Lorentz-Einstein transformation

[bernhard.rothenstein]

Textbooks devoted to the subject present separate derivations for the twoLorentz-Einstein transformations which relate the space-time coordinates of the same event E(x,0,t) and E'(x',0,t')
x=g(x'+Vt') (1)
t=g(t'+Vx'/cc) (2)
Equation (1) can be derived directly from length contraction
xg^-1=x'+Vt') (3)
Dividing both sides of (1) by c and taking into account the synchronization of the clocks in the involved inertial reference frames (x/c=t,x'/c=t',t'=x'/c) we obtain
tg^-1=t'+Vx'/cc (4)
i.e. (2).
Did you find that derivation in the literature? Please comment.
sine ira et studio

 

[nakurusil]

Textbooks devoted to the subject present separate derivations for the twoLorentz-Einstein transformations which relate the space-time coordinates of the same event E(x,0,t) and E'(x',0,t')
x=g(x'+Vt') (1)
t=g(t'+Vx'/cc) (2)
Equation (1) can be derived directly from length contraction
xg^-1=x'+Vt') (3)

Length contraction is a consequence of the LE transforms , not the other way around.

 

[Meir Achuz]

Textbooks devoted to the subject present separate derivations for the twoLorentz-Einstein transformations which relate the space-time coordinates of the same event E(x,0,t) and E'(x',0,t')
x=g(x'+Vt') (1)
t=g(t'+Vx'/cc) (2)
Equation (1) can be derived directly from length contraction
xg^-1=x'+Vt') (3)
Dividing both sides of (1) by c and taking into account the synchronization of the clocks in the involved inertial reference frames (x/c=t,x'/c=t',t'=x'/c) we obtain
tg^-1=t'+Vx'/cc (4)
i.e. (2).
Did you find that derivation in the literature? Please comment.
sine ira et studio

When one thing is derived from another, it is obvious that the derivatiion can be turned around as you do. One could say that GmM/r^2 can be derived from elliptical orbits if one were silly enough. Doing physics usually means presenting a general principle (e.g. Lorentz invariance) and deriving a large number of phenomenological effects from the general principle. Any one of those derived specific results could be used as a starting point if one wanted to engage in sophistry rather than physics. I hope that your derivation is not in the refereed literature.

 

[bernhard.rothenstein]

When one thing is derived from another, it is obvious that the derivatiion can be turned around as you do. One could say that GmM/r^2 can be derived from elliptical orbits if one were silly enough. Doing physics usually means presenting a general principle (e.g. Lorentz invariance) and deriving a large number of phenomenological effects from the general principle. Any one of those derived specific results could be used as a starting point if one wanted to engage in sophistry rather than physics. I hope that your derivation is not in the refereed literature.

i think that a derivation should start with something probably as you say with a general principle. but that is not enough. the derivations imply supplementary assmptions in order to satisfy the results of thought experiments or other requirements of Nature. do you think that we should start ad-hoc with the LET? physics is a democratic field where each participant could start ad-libitum. i know derivations which start with E=mcc, with the Doppler Effect, with length contraction and time dilation (de gustibus...) Concerning the style of your answer it is far from being elegant (do you use sily when you discuss with your students?) and the air of superiority you display is descouraging.
sine ira et studio

 

[bernhard.rothenstein]

Lorentz Einstein transformation

Length contraction is a consequence of the LE transforms , not the other way around.

Please delete from my message the sentence "(1) can be derived from length contraction" considering that it is derived in a way with which you aggree! What I wanted to underline was that (2) is a direct consequence of (1) if we consider the clock synchronization procedure in the two frames.
SINE IRA ET STUDIO

 

[yogi]

As to what is fundamental and what is secondary is not always obvious - for example, you can derive an expression of the Gravitational constant G starting with Friedmanns equation for an expanding critical density universe

While length contraction was the first idea proposed to explain MMx near null result, it may be more comfortable to consider length contraction as a necessary consequence of time dilation - an idea that came a bit later. Since the latter provides a residual record when clocks are compared after they have been brought to rest in the same frame, it may be confusion from a tutorial aspect, to start with length contraction.

 

[bernhard.rothenstein]

As to what is fundamental and what is secondary is not always obvious - for example, you can derive an expression of the Gravitational constant G starting with Friedmanns equation for an expanding critical density universe

While length contraction was the first idea proposed to explain MMx near null result, it may be more comfortable to consider length contraction as a necessary consequence of time dilation - an idea that came a bit later. Since the latter provides a residual record when clocks are compared after they have been brought to rest in the same frame, it may be confusion from a tutorial aspect, to start with length contraction.

thank you for your answer. my oppinion is that the best way to the transformation equations is Einstein's clock synchronization procedure. It leads to xx-cctt=x'x'-cct't' which at its turn leads to time dilation which leads to length contraction. time dilation per se is sufficient for deriving the LET. What i wanted to show was that once the LET for the space coordinates is derived in the way we like, the LET transformation for the time coordinates is a direct conseqeunce of the first one if we take into account clock synchronization.

 

[nakurusil]

Please delete from my message the sentence "(1) can be derived from length contraction" considering that it is derived in a way with which you aggree! What I wanted to underline was that (2) is a direct consequence of (1) if we consider the clock synchronization procedure in the two frames.
SINE IRA ET STUDIO

You are getting even worse: the Lorentz transform of time cannot be derived from the one for x. What gave you this idea?

 

[bernhard.rothenstein]

Let

You are getting even worse: the Lorentz transform of time cannot be derived from the one for x. What gave you this idea?

Could you prove your statement? You do not agree that as a result of clock synchronization in the invoved reference frames x/c=t, x'/c=t' and so
x/c=g(x'/c+Vt'/c) and finally
t=g(t'+Vx'/cc)?
The idea is mine. If it is not correct I am the single guilty! I think we are on the forum to help each other proving our statements.

 

[nakurusil]

Could you prove your statement? You do not agree that as a result of clock synchronization in the invoved reference frames x/c=t, x'/c=t' and so
x/c=g(x'/c+Vt'/c) and finally
t=g(t'+Vx'/cc)?
The idea is mine. If it is not correct I am the single guilty! I think we are on the forum to help each other proving our statements.

Look at the original derivation:
From the clock synchronization equation follows the transformation for t.
From the transformation for t follows the transformation for x.
This is the natural chain of derivations.

 

[bernhard.rothenstein]

Lorentz-Einstein transformations

Look at the original derivation:
From the clock synchronization equation follows the transformation for t.
From the transformation for t follows the transformation for x.
This is the natural chain of derivations.

Concerning the chain of derivatios we go to C.Moller 'The Theory of Relativity" Oxford at the Clarendon Press 1952 pp.36-41. We see that the derivations of space and time coordinates go in parallel, guessing theirs shapes in order to be in accordance with the invariance of xx-cctt=x'x'-cct't' and so i think that there is not a preference for the succession in which we derive the two transformation equations. Once derived the equations
x=g(x'+Vt')
x'=g(x-Vt)
lead with some algebra to
t=g(t'+Vx'/cc)
t'=g(t-Vx/cc)
and so the vice-versa to your statement is proved.
Thank you for your participation to the discussion from which and many readers could learn. I think that is for what we are there.

 

[JM]

Review of Einsteins 1905 paper shows that his derivation is based on the properties of light waves as modified by the Light Postulate. His process produces all four relations, x,y,z,t, together. Has anyone disagreed with his LET or with his analysis of the Maxwell equations? The ideas of slow clocks and contraction play no active part in his LET derivation or his Maxwell analysis. It appears that there is still a question whether dilation and contraction actually occur or whether they are connected with the measurement procedure.

 

[Meir Achuz]

Concerning the style of your answer it is far from being elegant (do you use sily when you discuss with your students?) and the air of superiority you display is descouraging.
sine ira et studio

I did not say you were silly. I was referring subjunctively to a hypothetical "one". I am very careful in redressing students. I consider you more of an equal. I just wanted somehow to emphasize the importance of going from one fundamental principle, rather than Fitzgerald's patchwork attempt. Now I've insulted him. Anyway, I will not interfere with this thread again.

 

[nakurusil]

Please delete from my message the sentence "(1) can be derived from length contraction" considering that it is derived in a way with which you aggree! What I wanted to underline was that (2) is a direct consequence of (1) if we consider the clock synchronization procedure in the two frames.
SINE IRA ET STUDIO

I don't understand your post.

I do not agree with your attempt to derive the transforms from length contraction. Length contraction is a consequence of the transforms, if you are attempting to start from the Lorentz-FitzGerald contraction that is a very bad idea.

I do not agree with your attempt to change the original Einstein derivation , i.e. the proper order is clock synchronization equation -> t transform -> x transform

The original Einstein derivation is excellent and doesn't need any modifications.

 

[bernhard.rothenstein]

Let

I don't understand your post.

I do not agree with your attempt to derive the transforms from length contraction. Length contraction is a consequence of the transforms, if you are attempting to start from the Lorentz-FitzGerald contraction that is a very bad idea.

I do not agree with your attempt to change the original Einstein derivation , i.e. the proper order is clock synchronization equation -> t transform -> x transform

The original Einstein derivation is excellent and doesn't need any modifications.

My intention was not to derive the LET. Einstein did it for all of us. My intention is to show that the direct and the inverse transformations for the space coordinates lead with some simple algebra to the direct and the inverse transformation for the time coordinate and vice-versa. Concentrate please your answer on this side of the problem. In a period when special relativity is a rara avis in the curriculum, I think that Einstein, still alive, would invent a short and transparent enough derivation. I know a nice story which asks if the missionary who was eaten by the natives did his job well? The answer is no, because he did not well his job or he has tried to impose his faith by force. I think the same question aplies in the case of the teacher who starts teaching relativity with four vectors or tensors...
Thanks for your participation.

 

[yogi]

I would agree Bernhard - it is more important to first obtain the physical connotation rather than start with a mathematical abstraction - we know that Einstein arrived at a result that he did not properly explain and may not have fully comprehended - In part IV of the 1905 paper he first gives an example of two clocks synchronized in one frame then states that when one is moved to the position of the other, there is a peculiar result - the clock that moved will be found to lag behind the one which has not moved - after giving a few more examples which consider both one way and round trip journeys he concludes that a clock at the equator will run slower than a clock at the pole!... but in actuality all clocks run at the same speed - and we know that one inertial frame is no better than another... so he implies something that contradicts the very foundation of SR. If he had said "The moving clock logs less time relative to the clock which is considered to be at rest" it would have generated less debate. The fact is, the moving clock does not run slower - but you do not get this from the equations per se - and that is why it is important to look at these things from perspectives that reveal new insight .. starting with synchronization and length contraction allows you to recover time dilation - and it is easier to see the time difference as being the result of a total accumulation of time in the length contracted frame rather than an alteration of the clock rate.

 

[bernhard.rothenstein]

time dilation and length contraction from LET or vice versa

Length contraction is a consequence of the LE transforms , not the other way around.

Please have a look at Asher Peres "Relativistic telemetry" Am.J.Phys. The Author derives the formulas that account for the radar echo, for time dilation, Doppler Effect and for the addition law of velocities without using the LET, considering that using them we obscure the physics behind the mentioned fundamental effects. Personally I learned a lot from the quoted paper which shows how mighty are the two postulates.
love was invented by a vendor of flowers

 

[nakurusil]

Please have a look at Asher Peres "Relativistic telemetry" Am.J.Phys. The Author derives the formulas that account for the radar echo, for time dilation, Doppler Effect and for the addition law of velocities without using the LET, considering that using them we obscure the physics behind the mentioned fundamental effects. Personally I learned a lot from the quoted paper which shows how mighty are the two postulates.
love was invented by a vendor of flowers

An exercise in futility. Not even worth the time finding out what is wrong with such papers.

 

[Daverz]

An exercise in futility. Not even worth the time finding out what is wrong with such papers.

Why are you assuming it's wrong? It's in a very reputable journal (Am. J. Phys. is about as vanilla as you can get) and written by a well-known physicist.

 

[nakurusil]

Why are you assuming it's wrong? It's in a very reputable journal (Am. J. Phys. is about as vanilla as you can get) and written by a well-known physicist.

"without using the LET, considering that using them we obscure the physics"

Really? Either the paper is wrong or Bernhard is misquoting the author. Either way, such papers are not useful for anything, they generally hide some flaw and they bring nothing over the standard derivation. AmJPhys publishes a lot of this stuff because it doesn't publish any original research (by declared charter).

 

[bernhard.rothenstein]

read the paper not the journal

"without using the LET, considering that using them we obscure the physics"

Really? Either the paper is wrong or Bernhard is misquoting the author. Either way, such papers are not useful for anything, they generally hide some flaw and they bring nothing over the standard derivation. AmJPhys publishes a lot of this stuff because it doesn't publish any original research (by declared charter).

the exact quotation of the paper Asher Peres, "Relativistic telemtry,' Am.J.Phys. 55 516 1987 is
"The Lorentz transformation is the standard way to derive formulas for relativistic phenomena, such as time dilation, addition of velocities, the Doppler Effect, optical aberration etc. Although the derivation of these formulas is straightforward, it is rather formal and not very transparent from the point of view of physics. In this article I show how thwy can be derived very simply from Einstein's relativity principle :All physical laws are the same for all inertial observers. "
I would highly appreciate if you could show me which are the week points of Ashers' paper as probably many Forumists would do. I did not discover anyone but that is my fault.
I think that many of us have a feeling of frustration being not published by Am.J.Phys. to which of course apply " nobody is perfect".
Thanks for participation on the thread.

 

[nakurusil]

the exact quotation of the paper Asher Peres, "Relativistic telemtry,' Am.J.Phys. 55 516 1987 is
"The Lorentz transformation is the standard way to derive formulas for relativistic phenomena, such as time dilation, addition of velocities, the Doppler Effect, optical aberration etc. Although the derivation of these formulas is straightforward, it is rather formal and not very transparent from the point of view of physics. In this article I show how thwy can be derived very simply from Einstein's relativity principle :All physical laws are the same for all inertial observers. "
I would highly appreciate if you could show me which are the week points of Ashers' paper as probably many Forumists would do. I did not discover anyone but that is my fault.
I think that many of us have a feeling of frustration being not published by Am.J.Phys. to which of course apply " nobody is perfect".
Thanks for participation on the thread.

I do not have the paper , if you would care to post a scan I might spend some time to look for the flaw. Either way, what is the use of such papers?

 

[bernhard.rothenstein]

supposing a flaw in a not seen paper

I do not have the paper , if you would care to post a scan I might spend some time to look for the flaw. Either way, what is the use of such papers?

i am surprised by your point of view supposing a flaw in a paper you have not seen. but that is your problem.

 

[bernhard.rothenstein]

paper

I do not have the paper , if you would care to post a scan I might spend some time to look for the flaw. Either way, what is the use of such papers?

if you give me an email address I could forward you the paper. as I see on the forum you are no the single one who considers that there are futil papers. your comment would help me to find out which are in your oppinion the usefull papers.

 

[JM]

I would agree Bernhard - it is more important to first obtain the physical connotation rather than start with a mathematical abstraction - we know that Einstein arrived at a result that he did not properly explain and may not have fully comprehended - In part IV of the 1905 paper he first gives an example of two clocks synchronized in one frame then states that when one is moved to the position of the other, there is a peculiar result - the clock that moved will be found to lag behind the one which has not moved - after giving a few more examples which consider both one way and round trip journeys he concludes that a clock at the equator will run slower than a clock at the pole!... but in actuality all clocks run at the same speed - and we know that one inertial frame is no better than another... so he implies something that contradicts the very foundation of SR. If he had said "The moving clock logs less time relative to the clock which is considered to be at rest" it would have generated less debate. The fact is, the moving clock does not run slower - but you do not get this from the equations per se - and that is why it is important to look at these things from perspectives that reveal new insight .. starting with synchronization and length contraction allows you to recover time dilation - and it is easier to see the time difference as being the result of a total accumulation of time in the length contracted frame rather than an alteration of the clock rate.

Yogi, I find your comments intrigueing, and I sense that you have some original viewpoints. I like what you say and I would like to hear more.I note you say "all clocks run at the same speed", I agree, but this seems to disagree with the common statement ' moving clocks run slow". Can you say what references you use or what you have published?

 

[Chris Hillman]

Asher Peres

i am surprised by your point of view supposing a flaw in a paper you have not seen. but that is your problem.

Bernhard, I am trying to avoid debunking in this forum, but it might help to recall that the MR review (23 B1527), by Felix Pirani, of the paper

Asher Peres, Null electromagnetic fields in general relativity, Phy. Rev. 118 (2) (1960): 1105-1110

states in part "The reviewer (Pirani) disagrees with the author's (Peres's) view, based on coordinate-dependent considerations, that pp waves are 'purely longitudinal'". Indeed, that claim (by Peres) is not only just plain wrong, but obviously wrong. In fact, pp waves represent purely transverse radiation.

Pirani was one of the founders of the theory of gravitational radiation in gtr, and one of the tiny handful of physicists who correctly understood such basic issues as the role of Riemann curvature tensor in gtr, as early as 1959 or so. Among other things, he independently discovered what we now call the Petrov types; in the Petrov classication, pp waves are type N and purely transverse; type III vacuums can include a kind of longitudinal component, which is revealed by examining the Bel decomposition of the Riemann tensor with respect to some timelike congruence.

I don't know what nakurusil was thinking of, but certainly this kind of bizarre claim makes me look quite a bit more suspiciously at any claims by the same author on similar topics. Or if time is short, to dismiss claims by that author as "unverified, and possibly not worth the time I would spend checking up on his claims".

Hope this makes sense, and that you take it in the spirit intended!

 

[bernhard.rothenstein]

relativistic clocks and time intervals

Yogi, I find your comments intrigueing, and I sense that you have some original viewpoints. I like what you say and I would like to hear more.I note you say "all clocks run at the same speed", I agree, but this seems to disagree with the common statement ' moving clocks run slow". Can you say what references you use or what you have published?

please have a critical look at
arXiv.org > physics > physics/0511062
Search for(Help | Advanced search)


We present a relativistic space-time diagram that displays in true magnitudes the readings (date-times) of two inertial reference frames clocks. One reference frame is the rest frame for one clock. This diagram shows that two events simultaneous in one reference frames are not compulsory simultaneous in the other frame. This approach has a bi-dimensional character.
Full-text: PDF only

 

[nakurusil]

Bernhard, I am trying to avoid debunking in this forum, but it might help to recall that the MR review (23 B1527), by Felix Pirani, of the paper

Asher Peres, Null electromagnetic fields in general relativity, Phy. Rev. 118 (2) (1960): 1105-1110

states in part "The reviewer (Pirani) disagrees with the author's (Peres's) view, based on coordinate-dependent considerations, that pp waves are 'purely longitudinal'". Indeed, that claim (by Peres) is not only just plain wrong, but obviously wrong. In fact, pp waves represent purely transverse radiation.

Pirani was one of the founders of the theory of gravitational radiation in gtr, and one of the tiny handful of physicists who correctly understood such basic issues as the role of Riemann curvature tensor in gtr, as early as 1959 or so. Among other things, he independently discovered what we now call the Petrov types; in the Petrov classication, pp waves are type N and purely transverse; type III vacuums can include a kind of longitudinal component, which is revealed by examining the Bel decomposition of the Riemann tensor with respect to some timelike congruence.

I don't know what nakurusil was thinking of, but certainly this kind of bizarre claim makes me look quite a bit more suspiciously at any claims by the same author on similar topics. Or if time is short, to dismiss claims by that author as "unverified, and possibly not worth the time I would spend checking up on his claims".

Hope this makes sense, and that you take it in the spirit intended!

I said what I said in reference to this:

"the exact quotation of the paper Asher Peres, "Relativistic telemtry,' Am.J.Phys. 55 516 1987 is
"The Lorentz transformation is the standard way to derive formulas for relativistic phenomena, such as time dilation, addition of velocities, the Doppler Effect, optical aberration etc. Although the derivation of these formulas is straightforward, it is rather formal and not very transparent from the point of view of physics. In this article I show how thwy can be derived very simply from Einstein's relativity principle :All physical laws are the same for all inertial observers. "..meaning that there are many such papers that made claims about a novel derivation of the Lorentz transforms and that in most cases they are uninteresting or contain hidden flaws. You got the wrong Asher Peres paper, the one I'm talking about is an sr , not a gtr paper.

 

[bernhard.rothenstein]

special relativity

So, you are a coauthor of that paper, right?

Uhm... did you just change the subject? What does this have to do with why someone might be suspicious about claims concerning gtr made by the late Asher Peres?

Yes I am. Proposing my humble contribution to physics teaching I always mention "critical look". My message you answer was not intended to you and so why do you consider that I have changed the subject?. The present is. I consider that in a period when every thing in physics and in particular in special relativity can be contested, it is hard for a humble physicist to teach it. I have in mind those who renegate special relativity start from the begining, those who revive the ether, those who consider that the propagation of light in empty space is not isotropic, those who invent new transformation equations for the space time coordinates...In what concerns Asher Peres I think that the facts you quote have nothing to do with his short and concise paper from which I have learned so much and probably many others did. Your large scale information (which is very impresive) would be more usefull for us if you would use it showing what is wrong with Asher's paper and of others in the same style published by journals devoted to teaching physics. Would you be so kind to do that? I consider that such an attempt would illustrate why some like (cool) "two line derivations" illustrating the simplicity of special relativity theory and why others like better (hot) complicated approaches using concepts which are not in an easy reach for the beginers. Being democratic physics should ensure access for all, of course up to a given level which depends on theirs ability.
sine ira et studio

 

[bernhard.rothenstein]

asher peres' sr paper

show h

I said what I said in reference to this:

"the exact quotation of the paper Asher Peres, "Relativistic telemtry,' Am.J.Phys. 55 516 1987 is
"The Lorentz transformation is the standard way to derive formulas for relativistic phenomena, such as time dilation, addition of velocities, the Doppler Effect, optical aberration etc. Although the derivation of these formulas is straightforward, it is rather formal and not very transparent from the point of view of physics. In this article I ow thwy can be derived very simply from Einstein's relativity principle :All physical laws are the same for all inertial observers. "


..meaning that there are many such papers that made claims about a novel derivation of the Lorentz transforms and that in most cases they are uninteresting or contain hidden flaws. You got the wrong Asher Peres paper, the one I'm talking about is an sr , not a gtr paper.

please take note that Peres did not propose a novel derivation of the Lorentz transformation. he derives some relaivistic formula without using them. is there something wrong?
sine ira et studio

 

[Chris Hillman]

Distinct papers by Asher Peres

Hi all,

..meaning that there are many such papers that made claims about a novel derivation of the Lorentz transforms and that in most cases they are uninteresting or contain hidden flaws. You got the wrong Asher Peres paper, the one I'm talking about is an sr , not a gtr paper.

I apologize if I have caused unneccessary confusion. Actually, I DID realize that you and Bernhard are discussing a different paper on an entirely different topic. I noticed that Bernhard had apparently taken umbrage at what he seemed to feel amounted to someone such as myself dismissing a paper by Peres as "possibly not worth my time", and I was trying to briefly explain why such an attitude, on the part of someone familiar with some other papers by this author, might not be unreasonable.

 

[Chris Hillman]

Yes I am. Proposing my humble contribution to physics teaching I always mention "critical look". My message you answer was not intended to you

Sorry, Bernard, I realized that just before I saw this and have deleted that post.

I tend to avoid discussions of special relativity, particularly ones which do not appear to me to involve a clear issue of what I would consider to be genuine interest. However, I acknowledge that to some degree this preference is a matter of taste.

Hope this has cleared the air!

 

[JM]

Prof. Rothenstein, The point here is the rate of the clocks. If the motion of a light ray is analysed the readings of the two clocks will disagree, because of the corrections required to satisfy the Light Postulate, but the rates of the clocks will be the same, I think.

 

[Doc Al]

The point here is the rate of the clocks. If the motion of a light ray is analysed the readings of the two clocks will disagree, because of the corrections required to satisfy the Light Postulate, but the rates of the clocks will be the same, I think.

Not sure what you are saying here, but if you are thinking that once you correct for the travel time of the light that you will find that all clocks run at the same rate--not so.

 

[Meir Achuz]

Against my better judgement, I have been looking at parts of this thread from time to time. Now, against my sworn promise, I will enter it once more. Asher Peres has been attacked and defended, in both cases unfairly.
In another life, I knew Asher Peres; I was a friend of Asher Peres.
Asher Peres and I had numerous, contentious but friendly, discussions, mostly about quantum mechanics where he also enjoyed outraging his peers.
(His thesis adviser was R of EPR.) The GR reviewer would not have attacked Asher so brutally if he did not also have good respect for Asher. That is the nature of Mediterranean physics. Asher would love this heated debate over his now dead body. I think the reason is that Asher (as expresssed in an autobiographical essay published as part of his seventieth birthday feldschrift) revelled in presenting physical insights that were nontraditional and considered outrageous by some of his peers.
He particularly liked to undercut his teachers, and told of one who promised him an A "if you would just stop coming to my class."
[This has been so long that I will put the physics in my next post.]