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Re: the famous formula

From Thomas Heger <ttt_heg@web.de>
Newsgroups sci.physics.relativity
Subject Re: the famous formula
Date 2018-12-14 15:13 +0100
Message-ID <g7hs52Ff4t7U1@mid.individual.net> (permalink)
References (13 earlier) <pummhj$vf2$2@gioia.aioe.org> <g7a3hoFoc5dU1@mid.individual.net> <puovcb$1mbf$1@gioia.aioe.org> <g7co0oFbh39U1@mid.individual.net> <purcte$1tqu$2@gioia.aioe.org>

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Am 12.12.2018 um 17:27 schrieb Odd Bodkin:

>>>>>>>> https://examples.yourdictionary.com/examples-vector-scalar-quantity-physics.html
>>>>>>>>
>>>>>>>>> The acting force has direction.
>>>>>>>>> The path along which the force is acting has direction as well
>>>>>>>>> But the work as integral of scalar product of these 2 vectors is a
>>>>>>>>> scalar, without direction.
>>>>>>>>
>>>>>>>> work is NOT 'forth times path'
>>>>>>>>
>>>>>>>> but ' force times distance'.
>>>>>>>
>>>>>>> No, it is not that either. It is the integral of the scalar product between
>>>>>>> two vectors, the force and the differential displacement.
>>>>>>
>>>>>>
>>>>>> 'Work' is the name of a quantity in physics.
>>>>>
>>>>> As is velocity.
>>>>>
>>>>>>
>>>>>> It relates to the real world, hence is not a product of either one or
>>>>>> two vectors.
>>>>>
>>>>> I disagree. There are LOTS of real world quantities that are related in
>>>>> some way to other real world quantities. Velocity (a vector) is related to
>>>>> differential displacement and differential time. Momentum is related to
>>>>> mass and velocity.
>>>>
>>>> This is correct. But I had something against this statement:
>>>>
>>>> ".. It is the integral of the scalar product between two vectors..."
>>>>
>>>> I said: no, it is not, since a vector is a mathematical construct.
>>>
>>> I disagree. A vector is a way to characterize a physical quantity. Velocity
>>> is a vector, momentum is a vector, force is a vector. All of those are
>>> real.
>>
>> There is still a difference between 'vector' and 'physical quantity
>> characterized by a vector'.
> 
> Not in a physics discussion, normally.

What you are apparently trying to say is, that if physicists chat at 
lunch brake or in a bar with a bear, they take the numbers for the thing 
and the vector for the quantity.

Well, maybe..

In my view there is a difference between a model and the system it tries 
to model. There is also a difference between the mathematical 
representation of some type of behavior and the mechanisms acting in 
that system.

The statement, that I disagreed with was, that work is a scalar, because 
it is a product of two vectors.

This is wrong, since it is not a product of two vectors, but a product 
of a physical quantity called 'force', which behaves like a vector, and 
something we are still debating.

You said, this second term should be a vector, too, while I wanted to 
use a scalar.

> When I talk about velocity, I can refer to it as a vector and that means
> the physical quantity characterized as a vector. The two are synonymous and
> understood. Maybe not by you.

Sure.

But where is the connection to the problem in question?

>>
>> A vector is a mathematical construct, while quantities have units and a
>> physical meaning.
>>
>> You may characterize that quantity by an appropriate vector, but this
>> does not make a vector a quantity.
>>
>>
>>>>
>>>> A number is also a mathematical construct. And you cannot multiply two
>>>> brainchilds and hope to get something real.
>>>>
>>>>
>>>> First statement: a quantity in physics (work) is defined as being the
>>>> product of one quantity (force)and some sort of length.
>>>
>>> “the product” is too vague. Given that the two things you are multiplying
>>> are vectors, you have to be precise about what you mean by “product”. In
>>> this case “product” means scalar- or dot-product.
>>
>>
>> I was trying to show, that the product of a force and a path is not the
>> right idea.
> 
> If you want to redefine work, using the same term that has been used with a
> particular understanding for centuries, good luck with that.

You must distinguish between the 'metaphysical' definition and the 
technical.

If a certain term is used, we need to talk about its meaning.

In case of 'work' we have something in mind. This would be somehow like 
"work is the quantity we have, if we lift a stone for a certain hight".

That is a little rough, but gives an idea about what we are actually 
trying to define.

A more technical definition would be like this:

work for lifting a stone in Earth gravitational field is equal to weight 
times additional hight (by what the stone is lifted).


This is still not very good, but defines, what we are trying to define: 
the physical quantity 'work'.


Now we should look, whether or not a certain definition would actually 
fit to what we had in mind.

'additional height' is not a vector and it is also not a path.

It is not a vector, because 'height' is meant as radius of the Earth 
surface at a certain point (where the thing to lift is right now).

The larger radius with additional height is actually the former radius 
multiplied by a scalar.

'additional height' is also not a path, because 'path' is meant as set 
of points, which are reached one after the other at certain times.

These points and the times, when they are passed are not interesting in 
this context and do not belong to the metaphysical construct 'work'.




...


TH

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                Re: [OT] Work Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2018-12-10 22:28 +0100
                Re: [OT] Work Thomas Heger <ttt_heg@web.de> - 2018-12-11 16:36 +0100
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