Hardware parameters of computer for developing double of reality.

by Dr. Leonid Sakharov

Hardware specifications to create virtual reality of our physical reality are discussed. Upon characteristics of physical constants it looks like precision of computation can be no more than 12^12 that is about ten decimal digits. Memory storage has to be thousand times better comparing to needed Google Map and Google Sky. It can be available in very near future about three decade ahead. If we can develop virtual reality indistinguishable from physical reality how one can be sure that he lives in real reality?
If our world is virtual reality game it must be implemented at the computer and software that is power enough to reproduce physical effects with precision equal or better than physical experiments in our reality produce.

There are more than few phenomenons these can be used to define minimum parameters of software that emulates our reality.

Precision of defining any physical constant should be no better compare to number of significant digits for its presentation in virtual software.

The Rydberg constant, that is fundamental in spectrometry, is defined with the virtually best precision that is about 12 decimal digits.

Speed of light is paradoxically is not measured physical constant. It has now axiomatically defined value: 299792458 meters per second. It means that 9 decimal digits defining speed of light is enough from scientific community point of view to adequate describe physical reality.

Plank’s constant, h = 6.62606983 × 10−34 J•s, is also defined with precision about 9 decimal digits similar to speed of light.

The Fig 1 presents distribution of precision of determination of physical constants described in the Wikipedia article: Physical constant https://en.wikipedia.org/wiki/Physical_constant.

Distribution of precision for physical constants.

The binary number 2^42 looks like is about to be enough for presentation even the best defined Rydberg constant.

So if we talking about our world as computer we can say that the mathematical calculations could be performed with enough accuracy using at least 2^42 binary digits numbers. Here is the place for humbleness. If we use binary system for computer calculation it doesn’t mean that everybody must to. For example numerical system based on dozens with maximum value 12^12 = 8.9161E+12 is quite fit for numerical mimicking of any physical phenomena. Any specific guess about what exact base for numerical system used in our virtual reality will be pure guess based maybe only on coincident like the fact that Standard Model of elementary particles contains 12 fermions. Is this fact meaningful or not? Some argues that duodecimal (based on dozen) system is the better compare to decimal because it has better presentations of rational fractions.

In context of discussion of mathematical architecture of our virtual reality we can take one definite fact. Already routine used computers can perform calculations with precision much excessive that necessary for adequate simulation of any physical process. Even more bizarre is the fact that numerical simulation of reality demands incorporating into random number generator that in some way the tool for limiting accuracy of calculation. There is strong temptation to declare that quantum mechanics is the simple byproduct of rounding during calculation of small integers. But even it is because rounding effect the rules for rounding are much more sophisticated compare to trivial math.

So precision of calculation for our reality is more than easy to reach. It is not a problem for implementation. What about speed of computing? What should be clock frequency of reality simulator? In other formulation of the same question – what time between two consecutive states of the reality? Time measured in what units? This is key question for understanding time as the concept. The question is there Chronon, that is quantum of time? If world is virtual reality the answer is yes, of course. It is there a smallest step between two states of reality. In movie picture it is 1/25 second between two consecutive cadres.

Moving with speed V along one of the space axis bullet has space coordinate x1 in one moment of time and x2 at the next moment these are separated by one Chronon, let name label it as Chr . The value v*Chr is the change of position of bullet at next step of calculation. Its not too difficult to understand that if there is fundamental minimum Chonon it will means that time is unitless integer parameter of reality. It means that passing of time for computer making numerical experiment and subjective interval of time has no connection. Computer can calculate new situation for next step that is one plus to the current (present) for thousand our subjective years or much faster that one Chonum lasts on one mind. This calculation time from one cadre of reality to next one could be lopsided. It will make no difference in our subjective comprehension.

The conclusion from reasoning about time is that from point of view hardware for simulation our reality is the fact that speeds passing time in our reality and factual time for calculation are not directly correlated. It is very easy illustrate by the following example. Let scientist develops a software program for numerical simulation of the crystal growth as I did. The same program on computer twenty years ago works several minutes to perform simulation of crystal surface adds 100 layers. At modern computer the same calculation takes seconds. At modern supercomputers it could be done for microseconds. But time of the physical simulated process is the same no matter how fast it is simulated. It means that speed of computer hardware our reality implemented in does not matter until it doing the trick.
If to fantasize that our world is computer game that was gift for boy of seven years old for occasion starting education in elementary school and dark ages corresponded to his puberty when the game was temporary abandoned because first sexual experiments consuming all his attention we could estimate that our seven thousand years corresponds to ten years of higher world. Maybe? Maybe not.

Memory storage for the virtual world is the most troubled question about its architecture. There are several close to definite true statements about how much memory is needed for construction our reality as computer software.

For naïve straightforward description when position and other characteristics of each elementary particle in universe is remembered separately there cannot be big enough memory storage. It is disputable question how many atoms is needed to store one bit information in best possible devises. One thing is obvious it would take more than two of them. And it is overboard generous estimation. One can argue that at the temperature close to absolute null one can store information in the crystal by one bit per atom if to distinct them by stable isotopes of one atom. For example in the diamond 0 and 1 can be distinct by two stable isotopes of the carbon with 12C and 13C Daltons. But how to read it? Some detector containing additional atoms has to be presented. This mental excise about completely hypothetical dream memory storage is needed only to be sure that there is no way to have full description of universe particle by particle at one memory device. In practice only minuscule part of physical reality can be remembered in such meticulous manner. If understand that most matter in universe exists in form of star plasma, light, separate particles and nobody knows what is in black holes. So what we can be sure about that it is completely unrealistic to have and operate with whole information about universe on the elementary particle level. Not even close to the ratio sun to grain of sand. It means one thing namely memory presentation of virtual reality must be structures on several levels.

One can think from other prospective about memory problem from point of view of software developer constructed virtual replica of our observed reality. The critical part of such software is the flow information to the observer. No matter what we argue about existence of objective world outside of our conscious we can make arguments about the problem only inside of our mind. In practice of modeling virtual reality it means that basic element of it could be observer and flow information to him. According researchers of visual systems of animals the flow of information from eye to brain is about from 10 to 100 millions bits per second. Such speed is already achieved by Ethernet systems. Nothing extraordinary it is.

If accept notion that short term memory lasts about 30 seconds and it is pool of information filled up with our senses and then in small part in aggregate way moving into long memory storage or mostly deleted to free space for new impressions. The capacity for short memory must be at least 0.3 Gb that is less than 10% of very ordinary flash drive ten years ago. It is very durable even if this number had happen to be underestimated.

To get number for long term memory is much more difficult but possible. Let presume that part of short memory that goes to permanent memory is about one to million. It means that to remember one year of life a human needs 3.154e+7 s * 1e+8 bits = 2860 TB. It is about thousand good external drives (close enough for such speculative considerations.) It is expensive but affordable even now.

Obvious except raw human experience for virtual reality developer has to make software remembering at least position of all objects at the service of the earth. Wait a second the Google Map did sort of such thing already decades ago. Sure that for construction of real virtual reality representing Earth as game field just Google Map level information is not sufficient, not even close. But combination of the detailed 3D map of positions typical software objects with unique characteristics stored in database can do the trick.

Interesting that for description of outer universe with all galaxies and stars the same level of information should be required. What astronomers were able to observe up to very recent time was two dimensional pictures at sky sphere around our planet. Google Map and Google Sky are like two border spheres bordering game field of our reality. No argue it is enormous amount of information to store. Very, very big but far from been defined as infinite. As very lose comparison the value of computer memory needed for description of habitant area of humanity to whole universe is as information about position of gas tank compare to information about position and velocity of every single molecule in it. And in this comparison information for molecules is miniscule compare to whale universe.

The practical question is when our virtual reality can be duplicated in our reality and can it at all. Progress in visual effects in cinematography provides some guidance. Star Trek franchise started in 1979 and lasted more than four decades. We can argue about script, how charismatic actors, connection to moral problems of present days. We can argue about everything except the undeniable fact of startling progress in special effects. The presentation of imaginary world is as realistic as it could be after 2009 reboot of the series. If one has doubt in possibility to do the same for gamer of virtual reality he can be right for now but due cost only. The price for one arithmetic operation drops at least thousand times for last three decades (price of computer is always around one grand in dollars but productivity doubles every two years). And rather primitive virtual reality exists already. It is nothing but waiting game until full experience virtual reality will be developed and procurable for society elite. And this time could be much sooner for comfort than any traditionalist could hope.

Now creation of virtual reality is the matter of straightforward software industry work. Nothing principally new needs to be developed. Most future job relates to sensor interface to mimic all senses and fast update of virtual reality comparable to speed of transfer signals via nerves of the player. No more than three decades needs to improve current video games in thousand times. That will be enough to trick gamer in full illusion of real reality. It is very soon. It is just one generation ahead.

If virtual reality equivalent to physical reality can be developed in our reality how we can be sure that our reality was not developed by anybody else? I cannot disprove this hypothesis by pure logic. So it is matter of faith or for brave minds like mine the open problem to live with.

Mar. 14, 2019; 11:31 EST

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