Time saving and not obscuring way of teaching special relativity theory?

[bernhard.rothenstein]

time saving and not obscuring way of teaching special relativity theory??

Events could be generated by tardyons in motion. A tardyon moving with speed u in the positive direction of the OX axis of the I frame generates the event E(x=ut,t=x/u). Detected from I' the same event is characterized by the space-time coordinates (g=gamma)
x'=gx(1-V/u) (1)
t'=gt(1-Vu/cc) (2)
Extending (1) and (2) to relativistic dynamics the tardyon has an energy E and a momentum p=Eu/cc. Momentum being a space-like physical quantity (the vector component of the (E,cp) "four" momentum it transforms as
p'=gp(1-V/u)=g(p-VE/cc) (3)
whereas energy as a time like physical quantity and the scalar component of a four vector it transforms as
E'=gE(1-Vu/cc)=g(E-Vp/cc) (4)
The method could be extended to all the four vectors involved in special relativity theory and also in the case of the electric and magnetic fields.
Do you consider that such a way of teaching, complemented with some explanations is time saving and not obscuring?

 

[JustinLevy]

I don't understand what you are trying to accomplish here.
If you are presenting those as the transformations they incorrectly give the impression that x and x' for events are merely related by a scale factor (ie. the transformation doesn't need t and t'). If you already have the Lorentz transformations and then derive these, why not just stick with the lorentz transformations. In particular, if the point of this excersize is to derive the transformation of E and p, you assume p=Eu/cc which will not be obvious to them at all (since it requires SR) and thus seems to defeat the point of this derivation.


Many of your posts seem related to such matters, containing bizarre looking ways to represent things to reduce the number of steps in deriving something. If that works, for you, great. However when one is trying to learn physics, the teacher should first focus on the concepts ... otherwise students get the impression that physics is just an "equation sheet". They need to understand the meaning / concepts so that they can apply physics to problems they have not seen yet.

All methods of teaching SR I have seen (while differring on the level of mathematical tools employed) still start by explaining the concepts (however they word the postulates) and deriving things using these concepts. This way if a student ever gets confused, they can still trace it back to something they understand.

Furthermore, especially when teaching SR (I have helped teach at a univeristy level for the SR section of a classical mechanics course), it seems very important to either just state the result or give a clear mundane derivation. Many students have trouble wrapping their mind around SR, and it would be useful to avoid tripping them up by using some math trick ... or even worse, have them come away thinking SR is merely a "useful math trick", as that betrays the insight SR gives us on the physical world (and you're basically back at Lorentz's view of SR).

As with any subject that is difficult to approach initially, there will be as many opinions about how to teach it as there are people that have learned it. This is merely mine, so take it as you will. It is your class, not mine.

I don't believe using velocity addition as a starting point is useful (which many of your posts and approaches seem to use), for it is MUCH more complicated when considering more dimensions than 1 spatial, 1 time. The conventional approach of starting with either symmetry or Einstein's postulates is much more trivial to understand the addition of more dimensions to get to our 4d world. Furthermore, focussing so much on velocity addition can make the transition later to a geometric understanding more difficult.

 

[bernhard.rothenstein]

I don't understand what you are trying to accomplish here.
If you are presenting those as the transformations they incorrectly give the impression that x and x' for events are merely related by a scale factor (ie. the transformation doesn't need t and t'). If you already have the Lorentz transformations and then derive these, why not just stick with the lorentz transformations. In particular, if the point of this excersize is to derive the transformation of E and p, you assume p=Eu/cc which will not be obvious to them at all (since it requires SR) and thus seems to defeat the point of this derivation.

x and x' and t and t' are not related by a scale factor but by a function which depends on the speed of the tardyon in one of the involved reference frames.

Many of your posts seem related to such matters, containing bizarre looking ways to represent things to reduce the number of steps in deriving something. If that works, for you, great. However when one is trying to learn physics, the teacher should first focus on the concepts ... otherwise students get the impression that physics is just an "equation sheet". They need to understand the meaning / concepts so that they can apply physics to problems they have not seen yet.

With supplementary explanations between the steps everything becomes clear.

All methods of teaching SR I have seen (while differring on the level of mathematical tools employed) still start by explaining the concepts (however they word the postulates) and deriving things using these concepts. This way if a student ever gets confused, they can still trace it back to something they understand.

Furthermore, especially when teaching SR (I have helped teach at a univeristy level for the SR section of a classical mechanics course), it seems very important to either just state the result or give a clear mundane derivation. Many students have trouble wrapping their mind around SR, and it would be useful to avoid tripping them up by using some math trick ... or even worse, have them come away thinking SR is merely a "useful math trick", as that betrays the insight SR gives us on the physical world (and you're basically back at Lorentz's view of SR).

As with any subject that is difficult to approach initially, there will be as many opinions about how to teach it as there are people that have learned it. This is merely mine, so take it as you will. It is your class, not mine.

I don't believe using velocity addition as a starting point is useful (which many of your posts and approaches seem to use), for it is MUCH more complicated when considering more dimensions than 1 spatial, 1 time. The conventional approach of starting with either symmetry or Einstein's postulates is much more trivial to understand the addition of more dimensions to get to our 4d world. Furthermore, focussing so much on velocity addition can make the transition later to a geometric understanding more difficult.

Starting with the addition law of velocities I am in a good company.
David Bohm "The Special Theory of Relativity" Routledge London New York 1996 pp.116-120.

Thank you for telling me your point of view. I appreacite it. I have inserted my point of view.
.
Do you think that presenting collisions and using conservation laws is a better way to introduce the student in the subject?
I am interested in the oppinion of other participants on PHF

 

[Moonbear]

With supplementary explanations between the steps everything becomes clear.

This is a subject I know nothing about, but that part of your response struck me as important. If you're providing additional explanation between the steps, then it seems if you're going to present this as a new approach to teaching material, you must be explicit about what those added explanations are, especially if they are non-trivial. What are the supplementary explanations you would include that would satisfy Justin's concerns? Being explicit about every step of your thought process is an important part of teaching, because that's what you need to model for your students. This is true no matter what subject you teach. If you skip steps and take shortcuts, they don't yet know the subject to keep up and will quickly become confused. So, if there are more explanations than what you've presented, please elaborate for the benefit of those who might be tempted to use your approach else they wind up shortchanging their students.

 

[bernhard.rothenstein]

This is a subject I know nothing about, but that part of your response struck me as important. If you're providing additional explanation between the steps, then it seems if you're going to present this as a new approach to teaching material, you must be explicit about what those added explanations are, especially if they are non-trivial. What are the supplementary explanations you would include that would satisfy Justin's concerns? Being explicit about every step of your thought process is an important part of teaching, because that's what you need to model for your students. This is true no matter what subject you teach. If you skip steps and take shortcuts, they don't yet know the subject to keep up and will quickly become confused. So, if there are more explanations than what you've presented, please elaborate for the benefit of those who might be tempted to use your approach else they wind up shortchanging their students.

Following your encouraging hint the additional explanations are
Consider a particle (tardyon) detected from the inertial reference frames I and I' in the standard arrangement. Knowing classical mechanics observers from I and I' will consider that the momentum of the particle is (OX,O'X' components)
p=mu (1)
p'=m'u' (2)
respectively. From relativistic kinematics they know that u and u' are related by
u=(u'+V)/(1+Vu'/cc). (3)
Combining (1) and (2) and taking into account (3) the result is
(p/m)=(p'/m')(1+V/u')/(1+Vu'/cc) (4)
Equation (4) suggests to consider that
p=Gp'(1+V/u') (5)
m=Gm'(1+u'V/cc) (6)
where G is a function of the relative velocity V but not of the physical quantities involved in the transformation process.
Performed experiments and thought experiments confirm that the rest mass m(0) of the tardyon measured by observers of I' when it is at rest relative to them and its relativistic mass m measured by observers from I relative to whom it moves with speed V are related by
m=gm(0) (7)
where g=1/sqr(1-V*2/c*2).
Imposing condition (7) to (6) the result is
G=g (8)
(5) and (6) becoming
p=gp'(1+V/u')=g(p'+Vm') (9)
m=gm'(1+Vu'/cc)=g(m'+Vp'/cc). (10)
Taking into account that the the OY(O'Y') components of the electric field and the OZ(O'Z')
components of the magnetic field are related by
E(y)=uB(z) (11)
E'(y)=u'B'(z) (12)
the strategy followed above could lead to the transformation equations that work there.
Your criticism is hyghly appreciated.
During the presentation the instructor could provide more information if needed.

 

[Hurkyl]

Consider a particle (tardyon)

How would a student, just starting to learn SR, know what a tardyon is?

detected from the inertial reference frames I and I'

How would a student, just starting to learn SR, know what the inertial reference frames are in SR?

in the standard arrangement.

How would a student, just starting to learn SR, know what the standard arrangement is? (Heck, I know SR, and I don't know what you mean by that!

Knowing classical mechanics observers from I and I' will consider that the momentum of the particle is (OX,O'X' components)
p=mu (1)
p'=m'u' (2)
respectively.

Mixing classical and relativistic mechanics in the same argument seems like a very bad idea to me, but anyways...

[quote\From relativistic kinematics they know that u and u' are related by
u=(u'+V)/(1+Vu'/cc). (3)[/quote]
How would a student, just starting to learn SR, know that u and u' are related in that way?



Honestly, this sounds more like an exercise you would give an advanced theoretical physics student -- something like "Show that Special Relativity follows from hypothesis X". This doesn't sound at all like a programme for teaching a total beginner.

 

[bernhard.rothenstein]

How would a student, just starting to learn SR, know what a tardyon is?


How would a student, just starting to learn SR, know what the inertial reference frames are in SR?


How would a student, just starting to learn SR, know what the standard arrangement is? (Heck, I know SR, and I don't know what you mean by that!



Mixing classical and relativistic mechanics in the same argument seems like a very bad idea to me, but anyways...

[quote\From relativistic kinematics they know that u and u' are related by
u=(u'+V)/(1+Vu'/cc). (3)

How would a student, just starting to learn SR, know that u and u' are related in that way?



Honestly, this sounds more like an exercise you would give an advanced theoretical physics student -- something like "Show that Special Relativity follows from hypothesis X". This doesn't sound at all like a programme for teaching a total beginner.[/QUOTE]
Thank you for your answer. I think that you should guess that the approach is intended to students who master relativistic kinematics and all the chapters of physics in general. Latin where from my first language starts
uses to say ex nihilo nihil.
I think that it is illusory to start teaching special relativity to a total beginner. There is a logical evolution in teaching a subject: General physics, relativistic kinematics, relativistic dynamics, relativistic electrodynamics...Would you start teaching SR to a total beginner?
Of course, during the lecture the instructor could explain all the notions you suppose the student do not know. Anyway I am happy that I have received a single good point from such a strong participant, without discovering errors in the derivations.

 

[Hurkyl]

What do you consider SR to be? I would have said that the moment you start teaching relativistic kinematics (or dynamics or electromagnetism) is when you are teaching SR.

 

[Phrak]

I think a box of crayons, some craft paper and drawing scissored coordinates is the way to go.

 

[bernhard.rothenstein]

I think a box of crayons, some craft paper and drawing scissored coordinates is the way to go.

To go where?