Announcement

Collapse
No announcement yet.

Heisenberg and Uncertainty

Collapse
X
 
  • Filter
  • Time
  • Show
Clear All
new posts

  • Heisenberg and Uncertainty

    THE FABRIC of the COSMOS, Brian Greene, 2004
    ```(annotated and with added bold highlights by Epsilon=One)
    Chapter 4 – Entangling Space
    Heisenberg and Uncertainty
    The uncertainty principle provides a sharp, quantitative measure of how tightly probability is woven into the fabric of a quantum universe. annotation 1: click To understand it, think of the prix-fixe menus in certain Chinese restaurants. Dishes are arranged in two columns, A and B, and if, for example, you order the first dish in column A, you are not allowed to order the first dish in column B; if you order the second dish in column A, you are not allowed to order the second dish in column B, and so forth. In this way, the restaurant has set up a dietary dualism, a culinary complementarity (one, in particular, that is designed to prevent you from piling up the most expensive dishes). On the prix-fixe menu you can have Peking Duck or Lobster Cantonese, but not both.

    Heisenberg's uncertainty principle is similar. It says, roughly speaking, that the physical features of the microscopic realm (particle positions, velocities, energies, angular momenta, and so on) can be divided into two lists, A and B. And as Heisenberg discovered, knowledge of the first feature from list A fundamentally compromises your ability to have knowledge about the first feature from list B; knowledge of the second feature from list A fundamentally compromises your ability to have knowledge of the second feature from list B; and so on. Moreover, like being allowed a dish containing some Peking Duck and some Lobster Cantonese, but only in proportions that add up to the same total price, the more precise your knowledge of a feature from one list, the less precise your knowledge can possibly be about the corresponding feature from the second list. The fundamental inability to determine simultaneously all features from both lists — to determine with certainty all of these features of the microscopic realm — is the uncertainty revealed by Heisenberg's principle.

    As an example, the more precisely you know where a particle is, the less precisely you can possibly know its speed. Similarly, the more precisely you know how fast a particle is moving, the less precisely you can possibly know about where it is. annotation 2: click Quantum theory thereby sets up its own duality: you can determine with precision certain physical features of the microscopic realm, but in so doing you eliminate the possibility of precisely determining certain other, complementary features.

    To understand why, let's follow a rough description developed by Heisenberg himself, which, while incomplete in particular ways that we will discuss, does give a useful intuitive picture. When we measure the position of any object, we generally interact with it in some manner. If we search for the light switch in a dark room, we know we have located it when we touch it. If a bat is searching for a field mouse, it bounces sonar off its target and interprets the reflected wave. The most common instance of all is locating something by seeing it — by receiving light that has reflected off the object and entered our eyes. The key point is that these interactions not only affect us but also affect the object whose position is being determined. Even light, when bouncing off an object, gives it a tiny push. Now, for day-to-day objects such as the book in your hand or a clock on the wall, the wispy little push of bouncing light has no noticeable effect. But when it strikes a tiny particle like an electron it can have a big effect: as the light bounces off the electron, it changes the electron's speed, much as your own speed is affected by a strong, gusty wind that whips around a street corner. In fact, the more precisely you want to identify the electron's position, the more sharply defined and energetic the light beam must be, yielding an even larger effect on the electron's motion.

    This means that if you measure an electron's position with high accuracy, you necessarily contaminate your own experiment: the act of precision position measurement disrupts the electron's velocity. You can therefore know precisely where the electron is, but you cannot also know precisely how fast, at that moment, it was moving. Conversely, you can measure precisely how fast an electron is moving, but in so doing you will contaminate your ability to determine with precision its position. Nature has a built-in limit on the precision with which such complementary features can be determined. And although we are focusing on electrons; the uncertainty principle is completely general: it applies to everything. annotation 3: click

    In day-to-day life we routinely speak about things like a car passing a particular stop sign (position) while traveling at 90 miles per hour (velocty), blithely specifying these two physical features. In reality, quantum mechanics says that such a statement has no precise meaning since you can't ever simultaneously measure a definite position and a definite speed. The reason we get away with such incorrect descriptions of the physical world is that on everyday scales the amount of uncertainty involved is tiny and generally goes unnoticed. You see, Heisenberg's principle does not just declare uncertainty, it also specifies — with complete certainty — the minimum amount of uncertainty in any situation. If we apply his formula to your car's velocity just as it passes a stop sign whose position is known to within a centimeter, then the uncertainty in speed turns out to be just shy of a billionth of a billionth of a billionth of a billionth of a mile per hour. A state trooper would be fully complyng with the laws of quantum physics if he asserted that your speed was between
    89.99999999999999999999999999999999999
    and
    90.00000000000000000000000000000000001

    miles per hour as you blew past the stop sign; so much for a possible uncertainty-principle defense. But if we were to replace your massive car with a delicate electron whose position we knew to within a billionth of a meter, then the uncertainty in its speed would be a whopping 100,000 miles per hour. Uncertainty is always present, but it becomes significant only on microscopic scales.
    Figure 4.6 A probability wave with a uniform succession of peaks and troughs represents a particle with a definite velocity. But since the peaks and troughs are uniformly spread in space, the particle's position is completely undetermined. It has an equal likelihood of being anywhere.
    The explanation of uncertainty as arising through the unavoidable disturbance caused by the measurement process has provided physicists with a useful intuitive guide as well as a powerful explanatory framework in certain specific situations. However, it can also be misleading. It may give the impression that uncertainty arises only when we lumbering experimenters meddle with things. This is not true. Uncertainty is built into the wave structure of quantum mechanics and exists whether or not we carry out some clumsy measurement. As an example, take a look at a particularly simple probability wave for a particle, the analog of a gently rolling ocean wave, shown in Figure 4.6. Since the peaks are all uniformly moving to the right, you might guess that this wave describes a particle moving with the velocity of the wave peaks; experiments confirm that supposition. But where is the particle? Since the wave is uniformly spread throughout space, there is no way for us to say the electron is here or there. When measured, it literally could be found anywhere. So, while we know precisely how fast the particle is moving, there is huge uncertainty about its position. And as you see, this conclusion does not depend on our disturbing the particle. We never touched it. Instead, it relies on a basic feature of waves: they can be spread out.

    Although the details get more involved, similar reasoning applies to all other wave shapes, so the general lesson is clear. In quantum mechanics, uncertainty just is.
    Last edited by Epsilon=One; 10-16-2012, 08:41 AM. Reason: Add Annotation

  • #2
    Heisenberg's Uncertainty is a manifestation of the Pulsoid's pulse

    (Return to Annotated Thread)

    Originally posted by Reviewer View Post
    The uncertainty principle provides a sharp, quantitative measure of how tightly probability is woven into the fabric of a quantum universe.
    Annotation 1
    Heisenberg's Uncertainty results from the pulse of the Pulsoid. When Resoloids form, the Pulsoid collapses to a dimensionless point within a dimensionless sphere. The subsequent pulse will have it's major diameter oriented in any of infinite directions about the identical singular point which would be the identical point for every Pulsoid that exists as the "space quantum" that can be said to be the "Fabric of the Cosmos."

    Originally posted by Reviewer View Post
    ...the more precisely you know where a particle is, the less precisely you can possibly know its speed. Similarly, the more precisely you know how fast a particle is moving, the less precisely you can possibly know about where it is.
    Annotation 2
    Pulsoids are of a size and speed that is beyond the quantitative (measurement) of today's instruments, which is a limit that the discipline of physics sets for itself. Reality knows no such limit. Philosophical Logic (Philogic) is a discipline at the top of knowledge. Philogic is where the unification of relativity and quantum mechanics is found.

    Originally posted by Reviewer View Post
    ...the uncertainty principle is completely general: it applies to everything.
    Annotation 3
    This is because the basic pulse of the seminal quanta of all that exists is what underlies the phenomenon that is observed as the Heisenberg Uncertainty Principle (HUP); therefore, like the Inverse Square Law (ISL), HUP is most fundamental.

    (Return to Annotated Thread)
    Last edited by Epsilon=One; 06-17-2013, 06:26 AM.
    ..."Click" to E-mail Me Directly
    ......Or, use a Forum Private Message

    ....."Seek simplicity; and
    ....... . . Natural integers."

    ..........Challenge to Academe
    ...The Purpose of Pulsoid Theory
    ..........
    ...........Forum Designer

    Comment

    Working...
    X