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I agree with a concept of consciousness that is defined by being fully engaged (aware, living in the moment etc.) and marvel that the brain can take these highly focussed learning processes and (as they become more automatic) efficiently park them elsewhere in the brain, leaving us more time/space to fully attend to new experiences.
It is now the end of May, I have completed the course, and am revising prior to attempting the final exam. I tried to derive the Lorentz Transformations from first principles and failed, emphasizing Brian Greene’s warning that the “mindless” turn of the crank application of these formulae would detract from a deeper understanding of the underlying principles! Oh so true – back to basics for me. Nevertheless a derivation of the formulae in the context of this ‘heavy’ unit might not have been advisable.
But it has been a really worthwhile journey – Many Thanks 🙂 My (limited) understanding is that this video was developed as part of the short (intuitive) course, and that its value is as an introduction, a teaching aid, to an element of the full math version.
The use of teaching aids should be selected to be appropriate for the intended audience – as a member of that audience I find the material challenging enough – nevertheless the Don Lincoln videos do make for a useful short, sharp shock of insight. It is fascinating to see graphically the relative progression of each observer’s experiences: At the turn around point in Gracie’s journey she has aged five years and sent out 5 annual greeting messages but received only 1 from George. George on the other hand has aged thirteen years and sent out 13 annual greeting messages but received only 2 from Gracie.
But what an eventful homecoming and reunion! It is fascinating to see graphically the relative progression of each observer’s experiences: At the turn around point in Gracie’s journey she has aged five years and sent out 5 annual greeting messages but received only 1 from George. George on the other hand has aged thirteen years and sent out 13 annual greeting messages but received only 2 from Gracie.
But what an eventful homecoming and reunion! My intuition tells me that in this simplified reality the result would be that there would be no paradox. Gracie would continue in constant velocity motion with respect to George for a fixed distance from and on to George. Similarly George would make the same journey from the perspective of Gracie. From each point of view they could both measure the distance, velocity and thus time from each perspective, and each could understand (post process) the alternative view – time dilation and length contraction would be experienced in identical fashion – therefore no paradox 🙂
Sadly my text (above) became scrambled when I copied it across!
However, I am now more enlightened – the original definition of the invariant interval (when c = 1) does readily transpose into (△t)² – (△x)² but, of course, the outcome must also be transposed.
So a negative value (less than 0) that relates to a potential causal connection in the original definition becomes a positive value (greater than 0) for a potential causal connection in the transposed version 🙂 I have struggled to follow the explanation of this Unit as there seems to be an inconsistency that I cannot understand!
Throughout the introductory sections of Unit 30 it was established that if the invariant interval between two events on a space-time diagram given by the condition: −(c∆t)2 + (∆x)2
is 0 then they can’t, they are causally disconnected
if =0 then they are at a causal boundaryHowever throughout the exercises (30.5) and the problem (30.6) it was stated that the invariant interval was given by: ∆t2 − ∆x2 and that if the resultant value:
is 0 the events can be causally connected
if =0 the events are at a causal boundaryNevertheless I did follow the initial version for the invariant interval to a correct conclusion.
My natural (lazy) preference has always been to first get a generalised, pictorial overview – and the mathematical derivations subsequently. However, I undertook this course to get a deeper understanding of the mathematics that underpins the concepts. Much as I dislike floundering through the mathematical mire, it is good for me (no pain, no gain) ¯\_( ͡❛ ͜ʖ ͡❛)_/¯
OK, I get it that the co-ordinates of the moving ‘object’ were taken from the perspective of the stationary ‘platform’. And that when these are translated to the perspective of a frame of reference moving at velocity V in the x direction the spatial co-ordinates of the y and z components remain unaffected but the time component will be, and as Velocity = Distance/Time then the Velocity must therefore be affected. So far, so good – but much more of this and my brain will boil!
I merrily progressed to unit 23 and found myself floundering in confusion – I had lost the internalisation of the constant nature of the speed of light! So I’m back here again (and doing other reading) to get a better grip on the concept, not just an acceptance of the ‘reality’. I figured that if one were to whack a rock or lead ball with a bat, it would shoot off at a measurable speed. If the ball were replaced with a golf ball, it would move faster. If the ball had zero mass and in a vacuum, just a light blow would cause it to shoot off really fast – if it were of truly zero mass then the speed should be infinitely fast!? So why is the zero rest mass photon restricted to the finite speed of light? Energy and Mass are related so perhaps the energy of the photon gives rise to pseudo-mass??
The platform perspective has the train moving to the right along the positive axis of x. The train perspective (from our bird’s eye view) has the platform moving to the left along the negative axis of x. Therefore it seems reasonable that the respective views of Lorentz Transformation will be identical except for the direction of velocity. However, the platform view sees the train moving to the right just as the view from the train window also has the platform scooting off to the right!