Refutation of Special Relativity for Dummies

[Darwin123]

I must admit that what you write here seemed at first completely misguided to me, because it is possible to make the acceleration period of direction-reversal arbitrarily short in comparison with the two periods of inertial motion, by increasing the distance from resting U1 to the reversal point of travelling U2. Therefore the effect of time contraction due to acceleration can be made negligibly small compared to the effect of time dilation due to inertial motion.

You never showed this. In fact, it is not completely true even in terms of Newtonian physics.

A force acting over any finite length of time generates a finite impulse In Newtonian physics . The impulse represents a change in momentum no matter how small you make the time interval. If you halve the time interval but double the force, you get the same impulse. No matter how many times you do this, the impulse remains constant.

The same logic applies to time contraction. You can halve the interval of time any number of times as long as you double the force an equal number of times. The time contraction would be the same.

Acceleration can still be significant even if it occurs on a very short time period. Acceleration in a round trip is significant no matter how short that you make the acceleration. Your denial of this fact doesn’t invalidate the fact.

Yet from Wheeler's formula of your post #78 I had to learn that my above conclusion is based on a premise, namely that time contraction due to acceleration is independent of the location where it takes place. In any case, I'll comment on Wheeler's formula.

.

There is no need to restrict oneself to ‘uniform acceleration’ to show the self consistency of sSR. The uniform acceleration case has a very simple expression. The more general case of an acceleration that is changing is more complicated.


I only gave you the Wheeler formula because you said that you didn't want to get into the advanced mathematics. I interpreted this to mean that you didn't want to see calculus. Even you have the mathematical background to evaluate the simple case of uniform acceleration. I could show you another case which has a simple expression. However, you are making a very concrete error even when 'analyzing' Wheelers expression.

Note that I have not used 'the Lorentz-factor mass energy-increase'. I don't think that Wheeler even used it. Yet, you wrote the following:

I Thus, insofar as we derive Lorentz-factor mass-energy-increase from the Lorentz transformation, the transformation is the premise, and mass-energy-increase is the conclusion.

This has nothing to do with your conclusions. It doesn't really matter whether the mass-energy relations are a premise or a conclusion. Acceleration is still significant in SR.


I note another mistake in your analysis.


You keep on claiming that 'we' used the Lorentz transformation. In fact, you never derived anything using the complete Lorentz transformation.

The Lorentz transformation is not what you think it is. You keep on conflating ‘Lorentz time dilation’ with the ‘Lorentz transform’. Your schedule of events does not include all the terms of the Lorentz transform. Premise or not, you never used it.

https://en.wikipedia.org/wiki/Lorentz_transformation
‘These are the simplest forms. The Lorentz transformation for frames in standard configuration can be shown to be…
<Complete Lorentz transformation, not the time dilation formula>’

You are claiming to have found a logical contradiction in the Lorentz transformation. Premise or not, you can't have found such a contradiction because you never used it.

I suspect that you haven't even read the expressions for the Lorentz transformation. You don't know the Lorentz transformation. I will bet that you don't even know the Lorentz transformation.

I will bet that you can't even cut and paste the Lorentz transformation into a post. You are so invested in your emotional position, that you can't even show the Lorentz transformation.

I have noted that you have provided your 'analysis' more than ten times. You have never once shown us the real Lorentz transform. Your calculations use a truncated version of the Lorentz transform.

Your claim that the acceleration is insignificant is effectively truncating the Lorentz transform. This is a concrete mistake. Every time you ignore the 'vx/c^2' term, you are truncating the Lorentz transform.

That is my concrete point. Tell us why you are ignoring the 'vx/c^2' term. Or admit that you don't even know what the Lorentz transform is.

You can't tell us that Einstein is a 'con man' if you haven't examined the 'con'. The Lorentz transformation isn't completely Einstein's, anyway. They were derived by H. A. Lorentz.

Einstein only worked out some of the physical consequences of the Lorentz transformation. It seems rather silly to slam Einstein for a set of equations called 'the Lorentz transform'. If you think then 'Lorentz transformation' is a con, then you should call Lorentz a con man.

Lorentz gave Einstein credit for relativity, by the way. Lorentz himself pointed out that he had not worked out the physical consequences of his equations. Relativity is actually the physical interpretation of the Lorentz transform. However, the equations themselves were from Lorentz.

BTW: I have read and own books and articles by H. A. Lorentz. You could call me a Lorentz fan. Lorentz wrote a book entitled: The Einstein Theory of Relativity. Really, the book is in front of me now! So if SR is a con, then Lorentz is one of the con men!

You should do your calendar using the full Lorentz transformation. If you don’t use the full Lorentz transformation, then you are not using SR.


Maybe your biggest mistake is your use of the word 'we'. Please use the word 'I' next time!

 

[wogoga]

... it is possible to make the acceleration period of direction-reversal arbitrarily short in comparison with the two periods of inertial motion, by increasing the distance from resting U1 to the reversal point of travelling U2. Therefore the effect of time contraction due to acceleration can be made negligibly small compared to the effect of time dilation due to inertial motion.

Yet from Wheeler's formula of your post #78 I had to learn that my above conclusion is based on a premise, namely that time contraction due to acceleration is independent of the location where it takes place. In any case, I'll comment on Wheeler's formula.

This is Wheeler's time-dilation formula presented by Darwin in post #78:

dt' = dt (1-a*x/c²) / sqrt(1-v²/c²)​

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 dynamic acceleration of the observer.​

The formula implies that time dilation depends on distance x between U1 and travelling clock or twin U2. And this implication is impossible:

Let us assume some space stations on the way from U1 on Earth to the target of travelling U2. All these space stations are at rest relative to the Earth, and time runs identically (apart from small gravitational effects) with identical simultaneity. Therefore, the trip of U2 from the Earth to the target must take the same time with respect to all of them. This is only possible if the factor of time dilation of U2 is the same. According to the above formula however, this factor depends on distance x from U2, which is different for every space station.

There are further problems. In the case of an acceleration of a = c²/x the formula reduces to: dt' = 0 dt. This means: Time of U1 runs infinitely fast with respect to U2. And if acceleration a is bigger than c²/x (or smaller than -c²/x) then time of U1 runs from the future to the past!

By the way, acceleration a = c²/x, necessary for such strange effects, is very small if distance x is big enough. In case of a distance of 100 LY we get:

a = c² / (100 year * c) = c / 100 year = 0.095 m/s²​

Note that my formula reduces to the traditional 'Lorentz time dilation formula' when ... a = 0. ...

I first got a simple version of it in the book, 'General Relativity' by Wheeler. However, he used both Greek letters and units where c=1. He also didn't really make the role of forces very clear. ...

I found the formula easy to derive from the Lorentz transform and the definition of force common to both Newtonian physics and special relativity. It just took a little calculus. Perhaps you can show how I am wrong without calculus using your incredible insight.

Actually your formula is very interesting. I've never seen it before and unfortunately I cannot find it elsewhere, so I fully rely on your presentation. The formula could result from an attempt to resolve the twin paradox along the lines of Einstein 1918 with a significant difference:

According to Einstein, acceleration of travelling clock U2 has no effect on time dilation. Therefore he uses a fictitious gravitational field acting on resting clock U1. The inventor of the formula seems to replace Einstein's fictitious field acting on U1 with U2's own acceleration.

During inertial motion acceleration a is zero, and as you have stated, the formula reduces to "normal time dilation":

dt' = dt /sqrt(1-v²/c²) = y dt​

where y ("gamma") is the Lorentz factor. In the special case discussed here, where v = 0.99995 c and y = 100, we get:

dt' = 100 dt​

This means that a time interval dt' = 100 sec of the travelling twin corresponds to an interval dt = 1 sec passing on Earth. This is time dilation (slowing) of resting U1 with respect to travelling U2. We conclude that this relates to Einstein's:

"During the partial processes 2 and 4 the clock U1, going at a velocity v, runs indeed at a slower pace than the [in K'] resting clock U2."​

Thus, also this formula agrees with Einstein and my analysis: With respect to U2, during inertial motion of totally 2.0001 year, only 0.02 year pass in U1. (Otherwise, if U1 were a light-clock then its inside light-pulse would not move at c relative to U2, see #43).

Now let us deal again with the whole of the formula presented by you:

dt' = dt (1-a*x/c²) / sqrt(1-v²/c²)​

A formal analysis shows that, by replacing a*x with v², the formula results in

dt' = dt * sqrt(1-v²/c²) = dt / y​

which is the exact opposite of "normal time dilation". In this way, the inventor of the formula pays tribute to the fact that insofar as time of A runs slower with respect to B, time of B runs faster with respect to A, and insofar there is time dilation of B with respect to A, there is also time contraction of A with respect to B (see SR Simultaneity, Contraction & Expansion).

In any case, the formula presented by you in no way refutes my analysis of the twin paradox. The formula cannot even be a direct consequence of the Lorentz transformation, as this transformation does not deal with acceleration (maybe apart from proper acceleration). The formula is probably only a failed attempt to resolve the twin paradox or similar SR problems.

Cheers, Wolfgang

Exaggeratedly worded: Insofar as Einstein is overestimated, he was wrong; insofar Einstein was right, he is underestimated

 

[aleCcowaN]

dt' = 100 sec

 

[Reality Check]

...
In any case, the formula presented by you in no way refutes my analysis of the twin paradox. ...

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

 

[Reality Check]

According to Einstein, acceleration of travelling clock U2 has no effect on time dilation.

According to Einstein and every other person who has learned Special Relativity, wogoga, acceleration of travelling clock U2 has no effect on SR time dilation because SR is for inertial frames of reference!
Therefore he uses an equivalent gravitational field as in General Relativity.

 

[Darwin123]

According to Einstein and every other person who has learned Special Relativity, wogoga, acceleration of travelling clock U2 has no effect on SR time dilation because SR is for inertial frames of reference!
Therefore he uses an equivalent gravitational field as in General Relativity.

I have to disagree with you, there. You are wrong because a clock does not have to be part of an inertial frame of reference, even in SR. A clock that is part of an inertial frame are not affected by dynamic acceleration because there is no force on the clock. However, a clock that in an accelerated frame is being acted on by a force that can be expressed in a Lorentz invariant form.

The clock, whether or not it is in an inertial frame, can be analyzed by dynamic part of SR. The kinematics of SR may be insufficient to describe the workings of the clock. The phrase 'time dilation' is often restricted to the kinematic part of SR. However, the phrase 'time dilation' does not apply to all clocks. So identifying 'time dilation' with the workings of a clock is not valid.


The difference between kinematic and dynamic becomes important here. The kinematic part of SR is the part of SR which does not vary in any way with the forces between particles (or whatever is equivalent to forces). The kinematic part of SR is sufficient to compare clocks that are never acted on by an external force. However, the kinematics of SR are insufficient to compare clocks which have ever been acted on by an external force. The formula for time dilation was derived using only the kinematics of SR. Therefore, the standard formula for time dilation can onl be used to compare clocks that are never subject to an external force. Both kinematics and dynamics are necessary to compare clocks where at least one clock has been acted on by an external force.


So your statement is a little bit wrong because SR applies to all clocks, whether or not they are in an inertial frame. However, the standard formula for time dilation applies ONLY to those clocks that are part of an inertial frame. Some clocks are not part of an inertial frame.

So time dilation in the standard form does not apply to all clocks. Einstein did not say that time dilation applies to all clocks. Wogoga is making the claim that Einstein said that time dilation applies to all clocks.

Time dilation for clocks without external forces IS ALWAYS symmetric. However, time dilation is SOMETIMES NOT symmetric if any of the clocks are being acted on by an external force.

Hey, I am not saying that you really got it wrong. I am saying you are not being precise. Certain people we know can twist a minor imprecision into a major error.

I think the fun of the forum is correcting a common misconception. I think a lot of people, including scientists outside the field of physics, often confuse dynamics with kinematics. I think there a many lurkers who don't realize that SR has two parts: kinematics and dynamics.

The real physics is always in the dynamics. Kinematics is just geometry. You need kinematics to describe the dynamics. Dynamics does not stand on its own. However, kinematics without dynamics is only good for mathematical play. Kinematics by itself is insufficient to describe what a physical system does.


Einstein gave a very good analysis of a set of clocks being acted on by external forces. These forces were being exerted by the earths surface. To do this, he compared the action of each clock to a clock that was not being acted on by any significant force. This clock was one the pole of the spinning earth. Ti

Please note that in this analysis Einstein uses the formula for centripetal acceleration. He doesn't make a big deal about it. He doesn't call it to the readers attention. However, he does use it. That is why the clocks are not in an inertial frame.

 

[Darwin123]

In any case, the formula presented by you in no way refutes my analysis of the twin paradox. The formula cannot even be a direct consequence of the Lorentz transformation, as this transformation does not deal with acceleration (maybe apart from proper acceleration).

Precisely! This is your ‘concrete error’. You have been assuming that the ‘proper acceleration’ is insignificant. The proper acceleration can not be insignificant in a round trip!

Thank you for introducing the term, ‘proper acceleration’, to me. I have never heard the term 'proper acceleration' though I have used the concept often. I had come to call it the ‘dynamic acceleration’ since it is intimately connected with force. 'Proper acceleration' is 'dynamic acceleration'. It is part of the dynamics of SR.

So here is a concrete example of how a mistake you made. The proper acceleration is not negligible in the examples that you gave. You can not keep cutting the duration of an impulse down without increasing the proper acceleration caused by the impulse. Thus, the proper acceleration can NEVER be negligible in a round trip.

An accelerometer measures the quantity ‘F/m’. So that is the connection to my formula. When I said that ‘a=F/m’, I meant the acceleration measured by an accelerometer.

https://en.wikipedia.org/wiki/Proper_acceleration
In relativity theory, proper acceleration[1] is the physical acceleration (i.e., measurable acceleration as by an accelerometer) experienced by an object. It is thus acceleration relative to a free-fall, or inertial, observer who is momentarily at rest relative to the object being measured.
…
For constant unidirectional proper-acceleration, similar relationships exist between rapidity η and elapsed proper time Δτ, as well as between Lorentz factor γ and distance traveled Δx. To be specific:
,
where the various velocity parameters are related by
.’

…
Hence the round-trip time on traveler clocks will be Δτ = 4(c/α) cosh−1(γmid), during which the time elapsed on map clocks will be Δt*= 4(c/α) sinh[cosh−1(γmid)].’

The above formulas are a generalization of the formulas that I presented. When the article says ‘measurable by an acceleration’ it means ‘caused by a force on the observer.’ The observer can only measure an acceleration if it is caused by a force.


So you knew the concept all along. How come you never used it in your calculations before?

Since you are apparently knowledgeable about ‘proper acceleration’, I will from now on use the concept to rebut your claims. I will do this in one of seven ways.

1) I will use the formulas given in the Wikipedia link that I just posted for ‘proper acceleration’.

2) I will use the full Lorentz transformation rather than the dilation formula that you use.

3) I will no longer respond to your claims that ‘acceleration is insignificant’ or ‘I used the Lorentz transformation’.

4) Every time you use a noninertial reference frame, I will point out that the proper acceleration is nonzero.

5) Every time I read a post where you claim to use the Lorentz transform, I will ask you to write the full Lorentz transform out.

6) I will occasionally calculate the proper acceleration for you, especially when you claim the acceleration is insignificant.

7) Instead of writing the SR formulas out, I will merely link to the appropriate Wikipedia article.


You can access Wikipedia as well as I can. So you can't claim that I haven't written out the formula clearly.

To start with, read the link that you just posted. Look up 'proper acceleration'. See how 'proper acceleration' is used in SR. I suggest anyone interested in this thread also read that article on 'proper acceleration.' Proper acceleration is an important concept in SR. Popular science texts don't place enough emphasis on it. However, the concept is available to anyone who could open up a Wikipedia article.


Anyone can find the full ‘Lorentz transformation’ and the definition of ‘proper acceleration’ in Wikipedia. The formulas for both are there. In fact, the full Lorentz transformation is in Einsteins 1905 article. Anyone who has actually read articles by Einstein will have read the ‘Lorentz transformation.’


In fact, I have asked you in previous posts to produce the full ‘Lorentz transformation’. I have challenged you and others to write the Lorentz transformation out. You never wrote it out. You only repeat the false claim that ‘I used the Lorentz transformation.’ I assumed that you merely did not know what it was. Now I realize that you have been holding out on us!

 

[Darwin123]

According to Einstein, acceleration of travelling clock U2 has no effect on time dilation.

That is absolutely not true. In fact, section 4 of his 1905 article uses a formula for centripetal acceleration. He derives the 'time dilation' of clocks rotating with the earth on the assumption that the clocks on the surface are subject to centripetal acceleration. '

This is another 'concrete mistake' that you made. You apparently have not actually read any of Einstein's articles. Or at least you did not read them carefully. You certainly have not paid Einstein's 1905 article with much attention.

'Centripetal acceleration' in this case is equivalent to 'proper acceleration'. However, lets deal with that after I talk about another concrete mistake.

In any case, the formula presented by you in no way refutes my analysis of the twin paradox. The formula cannot even be a direct consequence of the Lorentz transformation, as this transformation does not deal with acceleration (maybe apart from proper acceleration).

Everybody, please note. Wogoga himself found an article which shows how SR deals with acceleration. In fact, he acknowledged in the above paragraph that SR deals with 'proper acceleration'.

Wogoga has admitted that SR deals with some type of acceleration. Please, don't let him forget it!

The article that YOU cited describes how force is included in SR. The ‘proper acceleration’ has a ‘proper force’ associated with it. It is this ‘proper force’ that breaks the symmetry in special relativity problems.

The concrete error in your calculations are that your calculations did not include either ‘proper acceleration’ or ‘proper force’. You didn’t actually quote from the article that you cited. Allow me to quote the part that connects mechanical force with acceleration.

https://en.wikipedia.org/wiki/Proper_acceleration
‘The total (mechanical) force which is calculated to induce the proper acceleration on a mass at rest in a coordinate system that has a proper acceleration, via Newton's law F = m a, is called the proper force. As seen above, the proper force is equal to the opposing reaction force that is measured as an object's "operational weight" (i.e., its weight as measured by a device like a spring scale, in vacuum, in the object's coordinate system). Thus, the proper force on an object is always equal and opposite to its measured weight.’


I conjecture that when you said that the acceleration was insignificant, you were talking about the ‘coordinate acceleration’. Coordinate acceleration is all acceleration including ‘point of view’ acceleration which doesn’t depend in forces.


Everyone has remarked that you are not distinguishing between inertial and noninertial frames. You don’t seem to know the difference.

Well, here is a concrete definition of ‘inertial frame’.

https://en.wikipedia.org/wiki/Proper_acceleration
‘A corollary is that all inertial observers always have a proper acceleration of ZERO.’


Your concrete mistake can be stated another way. Some of the ‘inertial reference frames’ that you have used have a NONZERO proper acceleration. For example, the rocket which turns on its engines has a proper force equal to the thrust.

I also have also presented a concrete imprecision in your critics in order to be fair.

One does NOT have to use all of GR to determine the effect of acceleration. One can use the SR part of GR to include the effect of all forces that are not gravitational. The salient point is that in SR only the ‘proper force’ affects time and space.

So it is wrong to say that SR can not handle physics in a noninertial frame. Sorry, RealityCheck and all the other posters who have said otherwise.

In fact, SR has proven very useful in understanding the dynamics of accelerating electric charges. The title of Einstein’s paper was ‘On the Electrodynamics of Moving Bodies.’ The moving bodies referred to in the title were accelerating. Otherwise, there would be no electrodynamics.

In this 1905 paper, Einstein uses the word ‘force’ exactly 7 times. He is actually referring to what we now call the ‘proper force’. If Wogoga hadn’t found that Wikipedia reference, I would not know that there was a newly coined name to ‘mechanical force’. Hence, I have to thank Wogoga even though he is still wrong!


I and others have played with an approximation where gravity is treated as a force like any other force. This approximation is not entirely accurate because of the equivalence principle. This is not even accurate to first order in velocity (v/c), as the solar occultation experiment showed. However, I believe this approximation is a good heuristic for explaining how the twin conundrum is resolved in relativity.


Let it suffice to say that gravity is like other forces IN SOME WAYS but not in others. If you understand how the rockets thrust affects the perception of time, then we can start on how gravity affects the perception of time. When you are done understanding proper acceleration in special relativity, we can discuss space time curvature in general relativity.

You need more concrete?

 

[wogoga]

According to Einstein, acceleration of travelling clock U2 has no effect on time dilation.

That is absolutely not true. In fact, section 4 of his 1905 article uses a formula for centripetal acceleration. He derives the 'time dilation' of clocks rotating with the earth on the assumption that the clocks on the surface are subject to centripetal acceleration.

Darwin123, for quite some time now, I have been astonished at your ability to twist truth and reality. That other "skeptics" normally won't correct you as long as you fight for orthodoxy and against heresy, only shows that "skeptics" are more interested in fighting heterodoxy than interested in truth.

Einstein in "section 4 of his 1905 article" even tries to avoid acceleration by arriving at a "continuously curved line" via a "polygonal line" to which acceleration cannot be applied.

Einstein in §4 Physical Meaning of the Equations Obtained in Respect to Moving Rigid Bodies and Moving Clocks:

"What is the rate of this clock, when viewed from the stationary system?

Between the quantities x, t, and t', which refer to the position of the clock, we have, evidently, x = v t and

t' = (1–v²/c²)^-1/2 (t – v x/c²)​

Therefore,

t' = t (1–v²/c²)^1/2 = …​

… It is at once apparent that this result still holds good if the clock moves from A to B in any polygonal line, and also when the points A and B coincide.

If we assume that the result proved for a polygonal line is also valid for a continuously curved line, we arrive at this result: … Thence we conclude that a balance-clock at the equator must go more slowly, by a very small amount, than a precisely similar clock situated at one of the poles under otherwise identical conditions."​

Cheers, Wolfgang

Exaggeratedly worded: A typical "skeptic" is a reincarnated religious zealot confounding science with religion

 

[wollery]

Darwin123, for quite some time now, I have been astonished at your ability to twist truth and reality. That other "skeptics" normally won't correct you as long as you fight for orthodoxy and against heresy, only shows that "skeptics" are more interested in fighting heterodoxy than interested in truth.

Einstein in "section 4 of his 1905 article" even tries to avoid acceleration by arriving at a "continuously curved line" via a "polygonal line" to which acceleration cannot be applied.

Einstein in §4 Physical Meaning of the Equations Obtained in Respect to Moving Rigid Bodies and Moving Clocks:

"What is the rate of this clock, when viewed from the stationary system?

Between the quantities x, t, and t', which refer to the position of the clock, we have, evidently, x = v t and

t' = (1–v²/c²)^-1/2 (t – v x/c²)​

Therefore,

t' = t (1–v²/c²)^1/2 = …​

… It is at once apparent that this result still holds good if the clock moves from A to B in any polygonal line, and also when the points A and B coincide.

If we assume that the result proved for a polygonal line is also valid for a continuously curved line, we arrive at this result: … Thence we conclude that a balance-clock at the equator must go more slowly, by a very small amount, than a precisely similar clock situated at one of the poles under otherwise identical conditions."​

Cheers, Wolfgang

Exaggeratedly worded: A typical "skeptic" is a reincarnated religious zealot confounding science with religion

Actually that's one way that centripetal acceleration is derived, by looking at circular motion as a series of straight line segments and looking at what happens to the velocity vectors, then taking the limit as the line segments decrease in length to form a circle rather than a polygon. Einstein was using centripetal acceleration, he just wasn't saying so explicitly.

And you'll note that he derives a time dilation for the clock at the equator.

Which is under centripetal acceleration.

 

[Reality Check]

...Einstein in "section 4 of his 1905 article" even tries to avoid acceleration by arriving at a "continuously curved line" via a "polygonal line" to which acceleration cannot be applied.

Which is basically the definition of acceleration, wogoga !
Velocity is a vector.
A vector has both size and direction.
A change in direction s a change in velocity
A change in velocity is acceleration!
That is the segments in the polygonal line. Taking the limit to get a continuously curved line is basic mathematics.

This is the paper that created SR so no one expects Einstein to have a treatment of acceleration within SR. He has a series of velocity boosts (the polygonal line) and extends it to a continuously curved line.

This is repeated in the second Einstein citation.

We have to wonder abut the emphasis on Einstein and paper a century old - why are you not citing modern textbooks, wogoga?

 

[Darwin123]

Einstein in "section 4 of his 1905 article" even tries to avoid acceleration by arriving at a "continuously curved line" via a "polygonal line" to which acceleration cannot be applied.

Einstein in §4 Physical Meaning of the Equations Obtained in Respect to Moving Rigid Bodies and Moving Clocks:

"What is the rate of this clock, when viewed from the stationary system?

Between the quantities x, t, and t', which refer to the position of the clock, we have, evidently, x = v t and

t' = (1–v²/c²)^-1/2 (t – v x/c²)​

Therefore,

t' = t (1–v²/c²)^1/2 = …​

… It is at once apparent that this result still holds good if the clock moves from A to B in any polygonal line, and also when the points A and B coincide.

If we assume that the result proved for a polygonal line is also valid for a continuously curved line, we arrive at this result: … Thence we conclude that a balance-clock at the equator must go more slowly, by a very small amount, than a precisely similar clock situated at one of the poles under otherwise identical conditions."​

<I removed your ad hominem remark and ill-posed accusation.>

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What you said isn’t true. Einstein has not removed acceleration by replacing the curve with a polygon. Einstein is using the definition of acceleration as first presented by Newton in Principia.

If Einstein is trying to remove acceleration by replacing the curve with a polygon, then Newton is removing acceleration by replacing the curve with a polygon. Because Newton first used this replacement operation to calculate acceleration. Acceleration is merely the limit of this operation where the number of sides of the polygon is increased indefinitely.

This is actually the beginning of calculus. Einstein is repeating the first steps with a slight change to take into account the delay time of EM forces. He could have used calculus notation, but he decided to use basically the same diagram as Newton used.

Einstein is using the same hypothesess as Newton with regards to acceleration. Newton in ‘Principia’ calculates acceleration by replacing curves with polygons. If relativity is wrong with regards to this hypothesis, then so is Principia.

The hypothesis that a polygon can approximate a curve is part of calculus, not relativity. Einstein did not invent calculus. He only uses it as does every physicist from Newton on. In fact, Newton is often given credit for ‘inventing’ calculus. You are not disagreeing with anything particular to Einstein.

You are showing that you really don’t understand either calculus or Newtonian physics. You say that you are busting Einstein but you are really attacking simple calculus. Basically, Einstein is reviewing the concept of limit using geometric pictures.

So it isn't really relativity that you object to, it is calculus. It isn't really Einstein that you object to, it is Newton. You may be right that I am defending the orthodoxy of science. However, it is not the orthodoxy of Einstein. It is the orthodoxy of calculus.

I have a copy of ‘Principia’ in my hand. I am looking at a dozen figures where smooth curves are approximated with polygons. However, I can’t post the entire book. So I present the following link with an appropriate quote from that link.

http://nonagon.org/ExLibris/newton-keplers-laws
‘The polygon ABCD ... approximates the orbit and all the more closely the shorter the intervals between impulsive forces in this thought experiment.
<see associated illustrations where a curve is approximated as a polygon>.
…
These diagrams are from Brackenridge, the big one based on the Principia. Bc is the course the motion would take were there no impulsive force acting at B. Since the time intervals are equal, AB = Bc, SB is a median of ΔSAc, and ΔASB has the same area as ΔBSc. The action at B is the result of two effects, much like projectile motion on the surface of the earth is a result of a horizontal or slanted displacement as the projectile moves along that direction at constant velocity, combined with the downward displacement caused by the earth's gravitational acceleration. The first, non-accelerating motion is analogous to that experienced by the planet in moving from B to c, as it would unimpeded by any acceleration; the second, accelerated motion is analogous to that imparted by the earth's gravity, but now it is an impulsive force acting at B and directed towards S. ‘


Read the above link, please. Read 'Principia' if you can. If you think that Newton is wrong, then please tell us.


You have never directly rebutted a single objection that has been presented to you. Every time that someone points out a concrete mistake that you have made, you start to malign Einstein. It doesn't matter what the mistake was. The poster seldom mentions the name of Einstein.

So I don't think you challenge is real. You have never presented a scientific rebuttal to the corrections we send you. You throw sand in our eyes by naming Einstein.

You never make a direct accusation of Newton or Leibnitz, the makers of calculus. However, you keep on slamming mathematics. Most of your objections are consistent with someone who doesn't understand formal mathematics.

Just now, you rebutted the concept of limit. You blamed Einstein for using the concept of limits, as characterized by polygons. Sadly, Einstein was not the first to use the concept of limit. Perhaps he wasn't as smart as Newton. I don't know.

If you don't like the concept of limit, as used in Principia, then say so. This is worth another thread. I would be glad to discuss things in the 'Refutation of Principia for Dummies'. I would love to see what you think is better than calculus for characterizing a curve.

So far as I can tell, you don't understand Newtonian physics any better than you understand relativity. Tell me it isn't so!

I would recommend that you read a translation of Principia. Or if you read Latin, please read the original Principia. Principia gives dozens of examples where acceleration is calculated using a polygon. The link that I posted will be a good start. Then tell us how what Einstein did with acceleration was any less valid than what Newton did.

Okay, you didn't understand calculus. It wasn't Einsteins fault!

 

[aleCcowaN]

So far it looks like wogoga intersection calculus equals empty set.

Why do I have the feeling this is yet another version of "that is much simpler, I can explain it without using (insert specific and somewhat basic knowledge here) [which the proponent didn't study because they dropped out / were rusticated for being party people / never felt the need to study / never had the resources -from cranium to pocket- to study <delete as applicable>]

"Lost in Minkowski spacetime" would be a fair thread title for this arithmetical approach to relativity and it seems no (pseudo-Riemannian or other) manifold is going to breathe life into it.

 

[wogoga]

Einstein in "section 4 of his 1905 article" even tries to avoid acceleration by arriving at a "continuously curved line" via a "polygonal line" to which acceleration cannot be applied.

Clarification: On a "polygonal line", acceleration is not defined (or infinite) at the edge points, and zero in between.

Actually that's one way that centripetal acceleration is derived, by looking at circular motion as a series of straight line segments and looking at what happens to the velocity vectors, then taking the limit as the line segments decrease in length to form a circle rather than a polygon.

In my opinion, you somehow confuse "acceleration" with "infinitesimal". From Wikipedia on Infinitesimal:

"The 15th century saw the work of Nicholas of Cusa, further developed in the 17th century by Johannes Kepler, in particular calculation of area of a circle by representing the latter as an infinite-sided polygon."​

The problem, Cusanus and Kepler had dealt with was to approximate a curved line by a "polygonal line".

In the Wikipedia article on acceleration however, polygon is not even mentioned. Instead, a somehow related concept, namely the parallelogram law is mentioned. This law is used to explain movement on a curved line by continuous acceleration, as done e.g. by Newton. The two basis vectors involved are v dt and a/2 dt².

Yet in case of time-dilation of a movement at v along a "continuously curved line", one has to show that the time-dilation formula derived for inertial motion at v, is still valid.

Einstein was using centripetal acceleration, he just wasn't saying so explicitly.
And you'll note that he derives a time dilation for the clock at the equator. Which is under centripetal acceleration.

Einstein derives time dilation at the equator only from sidereal rotation speed of around v = 465 m/s. Acceleration of a = v²/r = 5.4 mm/s² is totally irrelevant. If acceleration had a relevant effect on time dilation then this effect should show up in curved particle accelerators, where accelerations become extremely high.

Correlation with acceleration does not imply causation by acceleration.
This whole detour in the discussion started with the easily refutable claim (see #82) that the correct time-dilation formula depends on acceleration. If you think that this claim agrees with either SR or GR, then please explain how centripetal acceleration of 5.4 mm/s² affects time dilation at the equator.

Cheers, Wolfgang
pandualism.com

 

[Darwin123]

Clarification: On a "polygonal line", acceleration is not defined (or infinite) at the edge points, and zero in between.

Newton did not have our modern notation for derivative. He did not write 'F=ma'. He derived all his theorems geometrically, using diagrams that contained polygonss. The concept of infinitesimal was introduced by him, or at least revived by him,

I can give many counter examples from Principia. I have an English translation of the book by Andrew Motte in front of me.


Let me just quote from page 41, Propostion II, Theorem II:
'Every body that moves IN ANY CURVE LINE described in a plane, and by a radius, drawn to a point either immovable, or moving forward with rectilinear motion, describes about that point areas proportional to the times, is urged by a CENTRIPETAL FORCE directed to the point.'

Then look at the Figure that is next to it. The Figure shows a polygon with labeled vertices.

Then we come to page 42, Prepostition III Theorem III:
'Every body, that by a radius drawn to the centre of another body, howsoever moved, describes areas about the point proportional to the times, is urged by a force compounded out of the centripetal force tending to that of anther body, and of ALL THE ACCELERATIONS, force by which the body is impelled.'

There. Centripetal force and acceleration is defined using a diagram which contains a polygon.

Of course, the modern physicist simply uses the formula for centripetal force 'a= v^2/r' which is a short cut for all of that.

The 'proper acceleration' in Einstein paper (section 4) is caused by the centripetal force.

Einstein derives time dilation at the equator only from sidereal rotation speed of around v = 465 m/s. Acceleration of a = v²/r = 5.4 mm/s² is totally irrelevant. If acceleration had a relevant effect on time dilation then this effect should show up in curved particle accelerators, where accelerations become extremely high.

The effect does show up in cyclotrons. The effect is asymmetry. Particles traveling the curved path decay slower than their counterparts in the frame of the laboratory.

The observers standing on the surface of the earth are not accelerating. There is no significant force acting on the observer standing on the ground. Thus, the proper acceleration of this observer is zero. Therefore, the observer standing on the ground sees a time dilation of the particles on the circular path as though there is no acceleration.

The particles in the accelerator are being acted on by the magnetic force. The magnetic force causes a proper acceleration which is equal to the centripetal acceleration.

Lets reverse the pimed and unprimed coordinates.

Plug the expression for centripetal acceleration into the formula that I gave you. In other words,
t2'-t1' =(t2-t1)(1-ax/c^2)/sqrt(1-(v/c)^2)
where
a=v^2/x.

The result is actually a large time contraction:
t2'-t1'=(t2-t1)sqrt(1-(v/c)^2)

The x's cancelled out. An observer moving with the particles sees the rate of clocks tied to the earths surface as speeding up.

There would be no asymmetry in the case of a cyclotron accelerator if the particles were not acted on by a magnetic force. The magnetic force causes the 'proper acceleration' which breaks the symmetry of the observers.

Same for the clocks in Eisnteins example. A clock in the center of the earth is ticking faster than the clocks on the equator surface because of the centripetal acceleration of the equator surface. The contact force of the ground on the clocks causes a proper acceleration that breaks the symmetry.

Correlation with acceleration does not imply causation by acceleration.

Who cares about 'cause'? The only thing one can measure is correlations!

Wait, I think I know what you mean by cause. You are talking about the forces, right? Because the only way a particle can move on a curved path is when a real force is acting on the particle.

Actually, the acceleration doesn't cause the effects of relativity. The only cause relevant in relativity are the forces. The 'forces' can cause something.

Acceleration can not be correlated with anything unless it is correlated with a body-to-body force. The body-on-body force causes clocks to go out of syn. An acceleration associated with a force is a proper acceleration.

In the case of the cyclotron, the asymmetry in the rate of clocks is caused by the magnetic force. The magnetic force keeps the particles moving in a circle. So the only acceleration that really causes anything is the magnetic force.

There is a magnetic force generated by the magnet on the electrically charged particle. This magnetic force determines the 'proper acceleration'. So this magnetic force is really the cause of the clocks being out of sync.

This whole detour in the discussion started with the easily refutable claim (see #82) that the correct time-dilation formula depends on acceleration. If you think that this claim agrees with either SR or GR, then please explain how centripetal acceleration of 5.4 mm/s² affects time dilation at the equator. Cheers, Wolfgang pandualism.com

Once again with feeling! The clocks on the equator are being acted on by the contact force of the surface acting on the clock. The speed of the clock relative to the center of the earth determines the proper acceleration of the clock which was 'caused' by the contact forces. Let the primed coordinates are describe the time as measured by the clock at the center of the earth, and the unprimed coordinates be time as measured by the clock attached to the surface of the earth. This time I will call the radius of the earth 'r' instead of 'x'. Just for clarity in case you missed the point. Of course, the formula for proper acceleration is a = F/m. However, the formula for centripetal force is F=mv^2/r. So a=v^2/r. So we go back to my formula easily derived from the formulas in the Wikipedia article on 'proper acceleration'. Remember, it is YOU who found that Wikipedia article on 'proper acceleration'. t2'-t1' =(t2-t1)(1-ar/c^2)/sqrt(1-(v/c)^2) where a=v^2/r. The result is actually a large time contraction: t2'-t1'=(t2-t1)sqrt(1-(v/c)^2) If you try to go backwards with this, flipping primed and unprimed coordiantes, you have the same formulas where a = 0. Then, you will get a formula for time dilation: t2'-t1'=(t2-t1)/sqrt(1-(v/c)^2). To summarize: 1) Only a force can 'cause' something. The asymmetry in SR problems is caused by a FORCE. 2) The kinematic part of SR doesn't deal with 'cause' because it doesn't deal in forces. 3) Your concrete error is that you claimed that 'forces' insignificant in SR. BTW: It doesn't matter at this point of time that Einstein did not explicitly name the centripetal force. The Wikipedia article that YOU cited show that modern day relativists ARE using explicit expressions for FORCE. Hence, todays 'relativists' are using self consistent theory for SR. Please read the Wikipedia article on 'proper acceleration' that YOU cited.

 

[Slings and Arrows]

Newton did not have our modern notation for derivative. He did not write 'F=ma'. He derived all his theorems geometrically, using diagrams that contained polygonss. The concept of infinitesimal was introduced by him, or at least revived by him,

I can give many counter examples from Principia. I have an English translation of the book by Andrew Motte in front of me.

"Isaac Newton's Philosophiae Naturalis Principia Mathematica (The mathematical principles of natural philosophy), hereafter referred to as the Principia, justifiably occupies a position as one of the most influential works in Western culture, but it is a work more revered than read. Three truths concerning the Principia are held to be self-evident: it is the most instrumental, the most difficult, and the least read work in Western science. A young student who passed Newton on the streets of Cambridge is reported to have said, "There goes the man who writ the book that nobody can read."" -- J. Bruce Brackenridge

Free online access:

Isaac Newton : Principia
Translated and annotated by Ian Bruce
http://www.17centurymaths.com/contents/newtoncontents.html

The Key to Newton's Dynamics
by J. Bruce Brackenridge
http://publishing.cdlib.org/ucpressebooks/view?docId=ft4489n8zn;brand=ucpress

 

[Darwin123]

So I found a second concrete example of where he is wrong. He is wrong about potential and field being the same.

The first concrete error is saying that acceleration is negligible in SR. 'Proper acceleration' is very important in SR. The second concrete error is assuming that potential and field are the same.

The following is a discussion where I demonstrate his second concrete error.

....

I'm genuinely flabbergasted by Einstein's continuation:

"According to the general theory of relativity, a clock will go faster the higher [weaker] the gravitational potential of the location where it is located, and during partial process 3 U2 happens to be located at a higher [weaker] gravitational potential than U1."​

In contrast, I am unsurprised at your your inability to distinguish between the words 'potential' and 'field'. The potential is not the same as a field, either for electromagnetic or gravitational interactions. The potential and the field are even in different units.

Any electrical engineer knowing classical physics would know the difference between electric potential and electric field. The absolute electrical potential has no physical meaning in classical physics. Let me use MKS units. The electric potential is measured in Volts. The electric field is in units of Volts per meter. If you multiply the electric field at a point by the electric charge at a point, you have the force in Newtons.

Any astronomer or ballistics expert would know the difference between gravitational potential and gravitational field. The absolute gravitational potential has no meaning by itself. The units of gravitational potential are Joules per kilogram. The units of gravitational field are Joules per kilogram per meter.

I had to read this several times on different days before noticing and becoming (almost) certain that already this statement stems from confusion and wishful thinking. Einstein must have confused "higher gravitational potential" with "stronger gravitational potential" or "[in K'] resting clock U2" with "clock at rest U1".

You seem to hypothesize that a large gravitational potential is always associated with a large gravitational field. There is a rather famous counterexample to your assumption. It is quite possible to have a huge potential and a zero field. The gravitational field inside in the hollow cavity is zero. The gravitational potential inside the hollow cavity is huge and homogeneous.

Newton examined this example as it relates to mass. Benjamin Franklin examined this example as it relates to electrostatic charges. This example was commonly understood by scientists and engineers WAY before Einstein.

Anyone with any knowledge of Newtonian mechanics knows this.

If clock U1 is accelerated by a gravitational field, then U1 is located at a lower (stronger) gravitational field.

Reader, please note the sleight of hand here. The anti-relativist (!?) just replaced potential with absolutely no indication that he knows the difference.

The mistake was not Einstein's. The mistake was made by the 'anti-relativist'.

A particle that falls because of a gravitational field is moving into regions with a higher gravitational potential. The gravitational field on the surface of the earth is very large, and is pointed toward the center. However, the gravitational potential is not at its maximum. A particle at the center of the earth is in a region with zero gravitational field. However, it has a much larger gravitational potential. The clock at the center of the earth really has to run faster than the clock at the surface of the earth due to the higher gravitational potential.

Note this mistake has nothing to do with SR. The critic is switching the concepts of potential and field, which is preSR. He made this mistake after several days of contemplation, after which he was 'flabbergasted'. I will bet you that he doesn't even acknowledge his mistake.

I know from personal experience that all too willingly one accepts the result of a superficial calculation or reasoning, if it agrees with one's expectation, for whatever reason.

The condescending statement above is self explanatory. The made a superficial calculation for the reason that he thought 'potential' and 'field' were the same thing. He did not check the units. He did not examine the definition of potential. He made the hypothesis that they are the same based on his expectation.

So I found a second concrete example of where he is wrong. He is wrong about potential and field being the same. He expects everyone to accept his calculation only because it fits his expectation of how 'Einstein is wrong'.

Our critic is wrong because:

1) Proper acceleration is significant in SR, GR and Newtonian physics.

2) Field and potential are two different physical concepts with two different different units regardless of subject.


The critic promised to show me how I was wrong if I gave a concrete reason he was wrong. So here are TWO concrete reasons that the critic is wrong. I am asking him to keep his promise by refuting both statement #1 and statement #2 without once mentioning the name of Einstein.

 

[wogoga]

According to Einstein and every other person who has learned Special Relativity, wogoga, acceleration of travelling clock U2 has no effect on SR time dilation because SR is for inertial frames of reference!

Yes, that should be obvious!

Therefore he uses an equivalent gravitational field as in General Relativity.

In 1918, Einstein still believed in the validity of Special and General Relativity. Therefore he concluded by logical necessity that time-dilation ala General Relativity must be the cause of the time-dilation asymmetry in the twin paradox.

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".

Cheers, Wolfgang

 

[Reality Check]

In 1918, Einstein still believed in the validity of Special and General Relativity.

And in 1919, Einstein believed in the validity of Special and General Relativity. etc. until his death.
And in 1918, most scientists believed in the validity of Special and General Relativity, wogoga.
Today it is only ignorant people and science cranks who do not in the validity of Special and General Relativity became they both have overwhelming evidence- including the twin paradox !

Therefore any person who has ever learned about Special and General Relativity will use Special and General Relativity where appropriate. That includes Einstein in Dialog about Objections against the Theory of Relativity where Einstein concluded from the physics that GR time-dilation is the cause of the time-dilation asymmetry in the twin paradox.

This is because of one fundamental bit of physics, wogoga. GR is derived from the equivalence principle - that an acceleration is equivalent to a uniform gravitational field.
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".

Cheers, Reality Check.

 

[Darwin123]

If my refutation (post #66) of Einstein's twin-paradox resolution was wrong then you would be able to show which point is wrong:
You have not addressed my last refutal. In my last post, I pointed out that you are conflating two concepts that all scientists would have know in Einstein’s day (and now).

You are conflating two concepts: field and potential. To facilitate the discussion, I present the units of these two physical quantities. The gravitational field is in units of acceleration, [ms^-2]. The gravitational field is in units of the square of velocity, [m^+2 s^-2].

The two have Newtonian analogs. The gravitational field is proportional to the gravitational force. Therefore, the field is a vector at every point which has direction in addition to magnitude. The potential difference is proportional to potential energy difference. Therefore, the potential is a scalar at every point with no direction associated with it.

The connection is that the gradient of the gravitational potential is equal to the gravitational force. So they are connected, but not the way you are claiming. The potential can be zero scalar when the field is nonzero. The field can be a zero vector when the potential is nonzero.

Every introduction to physics course presents the special case of a homogeneous gravitational field. The field is characterized by the proper acceleration, g, where,
g=F/m
If there is a homogeneous gravitational field in the z direction, then the field is ‘g’ everywhere in the universe. The potential is ‘g(Z2-Z1)’ where Z2 is the position of U2 and Z1 is the position of U1.

More complex cases require calculus to understand. However, this case is standard for anyone studying physics. Premed, engineer, everybody!

Gravitational time dilation refers to an explicit correlation between potential and rate of clocks. Gravitational time dilation does not refer to an explicit correlation between field and rate of clocks. The gravitational field at a point is uncorrelated with the rate of clocks. The gravitational potential is correlated with the rate of clocks.

Now lets look at your ‘points’.

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.

Okay.

2 This "faster pace" of U1 is explained by a fictitious "homogenous gravitational field" acting on U1.

No. The gravitational FIELD can not ‘explain’ the faster pace of U1 because it is acting on everything in the universe. 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.

3 Gravitational attraction implies (stronger, lower) gravitational potential.

No. Gravitational ‘attraction’ refers to the FIELD. Gravitational POTENTIAL refers to the accumulated effect.
Suppose one sets the arbitrary position of z=0 at the exact position of twin U1. Suppose U2 is in a position z=Z2. Then the potential difference between U1 and U2 is mg (Z2-Z1).

4 Gravitational potential leads to gravitational time dilation.

Yes. The gravitational POTENTIAL leads to gravitational time dilation. The potential difference between U2 and U1 leads to U2 and U1 not being synchronized.

5 Thus, Einstein explains the "faster pace" with gravitational time-dilation.


Yes. As the POTENTIAL increases, the pace decreases. The POTENTIAL is changing. However, ‘attraction’ is the same everywhere.

6 Yet gravitational time dilation of U1 is the opposite of "faster pace of U1”.

Which would be doubly strange if gravitational attraction (i.e., field) explicitly caused the difference. The attraction is the same everywhere (i.e., homogeneous). The field is ‘g’, which is the proper acceleration.

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


I am pointing out a very concrete mistake on your part. Attraction and potential are not the same thing. This mistake has nothing to do with Einstein. Instead of replying to the topic you have simply quoted Einstein and repeated the same mistake. I suppose you will keep ignoring this point.

Here is your concrete mistake again. Potential and attraction are not the same thing.