Saturday, November 22, 2014

Michio Kaku

http://www.cs.umd.edu/class/sum2003/cmsc311/Notes/Overall/clock.html

What's a Clock? © 2003 by Charles C. Lin. All rights reserved.

Background

When you buy a computer, one of the first things you probably look for is the speed of the computer. These days, it's not unusual to here rates as fast as 3 GHz. But what is 3 Ghz referring to? This is referring to the clock rate. The clock on a computer is not the same as the clock on the wall, which is used to tell time. A computer clock is more like a metronome, which keeps the beat for musicians to play music.

A Plot of a Clock

One way to understand a clock is to look at a plot of its behavior.
A clock changes its value from 0 to 1 every period. We use the letter T to designate the period. This signal repeats over and over again. Perhaps you remember, from a course in calculus, about sine waves. This wave repeats once per period. The difference between a sine wave and a clock is that a sine wave is curved. It gradually increases than decreases. A clock's signal is squarish in shape. Related to the period of the clock is the frequency. Frequency is defined as 1/T, and has units of s-1. When you hear clock rates, it's usually given by its frequencies. Thus, 2 Ghz means 2 x 109 cycles per second. A cycle is a signal for a single period. The period for this clock is 1/2 x 109 which is 5 x 10-10 seconds, which is half a nanosecond, which is a really, really short period of time. To give you an idea of how short this time is. Imagine that everyone in the world sang exactly one note, and exactly one person sings at a time. Suppose each note lasts one nanosecond. It would take 6 seconds to complete (assuming 6 billion people in the world).

A More Realistic Clock

A clock can't really instantaneously go from 0 to 1 and back to 0. A more realistic diagram looks like:
As you can see the clock signal has a positive slope from 0 to 1 and a negative slope from 1 to 0. This slope has been exaggerated so you can see it better. Normally, it wouldn't be quite so angled.

Features of a Clock

There are a few key features of a clock:
  • period This is the time it takes for a clock signal to repeat. Its unit of measurement is seconds. The symbol for the period is T.
  • frequency Frequency is 1/T. The unit of measurement is s-1, which is inverse seconds. This is also sometimes called Hertz (abbreviated Hz). Sometimes people say "cycles per second" instead of Hz or s-1. They all mean the same. When people refer to the "speed" of a CPU, they are usually talking about the clock frequency.
  • positive edge When the signal transitions from 0 to 1. It's circled above.
  • negative edge When the signal transitions from 1 to 0. It's circled above.
Each positive clock edge appears once per clock period. Each negative clock edge appears once per clock period.

Is It Always 50-50?

In the clock diagrams above, the amount of time the clock is at 1 appears to be T/2 (i.e., half the period). The amount of time the clock is at 0 also appears to be T/2. (There is a little time when it transitions from 0 to 1 or from 1 to 0, but let's assume this is a fairly small fraction of T). Must a clock always do this? The answer is no. We could have a clock where it stays 1 for 3T/4 (three quarters of a period) and 0 for T/4 (one quarter of a period), or any fraction x and T - x where x < T. If you're only using the positive edge, then it doesn't matter how long the signal stays at 1 or 0, since you only use the edge. However, if you want to use both positive and negative edges, then you're going to have to consider when you want the edges to occur.

A Simple Exercise

In order to get a feel for how a clock signal behaves, put your finger at the beginning of the clock signal in the diagram above. At this point, the signal should have a value of 0. Begin to move your finger to the right, but trace out the signal. Your finger should move from 0 to 1, and back again. If you happen to trace over the positive edge once a second, and you're steadily moving to the right (not going faster or slower) then the period is 1 second, and the frequency is 1 Hz. Tracing the signal with your hand gives you a better "feel" for how a continuous signal behaves. Usually, computer science majors have a more difficult time with this (unless you really like calculus or are in engineering) because we deal with quantities that are discrete, rather than continuous. At any point in time, someone can ask you the current value of the signal. If we use the "pipe" analogy, we can think of this signal alternating between pumping red soda (for 0) and green soda (for 1).

What's a Clock Used For?

We use a clock to synchronize the events of a CPU. Devices in a CPU can be categorized as sequential circuits or combinational circuits. Sequential logic devices use a clock. Basically, sequential logic devices can only change outputs once a period, usually during a positive or a negative edge. We'll assume that a sequential device can only change outputs on positive clock edges. To give you an analogy, imagine a music conductor tapping a beat with a baton (a stick) at regular intervals. Suppose you are playing a piano, and you're told to play a new note each time he taps his baton. Thus, how fast the conductor taps the baton controls how often you play notes. Similarly, the rate at which the positive clock edge appears controls how fast a sequential logic device can change outputs. It turns out that by using a clock, we can design a CPU more easily than if we don't use a clock. This is primary reason to use a clock.

Can't We Make It Faster?

If a CPU will run faster with a faster clock, then why not run it faster? The problem is that it takes time for signals to move around in a circuit. You can reduce this time in several ways. The main way is simply to make the circuit smaller. When the circuit is smaller, signals have less distance to travel, and therefore everything can happen more quickly.


Simple inference of time dilation due to relative velocity[edit]



Observer at rest measures time 2L/c.


Observer moving parallel relative to setup, measures longer path and thus, with same speed of light c, measures longer time 2D/c > 2L/c.
A: location of bottom mirror when signal is generated at time t'=0.
B: location of top mirror when signal gets reflected at time t'=D/c.
C: location of bottom mirror when signal hits bottom at time t'=2D/c.
Time dilation can be inferred from the observed fact of the constancy of the speed of light in all reference frames.[5][6][7][8]
This constancy of the speed of light means, counter to intuition, that speeds of material objects and light are not additive. It is not possible to make the speed of light appear greater by approaching at speed towards the material source that is emitting light. It is not possible to make the speed of light appear less by receding from the source at speed. From one point of view, it is the implications of this unexpected constancy that take away from constancies expected elsewhere.
Consider a simple clock consisting of two mirrors A and B, between which a light pulse is bouncing. The separation of the mirrors is L and the clock ticks once each time the light pulse hits a given mirror.
In the frame where the clock is at rest (diagram at right), the light pulse traces out a path of length 2L and the period of the clock is 2L divided by the speed of light
\Delta t = \frac{2 L}{c}.
From the frame of reference of a moving observer traveling at the speed v relative to the rest frame of the clock (diagram at lower right), the light pulse traces out a longer, angled path. The second postulate of special relativity states that the speed of light is constant in all frames, which implies a lengthening of the period of this clock from the moving observer's perspective. That is to say, in a frame moving relative to the clock, the clock appears to be running more slowly. Straightforward application of the Pythagorean theorem leads to the well-known prediction of special relativity:
The total time for the light pulse to trace its path is given by
\Delta t' = \frac{2 D}{c}.
The length of the half path can be calculated as a function of known quantities as
D = \sqrt{\left (\frac{1}{2}v \Delta t'\right )^2+L^2}.
Substituting D from this equation into the previous and solving for Δt' gives:
\Delta t' = \frac{\frac{2L}{c}}{\sqrt{1-\frac{v^2}{c^2}}}
and thus, with the definition of Δt:
\Delta t' = \frac{\Delta t}{\sqrt{1-\frac{v^2}{c^2}}}
which expresses the fact that for the moving observer the period of the clock is longer than in the frame of the clock itself.

NOVA | The Theory Behind the Equation - PBS

www.pbs.org/wgbh/nova/physics/theory-behind-equation.html
PBS
Loading...
Oct 11, 2005 - Michio Kaku explores the eureka moment when Einstein came up with special relativity, the theory that spawned E = mc2. ... Anyone who has ever gotten a ticket for speeding knows that. ... If only one of these assumptions were changed, it would unravel the entire theory in the same way that a loose thread ...

  • Challenging Einstein - USA Today

    www.usatoday.com/tech/science/story/2011-09-22/.../1
    USA Today
    Loading...
    Sep 22, 2011 - And all have failed. ... Physicist Michio Kaku of City College of New York called it "the ... results that at first seem to contradict relativity, only later to be found to fit ... He introduced the constant in his general relativity theory as a force that ... record are why nearly every one of the more than a dozen physicists ...

  • Borrowed Time: Interview with Michio Kaku - Scientific ...

    www.scientificamerican.com › ... › Features
    Scientific American
    Loading...
    Crichton cites theoretical physicist Michio Kaku of the City University of New York as ..... both Einstein's Special Theory and General Theory of Relativity are brazenly ..... Four methods have been used to estimate the Hubble Constant and age of the ..... Based on only ONE non-cyclic Big Bang, Michio Kaku's “String Theory” is ...

  • Essay—The Theory of One Revisited by Bek

    www.philosophymagazine.com/T1_thetheoryonerevisited.html
    Just as relativity had to abandon the concept of simultaneity, so too does ... —Michio Kaku ... Merging the two theories has consumed the Herculean efforts of scores of ... At this point in spacetime I would like to pay special tribute to my excellent ... My theory of one argues that lightspeed and Planck's constant are the same ...

  • Visual Language for Designers: Principles for Creating ...

    books.google.com/books?isbn=1592537413
    Connie Malamed - 2011 - ‎Design
    An explanation of Einstein's theory of special relativity for Discover magazine is ... segments so one concept can build on the next Nigel Holmes with Michio Kaku, United ... But the seed of relativity was planted when Einstein was only 16 years old, ... that the speed of light was always constant, no matter how fast you moved.

  • M-Theory: The Mother of all SuperStrings - Michio Kaku

    mkaku.org/home/.../m-theory-the-mother-of-all-superstring...
    Michio Kaku
    Loading...
    Cumrun Vafa at Harvard has said, “I may be biased on this one, but I think it is perhaps ... Einstein once said, “Nature shows us only the tail of the lion. .... simply blows up if we try to naively use perturbation theory for large coupling constant g. ... Einstein's theory of general relativity, for example, started from first principles.

  • Dr. Michio Kaku: "The Noose Around Relativity is Tightening ...

    www.democraticunderground.com/.../duboard....
    Democratic Underground
    Loading...
    Dec 6, 2011 - 15 posts - ‎11 authors
    OK, don't take my word for anything; this is from Dr. Michio Kaku at Bigthink.com: ... Now, they have done the experiment again, with a beam spread out over 3 ... person will never understand why he should believe opinions only because ... one usually learns when working with special relativity - mainly the ...

  • Beyond Einstein: The Cosmic Quest for the Theory of the ...

    myweb.rollins.edu/jsiry/Kaku_Beyond.html
    Michio Kaku and Jennifer Thompson ... "The only way to detect dark matter (invisible material) is by its weight: it has ... one of the particles, the other of the waves- are both incomplete and have ... "The mechanism by which theory manages to marry both special and general relativity with quantum mechanics ...is a fascinating ...

  • Hyperspace: A Scientific Odyssey through Parallel ...

    books.google.com/books?isbn=0191594067
    Michio Kaku - 1995 - ‎Science
    Michio Kaku ... light, She traveled one day, In a relative way, And returned on the previous night. ... General relativity has much wider validity than special relativity. While special relativity describes only objects moving at constant velocity far ...

  • Re: HOW EINSTEINIANS KILL AND THEN RESURRECT ...

    mathforum.org › ... › sci.math.* › sci.math.independent
    Math Forum
    Loading...
    Aug 20, 2014 - It is one of the most fundamental of the basic constants of physics. ... In recent years a few maverick scientists have claimed that the speed of light might not be constant at ... Philip Ball: "Einstein's theory of special relativity not only destroyed ... Featuring Michio Kaku, Brian Cox, Neil deGrasse Tyson, Brian ...
    • Posted by at

    No comments:

    Post a Comment

    Subscribe to: Post Comments (Atom)