## - Measuring the contracted train -

Einstein/Minkowski told us to look at it 4 dimensionally.

Consider a red train with rest length L0, measured by a red passenger carrying with him -at rest relative to the train- a red ruler as indicated.

L0 is the distance between events E1 (rear of the train) and E2 (front of the train) at red wristwatch time t'=43. The train fits exactly between the blue flag and the brown tree.

A green observer measures with his green ruler (at rest relative to him). The red and green rulers have different directions in 4D spacetime. This is due to the 'relativity of simultaneity'.

L1 is the green coordinate length (distance) from event E1 to event E2.

Lorentz tranformations give you that length x =g(x'+vt'))

Notice that this green coordinate length is

The green coordinate length does

The train is not only a 3D entity, but a 4-dimensional spacetime entity (made of all the events of past, present and future train existence), part of total 4D spacetime universe (made of all events, past, present and future of total universe from birth to death).

The left red worldline is made of all events ('past, present and future') of the rear of the train (the collection of all wristwatch events of a passenger sitting at the rear of the train).

The right red world line is made of all events ('past, present and future') of the front of the train.) The full pink area indicates the full 4D spacetime existence of the train and its passengers. But the passengers do not read the full 4D spacetime at once. They experience flow of time and consider successive 3D spaces of simultaneous events (red 3D worlds). (For clarity I do not indicate the area of green and red ruler's 4D existence.)

Relalivity of simultaneity means different observers -moving relative to each other- select out of all the 4D spacetime events different events as being simultaneous, happening "now", i.o.w. different 3D space worlds. Each observer's 3D world contains a different set of events of the train's life. Different cuts means different events, not just different coordinates:

(Note. For the green observer with wristwatch 50, the front of the contrated train with events E1 to E3 is not at the tree yet. It does

Similar procedure can be done for a red passenger and a contracted green train (not shown). The reciprocal shorter trains are different 3D cuts through real 4D spacetime existence, where all events are co-existing.

(Likewise, reciprocal time dilation is nothing else than physically real wristwatch time indication events in different 3D space world cuts through 4D spacetime existence (block universe).

Einstein:

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Consider a red train with rest length L0, measured by a red passenger carrying with him -at rest relative to the train- a red ruler as indicated.

L0 is the distance between events E1 (rear of the train) and E2 (front of the train) at red wristwatch time t'=43. The train fits exactly between the blue flag and the brown tree.

A green observer measures with his green ruler (at rest relative to him). The red and green rulers have different directions in 4D spacetime. This is due to the 'relativity of simultaneity'.

L1 is the green coordinate length (distance) from event E1 to event E2.

Lorentz tranformations give you that length x =g(x'+vt'))

Notice that this green coordinate length is

**LONGER**than L0 !The green coordinate length does

**not**give the green observer the length of the**contracted**train. The green coordinate system indeed measures the "train at rest relative to the red train passengers" from/with a different coordinate system ,**but does not give you the contracted train length of simultaneous train events in the green frame at t=0**(because the**contracted**train is not made of the events on the red line from E1 to E2).The train is not only a 3D entity, but a 4-dimensional spacetime entity (made of all the events of past, present and future train existence), part of total 4D spacetime universe (made of all events, past, present and future of total universe from birth to death).

The left red worldline is made of all events ('past, present and future') of the rear of the train (the collection of all wristwatch events of a passenger sitting at the rear of the train).

The right red world line is made of all events ('past, present and future') of the front of the train.) The full pink area indicates the full 4D spacetime existence of the train and its passengers. But the passengers do not read the full 4D spacetime at once. They experience flow of time and consider successive 3D spaces of simultaneous events (red 3D worlds). (For clarity I do not indicate the area of green and red ruler's 4D existence.)

Relalivity of simultaneity means different observers -moving relative to each other- select out of all the 4D spacetime events different events as being simultaneous, happening "now", i.o.w. different 3D space worlds. Each observer's 3D world contains a different set of events of the train's life. Different cuts means different events, not just different coordinates:

**The train, measured by the green observer with green wristwatch time indiacation t=0, is not the L0 train with events from E1 to E2, but the train made of events E5 to E6**. Or f.ex. events E1 to E3 (for a green observer with wristwatch time indication 50 ), etc.**The contracted train is not the red L0 train measured from a different angle! The contraction is not the result of using a different coordinate system measuring train E1-E2**. Measuring the events of the 'contracted' train between events E5-E6 gives the green observer a**shorter**length L3 (relative to the length L0 between events E1 and E2).(Note. For the green observer with wristwatch 50, the front of the contrated train with events E1 to E3 is not at the tree yet. It does

**not**only 'seems' or 'appears' that way. Nor is it only a coordinate effect. In Mr Green's physically real 3D space world of simultaneous events the front of the train is really not at the tree yet.)Similar procedure can be done for a red passenger and a contracted green train (not shown). The reciprocal shorter trains are different 3D cuts through real 4D spacetime existence, where all events are co-existing.

(Likewise, reciprocal time dilation is nothing else than physically real wristwatch time indication events in different 3D space world cuts through 4D spacetime existence (block universe).

Einstein:

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*From a "happening" in three-dimensional space, physics becomes, as it were, an "existence" in the four-dimensional "world".*>> Albert Einstein. "Relativity: The Special and the General Theory." 1916. Appendix II Minkowski's Four-Dimensional Space ("World") (supplementary to section 17 - last section of part 1 - Minkowski's Four-Dimensional Space).<<

*Since there exists in this four dimensional structure [space-time] no longer any sections which represent "now" objectively, the concepts of happening and becoming are indeed not completely suspended, but yet complicated. It appears therefore more natural to think of physical reality as a four dimensional existence, instead of, as hitherto, the evolution of a three dimensional existence.*>> Albert Einstein, "Relativity", 1952.