Energy Question

[chemguy]

Can anyone please identify this energy?

 

E = (ħc)^½

Are there any references to it in the literature?

 

Thank you.

 

P.S.

I prefer to write it as; E₀ = (ħc)^½

 

This energy may be inferred from Plank Units. The Plank force is; F_P = E_P²/ħc

 

A general definition of force magnitude is; F = E²/ħc = ħc/λ²

 

A unit vector of force (F₀) has a magnitude: |F₀| = F₀ = 1

 

A scalar definition is: F₀ = E₀²/ħc = ħc/λ₀² = 1

 

Giving; E₀ = ±(ħc)^½ and; E₀ = ħc/λ₀

 

Where; ħ is the reduced Plank constant; (ħ = h/2π)

 

h is the Plank constant

 

c is the light constant

 

λ is wavelength

[Robittybob1]

[latex]\hbar = \frac{h}{2 \pi} .[/latex]

 

[latex]E = \hbar \omega [/latex]

 

[latex]E_0 = \hbar^1/2,[/latex]

 

Doesn't seem to make sense.

Edited March 31, 2016 by Robittybob1

[Mordred]

Reduced Compton wavelength

 

The difference being [latex] 2\pi[/latex]

Edited March 31, 2016 by Mordred

[imatfaal]

Can anyone please identify this energy?

 

E = (ħc)^½

Are there any references to it in the literature?

 

Thank you.

 

P.S.

I prefer to write it as; E₀ = (ħc)^½

 

This energy may be inferred from Plank Units. The Plank force is; F_P = E_P²/ħc

 

A general definition of force magnitude is; F = E²/ħc = ħc/λ²

 

A unit vector of force (F₀) has a magnitude: |F₀| = F₀ = 1

 

A scalar definition is: F₀ = E₀²/ħc = ħc/λ₀² = 1

 

Giving; E₀ = ±(ħc)^½ and; E₀ = ħc/λ₀

 

Where; ħ is the reduced Plank constant; (ħ = h/2π)

 

h is the Plank constant

 

c is the light constant

 

λ is wavelength

 

The section starting "A Scalar definition...." is a bit like the cartoon "and then a miracle occurs". You cannot just ignore the fact that you have equated a force with a manipulated energy and suddenly claim that the LHS of the equation is equal to a dimensionless unit (or simple number as you have done).

 

A simple dimensional analysis shows your initial assertion is incorrect

 

Energy =>

L² M T^-2

 

 

Your formulation is Energy is =>

Sqrt ( [L² M T^-1] [L T^-1] )

Sqrt (L³ M T^-2)

L^3/2 M^1/2 T^-1

[chemguy]

Thank you imatfaal, for your posting.

Your dimensional analysis was convincing. I goofed here (wrong assumption).

 

I have a similar question concerning forces. I hope you will comment. So here it is;

 

The Plank force is; F_P = E_P²/ħc

 

Where; E_P is Plank energy

 

A general definition of force magnitude is; F = E²/ħc

 

An indexed force magnitude (F_nx) may be written as; F_nx = (m_nv_x²)²/ħc

 

A unit vector of force (F₀₀) has a magnitude: |F₀₀| = F₀₀ = 1

 

The indexed unit force magnitude is; F₀₀ = 1 = (m₀²v₀⁴)/ħc

 

Assume; m₀ is Plank mass

 

V₀⁴ = G

 

Then; F₀₀ = (m₀²G)/ħc = 1

 

Giving the definition of Plank mass; m₀ = (ħc/G)^½

 

Does this imply that v₀ is an invariant fundamental velocity somehow associated with gravity?

 

Please comment.

chemguy

[imatfaal]

This is the line I do not understand / agree with - and I got no further

 

"An indexed force magnitude (F_nx) may be written as; F_nx = (m_nv_x²)²/ħc"

 

When I use vector notation for Forces and end up with a expression such as F₁₂ it means the Force exerted on object two by object one; the most obvious example is Force due to Gravitation:

[latex]

\mathbf{F}_{12}=-\frac{G m_1 m_2}{\left |\mathbf{r}_{12} \right |^2} \cdot \hat{r}_{12}

[/latex]

 

The force on 2 due to 1 - and this makes it clear why gravitational force is shown as a negative as well; for the vectors to match then the force must be negative in order to be attractive

 

I would read F_nx as the force on x due to n - you could then not split this up to getting the velocity from one object and the mass from a second. Now it is clear you are using hte term in a different way - unfortunely I do not understand this way

[swansont]

 

Does this imply that v₀ is an invariant fundamental velocity somehow associated with gravity?

 

Please comment.

chemguy

 

 

No. In general trying to recreate an equation based on dimensional analysis or by throwing together terms that give you the right units isn't going to be valid. You need to derive equations based on physics principles and/or by justifiable assumptions.

 

You can, for example, show that force is a gradient of energy. But that has some physical meaning, while arbitrarily tossing in terms that have the units of energy (mv^2) and length (ħc) does not.

[chemguy]

I apologize to you imatfaal, for neglecting to explain the indexing in my previous post.

 

So here is my attempt to explain.

 

There are two types of interaction; primary and secondary. Forces are associated with each type of interaction.

 

The interaction you described in your previous post is a secondary interaction. This type may include the Newton gravitational equation, or the Coulomb equation. Two objects interact “indirectly”. A field of some sort is associated with each object. The fields interact directly if they are compatible. The force of secondary interaction represents an “indirect” force, and is the result of combining fields.

 

A primary interaction is due to stresses placed on the continuum by a massive (or charged) object. Assume also that a counter stress also acts upon the object. There are three basic types of stress; shear, pressure, and temperature (thermal stress). The EFE accounts for all types of stress. The result of such stress is a field of acceleration. This field may be represented as a deformation of the continuum. It represents the difference between the Schwarzschild metric and the Minkowski metric.

 

The origin of a reference system may (or may not) co-incide with the center of an object. If the object exists, assume they are co-incident. In order to deform the continuum a force must be distributed through it. This distribution of force is the primary interaction.

 

A force (associated with stress) acts upon the continuum and varies with distance ® from the center of the object. The distortional force of primary interaction (F_nx) may be represented as;

 

F_nx = m_ng_x

The indexing associates characteristics with and object (n) or with the continuum (x). A feature of the object is mass (m_n). A feature of the continuum is field acceleration (g_x).

 

g_x = v_x²/r

It may be assumed that the continuum experiences vibration.

 

Where; v_x represents an average velocity of vibration.

Assume; v₀ represents a special invariant velocity of vibration (v₀⁴ = G)

 

A distortional force may be represented as;

 

F_n0 = m_ng₀ = m_nv₀²/r = m_nG^½/r = E_n0/r = E_n0²/hc

The “deformation energy” (E_n0) is; E_n0 = m_nG^½

 

A “Plank object” has Plank mass (m₀).

 

The distortional force (F₀₀) is; F₀₀ = E₀₀²/hc = (m₀²G)/hc

 

Assume; F₀₀ is the magnitude of a unit vector of force. (F₀₀ = 1)

 

Giving: F₀₀ = 1 = (m₀²G)/hc

 

And; m₀ = (hc/G)^½

[swansont]

A primary interaction is due to stresses placed on the continuum by a massive (or charged) object. Assume also that a counter stress also acts upon the object. There are three basic types of stress; shear, pressure, and temperature (thermal stress). The EFE accounts for all types of stress. The result of such stress is a field of acceleration. This field may be represented as a deformation of the continuum. It represents the difference between the Schwarzschild metric and the Minkowski metric.

What is "the continuum"? What is it made of? Are we at rest with respect to it or moving through it?

 

It may be assumed that the continuum experiences vibration.

 

Where; v_x represents an average velocity of vibration.

Why is that a reasonable assumption?

 

Typically the average velocity of a vibration is zero. The average speed (or the rms velocity) is not.