Archive for the ‘spacetime’ Category

Noether-Pauli-Jung, V2

April 10, 2019

What happens when the fourfold of Noether’s Theorem is spliced together with the fourfold of Pauli-Jung? Both have Space-Time and Matter-Energy. The former has Conservation and Symmetry, and the latter has Causality and Synchronicity. And if Space-Time and Matter-Energy are both divided into Space and Time and Matter and Energy, one obtains this eight-fold.

Causality means that some action or cause in time (say a process) of things in space can have an effect (another process, say) on different things in space, and Synchronicity means that different events (say processes) separated in space can have non-causal relationships between them.  Conservation means the consistency of a quantity of matter or energy or matter-energy through time, and Symmetry means the consistency of a measure of a structure or form through space.

I am reminded of my fourfold Four Bindings, consisting of Chains, Grids, Blocks, and Cycles. Causality and Synchronicity are Chains (or non-chains for the latter) Space and Time are Grids (or flexible meshes), Matter and Energy are Blocks (or chunks of stuff), and Symmetry or Conservation are Cycles (of the group-theoretic kind or the equivalence class kind or just loops).

Further Reading:

https://en.wikipedia.org/wiki/Causality

https://en.wikipedia.org/wiki/Synchronicity

https://en.wikipedia.org/wiki/Symmetry

https://equivalentexchange.wordpress.com/2012/05/04/noethers-theorem/

https://equivalentexchange.wordpress.com/2018/01/23/atom-and-archetype/

https://equivalentexchange.blog/2016/04/06/four-bindings/

This is a reworking of a previous six-fold diagram that I believe is served better as an eight-fold.

https://equivalentexchange.blog/2018/03/29/noether-pauli-jung/

[*10.68, *10.155, *11.55]

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Noether-Pauli-Jung

March 29, 2018

What happens when the fourfold of Noether’s Theorem is spliced together with the fourfold of Pauli-Jung? Both have Space-Time and Matter-Energy. The former has Conservation and Symmetry, and the latter has Causality and Synchronicity.

I had to remind myself that Conservation means consistency (of matter or energy) through time (and space), and Symmetry means consistency (of form) through space (and time), so in some sense they are dualistic.

Combined, one has the three axes of dual concepts, represented above.

Further Reading:

https://equivalentexchange.wordpress.com/2012/05/04/noethers-theorem/

https://equivalentexchange.wordpress.com/2018/01/23/atom-and-archetype/

[*10.68]

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Four Dimensional Space-time

September 1, 2014

sq_4d_spacetime

Here’s a simple fourfold I’ve been ignoring just because it’s so trivial, but that triviality can be deceiving. Space-time as formulated in special relativity has four dimensions: three of space and one of time. Our everyday experience shows us the three dimensions of space: length, width (or breadth), and depth (or height), but time is a different kind of thing because we cannot see or move forward and backward through time with our eyes or body, like we can along the axes of space.

Personally, only our memory and imagination can let us range through time. Of course, after the invention of language and more recent technologies, the spoken word, writings, photographs, audio recordings, and videos can also be used. But it’s not the same as shifting one’s gaze along the length of something or moving one’s body across a width.

So, we can move semi-freely through the three spatial dimensions but our movement in time seems to be fixed into a relentless forward motion that we have no control over. And because gravity pulls us down onto the surface of the world, one of the spatial dimensions (depth or height) is more limiting than the other two.

sq_ll2Thus another interesting comparison to this fourfold is to that of linear logic. One observation is that length and width can be considered reversible but depth and time can be considered somewhat irreversible. That’s not true of course, but because of gravity it is easier to descend than to ascend, and it’s far easier to move into the future than into the past. But we can see into the distant past, just not our own, as we turn our telescopes to the heavens.

Space without time could have four or even higher dimensions, but we have no empirical evidence that it is so. Mathematically, however, we can easily construct multidimensional spaces. One representation of four dimensional space is by using quaternions, which have four dimensions to the complex numbers’ two. Tuples of real numbers or even vector spaces can also be used. However, the geometry of space-time is not Euclidean; it is described by the Minkowski metric.

Novels about characters living in different numbers of spatial dimensions are an interesting way to learn and think about them. The very first was Flatland by Edwin Abbott Abbott, about a being limited to two dimensions that learns about a third outside his experience when a three dimensional being comes to visit. Just recently I’ve finished reading Spaceland by Rudy Rucker, about an ordinary human person limited to the three dimensions of space that learns about the fourth dimension by similar reasons.

Links:

http://en.wikipedia.org/wiki/Special_relativity

http://en.wikipedia.org/wiki/Minkowski_space

http://en.wikipedia.org/wiki/Four-dimensional_space

http://en.wikipedia.org/wiki/Flatland

http://en.wikipedia.org/wiki/Flatland_%282007_film%29

http://en.wikipedia.org/wiki/Spaceland_%28novel%29

[*8.72]

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Matter, Energy, Space, and Time

February 17, 2014

sq_MESTThe first little ball is red and green
Oh it’s pretty, yes I know what you mean
I call it Substance, do dio dio do
And what it will do I just don’t know

The next little ball is silver and black
See it chase the first one forward and back
I call it Space, do dio dio do
What it will do I just don’t know

The next little ball is too hot to hold
I have to keep tossing it and I hope it gets cold
I call it Power do dio dio dio
What it will do I just don’t know

The next little ball is orange and blue
I can’t juggle four so I’ll toss it to you
And I call it Time…

— From “The Juggler’s Song” by The Incredible String Band

Here’s a nice little fourfold that I’ve overlooked until now, kind of like a four-leaf clover. If you search for images of matter, energy, space, and time, several websites show a diagram quite similar to this, and some have interesting things to say.

One shows free energy instead of energy in general. Free energy is energy that is able to do work, and that is an important distinction, especially if you are thinking about the Four Causes. Then the four can be considered fundamental resources.

There are some other things to consider from these references. One is that there is the familiar equivalence between matter and energy. Another is the equivalence principle between gravity and acceleration.

Also, there are obvious analogies between this fourfold and the Four Elements and the Four States of Matter. sq_Noether's TheoremI have also used the pairs space-time and matter-energy as two parts of the fourfold Noether’s Theorem, the other two parts being symmetry and conservation. There is also the fourfold Spacetime that has some similarities to this one. And let’s not forget the atomism of On the Nature of Things by Lucretius.

Be sure and watch the upcoming television series Cosmos: a Spacetime Odyssey, hosted by Neil deGrasse Tyson. I’m sure there will be much talk of Matter, Energy, Space, and Time.

Notes:

There is even a term coined for Matter-Energy-Space-Time: MEST. Of course, MEST also stands for Math, Engineering, Science, and Technology! No, sorry, that’s STEM!

http://lornaalkana.com/portfolio/graphic-design/ticket-space-time-energy-matter/

Links:

http://abyss.uoregon.edu/~js/ast123/lectures/lec09.html

http://www.zamandayolculuk.com/cetinbal/htmldosya1/ModernScience.htm

http://billmoyers.com/2014/01/10/the-new-cosmos-a-spacetime-odyssey/

[*7.90, *8.32]

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The Space-Time Tetrahedron

March 29, 2013

spacetime_tetrahedronIn honor of April Fool’s Day, I present the Space-Time Tetrahedron.

The Internet is full of crackpot and nutty websites, and one of the most famous concerns the so-called Time Cube.

Since the ideas expressed on this website are pretty much ignored, it is hoped that it could at least find some recognition as being slightly crackpot or somewhat nutty.

Let’s examine the similarities between Time Cube theory and my theory.

The number four is very important in each. In fact, the Time Cube is a fourfold, although quite a puzzling one.

The notions of space and time are crucial to Time Cube; many of my fourfolds involve some aspect of space and time or spacetime.

How about the differences? I don’t think one can find any common claims between the two theories. At least I hope not!

References:

http://en.wikipedia.org/wiki/Time_Cube

http://knowyourmeme.com/memes/the-time-cube

[*7.150]

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Spacetime

September 23, 2011

What is space? Is space merely extension? What makes up extension, but a set of locations?

What is time? Is time merely duration? What makes up duration, but a series of successions?

Is space a void for things to be located in, or do things create the space between them?

Is time a continuance for events to happen in, or do events create the time that joins them?

Does space and time exist objectively, or only subjectively? Are they absolute or are they relative?

Does space and time enframe all that exists? Does anything exist outside of space or time? How could we know if it did?

What is spacetime? Is it space plus time, disjoint, or is it a reciprocal enfolding of space and time, so that neither can exist without the other?

[*7.4]

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