vx/c^2.

I have the Lorentz transform correct now, anyway. You can check against the full Lorentz transform given in Einstein's 1905 article or against Lorentz's articles.

Anyway, you admitted to two concrete errors.
5) Time can be perceived discontinuously if the forces are discontinuous.
4) The potential is higher for the earth twin than for the rocket twin who is in the process of turning around.

So you still have three to go !-)

 

[Darwin123]

It looks like Darwin123 is right. You will continue to not understand the resolution of the twin paradox, confirm your existing concrete mistakes and make more concrete mistakes.

You are being a tiny bit unfair to Wogoga.

To be fair, Wogoga did admit at least one (two?) of his mistakes. He is right now with concerns to the ‘fictitious potential’ being larger near the earth than at the rocket which is turning around.

I also am fairly certain that he did not directly get that error from Einstein. I think he read the Wikipedia article, which got the theory just a little wrong.

https://en.wikipedia.org/wiki/Gravitational_time_dilation
‘The stronger the gravitational potential (the closer the clock is to the source of gravitation), the slower time passes.’

The writer should have said:
'The stronger the gravitational potential (which is equivalent be closer to a fictitious gravitational mass), the slower time passes.'

The text is stating that there is a literal mass which is the source of the gravitation. There is no literal mass, as you pointed out. However, Wogoga acknowledged that in his last post.

Another example of why Wikipedia should never be used as a sole reference!

However, we should both congratulate Wogoga for getting that far. I know it was hard work. I take just a little credit for this increment of progress. I also worked very hard for it!

 

[wogoga]

In this calculation, the "speeding ahead" of 199.9 year of U1 with respect to U2 during direction-reversal does not show up explicitly.

The reason obviously is a consequence of the necessary renaming of the direction-reversal event from the future to the past (see #106). Just before and just after direction-reversal, resting twin U1 is at x' = -1 LY (i.e. at a Lorentz-contracted distance of 1 light-year on the negative x-coordinate-side of travelling twin U2). From equation [4] of #75, valid before direction-reversal, we derive for a given time t' = T':

[4] t = 100 t' + 99.995 x' = 100 T' - 99.995 year
​

From equation [8], valid after direction-reversal, we derive for t' = T':

[8] t = 100 t' - 99.995 x' = 100 T' + 99.995 year
​

This means: Assuming simultaneity of travelling U2, U1 is 99.995 years in past just before direction-reversal. In the return-trip frame F'(-v) however, an object at rest with the same relative position x' = -1 LY is 99.995 years in the future. Thus, during direction-reversal of U2, the Earth with U1 migrates 199.9 years from the past to the future.

Such changes from the past to the future or the other way round are not more astonishing than huge distance changes inherent in Special Relativity:

Before U2 starts the journey, the target is 100 LY away. After having reached travel speed, the distance to the target is Lorentz-contracted to 1 LY. During the arbitrarily short period of direction-reversal, U1 together with the whole Earth makes a huge journey of 198 LY relative to U2. At first U1 moves away from Lorentz-contracted 1 LY to the normal distance of 100 LY (when U2 is at rest relative to U1) and then comes back to the contracted 1 LY.​

Just an infinitesimal amount of time BEFORE the rocket turns the thrust on and off,
t_A' = (t-[vx/c²])/sqrt(1-[v/c]²)
…
Just an infinitesimal amount of time AFTER the rocket turns the thrust on and off,
t_B' = (t+[vx/c²])/sqrt(1-[v/c]²)

If you replace v with 0.99995 c and c with 1, then your equations transform to [2] of #75 and [6] of #106:

[1] x' = 100 x - 99.995 t . . [3] x = 100 x' + 99.995 t'
[2] t' = 100 t - 99.995 x . . [4] t = 100 t' + 99.995 x'

[5] x' = 100 x + 99.995 t . . [7] x = 100 x' - 99.995 t'
[6] t' = 100 t + 99.995 x . . [8] t = 100 t' - 99.995 x'
​

The difference in ages is: t_B' - t_A' = -2vx/c²
Thus, the rocket twin at the end of the trip will be younger than the earth twin by 2vx/c².

With v = 0.99995 c and a one-way distance x = 100 LY (see #43) your 2vx/c² results in a "difference in ages" of Dt' = 199.99 year, which comes close to the time difference of standard textbooks: 198.0099 year = 200.01 LY – 2.0001 LY (see table of #75). However, without omission of the Lorentz-factor 1/sqrt(1-[v/c]^2) = 100, you get a time difference Dt' = 19999 year when using the event {x=100 LY, t=0}.

The event {100 LY, 0 year} of frame F is not direct part of the solution. Using the forward-trip equations [1] and [2], it transforms this way:

{x = 100 LY, t = 0} --> {x' = 10000 LY, t' = -9999.5 year}​

Using the return-trip equations [5] and [6] it transforms this way:

{x = 100 LY, t = 0} --> {x' = 10000 LY, t' = +9999.5 year}​

If you are interested in understanding this and why and where Special Relativity works and where not, then see: Reciprocity of SR Length Contraction for Dummies

Cheers, Wolfgang

 

[Darwin123]

However, without omission of the Lorentz-factor 1/sqrt(1-[v/c]^2) = 100, you get a time difference Dt' = 19999 year when using the event {x=100 LY, t=0}.

I confess that I am not following this. I can't say you are wrong since I don't understand your words.

For example, I don't know what you mean by 'without omission of the Lorentz-factor'.

The time interval measured in each reference frame is determined by the subintervals of time each serves. The minimum number of intervals needed to describe the trip varies with the reference.

In the case of the inertial frame (i.e., earth twin), one needs to look at only one interval of time. Since the thrust does not act on the earth twin, one doesn't need to assume more than one interval. The earth twin measures a total time elapsed of 2X/v where X is the distance from earth to star and v is the velocity of the space ship. There is no time expansion necessary to calculate the interval of time as experienced by the twin on earth.

The assumption for both twin is that their clocks are not resynchronized once the rocket is launched from earth. The clocks of both ground and rocket are synchronized once on the launch pad. Their biological clocks were synchronized slightly earlier, when they were born. The clocks are not resynchronized even when the rocket engines fire near the distant star where turn around occurs. Therefore, you can not let t=t'=T even when the rockets fire.

Furthermore, the gravitational potential determined by the twin on earth is effectively constant. There is no 'fictitious gravitational field'. In other words, there is zero 'proper acceleration' of the twin on earth. There is no 'gravitational time dilation'. Therefore, the twin on earth uses the same 'inertial frame' to determine where the rocket is located at all times. The twin determines that the clock in the rocket is ticking slower than his by the same time dilation factor at all times. The twin on earth doesn't need to consider 'time contraction'.

The twin in the rocket is in a noninertial frame that consists of three parts: The time interval from earth to star where the rocket is effectively in an inertial frame, the time interval from star to earth where the rocket is effectively in an inertial frame, and the interval where the rocket is turning around where the thrust is nonzero. During the two time intervals where the rocket is in an inertial frame, the gravitational potential of the entire universe is constant. During the single time interval where the thrust is nonzero, the gravitational potential of the earth is much HIGHER than the gravitational potential of the rocket. Thus, there is a gravitational time contraction observed by the twin in the rocket during this time interval.

The total time that passes for the rocket twin is provided by adding up the time intervals in each section of the trip. The total that time passes for the earth twin is determined by a single time interval.

If v<<c, then the difference in ages is approximately what I just gave, dt = 2vX/c^2.

The event {100 LY, 0 year} of frame F is not direct part of the solution. Using the forward-trip equations [1] and [2], it transforms this way:

{x = 100 LY, t = 0} --> {x' = 10000 LY, t' = -9999.5 year}​

Using the return-trip equations [5] and [6] it transforms this way:

{x = 100 LY, t = 0} --> {x' = 10000 LY, t' = +9999.5 year}​

If you are interested in understanding this and why and where Special Relativity works and where not, then see: Reciprocity of SR Length Contraction for Dummies

I have no interest in reading an 'critique of relativity' that doesn't include the gravitational time dilation and signal propagation velocities less than the speed of light. It may be a wonderful theory without these details, but it is not a 'critique of relativity'.

Let me put it another way. I said earlier that the proper acceleration can not be negligible. I qualify that a bit. The proper acceleration can't be negligible if the gravitational time dilation is not negligible.

I wasn't sure what you said. It almost sounded like you came to agreement that the gravitational time dilation could not be negligible. I am not sure that you said that. However, if you did that then you were admitting that the proper acceleration can't be negligible.

I think we are back to my original rebuttal of your 'theory'.

 

[Darwin123]

{x = 100 LY, t = 0} --> {x' = 10000 LY, t' = +9999.5 year}​

If you are interested in understanding this and why and where Special Relativity works and where not, then see: Reciprocity of SR Length Contraction for Dummies

Cheers, Wolfgang

Your post on 'length contraction' contains at least one concrete mistake.
You have ignored proper acceleration when you considered the length of time effect.

I am not sure in my earlier post whether I figured out the length contraction caused by acceleration correctly. Never mind, someone else did. The length contraction caused by both proper acceleration and gravitation has been determined.

Note that this is not the same as elastic distortion. Elastic distortion is second order in |ax/c|. Basically, it is a nonlocal effect. Basically, elastic distortion is caused by the tidal (i.e., dipole) component of gravity. The relativistic effect is caused by a gravitational field which is approximately homogeneous.

Here is a


http://www.farmingdale.edu/faculty/peter-nolan/pdf/relativity/Ch07Rel.pdf
‘…
Comparison of length contraction by Lorentz-Fitzgerald Contraction and the length contraction equation caused by an acceleration.
a. Using the Lorentz-Fitzgerald contraction equation. What is the length of a meter stick at rest on earth, when it is observed by an astronaut moving at a speed of v = 1.61  106 m/s = 3,600,000 miles/hr.
b. Length contraction for an accelerated rod. To arrive at the speed of 1.61  106 m/s, the rocket ship accelerates at 9.80 m/s2. How far must the rocket travel to arrive at this velocity. Find the length contraction of the meter stick caused by this acceleration.
c. Compare the results of the Lorentz-Fitzgerald length contraction and the accelerated length contraction.
…
Hence the results obtained by the Lorentz-Fitzgerald length contraction and the accelerated length contraction are the same. That is, the length observed by the accelerating astronaut is the same length that we obtained by the Lorentz- Fitzgerald contraction.
The important thing here to observe is that we get the same results by using the Lorentz- Fitzgerald contraction as we do by considering a contraction as the result of gravity or an acceleration.’


Here is another discussion on length contraction where the posters are better informed. This interchange discusses length contraction.

The OP compares time dilation and length contraction. The OP asks why time dilation is permanent by length contraction is not permanent. The surprising answer is that the effect of length contraction is just as permanent as time dilation when one of the observers has a nonzero proper acceleration.

Both time dilation and length contraction have irreversible effects due to proper acceleration. Although the time interval and the length interval snap back to their inertial values when the proper acceleration is turned off, the center of mass position has advanced when the proper acceleration has turned off.

Your example doesn't show this. You made the concrete error that the center of mass of the meter stick is in its original position when the length of the meter stick has 'snapped back' to it original position.

So I found another 'concrete error' in you analysis of special relativity.

http://physics.stackexchange.com/qu...action-permanent-even-though-time-dilation-is
‘

…
The length of space passed is in fact permanently contracted. Without loss of generality, consider a particle moving at C. For it the space passed contracted to 0 and the time passed was 0. If the space travelled were not permanently contracted, the particle would not be permanently at the new location after 0 time.

Or, to summarize things in an easy to remember way: The effect of length contraction has the same kind of permanency on your odometer as time dilation does on your clock.’


Again, the analysis supposes that there are only local effects. The measuring instruments, both meter sticks and clocks, have to be so small that 'constitutive effects' are negligible. Therefore, the meter stick isn't elastically deformed. The meter stick can't flow like a fluid, either.

I note that you haven't discovered constitutive properties, yet. Those are fun. We can discuss those once you have agreed that 'PROPER ACCELERATION IS NOT NEGLIGIBLE'!

 

[fuelair]

You do not refute the twin paradox - it has bee.\n resolved for almost a century, wogoga.
That continued ignorance needs a

Simpler to just say someone's posts here need the laughing dog ad infinitum!!

 

[Perpetual Student]

The reason obviously is a consequence of the necessary renaming of the ...
...
Cheers, Wolfgang

That you have wasted all the time and energy you have expended here and elsewhere on this fantasy is very regrettable. Think of all the real physics you could have learned in the meantime, with the same effort, if you had dedicated yourself to studying the work of the any of the thousands of physicists who have capably dealt with this subject.
Frankly, your stubbornness saddens me.

 

[wogoga]

Thus, the rocket twin at the end of the trip will be younger than the earth twin by 2vx/c².

However, without omission of the Lorentz-factor 1/sqrt(1-[v/c]²) = 100, you get a time difference Dt' = 19999 year [instead of 199.99] when using the event {x=100 LY, t=0}.

I confess that I am not following this. I can't say you are wrong since I don't understand your words. For example, I don't know what you mean by 'without omission of the Lorentz-factor'.

You had claimed in #111 that the age-difference in the twin-paradox is two times vx/c². This claim is wrong for several reasons, e.g. because the Lorentz-factor of Langevin's twin-paradox is as high as 100 and cannot be ignored. You also somehow confuse time shift vx/c² of the time-transformation with time dilation itself.

If you were right, and twin-paradox time-dilation directly stemmed from the vx/c² time-shift then time-dilation would be a universal effect and not only an effect relevant in case of "relativistic" speeds. If v << c, time-shift vx/c² is a first-order effect whereas time dilation according to the Lorentz factor 1/sqrt(1-v²/c²) is a much smaller second-order effect.

The time shift vx/c² is necessary to explain that e.g. the speed of light from an astronomical object near the ecliptic does not change from 0.9999 c to 1.0001 in the course of a year. Once in a year, the Earth moves with 30 km/s in direction to the object, and half a year later, with 30 km/s away from the object. In case of a galaxy at a distance of 10⁷ light-years, the galaxy makes according to SR every year a time-shift cycle with amplitude of 0.0001*10⁷ = 1000 year. This migration from 1000 years in the past to 1000 year in the future and back during one Earth year is a substantial, first-order effect. Yet length contraction is only a second order effect. A speed of 30 km/s (with Lorentz-factor 1+5*10^-9) reduces a distance of 10⁷ LY only by 0.05 LY.

The vx/c² time-shift as a first-order effect also exposes as a myth the claim that the Lorentz transformation turns into the Galilei Transformation, if v << c:

"For relative speeds much less than the speed of light, the Lorentz transformations reduce to the Galilean transformation in accordance with the correspondence principle." (Wikipedia)​

By dropping the Lorentz-factor as a second-order effect, the Lorentz transformation does not reduce to the Galilean transformation:

x' = x - v t . . . t' = t​

Instead, the Lorentz transformation (here with c = 1) reduces to:

x' = x - v t . . . t' = t - v x​

If we drop the first-order effect vx of the time transformation, then we must also drop the first-order effect vt of the x-transformation, and as result we get the "zero-order" transformation:

x' = x . . . t' = t​

An even more fantastic and theology-like myth is the so-called Lorentz invariance of Maxwell's theory of Electromagnetism. (Maxwell's completely inconsistent theory, based on the premise of naïve realism that instantaneous actions-at-a-distance are impossible, is a wild conglomerate of findings of Maxwell's predecessors, contemporaries and of himself. Consecration and benediction by and from "Lorentz invariance" absolved Maxwell's theory from sins and inconsistencies.)

Cheers, Wolfgang
Changing one's world view due to new findings, better understanding and logical reasoning should not be confused with surrendering part of one's identity when brutally forced to change religion

 

[Darwin123]

By dropping the Lorentz-factor as a second-order effect, the Lorentz transformation does not reduce to the Galilean transformation:

x' = x - v t . . . t' = t​

Instead, the Lorentz transformation (here with c = 1) reduces to:

x' = x - v t . . . t' = t - v x​

If we drop the first-order effect vx of the time transformation, then we must also drop the first-order effect vt of the x-transformation, and as result we get the "zero-order" transformation:

x' = x . . . t' = t​

[/COLOR][/B]

Therefore, physicists DON'T drop the first order effect in either distance (x) or time (t). They only drop effects that are second order or higher when they take the Galilean limit. However, you apparently haven't thought out which effect is which. With what expansion are the effects in any order?

The expansions are usually made in terms of 'v/c'. In your units where 'c=1', 'v'. Okay, let 'c=1'. The Galilean limit neglects terms like v^2 and (vx). We do not ignore first order terms like 'v' or 'vx'.

The expansions that you are obviously thinking of are Taylor expansions in terms of 'v'. The other quantities in the Lorentz transformation of independent of 'v'. So both 'v' and 'vx' are first order, not second order.

What disappears is terms like 'v^2'. So the Galilean approximation is really,
sqrt(1-v^2)=1.

The reason one that the 'vx/c^2' term disappears is because for the observer on earth looking at the rocket, 'x=vt'. This is subjective. So in this case:

xv=(vt)t
(vt)t=t v^2
xv =t v^2

Thus, 'xv' is second order in 'v' for this observation only.

 

[Reality Check]

The reason obviously is a consequence of the necessary renaming of the direction-reversal event from the future to the past ...
f you are interested in understanding this and why and where Special Relativity works and where not, then see: Reciprocity of SR Length Contraction for Dummies

There is no reason there, wogoga - just random mathematics not based on SR or GR.

Reciprocity of SR Length Contraction for Dummies is an argument from ignorance or incredibility and debunked in that thread in the very next post by WhatRoughBeast!
25th January 2015: Once you start applying non-relativistic common sense to relativistic scenarios, there's no telling what sort of trouble you can get yourself into. And it establishes that your ideas are not to be taken seriously.
Your response is a bit of a rant about religion/dogma without any actual science.

Now we have a track record of 10 months of ignorance of SR, wogoga.