2. Physical constraints |
Page = 2 |
"In every physical theory there is a rule which connects projections of the same object on different systems of reference, called a law of transformation, and all these transformations have the property of forming a group, i.e. the sequence of two consecutive transformations is a transformation of the same kind.
Invariants are quantities having the same value for any system of reference, hence they are independent
of the transformations".
The Lorentz transformations show, Born adds, that perspectival quantities "like distances in rigid systems, time intervals shown by clocks in different positions, masses of bodies, are now found to be projections, components of invariant quantities not directly accessible". We can therefore see that perspectivalism and invariance are two faces of symmetries.
A problem with the holist interpretation (b) is that it neglects the importance of constraints in Einstein's work. The presence of constraints and the concern for "fit" point in the direction of a stronger form of realism. Einstein is fond of the view that theoretical constructions are not inductive generalizations from experience but free inventions of the human mind. Nevertheless there must be a fit between the theoretical expressions and the external world. This compatibility is achieved, we suggested, through the introduction of constraints. If there is indeed a fit between what the theory says and what the material world presents, the question of realism returns. What counterbalances the strong holist interpretation of Einstein's views is Einstein's repeated insistence that out of many rival theories there is one with the best fit. Einstein did not believe that many
Absolute rest frame | page 15 |
Absolute space | page 4 |
Determine | page 3, page 5, page 15 |
Dimension | page 4 |
Euclidean | page 4 |
external world | page 4 |
four-dimensional | page 6, page 11 |
general coordinate system | page 4, page 5 |
Gravitational fields | page 3, page 5, page 15 |
GTR | page 4, page 5 |
inertial frame | page 7, page 95 |
Laws of motion | page 4 |
Laws of nature | page 2, page 4, page 5, page 10, page 12, page 16 |
Laws of physics | page 2, page 3, page 8, page 14, page 15, page 19 |
Laws of relativistic physics | page 14 |
Length contraction | page 4, page 15, ref 2.1 |
Length expansion | ref 2 |
Lorentz force | page 3 |
Lorentz transformations | page 3, page 5, page 7, page 8, page 10 |
Newton's Law | page 3, page 4 |
non-Euclidian | page 4 |
perpetual motion machines | page 16 |
perspectival | page 3, page 6, page 7 |
Philosophy | page 2, page 14, page 19 |
Popper (Karl) | page 16 |
pseudo-Euclidian | page 5 |
Quantum mechanics | page 15 |
Real world | page 2, page 5 |
Space-time | page 2, page 3, page 5, page 6, page 7, page 10, page 16 |
space and time | page 4, page 5 |
STR | page 5, page 14, ref 1 |
synchroneous | page 4 |
synchronised clock | page 5, page 14 |
Time dilation | page 4, page 6, page 15 |
Display 3b shows the results of a simulation of the movement of 10 stars around a Blackhole in time increments. That means at every moment tn the 10 positions x,y,z of the stars are calculated, and shown as 10 points px and py on the display. Those 10 points are considered simultaneous events. At tn = tn+1 the same proces is repeated.
In order to demonstrate possible length contraction (or expansion) a rod should move in a straight line through a grid of synchronised clocks at rest. Before the start of the experiment (at rest) an observer should be placed at both ends of the rod. When the experiment starts each observer should write the time on the clock he or she passes. The expectation is that all observers will write down the same sequence of numbers, implying there is no length contraction.
The easiest way to measure the length of a rod (a distance) at rest, is to place measurements rods along side this rod and count the number of measurement rods used. To measure the length of a moving rod, in side a frame at rest is more complicated. If you place the measurements along the moving rod, starting at one end of the rod, and the rod moves away, than the measured length will be longer as the length of the rod at rest. If you place the measurements along the moving rod, starting at one end of the rod, and the rod moves towards this point, than the measured length will be shorter as the length of the rod at rest. To solve this issue it is important that any measurement of a length should be done between two simultaneous events, this means the simultaneous events of the positions of both ends of the rod i.e. the total length of the rod. A practical solution is to place synchronised virtual clocks at equal (standard) distances within this grid. |
If the case of a rotating disc, as mentioned above, the first strategy is use measurement rods of size R.
There are two ways to do that:
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