# The Naked Scientists Forum

### Author Topic: Is the Length of Vectors a physical quantity?  (Read 3080 times)

#### Mr. Scientist

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##### Is the Length of Vectors a physical quantity?
« on: 24/10/2009 04:37:23 »
I propose this equation, which is new, but dimensionally-consistent as being;

P^aP^bη_ab=η^2_0 v^2_f(P_μ,η)-η^2_i v^2_i(P_μ,η)

This is mathematically-consistent as being a dispersion formula.

The left-hand side is in fact the physical equivalance of

P^aP^bη_ab=v^2 (\hbar c/G)

so that

E^2/c^2 - ∏_(n=1)^3 |p^2| = v^2 (\hbar c/G)

Then the equation can become:

E^2-|p^2c^2| = (v^2)^2 \hbar c/G

The relation can be found:

G(\hbar c/G)/ \hbar c = Fvt/Mc^2

and

P^aP^bη_ab = E^2/c^2 - p^2

#### Geezer

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##### Is the Length of Vectors a physical quantity?
« Reply #1 on: 24/10/2009 06:09:49 »
Fantastic!

#### Mr. Scientist

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##### Is the Length of Vectors a physical quantity?
« Reply #2 on: 24/10/2009 06:30:10 »
The question is bold. Due to the invariant relationship between matter and the presence of geometry, are there points on a spacetime metric which yields the exact fluctuation in question? In the case of only having the geometrical sense of the length of a vector, and no other information, might the solution of the length in question hold a physical importance to the structure of the particle in question, since \hbar c/G reverts to the description of a particle with mass M in a relativistically-invariant habitat?

#### syhprum

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##### Is the Length of Vectors a physical quantity?
« Reply #3 on: 24/10/2009 07:24:14 »
To me with only "O" level physics education this reads like the results of one of those jargon generating programs (Perhaps I should be off to university to complete my physics degree)

#### lightarrow

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##### Is the Length of Vectors a physical quantity?
« Reply #4 on: 24/10/2009 16:36:01 »
if it were PμPμ instead of P^aP^b, and without ηab (what is it? you haven't defined it), then it would have been an obvious relation.
If you don't define the terms and what you exactly mean, it's not so easy to understand your post...

#### Mr. Scientist

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##### Is the Length of Vectors a physical quantity?
« Reply #5 on: 24/10/2009 17:32:24 »
if it were PμPμ instead of P^aP^b, and without ηab (what is it? you haven't defined it), then it would have been an obvious relation.
If you don't define the terms and what you exactly mean, it's not so easy to understand your post...

P^aP^2P_ab - it refers to rest mass, or rest energy M_0c^2.

#### lightarrow

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##### Is the Length of Vectors a physical quantity?
« Reply #6 on: 24/10/2009 20:17:34 »
Then it is obvious: you have written E2 = (mc2)2 + (cp)2, which is a well known equation.

#### Mr. Scientist

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##### Is the Length of Vectors a physical quantity?
« Reply #7 on: 25/10/2009 06:36:22 »
Not quite what i was hoping for. Total fail.

I have more to say - but will do so later..

#### Mr. Scientist

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##### Is the Length of Vectors a physical quantity?
« Reply #8 on: 25/10/2009 06:50:26 »
Then it is obvious: you have written E2 = (mc2)2 + (cp)2, which is a well known equation.

Let's do this properly. The answer to your reply is no. I had to look for a corresponding equation to varify it's use. If it had dimensions of E^2, it would not fit the description P^aP^2P_ab - originally i gave this as M_0c^2, which was incorrect - whilst technically P^aP^2P_ab is rest mass, it has the dimensions M^2c^2.

Lorentz covariance - Wikipedia, the free encyclopedia.mht
« Last Edit: 25/10/2009 06:52:14 by Mr. Scientist »

#### lightarrow

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##### Is the Length of Vectors a physical quantity?
« Reply #9 on: 25/10/2009 12:17:54 »
I still don't understand what you mean.
Don't know, maybe it's me...

#### Mr. Scientist

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##### Is the Length of Vectors a physical quantity?
« Reply #10 on: 25/10/2009 20:46:26 »
I still don't understand what you mean.
Don't know, maybe it's me...

You don't know the expression P^2b^2n_ab? Did you follow the link for a reference to it?

#### The Naked Scientists Forum

##### Is the Length of Vectors a physical quantity?
« Reply #10 on: 25/10/2009 20:46:26 »