Reducing the time invested in teaching SR

[bernhard.rothenstein]

If
x=u(x)t
p(x)=u(x)t
k(x)=uf and probably many other such equations, then why it is not enough to derive the LT for x and t and to mimick the transformations for all the others?
Would that obscure or reduce transparence. Would that show the kinematic origin of all the relativistic effects (relative motion)?
Thanks for your answers.

 

[meopemuk]

If
x=u(x)t
p(x)=u(x)t
k(x)=uf and probably many other such equations, then why it is not enough to derive the LT for x and t and to mimick the transformations for all the others?
Would that obscure or reduce transparence. Would that show the kinematic origin of all the relativistic effects (relative motion)?
Thanks for your answers.

It would be nice if you can explain the meaning of your equations and notation. I barely recognize t as time and x as position. What is u? p? k?, f?

Eugene.

 

[bernhard.rothenstein]

lorentz transformation

It would be nice if you can explain the meaning of your equations and notation. I barely recognize t as time and x as position. What is u? p? k?, f?

Eugene.

u is the speed of a particle that moves with speed u in the positive direction of the OX axis going through the origin at t=0.
p is the OX component of the same particle whereas m is its mass
f and k represent the frequency of the electromagnetic oscillations in an electromagnetic wave, and k the OX component of the wave vector. I hope I have given the correct English terms.
So if I start with
x=ut in I and x'=u't' in I' the Lorentz transformations give
x=g(V)[x'+Vt'] (1)
t=g(V)(t'+Vx'/cc) (2)
If I start with
p=um in I and p'=u'm' then mimicking (1) and (2) I could say that p and m transform as
p=g(V)[p'+Vm'] (3)
m=g(V)[m'+Vp'/cc] (4)
and I could continue with all the pair of physical quantities related by
S=uT in I and S'=u'T' where S is a space-like physical quantity T being a time like physical quantity.
All further questions you could ask are in my benefit!
Regards

 

[lightarrow]

If
x=u(x)t
p(x)=u(x)t
k(x)=uf and probably many other such equations, then why it is not enough to derive the LT for x and t and to mimick the transformations for all the others?
Would that obscure or reduce transparence. Would that show the kinematic origin of all the relativistic effects (relative motion)?
Thanks for your answers.

If k is the wave number (= 2(pi)/lambda), f the frequency and u the particle's speed (= group velocity), shouldn't be k = 2(pi)uf/c^2 ?

 

[lightarrow]

u is the speed of a particle that moves with speed u in the positive direction of the OX axis going through the origin at t=0.
p is the OX component of the same particle whereas m is its mass
f and k represent the frequency of the electromagnetic oscillations in an electromagnetic wave, and k the OX component of the wave vector. I hope I have given the correct English terms.
So if I start with
x=ut in I and x'=u't' in I' the Lorentz transformations give
x=g(V)[x'+Vt'] (1)
t=g(V)(t'+Vx'/cc) (2)
If I start with
p=um in I and p'=u'm' then mimicking (1) and (2) I could say that p and m transform as
p=g(V)[p'+Vm'] (3)
m=g(V)[m'+Vp'/cc] (4)

I wouldn't talk about relativistic mass; I would write instead:

p=g(V)[p'+VE'/cc]

E/cc = g(V)[E'/cc+Vp'/cc]

E = energy.

 

[bernhard.rothenstein]

Lt

If k is the wave number (= 2(pi)/lambda), f the frequency and u the particle's speed (= group velocity), shouldn't be k = 2(pi)uf/c^2 ?

Thanks. I think it is a question of notation but that is not essential in the discussion I started.
REGARDS

 

[bernhard.rothenstein]

lt

I wouldn't talk about relativistic mass; I would write instead:

p=g(V)[p'+VE'/cc]

E/cc = g(V)[E'/cc+Vp'/cc]

E = energy.

Thanks. I am not so sensitive concerning the concept of relativistic mass. When I started learning SR I knew that p=mu (1) in I and p'=m'u' (2) in I'. I also knew from relativistic kinematics the way in which parallel speeds add. Starting with (1), (2) and the addition law we are able to derive the properties m (m') should have in order to do not violate the postulates of SR.
All that is not esential in the discussion I started.
Regards