wasting time?

[AntonioLao]

As a figure of speech, we heard quite often the phrases ‘you are wasting my time’ or ‘I’m wasting too much time’ and many others involving the word ‘wasting’ and the word ‘time.’ From these, it seems that time is like a material thing or personal possession auctioning for the highest bidder. This is truly a misconception about the concept of time. No one can optimize, stop, hurried, nor delay the passage of time.

On the other hand, each of us can control the usage of energy flowing into or out of our bodies. And energy is much closer to being a material thing than time. Moreover, everyone needs a constant daily supply of energy (from food stuff) to stay alive and healthy. So, now it is correct for me to say that ‘sorry, I might be wasting your energy reading this post.’ However, the important point I’m trying to make is that in physics the concept we called quantum of action is the scalar product of energy and time, which is an alternative expression for Heisenberg’s uncertainty principle. This alternative form was first noted by Einstein, which is really equivalent to the orginal scalar product of position and momentum by Heisenberg.

[Guille]

orginal scalar product of position and momentum by Heisenberg.

What is this in equations?

[AntonioLao]

A quantum mechanical principle due to Werner Heisenberg (1927) that, in its most common form, states that it is not possible to simultaneously determine the position and momentum of a particle. Moreover, the better position is known, the less well the momentum is known (and vice versa). The principle is sometimes known as the Heisenberg uncertainty principle, and can be stated exactly as

where is the uncertainty in position, is the uncertainty in momentum, and is h-bar (Landau and Lifschitz 1977, p. 48; Gasiorowicz 1995, p. 120). Care is necessary since versions of this equation using Planck's constant h instead of , omitting the factor of 2 (Cassidy 1991, p. 234), or both (Pais 1991, p. 305) are commonly found in the literature. Heisenberg's original paper does not attempt to rigorously determine the exact quantity on the right side of the inequality, but rather uses physical argument to show that the uncertainty between conjugate quantum mechanical variables is approximately h (Heisenberg 1927, p. 175, eqn. 1).

[Guille]

I know about Heisenberg's uncertainity principle, I jsut wanted to knwo about the equations used in it.

I have three questions for this equation:

1. I see there is no symbol between the triangle x and triangle Px. So, does this mean that they are multiplied?

2. What is the triangle? (please, define it with equations).

3. How did Heisenberg arrive to this equation? (if it was from other equations, can you give me what he did with them?)

[AntonioLao]

I know about Heisenberg's uncertainity principle

Ya, more power to you! As for me, I am looking for possible other conjugate variables that would satify this inequality.

1. I see there is no symbol between the triangle x and triangle Px. So, does this mean that they are multiplied?

First, we need to clarify that this is more than an equation. It is also an inequality, a positive definite inequality, to be precise. Since delta-x and delta-px are both scalars, the multiplication is implied without explicit symbols.

2. What is the triangle?

The delta symbol denotes 'change of' such as for a posions x1 and x2, delta-x = x1 - x2.

How did Heisenberg arrive to this equation?

He derived this principle from his matrix mechanics (basing on experimental data) and the anticommutation rules that emerged from his calculation. The anticommutation rule is that the product of x and px is not the same as the product of px and x.

[Guille]

Thanks for the info.

But I have a question:

He derived this principle from his matrix mechanics (basing on experimental data) and the anticommutation rules that emerged from his calculation. The anticommutation rule is that the product of x and px is not the same as the product of px and x.

Do you agree that such thing as non-cunmutative multiplication exists, I mean, is real, and is ok to explain the universe in such forms?

[AntonioLao]

Do you agree that such thing as non-cunmutative multiplication exists

Yes. In fact, all vector cross products are non-commutative or anti-communicative. Extending this concept to chirality, it is found that nonliving organic or inorganic compounds are mostly equal in left and right symmetry or what is called a racemic mixture. However, in contrast, life nearly always chooses only one of either left or right symmetry. For example, all protein molecules consist of left-handed amino acids, whereas DNA's and RNA's are always constructed using right-handed sugars. When a living thing dies and decays, thermal fluctuations randomize molecular shapes so that racemization again dominates.