Essay Abstract

Is it possible to render holographic spacetime starting from simple discrete building blocks? I will demonstrate that not only is the answer 'yes', but also that to do so, surprisingly simple building blocks suffice. Holographic 2D toy models result that you can play with and investi-gate in terms of De-Bruijn-type sequences, dual descriptions and path sums.

Author Bio

Johannes is a physicist who holds a PhD from Eindhoven University of Technology. He blogs on subjects including cosmology, relativity and quantum physics and is a featured writer on Science 2.0. Johannes is affiliated with a Fortune Global 500 company in the role of chief scientist.

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6 days later

Hello Ioannis -- thanks for your kind words.

A quick reaction to answer your questions.

1) The 'puzzle pieces' are constructed such that putting them together enforces a XOR relationship between the blue disks and the (yellow) voids. You can indeed build the same pattern using the puzzle pieces you proposed, but these can also fit together in many ways that violate the XOR relationship.

2) Not sure what you mean by 6 bits being only needed for the second configuration in figure 2. Can you elaborate please?

3) The superposition you can imagine as resulting from putting the left and middle configuration of figure 2 on top of each other. There where two blue disks are stacked on top of each other, you remove both disks. In all other circumstances (0 or 1 disks on top of each other) you leave the situation as is. The configuration that results is the one shown on the right-hand side of figure 2.

Regards,

Johannes

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  • Post #4

Dear Koelman,

Thank you for your informative respond.

1) OK although rule applied is said to be XOR and not enforcement is necessary (the difference to clarity is tremendous).

2) Sorry it is my fault (7 bits are needed).

3) So in superposition no XOR rule is used (instead: 11 >0, 00 >1, 01 >1, 10 >1)

4) I would insist for the meaning of "degrees of freedom" in your essay.

regards, narsep

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  • Post #5

3) I am wrong again. XOR rule is used in superposition as well.

narsep

Ok, with 1), 2) and 3) solved, let's see if we can also sort out 4).

In this essay, a 'degree of freedom' means a choice in filling a slot with a blue disk, or leaving it void. If you change a void in a blue disk (or vice versa), a whole new pattern emerges. If that pattern is essentially different (i.e. not related to the original pattern via a translation), but has the same shape of repeat unit, the choice in how to fill the slot represents a degree of freedom. So if a repeat unit has S degrees of freedom, it means that 2S different repeat patterns are possible that all have the same shape.

Dear Koelman,

The physical meaning of XOR rule may be that: local interactions are due to the differences between two static entities and when there are differences between two static entities global interactions occur. Any interaction (event) takes place in virtual part of our world while real part accommodates the static entities.

I wonder whether meaningful (and useful) results could be extracted if asymmetric rules (time asymmetry) are used in your systems (e.g. 00 -> 0, 11 -> 0, 10 -> 1, 01 -> 0 or 00 -> 0, 11 -> 0, 10 -> 0, 01 -> 1).

(I am absorbing your response for the "degrees of freedom"). It is needless to express my thanks for any of your replies.

Regards, narsep

    Dear Narsep -- the XOR rule is an example, and nothing more than that. Other rules can be chosen, and the same holographic statistics will result.

    However, you have to avoid selecting a rule that leads to some degenerate behavior. With two binary inputs here is not much room to maneuver. The XOR rules work quite well, but the (spatially asymmetric) variant you propose will lead to rather uninteresting straight line patterns.

    If you start working with two trinary inputs (or even higher number of allowed cell values) many more possibilities open up. Selecting a rule randomly will almost always lead to 'rich' patterns and holographic scaling.

    21 days later

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    • Post #9

    It seems to me the Holographic Universe only true answer.

    http://www.fqxi.org/community/forum/topic/946

    Good luck!

    18 days later

    Hello Johannes,

    congratulation for your essay!

    I don't know if we are exactly on the same line but I think you'll enjoy reading my essay because of my proposition for "simplexity" as a good answer to the"holographic" approach...

    (see my essay here http://www.fqxi.org/community/forum/topic/952)

    Best regards, good luck for the contest

    Ayind Mahamba

    2 months later

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    • Post #11

    So smart author no entry best 35.

    It is not fair play!

    Why did you went to industry?

    All the best.

    Yuri

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