Why is relativity theory counter-intuitive?

Siena, 1 June 2009 1

Why is relativity theory Why is relativity theory counter-intuitive?counter-intuitive?

A naturalistic approach to real time and A naturalistic approach to real time and time intuitiontime intuition

By Sandro NanniniBy Sandro Nannini

(UNiversity of Siena)(UNiversity of Siena)


Common sense and philosophy about timeCommon sense and philosophy about time

Real /Real /idealideal

Substance Substance /Relation/Relation

Does it Does it flow? flow? (Presentism (Presentism /eternalism)/eternalism)

Infinite / Infinite / FiniteFinite

Is present Is present extended?extended?

Absolute / Absolute / RelativeRelative

Is time Is time independent independent of space and of space and gravity?gravity?

Common Common sensesense

RealReal SubstanceSubstance Yes. Yes. PresentismPresentism

InfiniteInfinite YesYes AbsoluteAbsolute YesYes

AristotleAristotle (+)(+) (-)(-) -- ++ -- ++ ++

NewtonNewton ++ ++ ++ ++ -- ++ ++

KantKant -- ++ -- ++ -- ++ ++

EinsteinEinstein (+)(+) -- -- -- -- -- --


Common sense and relativity theoryCommon sense and relativity theory

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


Why is RT counter-intuitive?Why is RT counter-intuitive?A (too) reassuring replyA (too) reassuring reply

• SRT and GRT are difficult to accept not because SRT and GRT are difficult to accept not because they are odd but because obtaining empirical they are odd but because obtaining empirical confirmation of their validity is difficult.confirmation of their validity is difficult.• SRT: We have no possibility to observe in SRT: We have no possibility to observe in everyday life phenomena of time dilation or space everyday life phenomena of time dilation or space contraction because directly observable contraction because directly observable macroscopic objects always move slowly for their macroscopic objects always move slowly for their observers: therefore we never observe time observers: therefore we never observe time dilation or space contraction.dilation or space contraction.• For small values of For small values of vv (small in comparison to (small in comparison to cc) ) Lorentz transformations collapse into Galilean Lorentz transformations collapse into Galilean transformations.transformations.


A (too) reassuring replyA (too) reassuring reply

Galilean TransformationsGalilean Transformations


Why is RT counter-intuitive?Why is RT counter-intuitive?A (too) reassuring replyA (too) reassuring reply

• GRT: As for the implication of GRT that GRT: As for the implication of GRT that space-time “is curved” around masses, in space-time “is curved” around masses, in fact such curvature is so little not only on the fact such curvature is so little not only on the Earth with regard to observable Earth with regard to observable macroscopic bodies but also in the visible macroscopic bodies but also in the visible universe of stars and planets (because of its universe of stars and planets (because of its emptiness of matter) that the physical world emptiness of matter) that the physical world in which we human beings live is practically in which we human beings live is practically Euclidean and Newtonian.Euclidean and Newtonian.


An example of thisAn example of this(too) reassuring reply(too) reassuring reply

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


An example of thisAn example of this(too) reassuring reply(too) reassuring reply

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


An example of thisAn example of this(too) reassuring reply: an objection(too) reassuring reply: an objection

• Is the velocity of Earth small (in Is the velocity of Earth small (in comparison to the velocity of light) in an comparison to the velocity of light) in an absolute sense or only at a human scale?absolute sense or only at a human scale?

•If it is small only at a human scale, can one If it is small only at a human scale, can one speak of an absolute “cosmic time”? Or can speak of an absolute “cosmic time”? Or can one speak only, as it were, of a ‘human one speak only, as it were, of a ‘human cosmic time’?cosmic time’?


Einstein’s implicit criticism on the Einstein’s implicit criticism on the (too) reassuring reply(too) reassuring reply

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


Einstein’s criticism on the (too) Einstein’s criticism on the (too) reassuring replyreassuring reply

If the universe is Eucledean it is also Newtonian:If the universe is Eucledean it is also Newtonian:

““If we confine the application of the theory to the If we confine the application of the theory to the case where the gravitational fields can be regarded case where the gravitational fields can be regarded as being weak, and in which all masses move with as being weak, and in which all masses move with respect to the co-ordinate system with velocities respect to the co-ordinate system with velocities which are small compared with the velocity of light, which are small compared with the velocity of light, we then obtain as a first approximation the we then obtain as a first approximation the Newtonian theory” (A. Einstein, Newtonian theory” (A. Einstein, RelativityRelativity, chapter , chapter 29).29).


Einsteins’ criticism on the (too) Einsteins’ criticism on the (too) reassuring replyreassuring reply

““[…] But calculation shows that in a quasi-[…] But calculation shows that in a quasi-Euclidean universe the average density of Euclidean universe the average density of matter would necessarily be matter would necessarily be nil.nil. Thus such a Thus such a universe could not be inhabited by matter universe could not be inhabited by matter everywhere; it would present to us that everywhere; it would present to us that unsatisfactory picture which we portrayed in unsatisfactory picture which we portrayed in Section XXX.”.”

http://www.bartleby.com/173/30.html

http://www.bartleby.com/173/30.html



““According to the theory of Newton, the number of “lines of According to the theory of Newton, the number of “lines of force” which come from infinity and terminate in a mass force” which come from infinity and terminate in a mass mm is proportional to the mass is proportional to the mass m.m. If, on the average, the mass- If, on the average, the mass-density density 00 is constant throughout the universe, then a is constant throughout the universe, then a sphere of volume V will enclose the average mass sphere of volume V will enclose the average mass 00V. V. Thus the number of lines of force passing through the Thus the number of lines of force passing through the surface F of the sphere into its interior is proportional to surface F of the sphere into its interior is proportional to 00V. For unit area of the surface of the sphere the number V. For unit area of the surface of the sphere the number of lines of force which enter the sphere is thus proportional of lines of force which enter the sphere is thus proportional to to 00V/F or V/F or 00R. Hence the intensity of the field at the R. Hence the intensity of the field at the surface would ultimately become infinite with increasing surface would ultimately become infinite with increasing radius R of the sphere, which is impossible” (chapter 30, radius R of the sphere, which is impossible” (chapter 30, footnote 24).footnote 24).



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


Real time and time intuitionReal time and time intuition

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


The world as it is and as it The world as it is and as it appearsappears

One might be tempted to answer: ‘Well, it is so One might be tempted to answer: ‘Well, it is so because the velocity of the bodies that we can because the velocity of the bodies that we can observe is small in comparison to the velocity of observe is small in comparison to the velocity of light’. Therefore, although space-time light’. Therefore, although space-time is notis not absolute and flat it is inevitable that it absolute and flat it is inevitable that it appearsappears absolute and flat to us!’.absolute and flat to us!’.

All right, in a certain sense. But only in a certain All right, in a certain sense. But only in a certain sense since nothing is small in itself but only in sense since nothing is small in itself but only in comparison to something else!comparison to something else!


Brain and time intuitionBrain and time intuitionE. PE. Pöppel (e.g. öppel (e.g. The Brain’s Way to create “Nowness”The Brain’s Way to create “Nowness”, in H. , in H.

Atmanspacher & E. Ruhnau (eds.), Atmanspacher & E. Ruhnau (eds.), Time, Temporality, Time, Temporality, Now, BerlinNow, Berlin, Springer, 1997, pp. 107-120) maintains , Springer, 1997, pp. 107-120) maintains that our intuition of time is due to two brain that our intuition of time is due to two brain mechanisms. The intuition of time is a ‘mental mechanisms. The intuition of time is a ‘mental construction’ realized by two brain mechanisms:construction’ realized by two brain mechanisms:

1)1) ““a high-frequency processing system generating a high-frequency processing system generating discrete time quanta in the domain of approximately 30 discrete time quanta in the domain of approximately 30 milliseconds” (pp. 107-108)milliseconds” (pp. 107-108)

2)2) ““A low-frequency processing system, which is operative A low-frequency processing system, which is operative in the domain of 2 to 3 seconds” (p. 108).in the domain of 2 to 3 seconds” (p. 108).

The former system creates ‘atoms of simultaneity’. All The former system creates ‘atoms of simultaneity’. All events that happen within an interval of 30 ms. appear events that happen within an interval of 30 ms. appear simultaneous to us.simultaneous to us.

The latter system creates the ‘specious present’ and makes The latter system creates the ‘specious present’ and makes it possible that we perceive movements and not only it possible that we perceive movements and not only reconstruct them.reconstruct them.


Gaussian coordinatesGaussian coordinatesIn the GRT space-time Cartesian In the GRT space-time Cartesian

coordinates are substituted by Gaussian coordinates are substituted by Gaussian coordinates: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).


From Gaussian coordinates to From Gaussian coordinates to Euclidean coordinatesEuclidean coordinates

Some parts of a Gaussian continuum can be Some parts of a Gaussian continuum can be considered Euclidean if they are considered Euclidean if they are sufficiently sufficiently smallsmall. In such a case the distance square . In such a case the distance square between two points of a 4D-continuum is not between two points of a 4D-continuum is not expressed any more by (1) expressed any more by (1) dsds22=g=g1111dxdx11

22+2g+2g1212dxdx11dxdx22+…+g+…+g4444dxdx4422 but by the but by the

simplified formula (2) simplified formula (2) dsds22=dx=dx1122+dx+dx22

22+dx+dx3322+dx+dx44

22..

However, how small must this distance be to However, how small must this distance be to permit that (1) is reduced to (2)?permit that (1) is reduced to (2)?

Space-time and human sensesSpace-time and human senses““Small” means here “small in comparison to the capability of Small” means here “small in comparison to the capability of

human senses to discriminate events in space and human senses to discriminate events in space and time”.time”.

Let us remember that in our “phenomenal perceptual world” Let us remember that in our “phenomenal perceptual world” the temporal distance between all events happened the temporal distance between all events happened within the interval of 30 ms. is zero: such events appear within the interval of 30 ms. is zero: such events appear to us simultaneous.to us simultaneous.

Since light covers about 9,000 Km in 30 ms. the velocity of Since light covers about 9,000 Km in 30 ms. the velocity of light is for us, from a perceptual point of view, practically light is for us, from a perceptual point of view, practically infinite around us within a sphere whose radius is about infinite around us within a sphere whose radius is about 9,000 Km.9,000 Km.

Within such a sphere the Within such a sphere the of Lorentz transformations is of Lorentz transformations is for for usus identical to 1 and the identical to 1 and the is identical to 0; therefore, (1) is identical to 0; therefore, (1) is reduced to (2), that is, space and time seem to be is reduced to (2), that is, space and time seem to be absolute, independent of each other and independent of absolute, independent of each other and independent of gravity: their structure is Euclidean and the laws of gravity: their structure is Euclidean and the laws of mechanics that describe the motion of bodies in such mechanics that describe the motion of bodies in such Euclidean space-time are Newtonian.Euclidean space-time are Newtonian.


Space-time measures are observer-dependentSpace-time measures are observer-dependentIf this conclusion is true, the world around us appears to us If this conclusion is true, the world around us appears to us

Euclidean and Newtonian but it is not so. Einstein is Euclidean and Newtonian but it is not so. Einstein is clear about that.clear about that.

a)a) Gaussian coordinates have no physical meaning Gaussian coordinates have no physical meaning before measures are taken.before measures are taken.

b)b) Laws of nature are objective if they are covariant for Laws of nature are objective if they are covariant for transformations of arbitrary Gaussian coordinates. transformations of arbitrary Gaussian coordinates. Therefore they cannot be linear.Therefore they cannot be linear.

c)c) Single groups of measures are not objective but Single groups of measures are not objective but observer-dependent because they are the result of an observer-dependent because they are the result of an encounter between the movement of observed objects encounter between the movement of observed objects and the movement of ‘observing objects’ (the measure and the movement of ‘observing objects’ (the measure instruments).instruments).


Gaussian coordinates have no physical Gaussian coordinates have no physical significance in themselvessignificance in themselves

a) “a) “We refer the four-dimensional space-time We refer the four-dimensional space-time continuum in an arbitrary manner to Gauss co-continuum in an arbitrary manner to Gauss co-ordinates. We assign to every point of the ordinates. We assign to every point of the continuum (event) four numbers, continuum (event) four numbers, xx1, 1, xx2, 2, xx3, 3, xx4 4 (co-ordinates), (co-ordinates), which have not the least direct which have not the least direct physical significancephysical significance, but only serve the , but only serve the purpose of numbering the points of the purpose of numbering the points of the continuum in a definite but arbitrary manner. continuum in a definite but arbitrary manner. This arrangement does not even need to be of This arrangement does not even need to be of such a kind that we must regard such a kind that we must regard xx1, 1, xx2, 2, xx3 as 3 as “space” co-ordinates and “space” co-ordinates and xx4 as a “time” co-4 as a “time” co-ordinate […]”ordinate […]”


Space-time measures are Space-time measures are observer-dependentobserver-dependent

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


Covariant transformationsCovariant transformationsb) “Tb) “The co-ordinates now [in GRT] express only the he co-ordinates now [in GRT] express only the

order or rank of the "contiguity" and hence also order or rank of the "contiguity" and hence also the dimensional grade of the space, but do not the dimensional grade of the space, but do not express any of its metrical properties. We are express any of its metrical properties. We are thus led to extend the transformations to thus led to extend the transformations to arbitrary continuous transformations. This arbitrary continuous transformations. This implies the general principle of relativity: implies the general principle of relativity: Natural laws must be covariant with respect to Natural laws must be covariant with respect to arbitrary continuous transformations of the co-arbitrary continuous transformations of the co-ordinates. (ordinates. (A. EinsteinA. Einstein, Relativity and the , Relativity and the Problem of Space, Problem of Space, (1952)).(1952)).


Euclidean coordinates have no objective Euclidean coordinates have no objective significancesignificance

c) “c) “A space of the type A space of the type (1) (1) [[dsds22=dx=dx11

22+dx+dx2222+dx+dx33

22+dx+dx4422]], judged from the , judged from the

standpoint of the general theory of relativity, is standpoint of the general theory of relativity, is not a space without field, but a special case of not a space without field, but a special case of the gthe gikik field, for which – for the co-ordinate field, for which – for the co-ordinate system used, system used, which in itself has no objective which in itself has no objective significancesignificance – the functions g – the functions g ikik have values have values that do not depend on the co-ordinates. There that do not depend on the co-ordinates. There is no such thing as an empty space, i.e. a is no such thing as an empty space, i.e. a space without field” (A. Einstein, 1952).space without field” (A. Einstein, 1952).


The brain works as a watchThe brain works as a watchTherefore, if one thinksTherefore, if one thinksa)a) that that the brain is the first and fundamental watchthe brain is the first and fundamental watch by means of by means of

which measures of time (and space) are taken and the ‘manifest which measures of time (and space) are taken and the ‘manifest image’ of the world is constructed andimage’ of the world is constructed and

b)b) that the working of the brain with regard to the intuition of time is that the working of the brain with regard to the intuition of time is correctly described by Pöppel’s theory, thencorrectly described by Pöppel’s theory, then

one must conclude that the space-time around us appears to us one must conclude that the space-time around us appears to us Euclidean and Newtonian because of the kind of space-time Euclidean and Newtonian because of the kind of space-time measures taken by our brain: such measures “choose” such a measures taken by our brain: such measures “choose” such a description of the gravitational field that the Gaussian coordinates in description of the gravitational field that the Gaussian coordinates in which this description is formulated become Cartesian coordinates. which this description is formulated become Cartesian coordinates.

Such measures and such coordinates are observer-dependent (that is, Such measures and such coordinates are observer-dependent (that is, human brain dependent). They are not objective features of physical human brain dependent). They are not objective features of physical reality, although by means of them we can formulate and reality, although by means of them we can formulate and experimentally test laws of nature that thanks to certain experimentally test laws of nature that thanks to certain transformation principles are covariant for all possible Gaussian transformation principles are covariant for all possible Gaussian coordinates and therefore are objective (that is, observer-coordinates and therefore are objective (that is, observer-independent).independent).

In such laws time is not independent of space and gravity.In such laws time is not independent of space and gravity.


ConclusionConclusion..

We can understand now that the We can understand now that the counterintuitive character of RT has a counterintuitive character of RT has a biological basis in the way in which the biological basis in the way in which the human brain represents to itself the human brain represents to itself the external world (in orderexternal world (in order to successfully to successfully interact with it).interact with it).


Thanks for your attention!Thanks for your attention!

Why is relativity theory counter-intuitive?

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