Need for Fast . . . What Can We Do – In . . . Physical Phenomena . . . How to Use Special . . . Relativistic Effects Can Be Resulting Speedup . . . Used to Achieve a Universal This Is All We Can Get How Realistic Is This . . . Square-Root (Or Even This Is Similar to a . . . Possible General- . . . Faster) Computation Home Page Speedup Title Page ◭◭ ◮◮ Vladik Kreinovich ◭ ◮ Department of Computer Science Page 1 of 29 University of Texas at El Paso, El Paso, Texas 79968, USA, vladik@utep.edu Go Back (based on a joint paper with Olga Kosheleva) Full Screen Close Quit
Need for Fast . . . What Can We Do – In . . . 1. Need for Fast Computations Physical Phenomena . . . • At first glance, the situation with computing speed is How to Use Special . . . very good. Resulting Speedup . . . This Is All We Can Get • The number of computational operations per second How Realistic Is This . . . has grown exponentially fast, and continues to grow. This Is Similar to a . . . • Faster and faster high performance computers are be- Possible General- . . . ing designed and built all the time. Home Page • The only reason why they are not built even faster is Title Page the cost limitations. ◭◭ ◮◮ • However, there are still some challenging practical prob- ◭ ◮ lems that cannot yet been solved now. Page 2 of 29 • An example of such a problem is predicting where a tornado will go in the next 15 minutes. Go Back Full Screen • At present, this tornado prediction problem can be solved in a few hours on a high performance computer. Close Quit
Need for Fast . . . What Can We Do – In . . . 2. Need for Fast Computations (cont-d) Physical Phenomena . . . • However, by then, it will be too late. How to Use Special . . . Resulting Speedup . . . • As a result, during the tornado season, broad warning This Is All We Can Get are often so frequent that people often ignore them. How Realistic Is This . . . • And they become victims when the tornado hits their This Is Similar to a . . . homes. Possible General- . . . Home Page • There are many other problems like this. Title Page ◭◭ ◮◮ ◭ ◮ Page 3 of 29 Go Back Full Screen Close Quit
Need for Fast . . . What Can We Do – In . . . 3. What Can We Do – In Addition to What Is Physical Phenomena . . . Being Done How to Use Special . . . • Computer engineers and computer scientists are well Resulting Speedup . . . aware of the need for faster computations. This Is All We Can Get How Realistic Is This . . . • So computer engineers are working on new hardware This Is Similar to a . . . that will enable faster computations. Possible General- . . . • Computer scientists are developing new faster algo- Home Page rithms for solving different problems. Title Page • Some of the hardware efforts are based: ◭◭ ◮◮ – on the same physical and engineering principles ◭ ◮ – on which the current computers operate. Page 4 of 29 • Some efforts aim to involve different physical phenom- Go Back ena – such as quantum computing. Full Screen • Can we use other physical phenomena as well? Close Quit
Need for Fast . . . What Can We Do – In . . . 4. What Can We Do (cont-d) Physical Phenomena . . . • We are talking about speeding up computations, i.e., How to Use Special . . . about time. Resulting Speedup . . . This Is All We Can Get • So a natural place to look for such physical phenomena How Realistic Is This . . . is to look for physical effects that: This Is Similar to a . . . – change the rate of different physical processes, Possible General- . . . – i.e., make them run faster or slower. Home Page • In this paper: we will show how physical phenomena Title Page can be used to further speed up computations. ◭◭ ◮◮ ◭ ◮ Page 5 of 29 Go Back Full Screen Close Quit
Need for Fast . . . What Can We Do – In . . . 5. Physical Phenomena That Change the Rate of Physical Phenomena . . . Physical Processes: A Brief Reminder How to Use Special . . . • Unfortunately for computations, there are no physical Resulting Speedup . . . processes that speed up all physical processes. This Is All We Can Get How Realistic Is This . . . • However, there are two physical processes that slow down all physical processes. This Is Similar to a . . . Possible General- . . . • First, according to Special Relativity, if we travel with Home Page some speed v , then all the processes slow down. Title Page • The time interval s registered by the observer moving ◭◭ ◮◮ with the speed v is called the proper time interval. ◭ ◮ • It is related to the time interval t measured by the � 1 − v 2 Page 6 of 29 immobile observer by the formula s = t · c 2 . Go Back • Here c denotes the speed of light. Full Screen • The closer the observer’s speed v to the speed to the Close speed of light c , the larger this slow-down. Quit
Need for Fast . . . What Can We Do – In . . . 6. Physical Phenomena (cont-d) Physical Phenomena . . . • Second, according to General Relativity Theory, in the How to Use Special . . . gravitational field, time also slows down. Resulting Speedup . . . This Is All We Can Get • For immobile observer, the proper time interval s is equal to s = √ g 00 · t . How Realistic Is This . . . This Is Similar to a . . . • Here g 00 is the 00-component of the metric tensor g ij Possible General- . . . that describes the geometry of space-time. Home Page • In the spherically symmetric (Schwarzschild) solution, Title Page we have g 00 = 1 − r s r , where: ◭◭ ◮◮ – r is the distance from the center of the gravitating ◭ ◮ body and Page 7 of 29 = 2 G · M def – r s , where G is the gravitational constant c 2 Go Back and M is the mass of the central body. Full Screen • Both slow-down effects have been experimentally con- Close firmed with high accuracy. Quit
Need for Fast . . . What Can We Do – In . . . 7. How We Can Use These Phenomena to Speed Physical Phenomena . . . up Computations How to Use Special . . . • If these phenomena would speed up all the processes, Resulting Speedup . . . then it would be easy to speed up computations: This Is All We Can Get How Realistic Is This . . . – move the computers with a high speed and/or place This Is Similar to a . . . them in a strong gravitational field, Possible General- . . . – and we would this get computations faster. Home Page • In reality, these phenomena slow down all the pro- Title Page cesses, not speed them up. ◭◭ ◮◮ • So, if we place computers in such a slowed-time envi- ◭ ◮ ronment, we will only slow down the computations. Page 8 of 29 Go Back Full Screen Close Quit
Need for Fast . . . What Can We Do – In . . . 8. How to Speed up Computations (cont-d) Physical Phenomena . . . • However, we can speed up computations if we do the How to Use Special . . . opposite: Resulting Speedup . . . This Is All We Can Get – keep computers in a relatively immobile place with How Realistic Is This . . . a reasonably low gravitational field, and This Is Similar to a . . . – place our whole civilization in a fast moving body Possible General- . . . and/or in a strong gravitational field. Home Page • In this case, in terms of the computers themselves, Title Page computations will continue at the same speed, but: ◭◭ ◮◮ – since our time will be slowed down, ◭ ◮ – we will observe much more computational steps in the same interval of proper time, Page 9 of 29 – i.e., time as measured by our slowed-down civiliza- Go Back tion. Full Screen • In this talk, we analyze what speed up we can obtain Close in this way. Quit
Need for Fast . . . What Can We Do – In . . . 9. How to Use Special Relativistic Effects for a Physical Phenomena . . . Speed-Up: Reminder How to Use Special . . . • To get a speed-up, we can: Resulting Speedup . . . This Is All We Can Get – place the computer at the center, and How Realistic Is This . . . – start moving around this computer at a speed close This Is Similar to a . . . to the speed of light. Possible General- . . . • We cannot immediately reach the speed of light or the Home Page desired trajectory radius. Title Page • So, we need to gradually increase our speed and the ◭◭ ◮◮ radius. ◭ ◮ • Let v ( t ) denote our speed at time t , and let R ( t ) denote Page 10 of 29 the radius of our trajectory at moment t . Go Back Full Screen Close Quit
Need for Fast . . . What Can We Do – In . . . 10. Analysis of the Problem Physical Phenomena . . . • According to Relativity Theory: How to Use Special . . . Resulting Speedup . . . – a change ds in proper time This Is All We Can Get – is related to the change dt in coordinate time (as How Realistic Is This . . . � 1 − v 2 ( t ) measured by the computer clock) as ds = dt · c 2 . This Is Similar to a . . . Possible General- . . . • To make civilization with rest energy E 0 move with Home Page E 0 this speed, we need the energy E ( t ) = . Title Page � 1 − v 2 ( t ) ◭◭ ◮◮ c 2 • Thus, we can say that ds = dt · E 0 ◭ ◮ E ( t ) . Page 11 of 29 • We need to keep acceleration experienced by all moving Go Back persons at the usual Earth level g 0 . Full Screen Close Quit
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