Abstract
As it has been remarked repeatedly in the previous chapters, the theory of Special Relativity is not based on direct sensory experience, as it is the case with Newtonian Physics. This leads to situations which contradict the “common sense” in the way that the theory gives different results depending on the Newtonian observer (as we are) who observes a given phenomenon. It is a fundamental hypothesis of Physics, which makes Physics a unique science, that “reality” is observer independent. However one must use the appropriate class of observers for each “reality”.
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Notes
- 1.
Einstein in order to show the insufficiency of the “common sense” in various projections of the human mind has remarked that “Common sense is the aggregate of prejudices acquired by the age of eighteen”. However many years before him Heraclitus has remarked that “Toυ λoγoυ δ𝜖oντoς ξυνoυ ζωoυσιν oι πoλλoι ως ιδιαν εχoντες ϕρoνησιν″ which means “Although common sense is common, most people consider it as if it is their own”.
- 2.
For a different approach see G. Sastry (1987) ‘Is length contraction really paradoxical?’ Am. J. Phys. 55 , pp 943–46.
- 3.
We note that \(t_{2}^{\prime }>t_{1}^{\prime }\) therefore it is possible that for observer Σ′ the circuit remains open therefore the lamp will be turned off. The proof that \(t_{2}^{\prime }>t_{1}^{\prime }\) has as follows. It is enough to show that:
$$\displaystyle \begin{aligned} \frac{\gamma l_{0}}{c\beta_{s}}+\frac{\gamma\beta l_{0}}{c}>\frac{l_{0}}{\beta c}-\frac{l_{0}}{\gamma\beta c}\Leftrightarrow\frac{\gamma}{\beta_{s}}>\frac {1}{\beta}-\frac{1}{\gamma\beta}-\gamma\beta=-\frac{\gamma}{1+\gamma} \end{aligned}$$which is true.
- 4.
For a different approach see Hon-Ming Lai (1975) “Extraordinary shadow appearance due to fast moving light” Am. J. Phys. 43, pp 818–820.
- 5.
More on this paradox which has a long history in Special Relativity the reader can find in the following articles:
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1.
J. C. Nockerson and R. McAdory (1975), ‘Right-angle lever paradox’, Am. J. Phys. 43, 615
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2.
D. Jensen (1989), ‘The paradox of the L-shaped object’, Am. J. Phys. 57, 553.
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- 6.
For literature relevant to this paradox see for example D Greenberger (1972) ‘The Reality of the Twin Paradox Effect’ Am. J. Phys. 40, pp 750–754.
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Tsamparlis, M. (2019). Paradoxes. In: Special Relativity. Undergraduate Lecture Notes in Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-27347-7_8
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