… “Digital Physics”: An Essay That Uses Poetic License to Discuss A Few Theories in the Movie… by Jonathan Khanlian

Dear Jonathan,

I like your thought provoking essay. I would like to comment on one of your Dedekind cuts where you say " Show me one place where

infinity exists in the natural world! Show me one infinite or continuous process!" Isn´t the total seconds of the Universe and infinite amount? or do you think that because everything is finite, the Universe must recollapse in a singularity in the future such that no observer can experience an infinite amount of proper time?

Kind Regards,

Yafet

Dear Jonathan,

I did not see your above reply until just now. I revisited your blog to bring to your attention an essay by Tommaso Bolognesi which I thought you might enjoy because it has something of a movie script quality to it.

Now to answer your questions:

"Are you saying that you think light cones should really be depicted as warped images instead of perfect cones?"

No, I am saying that, in my view, the boundaries of lightcones should properly not be considered regions of spacetime. To give a somewhat misleading analogy, a zero-dimensional point cannot be considered a "region of space" because it cannot contain any objects in space.

Where the analogy is misleading is that Euclidean space has only one kind of object that is characterized by the fact that every neighboring point is separated from its center by zero distance: A zero dimensional point; but Minkowski space time has two: A zero-dimensional point and the boundary of a light cone. In this sense, the latter is a second type of "point- like object" for which we, who intuitively perceive ourselves as inhabitants of a 3D Euclidean space have absolutely zero intuition, and this is the reason, I think, that this has not been yet recognized.

If you accept that the boundaries of light cones are not regions of spacetime, then logically things which are constrained to exist only there, like photons, cannot be said to exist in spacetime. That special relativity gives us hints that this is indeed the case, starting from the fact that no spacetime observer can transform to a photon rest frame, was essentially what my vixra paper referenced above was driving at. Again, ultimately I think it will take a mathematical proof that the topology of spacetime really is intrinsically different from the topology of Euclidean space to convince others that this is the case.

"If so, that sort of makes sense in a world where matter warps spacetime... unless the warping of space and time perfectly offset each other so that the light cone looks normal for any object, whether it is near massive bodies or not. (I feel like my understanding is not right, so forgive me if I am off base)"

You are forgiven;) usually what people mean by the "warping" of space and time is that there are coefficients (and sometimes more involved combinations of terms) for the space and time terms different from the constant 1 (in Cartesian coordinates) which modify the metric relations at particular points. Importantly, these metrics are never expressed in such a way that the spacetime interval gains a coefficient different from 1 , because it is the invariant quantity, whereas space and time are separately not invariant. But even if you changed the coefficients of the space and time terms so that it would become equivalent to multiplying the metric interval by a coefficient not equal to 1, which amounts to scaling it, it would still be the case that ds=0 describes the boundary of a lightcone.

"I will try to respond to some of your explanations that you offered on your page to some of my questions, but I do remember thinking that some of it was a little over my head. Oh well, maybe I'll google some stuff and try to understand it a little better."

Well, I appreciate your interest in my ideas, if you have any questions let me know, you can also email me.

Best wishes,

Armin

Dear Jonathan,

My most recent paper is very close to Riemann idea of counting the primes statistically and of course connects to Riemann hypothesis (RH).

http://xxx.lanl.gov/abs/1410.1083

Also

http://xxx.lanl.gov/abs/1103.2608

(in particular the Hardy-Littlewood function and RH, and a connection to qudits)

Michel

Hi Jon,

I think our way of conceptualizing whether spacetime is continuous or not is shaped very strongly by our intuitions, which however mislead us into perceiving our existence to be in 3-D Euclidean space plus time. But once you accept that there are two kinds of "point-like" objects in Minkowski spacetime, then this has to be taken account when considering the answer to your question.

I believe the answer is that spacetime is continuous in terms of ordinary zero dimensional points, just as in the mathematical model (This implies, in particular, that all the spacetime symmetries are preserved, or, in some sense, fundamental). On the the other hand, lightcones are already characterized by discontinuity by virtue of how they separate time-like regions from space-like regions in certain directions (namely those which require crossing v=c either from below or from above).

My idea about spacetime emerging from areatime might at first give the impression that it requires spacetime to be discontinuous with respect to the former, but I think that is not necessary because I take the "substrate" from which the emergence takes place, or, in other words, the limit in which spacetime vanishes, to be the boundary of the lightcone (which brings me back to the point of my previous post).

I hope I could make things a little clearer.

Armin

Hi Jon,

me again. Maybe you missed my last reply. Anyhow I wanted to thank you for your comments and questions. I think I learned a lot in that dialog.

Best

Luca