A dangerous idea.  The problem is that if you do this accurately, you will find out that the concepts of space and time of quantum theory are quite different from the spacetime ideology of general relativity, but has a concept of space and time which is classical, with absolute time (which can be measured only approximately) and absolute space (independent of the matter in it).  This is something one tries to hide in relativistic QFT by using the Heisenberg instead of the Schrödinger picture (which is much less natural, it is the state which changes in time, not the measurements, but the fact that there is at every moment of time a global state becomes somehow invisible)

Quantum mechanics and Einstein's relativity theory present us with a great paradox. Quantum mechanics gives us the possibility of an indeterminate Universe with open possibilities in space-time. Relativity theory presents us with a deterministic Universe in which everything is spread out in time-space as fragments in 'a light cone'. Moreover, quantum mechanics is an area that is truly not understood and there's a lot of controversy even with the interpretations surrounding it, such as the Copenhagen theory that claims that time-space depends on the observer (sounds like a nuance of solipsism/post-modernism to me, but that's just my take!). This topic can truly take you on a wonderful journey, so happy exploring!

Following is a link to an emerging theory of space and time. In this theory space-time are considered imaginary mathematical tools which does not have any physical existence. The underlying oscillating energy has physical existence and human mind superimposes the idea of space and time on this oscillating energy. Time is strictly periodic in nature. T=1/f is the only connection between imaginary time and the physical oscillations. Length of space gives the extent of spread of the energy. For example wavelength of a particle wave.

Article Periodic relativity: Basic framework of the theory

The concepts of space and time are the most basic scientific concepts, as Kant has explained. We have the concept (meaning an abstract representation) of the location of a material body, and we relate the position to 4 scalars. Any map (in the most basic meaning) defining the location of an event from 4 scalars gives a chart, and if you have a set of compatible (meaning you have a way to go from one chart to another) charts you have an atlas, and the collection of compatible atlas defines the mathematical structure of a manifold, which is just the first assumption of general relativity. An affine space is a special manifold (as in special relativity).

There is a striking feature of this representation : because we cannot travel in time  there is a fundamental symmetry breakdown : one of the coordinate (time) is special, and this feature is specific to every observer (the presentis not the same for everybody). From there the usual assumption is to assume and additional structure, represented by a principal bundle with the Lorentz group.

As for space and time inQM, in the common interpretations you will find everything and its  converse : pick your choice. Actually QM has nothing to tell about space and time.

Hello Ruben,

As per my current papers to unite QM and relativity one needs to take time,momentum,position and energy to complex plane.

I have attached for your reference.

Regards,

Bhushan Poojary

Thesis Certainty Principle Using Complex Plane

Thesis Energy equation in complex plane

Since the question is about epistemologies for the notions of space and time, you may be interested in having a look on the theory of triune continuum.

Conference Paper A Report on the Triune Continuum Paradigm and on its Foundat...

Ruben,    As you probably know, the largest discrepancy in all of physics is the 10120 difference between the average energy density of spacetime obtained from general relativity (GR) and the vacuum energy density required by quantum mechanics (QM) and quantum electrodynamics (QED). For example, the "critical density" of flat spacetime from GR is roughly 10-9 J/m3. The energy density of zero point energy and vacuum fluctuations is roughly equal to Planck energy density (about 10113 J/m3). As John Archibald Wheeler said "Empty space is not empty... The density of field fluctuation energy in the vacuum argues that elementary particles represent percentage-wise almost completely negligible change in the locally violent conditions that characterize the vacuum". This discrepancy between GR and QM is usually assumed eventually to be resolved in favor of the GR because the energy density from QM seems ridiculous. However, I have written a paper that will be published in December that argues that the GR and QM energy densities are compatible because they represent different types of energy density of spacetime. A link to a preprint of this paper is available below. This model of spacetime leads to some predictions about gravity and the electrostatic force which were previously unknown but demonstrably correct. Also a description of the effect on spacetime produced by an electric field is given and subject to tests.   

http://onlyspacetime.com/QM-Foundation.pdf

After Kant a big number of people in philosophy has concentrated on phenomenological (in the philosopher's sense of the word) aspects of temporality. This attitude gave rise to philosophical constructions like those of Bergson and Husserl.  These informal theories are in a sense "richer" of elements but are, most of the times, not very rigorously framed and don't really deal with the core notions of contemporary physics - after all, for our experience of temporality the newtonian picture is a good approximation. It is true that some neokantians (Cassirer) attempted to make special and general relativity fit with kantian categories but it does not seem that these attempts have ever lead to a successful fusion. 

More interesting I find the work of philosophical logicians working on temporal logic. It all started with A.N. Prior using modal logic for reasoning about time and classical paradoxes. For what concerns space-time, you may take a look to the more recent work of Nuel Belnap (Branching space-time), Storrs McCall (A model of the Universe) or Nico Strobach. There is a stream of philosophical logicians working on space-time logics in the last decade. If you are really curious I also wrote a small paper on this topic (Time of Physics, Time of Logic) that you may find it in my profile as a dataset. 

Best,

Carlo

Hi Ruben, What a fascinating and challenging task! From the epistemological perspective I can recommend Barry Dainton's book 'Time & Space' for a good general and thorough overview of the main theories of both space and time.  However, at some point, you will need to consider the ontological position you wish to take on the nature of spacetime or, separately, space and time. As Jean Claude above discusses, you can take an approach that sees space and time as essentially a conceptual framework which is required in order for us to model reality and its causal connections via our best scientific theories.  Alternatively, you can accord an independent reality to spacetime (which appears to be an implicit assumption held by many physicists). Personally, I prefer the former option! Good luck with the project and keep us updated! Regards, Ruthie

To Ruthie,

I agree with your distinction. My comments :

1. To do Physics in relation with experiments, you just need to have a consistent representation of some container (the universe) in which everything lives. And this leads naturally to the manifold formalism : locally we need four parameters to locate an event. Further considerations (specificity of time, the fact that no observer sees phenomena going backwards, speed of light...) lead to precise the assumptions, as long as we stay in a limited region in the universe, we need just an efficient representation of the container, with respect to our experiments, including astrophysical observations.

However, if we can work efficiently in this framework, there are some facts that are disturbing. The main fact is that it is assumed, and I think that everybody agreeing with relativity would support this assumption, that material bodies travel along a world line. What is the power behind this motion ? So we are lead to have some look at cosmology.

 2. Cosmology raises many epistemological issues : the observers are part of the universe, we cannot experiment with different universes. So from the beginning we need to give to the universe some ontological meaning : the universe (space time) has properties, it can have an evolution, it obeys to some specific rules,...The models used in cosmology are almost all based on general relativity. Even if I am skeptical about them, I acknowledge their necessity. One disturbing question, about time, is linked to the expansion of the universe. Very sensible considerations lead to represent the universe as a warped product of a 3 dimensional manifold and time, so there is a universal time which has a physical meaning. But in the models the 4 manifold does not change, only the metric : the spatial distance between two points increases with the universal time (from the bing bang). But does that mean that the universe (where we are) is actually contained in a 3 dimensional submanifold which moves (and it would be an explanation to the power above) , or can we accept the possibility that it is not the only existing submanifold ?

Jean Claude,

Thank you for your extremely interesting and thought provoking comments.  I must admit that I am just starting out on my PhD research and am struggling with all the implications of what are currently merely intuitions.  I may turn out to be completely wrong but it is my intuition that the underlying reason preventing the unification of QM with GTR relates in some way to a misunderstanding of the ontological status of spacetime.  We know that the relation between space and time is very different in GTR than it is in QM.  (As you say under GTR material bodies move along a world-line and this accords spacetime a certain ontological status.) It is also my intuition that it will ultimately be more causally based theories of quantum gravity (e.g. Causal Dynamical Triangulation models, such as Smolin) that succeed, and precisely because they attempt to remove reference to space and time as ontological entities.

I think that STR provides illumination for this intuition.  Moving observers may disagree on the temporal order (and simultaneity) of events but what is not relative is their causal order.  The measurement of temporal intervals is always fundamentally a causal process (e.g. for caesium clocks this is defined by the emission of radiation in periodic energy level transitions, where ‘periodicity’ is determined by dE).  Thus for me causal processes are fundamental (and this is ontologically fundamental) and prior to any formulation of the concepts of time, or definition of a temporal interval. In terms of the ‘twin paradox’ STR tells us that there is no empirical fact of the matter as to which twin’s clock or ‘time interval’ is the correct one.  However, there is an absolute asymmetry between the twins, namely the different degrees of their ageing. This is related to the fact that Twin B’s (the travelling twin’s) caesium clock has, for argument’s sake, emitted e.g. 10 hv (the equivalent of an interval of 2 years) whereas Twin A’s caesium clock has emitted e.g. 70 hv  (the equivalent of an interval of 14 years). What the ‘twin paradox’ reveals is that time keeping or the measurement of temporal intervals is always and fundamentally a causal process and furthermore a process that occurs in 3 dimensions.  There is also a sense in which, under STR, from the point of view of the photon no time elapses and no distance passes (hence the null timeline) so in a sense photons do not travel in spacetime (as independently existing entity). I’m not sure that the full implications of this have been taken on board, especially in terms of the ontological significance of what is referred to as ‘spacetime’.  Yet photons do obviously ‘travel’ in some sense, and, by doing so, are fundamental to our measurement and definition of spatio-temporal intervals.

In terms of GTR I guess I would subscribe to an interpretation under which the left hand side of the Einstein Field Equations refers to the gravitational field not ‘spacetime’ (as independently existing entity) – I think it was Carlo Rovelli who once said "No more fields on spacetime: just fields on fields."

Dear Ruthie,

1. There is another thread on this site about causality. As usual there are many points of view but many share my belief that causality should not be given a key role in philosophy of science. The main reason is that it leads to single out a specific phenomenon prior to a change of states. What one actually follows in any experiment is a succession of states, with many parameters changing. Why finger one or another ? Take the desintegration of a meson in several pions (or any other particle), one of the most disturbing phenomon, it does not make real sense to say that the meson is the cause of the pion. What is interesting is what is the cause of the desintegration, at this place and time ?

2. Actually QM has no assumption about time and space. Read any common books, you will find the usual axioms (valid for any measure) and assumptions about the duality matter / fields. QM in his actual interpretation is an empiricist theory : it formalizes (with Hilbert spaces, operators,...) the relations occuring between measures. Space and time have no special places, but for the fact that QM considers successive measures (linked to the change of state). Space is seen only through coordinates. Space and time are commonly presented as linked to observables, thus to operators, but of course this is unconsistent because these operators are not compact : they cannot deliver a finite measure. So the need for a complicated interpretation of reality, with randmness,...

One can have almost all the results (meaning Hilbert spaces, operators, probability,...) deduced rigorously from some assumptions about the way models using quantitative variables are built. So the axioms of QM have no physical content. As it is obvious when it is said that the wave function does not represent a physical phenomenon (except for Bohm).

3. What is of interest in relativity is the concept of proper time. For millenia men have tried to measure time with clocks. So we have a concept of time, linked to observations. But because one cannot compare time as we do for space (one cannot proceed by surveying) time has a physical meaning only for each observer. So if, in spite of that, we want to keep a concept of time one has to 1) define a proper time 2) assume some law to compare proper times. This does not give an ontological meaning to time, it enables only the portability of the measures, and so its efficient use.

4. A thing which is not usually seen is the meaning of physical quantities linked to derivatives with respect to time, such as speed, momentum, force,...As we can measure only the state of a system at a given time, the genuine quantities are those which defines these states, the others (such as speed) are only deduced by comparisons between states. This is where all the machinery of frames appear. An example : contrary to what you read in the books, nobody use an orthogonal frame to locate a point : ask to the pilot of a plane. Frames are used not to locate points, but to measure directions (or angles),. And frames provide vectorial quantities (such as speed). So this a different use of time, meant as the way to compare the rate according to which phenomena changes.

Ruthie, I think it is good to bet on causality. But in this case I would recommend you to consider the violation of Bell's inequality and to think a lot about this. Because, essentially, this is a conflict between ontological, causal theories and relativity.  

If you have a correlation between A and B, it requires a causal explanation. This may be A->B, or B->A, or a common cause C->A,B.  The violation of Bell's inequality excludes a common cause as an explanation. Relativity excludes the direct causal influences.  This is not a quantum problem, because the ingredients are macroscopic (decisions of experimenters and the results of their measurements). 

The only choice which remains if you do not want to give up realism and causality is to accept a hidden preferred frame.  The violation of Bell's inequality, together with basic ideas about causality, tell us that or A->B, or B->A.  An exclusive or, because there should be no causal loops. But which of the alternatives is the correct one is - hidden.  

See http://ilja-schmelzer.de/realism/game.php for an introduction, but there are more considerations on http://ilja-schmelzer.de/realism/

Thank you both Jean Claude and Ilja for your comments, they have given me some very useful avenues for further exploration / analysis!