Why is relativity theory counter-intuitive?

1. Why is relativity theory counter-intuitive? A naturalistic approach to real time and time intuition By Sandro Nannini (UNiversity of Siena) Siena, 1 June 2009

2. Common sense and philosophy about time Siena, 1 June 2009

3. Common sense and relativity theory Relativity theory (SRT and GRT) is counter-intuitive first of all because it denies the absoluteness of time and its independence from space (and gravity). This double denial did not come out from philosophical reflection but from physics, that is, from the project of unifying classical mechanics and Maxwell’s theory of electro-magnetism. Why is accepting such a denial so difficult for the man in the street? Why are SRT and GRT so counter-intuitive and odd? Siena, 1 June 2009

4. Why is RT counter-intuitive?A (too) reassuring reply SRT and GRT are difficult to accept not because they are odd but because obtaining empirical confirmation of their validity is difficult. SRT: We have no possibility to observe in everyday life phenomena of time dilation or space contraction because directly observable macroscopic objects always move slowly for their observers: therefore we never observe time dilation or space contraction. For small values of v (small in comparison to c) Lorentz transformations collapse into Galilean transformations. Siena, 1 June 2009

5. A (too) reassuring reply Galilean Transformations Siena, 1 June 2009

6. Why is RT counter-intuitive?A (too) reassuring reply GRT: As for the implication of GRT that space-time “is curved” around masses, in fact such curvature is so little not only on the Earth with regard to observable macroscopic bodies but also in the visible universe of stars and planets (because of its emptiness of matter) that the physical world in which we human beings live is practically Euclidean and Newtonian. Siena, 1 June 2009

7. An example of this(too) reassuring reply “Because the (large scale) universe looks the same from every galactic cluster, and changes by expansion at the same rate everywhere, the effect on clocks is the same at all places, provided of course that the clock is not in rapid motion relative to the local group of galaxies […] (P.C.W. Davies, Space and time in moderne universe, Cambridge, C.U.P. 1977, p. 155; my italics). Siena, 1 June 2009

8. An example of this(too) reassuring reply “[…] For example, the Earth is moving only slowly (compared with light) relative to the local group of galaxies, so that Earth time is an accurate way of dating the large-scale condition of universe as seen by any distant observer travelling with his local galactic group. […] This universal clock time is called cosmic time, and because it happily coincides closely with Earth time it enables us to compare historical events on the Earth with various cosmic events (P.C.W. Davies, pp. 155-156; my italics). Siena, 1 June 2009

9. An example of this(too) reassuring reply: an objection Is the velocity of Earth small (in comparison to the velocity of light) in an absolute sense or only at a human scale? If it is small only at a human scale, can one speak of an absolute “cosmic time”? Or can one speak only, as it were, of a ‘human cosmic time’? Siena, 1 June 2009

10. Einstein’s implicit criticism on the (too) reassuring reply “But it is conceivable that our universe differs only slightly from a Euclidean one, and this notion seems all the more probable, since calculations show that the metrics of surrounding space is influenced only to an exceedingly small extent by masses even of the magnitude of our sun. We might imagine that, as regards geometry, our universe behaves analogously to a surface which is irregularly curved in its individual parts, but which nowhere departs appreciably from a plane: something like the rippled surface of a lake. Such a universe might fittingly be called a quasi-Euclidean universe. As regards its space it would be infinite […]” (A. Einstein, Relativity: the special and general theory, New York, Holt, 1920, chapter 32). [http://www.bartleby.com/173/32.html]. Siena, 1 June 2009

11. Einstein’s criticism on the (too) reassuring reply If the universe is Eucledean it is also Newtonian: “If we confine the application of the theory to the case where the gravitational fields can be regarded as being weak, and in which all masses move with respect to the co-ordinate system with velocities which are small compared with the velocity of light, we then obtain as a first approximation the Newtonian theory” (A. Einstein, Relativity, chapter 29). Siena, 1 June 2009

12. Einsteins’ criticism on the (too) reassuring reply “[…] But calculation shows that in a quasi-Euclidean universe the average density of matter would necessarily be nil. Thus such a universe could not be inhabited by matter everywhere; it would present to us that unsatisfactory picture which we portrayed in Section XXX.” Siena, 1 June 2009

13. Einstein’s criticism on the (too) reassuring reply “According to the theory of Newton, the number of “lines of force” which come from infinity and terminate in a mass m is proportional to the mass m. If, on the average, the mass-density 0 is constant throughout the universe, then a sphere of volume V will enclose the average mass 0V. Thus the number of lines of force passing through the surface F of the sphere into its interior is proportional to 0V. For unit area of the surface of the sphere the number of lines of force which enter the sphere is thus proportional to 0V/F or 0R. Hence the intensity of the field at the surface would ultimately become infinite with increasing radius R of the sphere, which is impossible” (chapter 30, footnote 24). Siena, 1 June 2009

14. Einstein’s criticism on the (too) reassuring reply “ If we are to have in the universe an average density of matter which differs from zero, however small may be that difference, then the universe cannot be quasi-Euclidean. On the contrary, the results of calculation indicate that if matter be distributed uniformly, the universe would necessarily be spherical (or elliptical). Since in reality the detailed distribution of matter is not uniform, the real universe will deviate in individual parts from the spherical, i.e. the universe will be quasi-spherical. But it will be necessarily finite” (chapter 32). Siena, 1 June 2009

15. Real time and time intuition If the real universe cannot be Euclidean and Newtonian, why is it so spontaneous and quasi inevitable – both for the man in the street and for all philosophers and physicist until Einstein published his famous article in 1905 - to represent it in such a way? Siena, 1 June 2009

16. The world as it is and as it appears One might be tempted to answer: ‘Well, it is so because the velocity of the bodies that we can observe is small in comparison to the velocity of light’. Therefore, although space-time is not absolute and flat it is inevitable that it appears absolute and flat to us!’. All right, in a certain sense. But only in a certain sense since nothing is small in itself but only in comparison to something else! Siena, 1 June 2009

17. Brain and time intuition E. Pöppel (e.g. The Brain’s Way to create “Nowness”, in H. Atmanspacher & E. Ruhnau (eds.), Time, Temporality, Now, Berlin, Springer, 1997, pp. 107-120) maintains that our intuition of time is due to two brain mechanisms. The intuition of time is a ‘mental construction’ realized by two brain mechanisms: “a high-frequency processing system generating discrete time quanta in the domain of approximately 30 milliseconds” (pp. 107-108) “A low-frequency processing system, which is operative in the domain of 2 to 3 seconds” (p. 108). The former system creates ‘atoms of simultaneity’. All events that happen within an interval of 30 ms. appear simultaneous to us. The latter system creates the ‘specious present’ and makes it possible that we perceive movements and not only reconstruct them. Siena, 1 June 2009

18. Gaussian coordinates In the GRT space-time Cartesian coordinates are substituted by Gaussian coordinates: Gaussian coordinates are not Euclidean and do not represent only space and time, but also gravity (and in principle they should include also electromagnetism and all other forms of interaction between particles). Siena, 1 June 2009

19. From Gaussian coordinates to Euclidean coordinates Some parts of a Gaussian continuum can be considered Euclidean if they are sufficiently small. In such a case the distance square between two points of a 4D-continuum is not expressed any more by (1) ds2=g11dx12+2g12dx1dx2+…+g44dx42 but by the simplified formula (2) ds2=dx12+dx22+dx32+dx42. However, how small must this distance be to permit that (1) is reduced to (2)? Siena, 1 June 2009

20. Space-time and human senses “Small” means here “small in comparison to the capability of human senses to discriminate events in space and time”. Let us remember that in our “phenomenal perceptual world” the temporal distance between all events happened within the interval of 30 ms. is zero: such events appear to us simultaneous. Since light covers about 9,000 Km in 30 ms. the velocity of light is for us, from a perceptual point of view, practically infinite around us within a sphere whose radius is about 9,000 Km. Within such a sphere the  of Lorentz transformations is for us identical to 1 and the  is identical to 0; therefore, (1) is reduced to (2), that is, space and time seem to be absolute, independent of each other and independent of gravity: their structure is Euclidean and the laws of mechanics that describe the motion of bodies in such Euclidean space-time are Newtonian.

21. Space-time measures are observer-dependent If this conclusion is true, the world around us appears to us Euclidean and Newtonian but it is not so. Einstein is clear about that. Gaussian coordinates have no physical meaning before measures are taken. Laws of nature are objective if they are covariant for transformations of arbitrary Gaussian coordinates. Therefore they cannot be linear. Single groups of measures are not objective but observer-dependent because they are the result of an encounter between the movement of observed objects and the movement of ‘observing objects’ (the measure instruments). Siena, 1 June 2009

22. Gaussian coordinates have no physical significance in themselves a) “We refer the four-dimensional space-time continuum in an arbitrary manner to Gauss co-ordinates. We assign to every point of the continuum (event) four numbers, x1, x2, x3, x4 (co-ordinates), which have not the least direct physical significance, but only serve the purpose of numbering the points of the continuum in a definite but arbitrary manner. This arrangement does not even need to be of such a kind that we must regard x1, x2, x3 as “space” co-ordinates and x4 as a “time” co-ordinate […]” Siena, 1 June 2009

23. Space-time measures are observer-dependent a) “[…] Let us consider, for instance, a material point with any kind of motion […] Corresponding to the material point, we thus have a (unidimensional) line in the four-dimensional continuum. In the same way, any such lines in our continuum correspond to many points in motion. The only statements having regard to these points which can claim a physical existence are in reality the statements about their encounters. […] After mature consideration the reader will doubtless admit that in reality such encounters constitute the only actual evidence of a time-space nature with which we meet in physical statements” (A. Einstein, Relativity, chapter 27). Siena, 1 June 2009

24. Covariant transformations b) “The co-ordinates now [in GRT] express only the order or rank of the "contiguity" and hence also the dimensional grade of the space, but do not express any of its metrical properties. We are thus led to extend the transformations to arbitrary continuous transformations.  This implies the general principle of relativity: Natural laws must be covariant with respect to arbitrary continuous transformations of the co-ordinates. (A. Einstein, Relativity and the Problem of Space, (1952)). Siena, 1 June 2009

25. Euclidean coordinates have no objective significance c) “A space of the type (1) [ds2=dx12+dx22+dx32+dx42], judged from the standpoint of the general theory of relativity, is not a space without field, but a special case of the gik field, for which – for the co-ordinate system used, which in itself has no objective significance – the functions gik have values that do not depend on the co-ordinates. There is no such thing as an empty space, i.e. a space without field” (A. Einstein, 1952). Siena, 1 June 2009

26. The brain works as a watch Therefore, if one thinks that the brain is the first and fundamental watch by means of which measures of time (and space) are taken and the ‘manifest image’ of the world is constructed and that the working of the brain with regard to the intuition of time is correctly described by Pöppel’s theory, then one must conclude that the space-time around us appears to us Euclidean and Newtonian because of the kind of space-time measures taken by our brain: such measures “choose” such a description of the gravitational field that the Gaussian coordinates in which this description is formulated become Cartesian coordinates. Such measures and such coordinates are observer-dependent (that is, human brain dependent). They are not objective features of physical reality, although by means of them we can formulate and experimentally test laws of nature that thanks to certain transformation principles are covariant for all possible Gaussian coordinates and therefore are objective (that is, observer-independent). In such laws time is not independent of space and gravity. Siena, 1 June 2009

27. Conclusion . We can understand now that the counterintuitive character of RT has a biological basis in the way in which the human brain represents to itself the external world (in orderto successfully interact with it). Siena, 1 June 2009

28. Thanks for your attention! Siena, 1 June 2009