Einstein's Train & Me.

[madmac]

I printed off a copy of an English translation of -- On The Electrodynamics of Moving Bodies (June 30, 1905).

I read it over a few days, to see what Einstein said about his train-thought-experiments. Alby didn't mention any train experiment of any sort.

 

There was a mention in Chapter 1 to explain the physical meaning of simultaneous events, here Alby says -- "That train arrives here at 7 o'clock" -- which he says means -- "The pointing of the small hand of my watch to 7 and the arrival of the train are simultaneous events". No experiment here.

And in Chapter 7 re Doppler etc Alby mentions a -- "wave-train". Nothing to do with choo-choo trains.

 

My copy is 24 pages long, but it felt like 240 pages (slow going), nicely written, but some wordage hurt my brain.

Alby mentions -- postulates -- but sometimes he calls them -- principles (confusing).

Alby mentions a -- line of thought -- (to synchronise clocks). Later -- the rule -- the manner -- the method.

Alby mentions -- operations -- (to ascertain the length of a moving rod). Later -- a criterion.

And as well as -- ascertained -- he later says -- determined -- discovered -- measured.

We have that observers -- find that -- and later -- declare that.

 

My math is a problem, especially when in equations i confuse v with u. And the snail-trails (Greek?) used for x, y, z etc are scary. But i was impressed, & would be more impressed if i understood more of it. Alby sure was clever (or was it Mrs Alby?).

Anyhow, i had more luck with Alby's book -- Relativity: The Special and General Theory (1920) -- lots of trains, tomorrow.

Edited February 1, 2017 by madmac

[madmac]

Relativity: The Special and General Theory (1920).

Has lots of imaginings. I am mostly interested in trains, but will mention a few of the others.

 

(a) Alby erects a pole perpendicularly on Trafalgar Square to reach a cloud, measuring its L with a rod, to specify position.

 

1. A moving railway carriage with a window, Alby, dropped stone, ground (embankment) -- to show that trajectories are relative.

 

2. 1 again, but with 2 clocks that tick, a man, a man on a footpath -- to better measure the stones falling trajectory.

 

3. Railway carriage, embankment, flying raven, 2 observers -- to show movement in a straight line in different frames of reference.

 

4. Embankment, railway carriage, organ-pipe (emitting a note when parallel)(& when perpendicular) -- showing effect of orientation.

 

5. Earth (orbiting the sun), railway carriage (v = 30 km/sec) -- to show that the laws of nature are not affected by orientation.

 

6. Railway carriage, rails, man (walking along carriage)(or standing still for 1 sec), embankment -- theorem of addition of vel (later to be shown false).

 

7. Embankment, air (removed), ray of light (like man walking), tip of ray (vel c), railway carriage (vel v), railway lines -- vel of ray relative to carriage is less than c.

 

8. (7 again). Advising that 7 conflicts with the principle of relativity set forth earlier.

 

9. Lightning (2 strokes), striking rails on embankment at A & B (far apart) simultaneously, Alby (commissioned to determine whether the 2 events took place simultaneously), meteorologist (with a theory for simultaneous lightning) -- requires a definition of simultaneity which includes a method to decide.

 

10. (9 again). Observer (at midpoint M of A-B), holding 2 mirrors (inclined at 90dg to see A&B) -- can see if simultaneous.

Alby says that 10 is ok if the lightning flash vel A-M is the same as B-M. Alby says....

"That my definition satisfies this demand is indisputable. That light requires the same time to traverse the path A-M as for the path B-M is in reality neither a supposition nor a hypothesis about the physical nature of light, but a stipulation which i can make of my own freewill in order to arrive at a definition of simultaneity". (Comment -- i don't understand).

 

11. (Further to 10). Clocks (placed at ABC of the railway line)(with pointers set simultaneously the same) -- give the time of an event if at an event.

Alby says that 11 is ok if clocks go at the same rate, ie if they are of identical construction, & at rest in that reference frame. Alby says....

"This stipulation contains a further physical hypothesis, the validity of which will hardly be doubted without empirical evidence to the contrary".

 

12. Railway embankment, a very long train (at least 100 carriages)(vel = v), people in the train, 2 strokes of lightning at A & B -- full details tomorrow.

 

13. (Further to 12). A 3D consideration, by means of a framework of rods, for 3 co-ordinate planes -- showing equations for the Lorentz transforms.

 

14. (Further to 6). Instead of a man walking inside a carriage, a point moving -- giving an equation for addition of vel in one direction.

 

15. (Further to 14). The Fizeau experiment, the vel of light in a moving liquid in a tube. The tube plays the part of the railway embankment, the liquid the carriage, the light plays the part of the man walking -- Zeeman's measurements accord with the above equation to within 1%.

 

16. Embankment, railway carriage -- either are ok for a reference-body re the general laws of nature.

 

17. (Further to 16). An occupant, brakes (giving a jerk & non-uniform motion) -- Galileain law does not hold (& mentions general principle of relativity).

 

(b) A spacious chest (in space), with hook & rope attached to lid, with a being pulling, observer inside chest (equipped with apparatus), observer fastened with strings to floor -- leading to law of equivalence of inertial & gravitational mass.

 

18. (Further to 17 & (b)). Re observer in carriage experiencing a jerk due to brake -- might interpret this to a gravitational field.

 

(c ) Alby, a gas range, with 2 pans (alike, half filled with water), steam emitting from only one pan, a luminous blueish color under this pan but not the other -- Alby is not astonished by the different behaviour.

 

(d) (Further to (b)). A ray of light in the accelerated chest -- the path is curvilinear -- we conclude that in general rays of light are propagated curvilinearly in gravitational fields. Alby says that the estimated curvature for rays grazing the sun is 1.7 seconds of arc, & should manifest by observing stars during eclipse. Alby says that the special theory holds only if no gravitational field.

 

(e). A plane circular disc rotating in its plane, an observer on the disc might think he was at rest & that the force was gravitational -- an outside observer would interpret it as an effect of inertia & centrifugal force.

 

(f). (Further to (e)). Observer on disc uses clocks & rods . A clock at the rim is in motion & ticks slower than a (stationary) clock at the center (for both observers), even though the observer on the disc thinks both clocks are at rest. Alby says that this shows that in a gravitational field a clock will tick more quickly or less quickly according to position.

 

(g). (Further to (f)). If the observer on the disc uses a short rod to measure the circumference & diameter, he will arrive at a ratio larger than pi, because the rod is contracted when measuring the circumference of the rotating disc, but not when measuring the dia. Alby says that this shows that Euclidean geometry cannot hold exactly on the rotating disc, nor in general in a gravitational field.

 

(h). Alby, a marble table (or slab), covered by lots of small rods forming squares giving Cartesian co-ordinates. We heat the central part of the slab, those rods expanding & giving disorder. Alby says that this corresponds to the situation brought about by the general postulate of relativity.

Edited February 2, 2017 by madmac

[swansont]

!

Moderator Note

It's unclear to me what it is you wish to discuss.

[madmac]

swansont.

I will be looking at the above No12 (Einstein's famous train (thought) experiment) in detail, & i expect that there will be lots of discussion.

 

I decided to do this as a result of looking at the sister-thread which is based on the youtube version showing a short bullet-train, & showing the observer on the platform standing about half the length of the train back away from the train.

 

The bullet-train version differs from Einstein's original in many ways (i assume that the 1920 book version is faithful to the original), which changes some things. And the bullet-train version is so badly described (re who saw what where & when) that it is almost impossible to analyse.

Edited February 2, 2017 by madmac