[TheCartographer]

So, I worked with Bergson's texts quite a bit in grad school, as he is heavily in vogue at the moment in certain disciplines. To break down his argument to its essentials, the whole concept he is railing against is the spatialization of time. That is, for Bergson, time cannot be subdivided into the "mechanistic time" of the ticking clock, and the idea of a timeline is an abomination.

Hence Bergson's framing of time as duration: for Bergson the essence of experiential time is that our consciousness is always experiencing the latest moment sliding smoothly into the next. Time, he says, cannot be spatialization and counted as can space. Bergson railed against the idea of time being extrapolated to just another metric dimension like the 3 dimensions of space. The spatial dimensions, to him, were static, fixed, dead. It is only duration that gives our existential experience of the lived experience that we know. Spatialization, to Bergson, was a dirty word; it was the spatialization of our lived experiences that rendered industrial life dead, static, mechanistic and uninteresting. Bergson was railing against the idea of a physics that could predict everything, a popular thought in the early 20th century.

After WWII, Bergson was largely forgotten until Deleuze & Guatarri ressurected him. Deleuze in particular was an enormous fan of Bergson and promoted his ideas heavily.

But what was revolutionary about Deleuze's handling of Bergson was his incorporation of post-war complexity/chaos theory and quantum mechanics to recover space as a dynamic and mutable. Influenced by such concepts as Reimman mana olds and fractal theory, Deleuze recognized that space wasn't a static and mechanistic concept at all, but instead, like Bergson's duration, can give rise to all types of unpredictable behaviors, experiences, and mathematics.

Rather than focus on one concept of "space" - the abstracted Euclidean grid - they classified space in two broad classes, the smooth and striated. Smooth spaces are spaces that are analogous to Bergson's duration: the experienced space of the journey, nomadic spaces, spaces that unfold rather than increment, that are uncountable and unexpected. Striated spaces are the class of spaces Bergson focused on exclusively: coordinate spaces, the countable spaces of the Euclidean grid and the map, or that of the timeline.

Essentially, D&G 'recovered' mathematical space as an exciting and unpredictable philosophical concept. All spaces arise from continuously recapitualtion of smoothing and striation, and counting spaces always give rise to the uncountable and to emergent behavior.

A good example is Conway's Game of Life: a simple set of rules played out on a metric space in countable time (striation) gives rise to emergent organizational patterns and a higher level of emergent behavior that simply cannot be predicted or quantified using the original simple set of rules alone (smoothing). Or, to take another case, the Mandlebrot set: a simple pattern gives rise to a recursive, self-similar-yet-never-identical structure that persists to infinity. For D&G it the uncountable always arises out of the act of counting.

This comment is somewhat outside the normal domain of HN, I know, so I hope you will excuse it. I rarely get to show off the hundreds of hours I dumped into D&G and Bergson in gradschool in my day job. :-D

[raattgift]

Interesting. The vocabulary disconnect with General Relativity (which is the more relevant theory of relativity here, I think) is pretty frustrating, although one thing that struck me is that at the time Bergson was making these arguments, there was a lot of GR jargon yet to be invented. Also, crucially, a formal process for foliating a "block universe" spacetime was decades off (the 3+1 Arnowitt-Deser-Misner formalism arose in the late 1950s), so a late 1910s criticism of GR as treating the timelike axis as "dead" like the spacelike ones was almost reasonable.

Other important and relevant tools were either extremely fresh (e.g. Noether's first theorem) or had yet to be formalized (e.g. gauge theory), and these put practical limits on conceptual attacks on dynamical spacetimes (that's one reason why externally static vacuum metrics, like Schwarzchild's, were popular at the time). Numerical relativity wasn't even a dream in the 1920s.

However, in spite of not-yet-existing tools, it was pretty clear that General Relativity's coordinate freedom combined with diffeomorphism-invariant models of matter would accomodate standard approaches to time-series evolutions of field content (e.g., initial values surfaces and physical laws). Additionally, "ticking clocks" that appeared in Einstein's and others' GR papers were meant as shorthand for much more general objects -- basically anything that has some state that isn't time-translation-invariant. Ideal gases and other thermodynamic composite "objects" count, as do fundamental particles, as does an entire expanding or contracting universe. "Ticking" is simply the application of some arbitrary coordinates (not necessarily linear or even uniform ones; in GR they only have to admit a diffeomorphism) on those "clocks".

One of the interesting things that was pretty fresh prior to Einstein's Nobel was the resolution of the hole argument, which essentially abandoned manifold substantialism. Spacetime without a clock is simply an irrelevance; it's only the presence of at least one (or more) "ticking clocks" that gives meaning to any system of coordinates one puts down on the manifold -- and in particular it's the "ticking clock" or clocks that generate the metric; it is not something that is a property of wholly empty space, and that in turn led to a deeper understanding of the G_{\mu\nu} + \Lambda g_{\mu\nu} side of the Einstein Field Equations (i.e. the curvature of spacetime determined by the metric).

There was undoubtedly some "philosophy" going on in the early days of General Relativity, but frankly most of the work was on modelling gravitational collapse in general, which was both fairly difficult technically and also a deep well of unexpected consequences that were even more strikingly different from Newtonian gravitation than the Kepler problem in GR.

I'm fairly confident that the ideas raised related to this Bergson-Einstein debate were uninteresting (and possibly even mostly unknown) to most of the scientists exploring the golden age of General Relativity (1960s & 1970s mainly). GR, especially post-Einstein, racked up some extremely precise quantitative predictions of the behaviour of large bodies (and small things near large bodies) that matched later observations with high precision.

By the 1980s, the space for thinking about the philosophy of General Relativity was already mainly at inaccessible energy-densities or at almost pointlessly timelike-separations from us (e.g. the earliest we could see the consequences of black hole evaporation is about a hundred billion years in the future), so what's more interesting (I think) is the study of the mechanisms that generate the metric and the exploration of non-exact solutions, rather than picking at the scabs of GR's unremovable background.

[TheCartographer]

This... was an amazing reply. Thank you for offering it, and taking the time to lay out such a long and thoughtful response. I think you are pretty much dead on, and your reply helped me connect some dots in my own mind about the meta-history of relativity.

Regarding the lack of interest in Bergson during 70s and 80s, I think you are precisely right, and the untestable nature of the time-like ramifications of relativity weren't something I had previously considered. Of course, by that time Einstein was so obviously right, and Bergson so obviously wrong, I think those physicists can be forgiven for not knowing, or for not giving a shit if they did know.

One of Bergson's chief objections to the Twin's Paradox was the idea of time slowing down for the twin sent on the relativistic journey. Such a thing made no sense to him, giving how he framed time: as an unrolling now that could not be subdivided into metric units.

Bergson's objections to time-like relativity are certainly understandable, I think, given the historical context. As you pointed out, the notion of a physics without a background of absolute space - the concept of the ether or an absolute background metric against which space time is measured - were the 'standard' model of the time. I would go even further, and say that many physicists at the time either had severe difficult in coming to terms with physics based on frames of reference, or they rejected it outright. So I don't think Bergson's objections to a relative experience of time are unreasonable, nor do I think you can fault him for his objections, given the difficulties physicists themselves had coming to terms with the implications of relativity. Something I hadn't really considered, however, is that we didn't have the laboratory apparati to test the hypothesis that time passes differently under acceleration until decades after Bergson himself was dead.

Regarding clocks, I certainly understand that a 'clock' in physics is a shorthand for a physical system undergoing periodicity: whether it is an actual clock, a cesium atom, or a gas, etc. For Bergson, however, it was the act of reducing the dimension of time to a countable metric itself that was problematic. For him, the idea that time can be subdivided like space was simply a trick of memory, not actual experience. If we focus only on the unfolding 'now' - something difficult enough to do Bergson wrote whole books on it - we only see one moment elide seamlessly and smoothly into the next.

Bergson had no problem with pointing out that metric time worked quite well in modeling physical systems; his objections were to using this approach to model human experience (particularly with regards to free will and the implications of determinism inherent in relativity). Bergson was a proto-postmodernist, and was trying to get at the idea that the 'map is not the territory.' Hence Bergson's focus on the Twins Paradox. Relativity allows for a space-like time that can be 'run in reverse,' but actual time isn't space-like, in the sense that it can be traversed in one direction only. So despite what Einstein's equations predicted, Bergson objected that the notion of the Twins experiencing time differently was non-sensical.

What I hadn't realized prior to reading your comment is the similarity of Bergson's objections to the objections/difficulties physicists themselves had in abandoning the idea of a fixed, background metric space. He is essentially arguing for a fixed background of indivisible non-metric time that everyone experiences universally and that unrolls at a fixed rate for all observers.

On a side note, I've always thought Bergson (and pretty much the entire history of the philosophy prior to Einstein) had it precisely backward. Thousands of works have focused on and prioritized time as a cornerstone philosophical concept. Bergson was not alone is his obsessive focus on it. And yet, time is the most ephemeral and intangible concept of them all. You can't see it, you can't hold it, there is nothing there. 'Time' as we know it is merely the periodic spatial change repetition of some physical phenomenon: the vibration of an atom; the periodic steps of a watch hand; the filling of a fixed volume of space with water (as in a water clock).

Perhaps it's only the fact that I take living in a post-Einsteinian space-time for granted, but I always found it strange that people -including Bergson - so obsessively abstract 'time' as something distinct from itself, when what they are really seeing is space itself unfolding into... well, more space I suppose.

Thanks again for the thoughts, it was a great read with my morning coffee!

[raattgift]

[continuation of too long comment]

"He is essentially arguing for a fixed background of indivisible non-metric time that everyone experiences universally and that unrolls at a fixed rate for all observers."

Right, that pre-Einsteinian picture has proven to be wrong. Accurate clocks at different altitudes and moving at different groundspeeds bear this out, even if people living on mountaintops or flying in jets don't notice the parts per billion difference in their day from the people living at sea level. The GPS tools they have with them do, though.

And, sadly, he did not live long enough to see 1971 ( https://en.wikipedia.org/wiki/Hafele%E2%80%93Keating_experim... ).

Penultimately, there are some theoretical physicists who think time is "real" in the sense that it is fundamental rather than just emergent. I think you are taking an emergentist position (which I agree with) when treating it as arising from observed periodicity. (Remember that your observation of something's period -- like the bouncing light pulse between the parallel mirrors -- is not necessarily the same as another person's observation of the same something.)

Finally, just to bend your brain a bit, in General Relativity in any universe which is even close to being like ours, you cannot have a system where a pair of mirrors with a light pulse bouncing between them can be forever parallel. The parallel mirrors and light pulse are a system of mass-energy that source very slight (but nonzero) curvature. That curvature means that the parallel mirrors, if close to one another, are on a converging path even in empty space far from all other matter. If far from one another, the metric expansion of space means that the parallel mirrors are on diverging path. In a completely empty universe with a finely tuned dark energy, one can set up a classical system in which the system is extremely finely balanced so that the mirrors will stay the same distance apart (measured locally by a notional mass-energy-less observer moving with the mirrors), but real mirrors and light, made out of parts of the Standard Model, will break that fine balance, and the mirrors will move onto either a converging or a diverging path eventually (maybe bet on diverging because of the relative strength of the electromagnetic interactions with the light pulse compared to the gravitational potential energy, and because real mirrors are imperfect reflectors so some photons will "leak away").

On top of that, a really long (approximately "straight-line") Twin Paradox journey in an expanding universe can put a cosmological horizon between the Twins, so they'll never be able to compare their wristwatches in person. Each will see the other slow down and grow dimmer, but only the one moving at near the speed of light (still locally constant everywhere) will live to see her twin disappear completely across the horizon.

(Of course a similar journey confined to the neighbourhood of the Milky Way, e.g., by zipping to and fro many times, will not involve a cosmological horizon.)

"post-Einsteinian space-time"

Well, we call it post-Newtonian. General Relativity's fundamental theory (and in particular the Einstein Field Equations) is very much Einsteinian still. We just understand it better than he did, mainly because we have newer calculational tools (and newer mathematical innovations), and because we have the advantage of access to many thousands of relativists' work over the sixty years or so since his death.

> Thanks again for the thoughts, it was a great read with my morning coffee!

Likewise.

[raattgift]

Thanks, I enjoyed your reply to my reply too.

The sequence of discoveries or formalisms weighs heavily on how we teach students; it's not just because earlier formalisms are necessarily easier or more intuitive, although they certainly appear to be when it comes young people who have grown up very close to the surface of the earth when it comes to classical mechanics and Newtonian gravity versus the post-Newtonian extensions.

Certainly lots of physicists took varying amounts of time coming to terms with Special Relativity; few today are au fait with General Relativity. Indeed, even relativists who are will tend to prefer to cast problems as Special Relativity ones, using (or even deliberately abusing) the approximately flat spacetime close by the strict definition of "local", because even when they are comfortable with General Relativity, it is faster to use SR where one can, even in cases where one has to manually put in corrections arising from slight curvature.

In an SR setting one usually teaches Lorentz transformations by trying to impart understanding about three things: firstly, the constancy of the speed of light for all observers in uniform motion everywhere, and secondly, thinking of a "clock" that is a pair of parallel mirrors with a pulse of light continuously bouncing back and forth between them. An observer moving with the parallel mirrors will see the pulse "forever" moving perpendicularly back and forth at the same frequency. An observer in any other uniform motion will see the pulse follow a non-perpendicular path (try it with your thumb and forefinger on one hand held parallel and representing the mirrors, with your index finger on your other hand pretending to be the front of the pulse of light -- hold your hands at a fixed distance in front of your face and watch, then try moving your arms left and right, or towards and away from you, or up and down.). The third thing to understand is that the zig-zagging of your finger between your moving thumb-and-finger appears to be a longer path because it is a longer path (think of a set of coordinates on a wall you see past your hands -- bricks or a wallpaper pattern may help). Moving-with-mirrors twin sums up the length traversed by the pulse of light and arrives at something shorter than not-moving-with-mirrors twin's sum, since the latter sees the pulse travelling along a zigzag between the moving mirrors. Since light always travels at a fixed speed, the longer zig-zagging path must take more time than the shorter always-parallel path. That is, each zig-zag "bounce" takes longer, i.e., the zig-zag bounce frequency is lower, or equivalently, the moving-with-mirrors twin's time is passing more slowly.

Einstein wrote about light bouncing between parallel mirrors, but unfortunately almost always in technical settings. I wonder if that would have helped people like Bergson.

'map is not the territory' -- funnily that's exactly what General Relativity is about; diffeomorphism invariance means that you can have arbitrarily many maps of the same matter, all exactly equivalent, and that you can apply arbitrary coordinates over the configuration of matter.

'Relativity allows for a space-like time that can be 'run in reverse'

Well, sorta. Flat spacetime is time-symmetric; since the symmetry group of flat spacetime is fundamental to the Standard Model, all Standard Model interactions are time-reversible.

BUT... the Hubble volume is extremely curved and in an expanding universe, time-reversibility is far from clear. Indeed, there is a pretty clear thermodynamic arrow-of-time, since the earlier universe, being hotter and denser, had less entropy than the later universe (which has lots of almost wholly empty space, and space with a tiny tiny tiny energy-density can be arranged in all sorts of ways and look the same macroscopically). As the metric expansion of space continues, entropy increase because of all that extra new practically empty space. The empty space can pop up all over the place and in almost any sort of configuration, and we get the same overall picture of the cosmos (in particular everything on Earth looks fundamentally, if not absolutely exactly, the same). Reversing the "movie" of the expanding universe with lots of galactic clusters in it requires very careful positioning of all the "almosts" in the empty space as it disappears, otherwise the overall picture of the cosmos diverges dramatically from our history of it. So at that scale, time-symmetry appears to vanish.

(You could also think of it this way: if you blow up the earth you get a cloud of dust and rocks and stuff. Following Boltzmann's definition of entropy as above, one cloud of dust and rocks and stuff can be pretty indistinguishable from another. But if you reverse the explosion (say, via gravitational collapse), you aren't going to get the dust and rocks coalescing into cities and coral reefs and the Himalayas as we know them unless you are very very precise. So even at that scale, time-symmetry vanishes.)

I am not certain that our brains are actually sensitive to those sorts of time-symmetry violations. Maybe we don't reconstruct the future as well as we reconstruct the past because some part of our brain was lost during the evolutionary periods in which we lost various features found in our common ancestors with birds (e.g., the ability to synthesize vitamin C in our own bodies; tails; nictitaing membranes on our eyes; ...). It'd be interesting to have a conversation with a corvid or a grey parrot or something, or a cetacean. Maybe they have a more symmetrical view of "past" and "future", in that they can remember both. Maybe we are good at playing catch because our brains actually "remember" where the ball will be, rather than doing some sort of calculative prediction.

General Relativity is not quite silent on these points; the theory is a "block world" one in which the whole of spacetime is fully determined. Formalisms that do a 3+1 foliation to look more like pre-Einsteinean physics can produce surprisingly bogus results, even though the "block world" suggests that if we know the entire configuration of the universe at any "slice", we know the configuration of the whole "block" history of the universe. (Why is the subject of a substantial amount of current research).

'actual time isn't space-like, in the sense that it can be traversed in one direction only'

So, above, I said that in an expanding universe, or in the presence of curvature near planetary masses, time-reversal fails, but it fails globally. The individual local interactions within atoms and within molecules are all fully time-symmetric (and we can more-or-less show this in labs).

Again, this is a hot topic in physical cosmology. However, I think everyone agrees that no humans are known to have travelled backwards in time, even if subatomic parts of humans may have (due to e.g. the presence of positrons from radionuclide decays within their bodies, or the uncertainty principle).

[comment too long, so dividing it here]