^{*}. If nothing happens now, if "now" is frozen, then nothing can be known "now".

Presentism originates in the fact that I cannot measure events that are a microsecond in the future or easily measure events that are a microsecond in the past, here, at the point of the measuring instrument (But electrons can interfere with their past "selves" - see Lindner et al. (2005). Attosecond double slit experiment. and Horwitz's analysis of these experiments).

The alternative to presentism is four dimensionalism in which there is an aspect of time that occurs as a dimension like the three dimensions of space. This aspect of time is sometimes called "dimensional time" and is another axis, or direction, for arranging things. Four dimensionalism is the modern interpretation of relativity theory, it not only holds that objects are arranged in space and dimensional time, it also says that space and time are interdependent. This interdependence of space and time seems odd until it is realised that Pythagoras' theorem is just a way of saying that distances are interdependent. In Pythagoras' theorem any two dimensions in space are related by:

h

^{2}= x

^{2}+ y

^{2}

The Ancient Greeks realised this was weird; why should two independent directions for arranging things be related to each other by an exact mathematical formula? It gets weirder. If we have three independent directions (left-right, forward-back and up-down) they are related by a grand form of Pythagoras' Theorem:

r

^{2}= x

^{2}+ y

^{2}+ z

^{2}

Any readers who are mathematicians will recognise that this is the equation that defines a sphere. The Pythagoreans got mystical about this and thought that spheres were a sacred form. Spheres are indeed odd, why should three independent directions be exactly related? Why is the universe uniform in all directions? Why does the surrounding volume grow in an exact way with distance from a point? In the nineteenth century mathematicians such as Riemann toyed with the idea of space and created powerful tools for analysing geometry. In 1905 Einstein came up with the Special Theory of Relativity and in 1908 Minkoswki, who was Einstein's maths teacher and knew Riemann's work, showed how Einstein's idea was equivalent to adding another direction for arranging things that some philosophers call "dimensional time". Minkowski expressed the relationship between the dimensions as:

s

^{2}= x

^{2}+ y

^{2}+ z

^{2}+ (ict)

^{2}

Where (ict) is the square root of minus one times the speed of light times the time elapsed. (See Wikibooks Special Relativity). The "speed of light" is just the number of metres that are covered by a single second of dimensional time. Nowadays the square root of minus one is replaced by a change of sign in a "metric tensor" but the significance of the Pythagorean form of the relation between time and space remains the same.

These equations that relate the dimensions are known as

**metrics**and they define a spacetime. In the Wikibook reference it shows how Minkowki's equation leads on to the whole of Special Relativity.

Presentists do not like Relativity Theory. Presentism also denies that we can hear whole words stretched through time rather than individual phonemes, or less, and rejects the idea that we can see movements. The idea that we might have both a question and its answer in our time extended minds is also considered absurd by presentism but no explanation is offered for how we could know anything in no time at all. (See Time and conscious experience for a description of how our minds extend through time). Presentism is "time blind", we hear whole bars of tunes but presentism declares that you coexist with less than a note.

Even those who accept that the universe is four dimensional often make a mistake in imagining the form of four dimensional spacetime. It is common for four dimensions to be represented as:

But this is a pseudo-three dimensional representation of four dimensions. Four dimensions cannot be portrayed on a sheet of paper, the nearest we can get is to consider the "light cone":

Image courtesy of Wikibooks: Special Relativity.

The light cone is a representation of the four dimensional equation:

0 = x

^{2}+ y

^{2}+ z

^{2}- (ct)

^{2}

which has a

**negative**sign in front of the term for time so what is happening is that, if dimensional time exists, all of those points on the surface of the cone are no distance at all from the centre point along the path represented by the cone. This four dimensional form is full of surprises and not at all intuitive, for instance the zero length path is the same path as that taken by photons, it has no length for something on the path but does indeed have a length and duration for any observer who is not on the path.

Unlike four dimensionalism, Presentism is not a scientific theory, it has no corpus of explanatory physics attached to it and has no experimental basis. There is no document anywhere that explains how Presentism can be integrated into science and there are only the vaguest of notions in the philosophical literature of the actual nature of Presentism, most 'Presentist' articles being attacks on four dimensionalism rather than manifestos for Presentism. Yet this unsupportable and barren idea is understood by large numbers of people to be the conventional 'wisdom' about time.

**Some speculations**

From the empirical viewpoint it is sufficient that we can see things move to know that presentism is false. It is, however, interesting to speculate upon potential physical models of our experience but the reader should be aware that if the speculation is wrong the experience remains. Unlike presentism, empiricism would not claim that the existence of your experience depends upon a scientific hypothesis!

Here is a possible idea for how four dimensionalism might explain experience. When dimensional time is introduced into the metric of spacetime time occurs as a negative factor. This can be seen when the square root of minus one is expanded:

0 = x

^{2}+ y

^{2}+ z

^{2}- (ct)

^{2}

Dimensional time subtracts from the distances specified by the other, spatial, dimensions and creates a geometry akin to the descriptions of conscious experience given by Descartes in which experience occurs at a point. In fact only those events that obey this equation can be 'known' at a given time and place because all other events have a net spatial or temporal separation. Notice that the equation allows events to stay at their proper locations in time and space and the 'point' is created by a disappearance of separation between the events as time progresses (See Some notes on projective geometry).

**Notes for physicists**

The general form of the metric is a differential equation, the form given here is applicable to the discussion however because it applies to coordinates relative to a point observer in flat spacetime. Minkowski's use of imaginary coordinates has now been replaced with an approach that uses a metric tensor. The bilinear form of the modern theory is important in General Relativity, but the metric remains the same so this removal of

*i*makes no difference to the argument given above which depends upon the fact of dimensional time and the negative sign in the metric.

The application of time extension to time intervals greater than a microsecond would seem to require Green's time-like fifth dimension (Green 2002) to create an appropriate time dilation, the time-like nature of this dimension might be due to the continuous appearance of experience.

* Some readers may realise that it is inconsistent to refer to time intervals when only the present is held to exist. I would suggest that presentism is inherently dualist with the philosopher or observer having time-like qualities that permit the inspection of the universe in the different states that we assign to "time" and "change". This would be a strange and unnecessary dualism because physicalist explanations such as that put forward by de Witt (of the Wheeler-de Witt equation) allow an inherently timeless universe to acquire "time" through the separation of a physical observer system.

See also:

Ashmead, J. 2010 Quantum Time. http://www.timeandquantummechanics.com/papers/single.pdf

Gopal et al. 2009 Three-Dimensional Momentum Imaging of Electron Wave Packet Interference in Few-Cycle Laser Pulses. Phys. Rev. Lett. 103, 053001 (2009). http://www.attosecondimaging.com/attosecimaging/pdf/Gopaletal.pdf

Hi,

ReplyDeleteEven though complex mathematics describes very accurately the fourth dimension of space-time continuous, let’s not forget that square root of -1 is an imaginary number and is introduced for theoretical reasons.

The problem with presentalism, seems to be the continuity of reality. The reality cannot be continuous and present in the same time. So you can think of reality as being rather discrete (a series of flashes) and not necessarily correlated to what is observed but with who is making the observation. So far, I found this to be in accordance with QM.

I know that there are cameras that can capture 500 images a second, however for human eye the visual reality is only at 50 images per second. 20 milliseconds is our sampling frequency that makes the visual reality appear continuous.

Hi Doru,

ReplyDeleteI was recording Minkowski's original approach to 4D in the article. Of course the metric is nowadays described using a metric tensor with a signature +++- or ---+. The use of a metric tensor is essential to preserve a bilinear form in General Relativity. However, the metric itself is preserved, it is still: ds^2=dr^2 - (cdt)^2, and the geometrical significance of this metric is unchanged if time exists.

You say "The reality cannot be continuous and present in the same time". Well, that is one way of defining "presentism". It is entirely contrary to the modern physical view of spacetime as a continuum.

Your statement that:

"So you can think of reality as being rather discrete (a series of flashes)"

is also a good piece of presentism. Now, suppose you are yourself one of these static flashes, how do you know anything? Or do you know things about the previous flash in the next flash?

Hi,

ReplyDeleteI'm thinking about your arguments here and I have a couple questions, if you feel like answering.

First: when you say that it's wrong to think of four-dimensional spacetime as a series of three-dimensional "frames," is your point simply that the time dimension is continuous (like the spatial dimensions) rather than discrete? Or are you saying that the geometry of spacetime is (per modern physics) not like the geometry that you get by simply adding one perpendicular dimension to 3D space?

Second: Is it correct to understand you as arguing that we should conceive of the "self" or "mind" as extended in the fourth (time) dimension, rather than as something existing simply within a single 3D slice of spacetime? That makes sense to me, but I don't quite follow where the argument goes from there, so I feel like I'm probably missing something at the basic conceptual level.

Thanks -- this is all very interesting, I have a strong feeling that you're onto something here, as I've felt for quite a while that dealing with the problem of consciousness was going to require a fundamental conceptual shift rooted in how modern physics tells us that the world works.

Going from 3D to 4D involves more than just proliferating 3D forms. Time is unlike the spatial dimensions because it enters the metric with an opposite sign (negative instead of positive in the convention that is used here). If time exists then this negative sign can give rise to a disappearance of separation between events. The equation:

ReplyDelete0 = x^2 + y^2 + z^2 - (ct)^2

describes all the events that have no net separation from a given point in spacetime where x,y,z are spatial separations from the point and t is the temporal separation. Notice that this equation describes a disappearance of separation between events on a sphere surrounding the point, not a flow into the centre of the sphere.

The clearest way to think of this is to consider the path of a photon. At the speed of light the whole universe has zero separation from an observer in the direction of motion. If dimensional time exists then the path of a photon is a geometrical entity, a line connecting two existent spacetime points. The length of this line is zero metres. If dimensional time exists then the path of a photon is actually like a door or bridge that directly connects two points in spacetime. Now for the interesting bit, if dimensional time exists then that path is there even without the photon to traverse it.

So, consider a sphere of events, perhaps a sphere of events in the brain. All those events that conform to:

0 = x^2 + y^2 + z^2 - (ct)^2

will have no net separation from each other at a point and in the directions specified by the lines from (0,0,0,0) to (x,y,z,t). The events will be measured as being spread out in space and time but will also be no distance from each other in the directions that correspond to the paths of photons connecting them. Green(2002) pointed out that our experience implies yet another, timelike, dimension so that:

0 = x^2 + y^2 + z^2 - (ct)^2 + T^2

which conjures up an image of a volume of brain activity rocketing along the positive time axis at near the speed of light so that time dilation would permit a second or two of four dimensional spacetime to be represented in a few cubic millimetres of brain.

Green's argument is interesting but I would like to keep the theorising in two separate stages. Firstly our experience is clearly multidimensional - just look and listen, stuff is distributed in time as well as space so we need a theory of this observation. Secondly our experience is due to our brains so we need another theory about how measurements of our 3D brain activity at an instant transform into our multidimensional experience.

I just realised that I havent tackled your second point:

ReplyDelete"Second: Is it correct to understand you as arguing that we should conceive of the "self" or "mind" as extended in the fourth (time) dimension, rather than as something existing simply within a single 3D slice of spacetime? That makes sense to me, but I don't quite follow where the argument goes from there, so I feel like I'm probably missing something at the basic conceptual level."

If the summary of Green's theory in my last comment is true then a spread out volume of brain activity would be in contact with its historical self through a point of connection in spacetime. The "self" would be a succession of brain states available now, at this instant. Spatial separations in our experience, such as those between the letter 'A' in the diagram: A------A being angular separations at the point of connection. Temporal extensions such as the extension of a whole word at the lips of a speaker being angular separations through time at the point.

The vectors that extend into the point and have angular separations from each other are, according to the equation given above, of no net length so might correspond to a sort of infinitessimal leaning over of brain activity at one instant into brain activity in the same volume of brain at another instant. The overall effect would be to create a sort of modern "monad" or Cartesian point-soul.

If dimensional time exists then there are some weird corollaries. For instance, if Green's five dimensional model were correct then I would be rocketing along but there is no reason why "I" should be at any particular point on the web of time. "I" would also be an hour ago and if "I" could be an hour ago then "I" could also be an hour in the future though each of these "Is" would be entirely separate.... My guess is that there are some rigid constraints not encompassed in Green's theory that prevent this weirdness.

Thanks, that was lucid & helpful. One more thing, if you have the time. On this understanding, a volume in my brain is in spacetime contact not only with other parts of my brain at earlier times, but with earlier points in the room, and the Earth, and the whole universe -- the connected points just get further back in time the further out you go, right? So why isn't there some more apparent interaction between my brain and points in the distant universe at long-ago times?

ReplyDelete"So why isn't there some more apparent interaction between my brain and points in the distant universe at long-ago times."

ReplyDeleteThis was Rauscher and Targ's "prediction" from a consideration of the possibility of multidimensional conscious experience. I say "prediction" because their paper was based on the, possibly dubious, US Remote Viewing experiments.

Green's theory is not dissimilar to Rauscher & Targ's and would also seem to allow the whole universe to be its own conscious experience.

However, these ideas would seem to be getting ahead of the empirical evidence. All that I know is that my mind is four dimensional - I can see and hear this - and, like Green, I can infer a fifth dimension from the layout of the four but this makes me uneasy. It makes me uneasy because we should always be able to check our inferences with predicted observations.