The Theory of Relativity

The Magical Flower of Winter is an essay series exploring reality and our relationship to it. It deals with philosophy, science and our views of the world, with an eye on the metacrisis and our future. Sign up to receive new essays here:

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…these concepts and relations, and indeed the postulation of real objects and, generally speaking, of the existence of "the real world," have justification only in so far as they are connected with sense impressions between which they form a mental connection.

Albert Einstein - Ideas and Opinions

In the previous essay I took a look at the break made with classical thinking and our experiential intuition by the quantum theory. Preceding the full development of the latter in the mid-1920s is the theory of relativity¹, largely developed by Einstein and collaborators² in the period from 1905 to 1916. We will see in this essay how relativity and the new conception of spacetime breaks with classical thinking, and what the insights from these developments have to say about the nature of reality, in particular towards illuminating its holistic aspects. The starting point will be the same as in the last essay:

Our day-to-day experience of the world is one of solid, determinate and extended objects interacting in a fixed space, with durations of time that, though psychologically subjective, are unerringly measured out by the ticking clocks around us. The legacy of Newton is a model of reality as a big unchanging and absolute box, space, acting as a static background in which things deterministically evolve in a time that is equally absolute.

What follows will be an overview of how this understanding of space and time was revolutionized, as well as a brief treatment of the domains of experience and science by which the theory of relativity is limited.

Figure 1. The classical picture: matter, represented by the orbiting system, is separate from spacetime, a slice of which is represented by the box of coordinates. The latter is an absolute background for the former to be in.

The Special Theory of Relativity

The special theory of relativity arose in part from the friction between the Newtonian model and the developments in electromagnetic theory in the late 19th century. In addition to space and time as absolute, the Newtonian paradigm saw forces and actions as carried out immediately at a distance. This means that there would be no delay in the effects in the rest of the universe by an action carried out here, that by moving or changing a single mass anywhere all the other masses in the universe are gravitationally affected instantaneously. The forces in electromagnetic theory on the other hand obeys a constraint, the speed of light, which limits the speed at which forces from one spacetime region affects another. This theory was developed in the 19th century by such titans as Faraday, Hertz and Maxwell, and describes the electric and magnetic phenomena of charged particles and light. The electromagnetic field is the central substance of the theory, and this field is the carrier of electromagnetic forces, limited in how fast they can affect separated regions. Forces and actions are now not instantaneous, but propagated at the speed of light through the field, such that a change in a charge over here propagates with the speed of light outwards to everywhere else. This limitation on the speed of light manifests as the theory being Lorentz covariant. This means that the form of the electromagnetic laws are invariant under Lorentz transformations of the coordinates. It was the great insight and work of Einstein in the special theory of relativity to extrapolate this property of the electromagnetic field to spacetime itself, thus refashioning the separately absolute space and time of Newton into a single absolute spacetime. This property of Lorentz covariance now encapsulates the two postulates of the special theory of relativity:

1. The laws of physics are the same in all inertial (uniformly moving, i.e. non-accelerating) frames of reference.

2. The speed of light (in vacuum) is the same in all frames of reference.

By frame of reference is meant a local (coordinate or physical) system by which dynamics can be measured (co-ordinated). The theory gets its name of relativity because in it, uniform (“special”) motions are relative and not absolute, a development on Galilean relativity compatible with the second postulate³. That motions are relative is simply stated in the following way: in the absence of anything else, one mass in uniform motion relative to a second mass at rest is indistinguishable and equal to the second mass being in an inverted motion relative to the first being at rest. Another important consequence of this new understanding of spacetime is the relativity of simultaneity. There is no longer an absolute and universal “now” that is equal for all frames of reference. What is “now” for me has no immediate connection to what is “now” for you, our now’s have to be mediated, and this mediation is limited by the speed of light. Everything (in the special case, everything in uniform motion) is connected spatiotemporally, and by this spatiotemporal connection we start to see the outlines of the interconnected whole. But what about things in spacetime? «In accordance with classical mechanics and according to the special theory of relativity, space (spacetime) has an existence independent of matter or field.»⁴ Spacetime is still an absolute and independent background to things in the special theory. In order to have a theory that encompasses both spacetime, matter and field, relativity must be extended to non-uniform, accelerated, frames of reference.

The General Theory of Relativity

Figure 2. The relativistic picture: matter is spacetime, the latter being an aspect of the former. 

The general theory arose out of expanding the framework of the special theory of uniformly moving frames of reference (special relativity) to accelerated frames of reference (general relativity), coupled with the insight that gravitational mass (the mass property in Newtonian gravitation) is the same as inertial mass (the mass property in Newtonian dynamics). It was due to Einstein’s great understanding that free fall in a gravitational field is indistinguishable from being in an accelerated frame of reference, meaning that these two situations are two sides to a single coin, thus that the mass in these two situations are the same. In the general theory, now encompassing accelerations, frames of reference transform according to non-linear continuous coordinate transformations, a consequence of the general principle of relativity: all frames of reference are equivalent with respect to the formulation of the fundamental laws of physics. In the special theory of relativity, spacetime was absolute, but in the general theory it no longer is, meaning there is no longer any absolute background against which anything can lean on, the background is itself dynamically constituted by the gravitational field and the generally covariant spacetime the field composes. «Space-time does not claim existence on its own, but only as a structural quality of the field.»⁵ This is important: there is no spacetime without the gravitational field, the gravitational field is spacetime. This means that a process is not in a spacetime-region, it is a spacetime-region⁶. That the gravitational field obeys general covariance is a symmetry of the theory that makes it independent of coordinates: there is no longer any absolute coordinate system, any coordinates we use is a choice, and can be transformed into any other coordinate system as long as the transformation adheres to local Lorentz covariance. General covariance can also be understood as diffeomorphism invariance⁷, meaning that the same physics can be obeyed by different gravitational fields as long as these transform into each other covariantly: the form of physical law is independent of coordinates. General covariance and diffeomorphism invariance both reflect the fact that there is no background: the general theory of relativity is a theory of background independence. The arena in which things happen is no longer separable from the things happening, they are mutually co-dependent and co-existing⁸. One is not prior to or constitute of the other, just as we in experience cannot conceive one without the other⁹. These properties of general covariance and background independence strongly indicate the holistic nature of reality, and the limitedness of particularism: that reality can be conceived of independently of our experience and that our experience reduces to this independent reality of things cannot be an adequate view of reality when we find that things and their background are inseparable, because the independence of things and their background is the very presupposition that particularism has been modelled on since Descartes. Furthermore, Einstein was a strong believer in Mach’s principle¹⁰, that local inertial frames are defined by the global distribution of masses, which we can see is a holistic principle: the parts depend on the whole.

Time

People like us, who believe in physics, know that the distinction between past, present and future is only a stubbornly persistent illusion.

Albert Einstein¹¹

As we saw in the previous essay on Quantum Theory, Einstein struggled with letting go of his relativistic model of spacetime as a model, which to some extent can explain his near dogmatic belief in local realism and a deterministic universe, for these are aspects of the relativistic model. Sadly, since almost everyone else also mistook the model for reality, this has led to the physical time that appears in general relativity being confused with time as we experience it. We must remember that our physical model must answer to our experience, and not the reverse. Thinking that our model of reality holds an ultimate answer leads to thinking that time is a “stubbornly persistent illusion”, while our experience tells us that time is both the most essential and the most undeniable aspect of what makes experience what it is. Our experience is inseparable from time, without time there would be no experience at all, because our experiencing is irreducibly temporal¹². Remove time from experience, and you lose both, for the latter cannot be recovered from individual “moments”, no experience can exist that does not have duration¹³. The “time” that appears in the equations of general relativity is a parameter, unobservable, which stands in for what a clock measures, but this is not the same as time in our experience¹⁴. Clocks measure and counts simultaneous events, their use presupposes a division of reality into a series of countable moments. The present in our experience is irreducibly extended as opposed to the mathematical present. Physical and mathematical time is as such thin and instantaneous, as opposed to thick and enduring experiential time. The great error lies in this presupposition of division, for experienced time is duration, and not a serialized succession of moments, this latter is the fallacy of viewing time as space, of spatializing time¹⁵. By breaking our experience apart into pieces, we inevitably treat of the pieces in space, we see “moments” of time laid out in a string, but this string is either in or constitutive of space, not time. Bergson saw the experientially essential nature of time and the limits to representing it: «But how can we help seeing that the essence of duration is to flow, and that the fixed placed side by side with the fixed will never constitute anything which has duration. It is not the states, simple snapshots we have taken once again along the course of change, that are real; on the contrary, it is flux, the continuity of transition, it is change itself that is real. This change is indivisible, it is even substantial.»¹⁶

The continuity of experiential time cannot be recovered from a series of infinitesimal moments, this is the trap laid by mathematization (which is an epistemisation) of continuity. «Immanent in our measurement of time, therefore, is the tendency to empty its content into a space of four dimensions in which past, present, and future are juxtaposed or superimposed for all eternity. This tendency simply expresses our inability mathematically to translate time itself, our need to replace it, in order to measure it, by simultaneities which we count. These simultaneities are instantaneities; they do no partake of the nature of real time; they do not endure. They are purely mental views that stake out conscious duration and real motion with virtual stops, using for this purpose the mathematical point that have been carried over from space to time.»¹⁷ By reducing experience we make of it something other, and the experience cannot be recovered from the parts, because experience is a whole, more than the sum of the parts. The theory of relativity, or any other theory, is always-already epistemised¹⁸, the analytical and theoretical, the sayable, only ever an approach to our experience, never capable of encompassing it unto completion. The spatiotemporal framework of general relativity is of course not wrong, it has been experimentally verified despite the criticisms of Bergson and others, but the theory is limited like all other frameworks, like all the epistemic is. It treats of those aspects of reality that are reducible to spatiotemporal coordinates and that are measurable by rods and clocks, but the theory cannot answer to our full experience of space and time, because the meaning of these terms in our experience covers over more than their meaning in the theory of relativity. Thus, it is not a case of either holding to the conception of physical time in general relativity or Bergson's experiential time as duration, but of holding to both: a coherent view of reality as a whole must account for both the physical and experiential aspects of space and time, while acknowledging the primacy of the latter. I will return to experience, time and Bergson in upcoming essays¹⁹.

Reality

Physics is an attempt conceptually to grasp reality as it is thought independently of its being observed. In this sense one speaks of "physical reality."

Albert Einstein - Ideas and Opinions

Einstein brought to light the pivotal importance of relativity to physical reality - that your frame of reference, your point of view and context in relation to the rest of the world, determines your view of that world and how you can measure and interact with it. This means that your experience of the world, understood in physical terms, is relational²⁰. The theory of relativity collapses the classical absoluteness of space and time, and is a statement to the fundamentally mutual dependence of spatiotemporal and material reality. Obviously, the picture of spacetime and reality painted by the theory of relativity is still a picture, a model. As I stated in the previous essay: «Any interpretation of physics is metaphysical, for it involves the interpreter, and interpretation is inevitable when faced with models of reality.» The aspects of the relativistic model of reality are radically different from our everyday naive conception of space and time, and necessarily so in order to account for the phenomena coherently. And it is this coherence that once again reveals itself as the criteria by which physical theory is measured. The theory of relativity is a coherent theory of those experiential phenomena that are spatially ordered in spatialized time, and as we saw above it meets one of its limits when faced with our experience of time as duration. General relativity further goes up against its limits in the regime of high energies and small scales where quantum phenomena become dominant: black holes and the physical origin of reality. The collection of unexplained phenomena going by the name “dark matter” is another domain where our current understanding points towards the incompleteness of general relativity as a theory of reality.

Background independence encapsulates an aspect of reality that any theory claiming to be fundamental must adhere to: the stuff out of which reality is made, whether substance, field or flow, cannot rely on anything other, some absolute background, on which it leans for its existence or its properties. Reality is self-sufficient, self-upholding, which our model of it must reflect if it aims to be “fundamental”. The quest for an “ultimate” theory that unifies or provides common ground for the theory of relativity and quantum theory is collectively called quantum gravity, examples being superstring theory and loop quantum gravity. Common to physical quantum gravity approaches must be that both spacetime and the things in it are constructed out of one and the same physics. The criteria of background independence (and general covariance) favors loop quantum gravity: «...we do not have a background-independent formulation of the [string] theory… The main merit of loop quantum gravity, on the other hand, is that it provides a well-defined and mathematically rigorous formulation of a background-independent, non-perturbative generally covariant quantum field theory.”²¹ I will return to the topic of in what sense we can expect success in uniting quantum theory and gravity, but as should be clear from the rest of this project, dreams of epistemic completion are incompatible with a view of reality as a whole on which the epistemic can only ever approach reality and where an independent ontic world is only ever the unreachable horizon of the epistemic.

General covariance expresses the contextual continuity of reality and how our spatiotemporal experience of reality is inseparable from the substance of our experience: there is no space without things to be extended in space, and there is no time separable from space or vice versa. Covariance further speaks to the immersive aspect of experience, how one’s experience is inextricably unique, yet fully coherent, cohesive and continuous. Nothing can be separated from its immersive context in reality without making it something else, which fact covariance captures: the form of physical laws is independent of coordinates, and physical systems are only defined by the whole they are part of. We thus see how spacetime and the things that make it are mutually dependent: «According to general relativity, the concept of space detached from any physical content does not exist.»²² Even though general relativity is a model, the fact that it explicates a picture of reality where space itself is made up of the very things we classically think it is a background to, should jolt our everyday intuition about the world. Just as the whole shows through in quantum theory as complementarity and non-separability, equally does it show through as background independence and general covariance in the theory of relativity. Our models approach reality in its wholeness, but can never encompass it to completeness, which is why we must take care not to confuse our models for reality. 

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References

Bergson, H. (2001). Time and Free Will: An Essay on the Immediate Data of Consciousness. Dover Publications. [1889]

Bergson, H. (1946). The Creative Mind: An Introduction to Metaphysics. The Philosophical Library. [1934]

Bergson, H. (1965). Duration and Simultaneity. Bobbs-Merrill. [1922]

Canales, J. (2015). The Physicist and the Philosopher: Einstein, Bergson, and the Debate That Changed our Understanding of Time. Princeton University Press.

Einstein, A. (1955). Letter to the family of Michele Besso.

Einstein, A. (1982). Ideas and Opinions. Three Rivers Press. [1954]

Einstein, A. (2006). Relativity: The Special and the General Theory. Penguin. [1916]

Huggett, N, Hoefer C. & Read, J. (2023). Absolute and Relational Space and Motion: Post-Newtonian Theories in The Stanford Encyclopedia of Philosophy (Eds. E. N. Zalta & U. Nodelman, Summer 2023 Edition), URL = <https://plato.stanford.edu/archives/sum2023/entries/spacetime-theories/>

Mach, E. (1919). The Science of Mechanics (Trans. McCormack, T. J.). The Open Court Publishing Co. [1883]

Rovelli, C. (1998). Loop Quantum Gravity. Living reviews in relativity, 1(1), 1.

Rovelli, C. & Vidotto, F. (2014). Covariant Loop Quantum Gravity: An Elementary Introduction to Quantum Gravity and Spinfoam Theory. Cambridge University Press.

Rovelli, C. (2021). General Relativity: The Essentials. Cambridge University Press. 

Smolin, L. (2013). Time Reborn: From the Crisis in Physics to the Future of the Universe. Houghton Mifflin Harcourt.

1. Einstein (2006).

2. Particularly Grossmann.

3. The development of the Galilean transformation to the Lorentz transformation.

4. Einstein (1982) p. 375.

5. Einstein (1982) p. 375.

6. Rovelli (2014) p. 52.

7. See Rovelli (2021) p. 69-70.

8. See World Views for an explication of these terms and how they apply to reality.

9. This is as such a dissolution of the dichotomy between “dynamical” and “geometrical” approaches to spacetime structure which are opposed to each other in whether the dynamics of matter explains the geometry of spacetime, or whether the geometry of spacetime explains the dynamics of matter. See the section The Dynamical Approach in Huggett et.al. (2023). As elsewhere in this project, it is not a question of “either/or”, but “both/and”.

10. Called Mach’s principle by Einstein, referring to the ideas in Mach (1919).

11. Einstein (1955).

12. This relates to Heidegger’s thought, which I will return to later.

13. See e.g. Bergson (1946).

14. Rovelli (2021) p. 71-72.

15. See e.g. Bergson (2001), Smolin (2013).

16. Bergson (1946) p. 15.

17. Bergson (1965) p. 60.

18. See World Views.

19. Bergson and Einstein did not fully understand each other in their discussion of time in 1922 (See e.g. Canales (2015)). Einstein did not believe in the existence of the “philosophers’ time”, and he stated that “there is only a psychological time different from that of the physicist”. I think their misunderstanding from Einstein’s side was his belief in his theory as objectively reality, and not as model. Einstein’s “win” over Bergson in this discussion in large part contributed to discrediting most of Bergson’s thought. Of course, Bergson was not correct in everything and did not fully understand Einstein or his theory either, as his misconceptions of relativity in Bergson (1965) attest to, but the discrediting of most of his contributions is one of the great losses to the development of thought. The general theory of relativity is perfectly compatible with a view of experiential time as duration (without Bergson’s single and absolute time) as long as the limits of theory in relation to reality are acknowledged.

20. It is debated whether general relativity is completely relational or whether there is some notion of the absolute left in it, see Huggett et.al. (2023). Based on my superficial reading of the debate, the arguments against general relativity being completely relational seem to rely on scenarios that while being allowed by the equations of general relativity, are impossible to realize, like the only existing matter in the universe being a lone spaceship accelerating or a singular rotating body. Such scenarios will break the symmetry between acceleration and gravitation, thus returning some notion of the absolute, but of course can only be imagined. As such I don’t think this debate carries too much weight. In addition, general relativity is an epistemic, thus limited, theory, so the fact that it isn’t completely relational just confirms this limitedness from another direction. Reality as we experience it is relational, and we have seen how it is irreducible to the epistemic, so that our model of it should be lacking is no surprise.

21. Rovelli (1998).

22. Einstein (1982) p. 348.