Refutation of Special Relativity for Dummies

[wogoga]

You continue to confuse yourself by setting c = 1.

With your choice of v = 10 m/s and the units meter and second, we get this time-shift (resp. deviation from simultaneity):

v/c² = 1.11*10^-16 sec per meter​

The analogous length-shift (resp. speed) is:

v = 10 meter per sec​

You claim that compared to 10 m/s, the 1.11*10^-16 s/m are negligible and can therefore be discarded when taking a first-order approximation. Yet the difference of 17 decimal powers is only the result of the (squared) numerical value of light-speed c expressed in meter per second.

The hallmark of a first-order effect is the following:

If we reduce an argument further by a factor, then the effect is also reduced approximately by the same factor. (In the second-order case, the effect would be reduced approximately by the square of this factor.)​

In our case:

If we reduce v from 10 m/s to 1 m/s then time-shift is reduced only from 1.11*10-16 sec/m to 1.11*10-17 sec/m.​

When dealing with our galaxy or the whole universe, the units second and light second, or year and light-year are rather better suited than second and meter.

In any case, if β = v/c << 1, we get for length-shift and time-shift:

v = β LS/s = β LY/year = (3*10⁸)⁺¹ β m/s
x/c² = β s/LS = β year/LY = (3*10⁸)^-1 β s/m​

Contrary to time dilation and length contraction, which are higher-order effects of v, relativity of simultaneity is a first-order effect. You should really try to understand what I wrote in #118:

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 [i.e. 0.0001c] 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.​

All I've said concerning Lorentz Transformation Reducing to Galilean Transformation is correct.

When v/c << 1 the Taylor series for the Lorentz factor can be truncated and we get Newtonian mechanics.

Do you assume one of the following hypotheses?

• Einstein's simultaneity concept is part of Newtonian mechanics.
• The speed of light is infinite in Newtonian mechanics.

If you do not subscribe to one of these two hypotheses, then your claim that Special Relativity reduces to Newtonian mechanics is simply wrong. Ask a mathematician or use a program for symbolic computation as shown in #135.

Cheers, Wolfgang

 

[Darwin123]

With your choice of v = 10 m/s and the units meter and second, we get this time-shift (resp. deviation from simultaneity):

v/c² = 1.11*10^-16 sec per meter​

The analogous length-shift (resp. speed) is:

v = 10 meter per sec​

You claim that compared to 10 m/s, the 1.11*10^-16 s/m are negligible and can therefore be discarded when taking a first-order approximation. Yet the difference of 17 decimal powers is only the result of the (squared) numerical value of light-speed c expressed in meter per second.

...
You claim that compared to 10 m/s, the 1.11*10^-16 s/m are negligible and can therefore be discarded when taking a first-order approximation. Yet the difference of 17 decimal powers is only the result of the (squared) numerical value of light-speed c expressed in meter per second...

I did not compare v and v/c^2 since they are in different units. You know that and I know that. You said that v is in m per sec and v/c^2 is in sec per meter. One can compare 'm per sec' with sec per meter'. You misrepresented me.

Let me restate it in your favorite units. The quantity v is 3.3(10^-8) LS/sec. The quantity v/c^2 is 1.1(10^-16) sec/LS. These are still in different units.

The number alone doesn't matter when comparing quantities. You can only compare quantities with the same units. LS/s is not the same as s/LS

An exception should be mentioned just for completion. You can drop 'ratio units' radians and nepers sometimes. However, we haven't been using them.

I will count this as a concrete error.

The quantities that I have been comparing is t and vx/c^2 ax measured between the stationary observer and the moving observer. These are both in the unit, sec. Since the rest of your argument doesn't really deal with these two quantities, we can ignore your argument.

 

[Darwin123]

I did not compare v and v/c^2 since they are in different units. You know that and I know that. You said that v is in m per sec and v/c^2 is in sec per meter. One can compare 'm per sec' with sec per meter'. You misrepresented me.

Let me restate it in your favorite units. The quantity v is 3.3(10^-8) LS/sec. The quantity v/c^2 is 1.1(10^-16) sec/LS. These are still in different units.

The number alone doesn't matter when comparing quantities. You can only compare quantities with the same units. LS/s is not the same as s/LS

An exception should be mentioned just for completion. You can drop 'ratio units' radians and nepers sometimes. However, we haven't been using them.

I will count this as a concrete error.

The quantities that I have been comparing is t and vx/c^2 ax measured between the stationary observer and the moving observer. These are both in the unit, sec. Since the rest of your argument doesn't really deal with these two quantities, we can ignore your argument.

This website keeps rejecting my long answers. Twice! So apparently, the software of teh forum agrees with you. However, software is noteriously unreliable in physics and real math. So let me summarize.

Concrete error: Newton did not assume that the speed of light was infinite. He included as part of his theory the idea of light corpuscles which traveled at a finite speed. So he definitely thought that light traveled at a finite speed.

However, Newton implicitly assumed that there was no upper limit to the speed of signal carrying information. We know this because the third law of motion is written in present tense. I don't know about other languages, but in English the present tense is restricted to signals that are transmitted so fast that it doesn't matter how fast they go. The reaction was always equal and opposite the reaction simultaneously. This is not always possible unless there is a force that is transmitted at infinite speeds.

I could quote the third law of motion to you, or at least an English translation of same. However, most scientists interpret that law to imply simultaneity between action and reaction. If I am wrong, then please tell me how!

Newtons laws of gravity are self consistent with his laws of motion only if gravity travels at an infinite speed. Therefore, Newtons mechanics are consistent with Einsteins hypothesis of simultaneity only if gravity moved at an infinite speed.

So Einstein's principle of simultaneity COULD apply to Newton's mechanics, but DOESN'T HAVE TOO. You claimed that Einstein's hypothesis of simultaneity HAS TO be consistent with Newtons mechanics. So that is a second concrete error.

The discrepancy in the hypothesis of simultaneity does not imply a logical contradiction in the Galilean limit of the Lorentz transformation. This is because the local speed of light in a vacuum IS MUCH FASTER than the propagation speed of any force ever measured. The speed of light in a vacuum is faster than a speeding bullet, faster than the speed of sound, and about the same speed of gravity. So the Galilean transformation can approximate the Lorentz transformation to first order in v/c.


So that is a third concrete error that you have made in this post alone.

In addition, you made an old concrete error. You ignored the proper acceleration of the earth. In your example, the earth is moving back and forth due to gravitational force. Therefore, it has a proper acceleration as described by SR.

That is a fourth concrete error made in this post. It is old but still good.

Hope this gets through.

 

[Perpetual Student]

With your choice of v = 10 m/s and the units meter and second, we get this time-shift (resp. deviation from simultaneity):

v/c² = 1.11*10^-16 sec per meter​

The analogous length-shift (resp. speed) is:

v = 10 meter per sec​

You claim that compared to 10 m/s, the 1.11*10^-16 s/m are negligible and can therefore be discarded when taking a first-order approximation.

<...>

You can stop right there. Yes, the difference is as negligible as the difference between 1 and the gamma function. Think! What do you think "reduces to the Galilean transformation means"? At speeds like 10m/s and spacial differences like 1m, time intervals like 10^(-16)s are irrelevant, and as far as I know, immeasurable. The rest of your post is nonsense.

 

[Darwin123]

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 [i.e. 0.0001c] 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.​

I dealt with the other things in two other posts. The website software doesn't accept my longer replies for some reason. So am splitting the analysis up.

You have just made an error in claiming comparing the orbital time of the earth as seen by an observer stuck to the earth and an observer in the at the galactic center. These two observers are a large distance apart.

1) You are ignoring the proper acceleration of the earth as it orbits.

The earth is not in an inertial frame since it is not undergoing uniform motion. A force is making the earth move back and forth. The accleration caused by mechanical force is called proper acceleration. The mechanical force makes the earth go back and forth. Therefore, the proper acceleration of the earth caused by the force is nonzero.

The earth can not be considered in an inertial frame because the proper acceleration is not zero. Therefore, the erth in this example is a NONINERTIAL FRAME.

2) You did not calculate the round time of a signal from the galactic center to the earth and back to the galactic center.

The round trip time of a signal in this circumstance is 30000 y. The murder occurred about 1000 y previous to the back and forth motion of the earth during the year that the murder occurred. The earth observer sees the murder 1000 years in the future. So the round trip time of the signal is 60000 y as determined by the Galilean transformation and 59000 y as determined by the Lorentzian transformation.

Therefore, the round trip time of the signal is the same to first order in v/c. The round trip time is the only time that can be objectively determined.


Basically, the simultaneity hypothesis of Einstein implies that ONLY ROUND TRIP TIMES are objective.


Your error is basically the same as before. The earth observer in this example is not an inertial frame. The galactic center is observer is in an inertial frame. The round trip time in the inertial frame is slightly longer (Galilean transformation) than the round trip time in the noninertial frame (Lorentzian transformation).

Please address these concrete errors

 

[Darwin123]

The round trip time of a signal in this circumstance is 30000 y.

Sorry. I made a typographical error. The ONE way signal time is about 30000 y because of the local speed of light in a vacuum is an upper limit to the speed of all signals. The round trip signal time is more like 60000 y, as I said before.

Actually, the round trip time as seem by the observer stationary at the galactic center is 60000 y. The round trip time as seen by an observer stationary with respect to the surface of the earth is more like 59000 y. The observer on the earth sees a shorter round trip time because the observer on earth has a nonzero proper acceleration. The observer fixed at the center of the galaxy has a proper acceleration that is effectively zero.

The observer at the center of the galaxy sees the same round trip time as an observer in a 'Newtonian' universe. Basically, you can derive 60000 y using a Galilean transformation. The observer moving with the earth sees a smaller round trip time because that is the observer that is undergoing proper acceleration. The observer on earth is subject to a 'real' force.

I have decided to restrict my calculations to special relativity (SR). I have ignored the inhomogeneous component of the gravitational field caused by the mass of the galaxy.

Relativity purists can do a more accurate calculation using general relativity (GR) if they wish. However, the OP initially claimed that it was SR that was not self consistent. Therefore, I am concentrating on proving that SR is self consistent. That means that I have to ignore the gravitational potential associated with massive gravitational sources. If I included the mass of the galaxy in my calculations, then I would be proving the self consistency of GR.

The OP has been caught with concrete errors uncorrected, anyway.

 

[Perpetual Student]

Darwin123, I find it troubling to say that this is a lost cause. If he can't see how readily the Lorentz transformation reduces to Newtonian physics at low velocities and short distances, how is he to fathom more complex issues like the twin paradox?
Understanding the basic Lorentz transformation requires simple high school algebra with minimal difficulty. Understanding how and why it reduces to Newtonian physics is straightforward and obvious. He must be completely out of his element. All these discussions of Taylor series expansions and first order/second order effects are just fluff and distractions.

 

[Darwin123]

Darwin123, I find it troubling to say that this is a lost cause. If he can't see how readily the Lorentz transformation reduces to Newtonian physics at low velocities and short distances, how is he to fathom more complex issues like the twin paradox?
Understanding the basic Lorentz transformation requires simple high school algebra with minimal difficulty. Understanding how and why it reduces to Newtonian physics is straightforward and obvious. He must be completely out of his element. All these discussions of Taylor series expansions and first order/second order effects are just fluff and distractions.

I know that. I have fun with lost causes.

Also, these discussions help reinforce my understanding of SR. For example, I knew about proper acceleration before I started arguing with the OP. However, I didn't know what it was called. I had to make up the concept myself in order to solve certain problems in SR. I was uncertain as to certain concepts in calculus. For instance, I wasn't sure how to differentiate a 'full differential' from a 'partial differential'. I was able to use certain 'rules of thumb' to pass my PhD qualifying exams. However, I didn't have a full understanding of how 'these rules of thumb' were related to the bigger scientific pictures.

It was actually the OP who cited a detailed article on proper acceleration. I read the article. Now I can articulate my thoughts better. Furthermore, his questions motivate me to examine some fundamental assumptions in calculus. When he showed ignorance of infinitesimals, I was inspired to examine the history of the infinitesimal concept.

The OP has demonstrated to me some reasons WHY the concept of infinitesimals was fought tooth and nail for so many centuries. In a way, the OP makes a good historical simulation.

The OP makes a good cautionary tale. When the OP shows confirmation bias, he usually supports it with a poor statistical argument. Examination of his thought processes helps me recognize poor statistical arguments. I have been more careful looking for similar errors in my own research projects.

There is also the vicarious thrill of outing someone. This OP makes grandiose claims of his own capabilities. He presents gambits and other false challenges to show how smart he is. I don't think he expects people challenging him directly. He wants generalized put downs. I enjoy showing him up by answering him seriously. I know it is a cheap thrill.

 

[Perpetual Student]

I know that. I have fun with lost causes.

Also, these discussions help reinforce my understanding of SR. For example, I knew about proper acceleration before I started arguing with the OP. However, I didn't know what it was called. I had to make up the concept myself in order to solve certain problems in SR. I was uncertain as to certain concepts in calculus. For instance, I wasn't sure how to differentiate a 'full differential' from a 'partial differential'. I was able to use certain 'rules of thumb' to pass my PhD qualifying exams. However, I didn't have a full understanding of how 'these rules of thumb' were related to the bigger scientific pictures.

It was actually the OP who cited a detailed article on proper acceleration. I read the article. Now I can articulate my thoughts better. Furthermore, his questions motivate me to examine some fundamental assumptions in calculus. When he showed ignorance of infinitesimals, I was inspired to examine the history of the infinitesimal concept.

The OP has demonstrated to me some reasons WHY the concept of infinitesimals was fought tooth and nail for so many centuries. In a way, the OP makes a good historical simulation.

The OP makes a good cautionary tale. When the OP shows confirmation bias, he usually supports it with a poor statistical argument. Examination of his thought processes helps me recognize poor statistical arguments. I have been more careful looking for similar errors in my own research projects.

There is also the vicarious thrill of outing someone. This OP makes grandiose claims of his own capabilities. He presents gambits and other false challenges to show how smart he is. I don't think he expects people challenging him directly. He wants generalized put downs. I enjoy showing him up by answering him seriously. I know it is a cheap thrill.

 

[Matthew Cline]

When he showed ignorance of infinitesimals, I was inspired to examine the history of the infinitesimal concept.

The OP has demonstrated to me some reasons WHY the concept of infinitesimals was fought tooth and nail for so many centuries. In a way, the OP makes a good historical simulation.

From Wikipedia:

Infinitesimals were the subject of political and religious controversies in 17th century Europe, including a ban on infinitesimals issued by clerics in Rome in 1632.

I, what? Religious controversies over math?

 

[Darwin123]

I, what? Religious controversies over math?

Oh, yes!

Here is a link to the Amazon webpage for a book relating some of the sorry history of this controversy.

http://www.amazon.com/Infinitesimal-Dangerous-Mathematical-Theory-Shaped/dp/0374534993
‘Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World
by Amir Alexander
…
On August 10, 1632, five men in flowing black robes convened in a somber Roman palazzo to pass judgment on a deceptively simple proposition: that a continuous line is composed of distinct and infinitely tiny parts. With the stroke of a pen the Jesuit fathers banned the doctrine of infinitesimals, announcing that it could never be taught or even mentioned. The concept was deemed dangerous and subversive, a threat to the belief that the world was an orderly place, governed by a strict and unchanging set of rules. If infinitesimals were ever accepted, the Jesuits feared, the entire world would be plunged into chaos.’


And you thought Darwinian evilution was sacrilegious! The evils of
infinitesimals were fought even before heliocentric theory!

Infinitesimals are the foundation of calculus. There would be no Newtonian mechanics, no relativity, no CALCULUS if there were no infinitesimals!

Life would be simple and good without calculus! Just the way God wanted life to be!

 

[Perpetual Student]

Infinitesimals, limits and calculus were on shaky ground until the 19th century. Many objected to their usage (on non-religious grounds) because of the lack of rigor in their usage.

LINK

Nevertheless, whenever I work with a differential equation, I furtively look around for fear of a manifestation of the Prince of Darkness.

 

[Darwin123]

Infinitesimals, limits and calculus were on shaky ground until the 19th century. Many objected to their usage (on non-religious grounds) because of the lack of rigor in their usage.

LINK

Nevertheless, whenever I work with a differential equation, I furtively look around for fear of a manifestation of the Prince of Darkness.

This differential equation requires the rigor of a mathematical exorcise!

 

[Perpetual Student]

This differential equation requires the rigor of a mathematical exorcise!

 

[wogoga]

You claim that compared to 10 m/s, the 1.11*10^-16 s/m are negligible and can therefore be discarded when taking a first-order approximation.

You can stop right there. Yes, the difference is as negligible as the difference between 1 and the gamma function. Think! What do you think "reduces to the Galilean transformation means"? At speeds like 10m/s and spacial differences like 1m, time intervals like 10^(-16)s are irrelevant, and as far as I know, immeasurable. The rest of your post is nonsense.

We cannot compare apples or m/sec to oranges or sec/m in the way you do.

One the one hand we have the "difference between 1 and the gamma function" (Lorentz-factor):

1 versus 1+10^-16​

On the other hand we have the difference in time-shift between Galilean transformation and "first-order reduced" Lorentz transformation:

0 s/m versus 10^-16 s/m​

The change from 1 to 1+10^-16 is actually minimal. However, no multiplication-factor is big enough to transform 0 s/m to 10^-16 s/m. The difference between simultaneity and time-shift (linearly depending on distance) is even qualitative.

Whereas a Lorentz-factor of 1+10^-16 does not depend on any units, the numerical value of a time-shift 10^-16 s/m can be increased by changing units, e.g. to around 1 sec/LY.

To the mathematical question whether the Lorentz transformation reduces to the Galilean transformation or not, it is irrelevant that one 1 sec per light-year may seem negligible to you. On a cosmic scale, the corresponding length-shift (resp. speed) of 1 m/s ≈ 10^-16 LY/sec could be considered negligible too.

Once again: All I've said concerning Lorentz Transformation Reducing to Galilean Transformation is correct.

I did not compare v and v/c^2 since they are in different units. You know that and I know that.

Should this be an invitation to read between the lines, or do you simply confuse written-by-Perpetual-Student with written-by-Darwin123?

Darwin123, I find it troubling to say that this is a lost cause.

I know that. I have fun with lost causes.

Cheers, Wolfgang

 

[Reality Check]

wogoga: Repeating a delusion about the Lorentz and the Galilean transformations

We cannot compare apples or m/sec to oranges or sec/m in the way you do. ...

Repeating a delusion about the Lorentz and the Galilean transformations does not make it true, wogoga. It is simple mathematics that the Lorentz transformation reduces to the Galilean transformation for v << c .

Have you read any physics textbooks, wogoga?
They state that that relativistic mechanics reduces to Newtonian mechanics when v << c.

Have you read Wikipedia, B]wogoga[/B]?
Lorentz transformation

Another important property is for relative speeds much less than the speed of light, the Lorentz transformations reduce to the Galilean transformation in accordance with the correspondence principle.

Have you learned basic mathematics, B]wogoga[/B]?
if v << c then

1. v/c is << 1 and
2. (v/c)² is even smaller and
3. 1- (v/c)² is very close to 1 and
4. The Lorentz factor is very close to 1 and
5. The Lorentz transformation reduces to the Galilean transformation when we ignore negligible terms in the expansion of the Lorentz transformation. Or simply look at the limit as v -> 0.

Have you learned the basic physics that relativistic effects appear when v is high compared to c, B]wogoga[/B]?

 

[Perpetual Student]

We cannot compare apples or m/sec to oranges or sec/m in the way you do.

One the one hand we have the "difference between 1 and the gamma function" (Lorentz-factor):

1 versus 1+10^-16​

On the other hand we have the difference in time-shift between Galilean transformation and "first-order reduced" Lorentz transformation:

0 s/m versus 10^-16 s/m​

<...>

NO! What are you talking about?

Your 0 s/m versus 10^(-16 )s/m is nowhere to be seen in the time dilation equation.

t' = γ(t - vx/c^2)

Gamma has no units and vx/c^2 has units of time only. All the distance factors (m) cancel out. There is no s/m or m/s. The result is t - 10^(-16)s.

Where are you getting all these misconceptions? As RC has suggested, learn some mathematics; buy a book, take a course. You are floundering!

 

[Darwin123]

The hallmark of a first-order effect is the following:

If we reduce an argument further by a factor, then the effect is also reduced approximately by the same factor. (In the second-order case, the eff​

This Forum adds all replies to the end of the thread, regardless of who the reply was for. Thus, the use of pronouns leads to confusion. I could very well have confused reply-for-Perpetual Student with reply-for-Darwin123. If PS made such a fundamental mistake in units, then I won’t defend him.

You still haven’t addressedany one of your (Woogoga) concrete error. Let me try again.

Here is a link to your webpage and a typical quote.
http://www.pandualism.com/d/myth_Lorentz_Galilean_transformation.html#p0135e
‘No objection can be raised against your choice of v = 10 m/s, leading to a negligible Lorentz factor, but the choice of x = 1 m and t = 1 sec is in principle completely arbitrary, and depends on the units meter and second. With your choices we get:
x' = x - vt = 1 m - 10 m
t' = t - vx/c2 = 1 s - 1.11*10-16 s’

Let me explain your error again.

You said the choice of x = 1 m and t = 1 sec is in principle completely arbitrary. This is wrong.

The choice of these two values is not arbitrary even in principle because x’=0. The observer can not observe his own translation. So if the position of the moving observer is x’, then x’=0.

Therefore,
0 = x - vt

So,
t=x/v.


So if x = 1 m and v=10 m/s, then t = 0.1 sec.

If I replace v by 100 m/s, then t = 0.01 sec.

So I see that the time has the earmark of a first order effect. By multiplying the value of v by a factor of 10, I reduced the value of t by a factor of 10. So the time t is a first order effect in v.

Lets us go back to v = 10 m/s so t=0.1 sec.

So t’= (0.1-1.11*10^-16) s

t=t’=0.1 sec.

Hence, the Lorentz transformation and the Galilean transformation are the same to first order.

Notice that x DOES NOT EQUAL x’. x=1 m and x’ = 0 m. As you pointed out, they are not nearly the same.

You are confused by the word 'effect'. Neither the Galilean transform nor the Lorentz transform are 'effects'. They are transformations.

Also notice that I (Darwin123) did not make an error in units. So again.

You made a concrete error by claiming that x' is not equal to zero.

Please address your (Wogoga) concrete error in any units you (Wogoga) chooses.​

 

[Perpetual Student]

This Forum adds all replies to the end of the thread, regardless of who the reply was for. Thus, the use of pronouns leads to confusion. I could very well have confused reply-for-Perpetual Student with reply-for-Darwin123. If PS made such a fundamental mistake in units, then I won’t defend him.
...Darwin123

Please enlighten me on my fundamaental mistake in units. I've missed it.

 

[Darwin123]

Please enlighten me on my fundamaental mistake in units. I've missed it.

Please forgive me if I made a mistake. He accused either you or me of making a mistake. When I said that he was the one who made the mistake, he said that I confused a reply meant for him with a reply meant for me.


Here is where I may have made a real mistake. I assumed that the mistake Wogoga corrected me on was a real mistake. It could have been Wogoga’s fantasies.


There I lost track of the thread before the following.
Start Quote
Originally Posted by Perpetual Student in #155
You continue to confuse yourself by setting c = 1.
END TEMPLATE: bbcode_quote
Originally posted by Wogoga in #161.
With your choice of v = 10 m/s and the units meter and second, we get this time-shift (resp. deviation from simultaneity):
v/c2 = 1.11*10-16 sec per meter
The analogous length-shift (resp. speed) is:
v = 10 meter per sec
Originally Posted by Darwin123
I did not compare v and v/c^2 since they are in different units. You know that and I know that. You said that v is in m per sec and v/c^2 is in sec per meter. One can compare 'm per sec' with sec per meter'. You misrepresented me.

Originally Posted by wogoga in #161
You claim that compared to 10 m/s, the 1.11*10-16 s/m are negligible and can therefore be discarded when taking a first-order approximation.
End quote

Maybe he was trying to derail the thread. He does that whenever I point out a concrete mistake. So I will remind everyone of the challenge I presented Wogoga.


Wogoga claims that the Lorentz tranform does not asymptotically approach the Galilean transform as v/c approaches 0. He used a numerical example of a moving observer at x’ watching a stationary observer at (x-vt)/sqrt(1-[v/c]^2)where x=1 m and v=10 m/s. He claimed that the choice of x and t was arbitrary. He made mathematical errors in his calculation, but I decided to concentrate on the physical error which I consider to be most ‘concrete’. Although he may have made another mistake in units, his choice of ‘arbitrary’ is also in question. This is an error that he made not only in the forum of this thread but on his own web page.

I claimed that his choice of values was not arbitrary since by the assumptions of both Galileo and Lorentz, x’=0. Therefore, he can’t chose x and t to be arbitrary values. If x’=0, then x = vt independent of the value of v. Even if he were to get all the units right, he is making a mistake by not realizing x’=0.

No other participant in this thread has called Wogoga out on this. They get derailed every time he switches units. Sometimes Wogoga tells us v is in m/s, and sometimes it is in LS/s, and sometimes it is in LS/year. Maybe he keeps track of this unitse and maybe he can’t. However, x’=0 in every system of units. Wogoga seems to think x’ is not 0 (x’><0).

Wogoga is assuming that x’ >< 0 when x’=0. This is his first concrete mistake.