| Topic: |
Science > Physics |
| User: |
"BD" |
| Date: |
08 Feb 2006 04:19:48 PM |
| Object: |
QUESTION - establishment of units of measurement |
Hey, all.
I've been bothered by this for awhile - it's not so much a physics
question, but I think it's relevant to physics.
Many of the principles and 'truths' in physics have been compressed and
summarized with very succinct mathematical equations - best example I
can think of is e=mc^2.
Each variable in this equation is measured in units that the human race
discovered or invented. A metre is a certain measurement of length, a
joule is a certain measurement of energy, a gram is a measurement of
mass (or is it weight? whatever), etc.
But when these units of measurement were discovered/created/invented,
were they not done so 'arbitrarily'? Did some 'council' not agree at
some point that a metre would be 'this long' and a 'joule' would be
'this much energy?
Is it not _extremely_ serendipitous (or even unlikely) that a
mathematical equation such as e=mc^2 could actually 'work', given how
the units of measurement used therein originated? It strikes me as
incredibly lucky that all the units of measurement we use here could
fit together so 'cleanly' unless there was something - dare I say -
unified about their acceptance.
Or maybe 'metres' and 'joules' weren't arbitrary in their origins...
Any comments? Is there something obvious about all this that nullifies
my question? In a way, I hope there is... ;)
Cheers,
BD
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| User: "Greg Neill" |
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| Title: Re: QUESTION - establishment of units of measurement |
08 Feb 2006 04:52:35 PM |
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"BD" <bobby_dread@hotmail.com> wrote in message
news:1139437188.085922.99490@f14g2000cwb.googlegroups.com...
Is it not _extremely_ serendipitous (or even unlikely) that a
mathematical equation such as e=mc^2 could actually 'work', given how
the units of measurement used therein originated? It strikes me as
incredibly lucky that all the units of measurement we use here could
fit together so 'cleanly' unless there was something - dare I say -
unified about their acceptance.
Or maybe 'metres' and 'joules' weren't arbitrary in their origins...
Fundamental units can be arbitrarily sized, but only
the fundamental units can be so defined; all derived
units must be based upon that small set of independent
fundamental units. In that way, the relationships
between the units is maintained and the formulae all work.
Exactly the same formulae would work using a completely
different set of sizes for the fundamental units, provided
that all the constants of proportionality were adjusted
accordingly.
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| User: "BD" |
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| Title: Re: QUESTION - establishment of units of measurement |
08 Feb 2006 10:43:11 PM |
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Exactly the same formulae would work using a completely
different set of sizes for the fundamental units, provided
that all the constants of proportionality were adjusted
accordingly.
So you accept that these 'sizes for the fundamental units' can vary and
still render formulae valid - I agree.
But the sizes of 'real-world' units cannot vary. A gram could have been
reckoned as the weight of 500 grains of rice... but what if it had been
700? or 100?
If the sizes of the fundamental units can vary in theoretical physics
without negating the validity of dependent formulae, then what
relevance does theoretical physics have to a 'real world', in which
sizes and measures do NOT vary???
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| User: "" |
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| Title: Re: QUESTION - establishment of units of measurement |
09 Feb 2006 01:38:49 AM |
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Check out my super long reply to your other post. I hope it will
address these points too.
Gianguido
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| User: "BD" |
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| Title: Re: QUESTION - establishment of units of measurement |
09 Feb 2006 11:07:15 AM |
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Check out my super long reply to your other post. I hope it will address these points too.
Oh, okay, I'll track that down. Thanks kindly!!
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| User: "" |
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| Title: Re: QUESTION - establishment of units of measurement |
08 Feb 2006 10:54:54 PM |
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In article <1139460191.026239.172520@f14g2000cwb.googlegroups.com>, "BD" <bobby_dread@hotmail.com> writes:
Exactly the same formulae would work using a completely
different set of sizes for the fundamental units, provided
that all the constants of proportionality were adjusted
accordingly.
So you accept that these 'sizes for the fundamental units' can vary and
still render formulae valid - I agree.
But the sizes of 'real-world' units cannot vary. A gram could have been
reckoned as the weight of 500 grains of rice... but what if it had been
700? or 100?
Wouldn't matter a thing. The formulas remain valid since you compare
things wiht the same dimensions (and that's the only thing you can
compare).
If the sizes of the fundamental units can vary in theoretical physics
without negating the validity of dependent formulae, then what
relevance does theoretical physics have to a 'real world', in which
sizes and measures do NOT vary???
The level of ignorance required by a denizen of the modern world who
freely enjoys all the goods and amenities provided him courtesy of
theoretical physics and then asks "what relevance it does have to the
real world" is, frankly, mindboggling.
Mati Meron | "When you argue with a fool,
meron@cars.uchicago.edu | chances are he is doing just the same"
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| User: "" |
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| Title: Re: QUESTION - establishment of units of measurement |
09 Feb 2006 12:32:35 AM |
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wrote:
If the sizes of the fundamental units can vary in theoretical physics
without negating the validity of dependent formulae, then what
relevance does theoretical physics have to a 'real world', in which
sizes and measures do NOT vary???
The level of ignorance required by a denizen of the modern world who
freely enjoys all the goods and amenities provided him courtesy of
theoretical physics and then asks "what relevance it does have to the
real world" is, frankly, mindboggling.
Mati,
What is mind boggling is that despite the unfortunate ignorance of the
general public with respect to the usefulness of physics, despite the
gravity of the consequences of this ignorance to culture, perception,
policy, funding etc. some seem to think condescension is a better
"cure" than education and mentoring. I do not know you and for all I
know, you are a visionary of Physics. But I do not know BD either, and
for all I know, he's just some kid trying to get it.
It is mind boggling for sure.
Gianguido
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| User: "BD" |
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| Title: Re: QUESTION - establishment of units of measurement |
09 Feb 2006 12:42:52 AM |
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for all I know, he's just some kid trying to get it.
Actually, I'm 38 and reasonably well educated.
If my question is fundamentally 'ignorant' or 'elementary', then either
I have yet to be visited upon by an epiphany, or I am not communicating
myself well enough.
Either way... this is the SECOND time I've come to this group with a
genuine question and gotten abuse as a result.
I appreciate yours and physicsboy's responses, but Mati does not make a
very good ambassador to us poor simpletons.
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| User: "" |
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| Title: Re: QUESTION - establishment of units of measurement |
09 Feb 2006 12:56:28 AM |
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Asking basic questions at 38? (we like to call them fundamental ;-0)
Great!! Wish everyone were so. I hope *I* will... I am writing a
lengthy reply to your message. gimme a few more minutes... don't get
discourged by the way for every Mati there are many of us who enjoy
explaining stuff... by the way, nothing to do with epihpany... I have
been thinking (read obsessed :-D ) about things like this for a long
time... been studying physics exclusively for ~10 years now.
G
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| User: "" |
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| Title: Re: QUESTION - establishment of units of measurement |
09 Feb 2006 01:46:06 AM |
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In article <1139466755.809808.264280@z14g2000cwz.googlegroups.com>, writes:
mmeron@cars3.uchicago.edu wrote:
If the sizes of the fundamental units can vary in theoretical physics
without negating the validity of dependent formulae, then what
relevance does theoretical physics have to a 'real world', in which
sizes and measures do NOT vary???
The level of ignorance required by a denizen of the modern world who
freely enjoys all the goods and amenities provided him courtesy of
theoretical physics and then asks "what relevance it does have to the
real world" is, frankly, mindboggling.
Mati,
What is mind boggling is that despite the unfortunate ignorance of the
general public with respect to the usefulness of physics, despite the
gravity of the consequences of this ignorance to culture, perception,
policy, funding etc. some seem to think condescension is a better
"cure" than education and mentoring. I do not know you and for all I
know, you are a visionary of Physics. But I do not know BD either, and
for all I know, he's just some kid trying to get it.
Well, the first step in "trying to get it" is some dose of humility.
Meaning, faced with something elementary that "doesn't add up" you
ask "am I getting something wrong". Starting with assuming that
everybody else got it wrong is offensive.
As for "eduction and mentoring", you haven't been on this ng long
enough. People have to prove themselves being worth the time
investment involved in education and mentoring. YMMV.
Mati Meron | "When you argue with a fool,
meron@cars.uchicago.edu | chances are he is doing just the same"
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| User: "" |
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| Title: Re: QUESTION - establishment of units of measurement |
09 Feb 2006 01:57:21 AM |
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Or maybe 'metres' and 'joules' weren't arbitrary in their origins...
Any comments? Is there something obvious about all this that nullifies
my question? In a way, I hope there is... ;)
I think the above is humble enough... it did not offend me anyway. I am
not sure how BD could proove his worthiness. If your time is so
precious why waste it denigrating someone who is trying to express a
question without being sure of the surrounding vocabulary?
I'll take a hint from your excellent signature now.
G
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| User: "physicsboy" |
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| Title: Re: QUESTION - establishment of units of measurement |
09 Feb 2006 08:22:39 AM |
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The discussion is interesting folks. But, please, let us remind
ourselves that there is no reason to throw stones at each other. We are
all in this world to learn. We are all on the same boat. We don't have
all the answers. We are all educated enough. In my case, I hold two
PhDs and I am sure all of you do too. For this reason, jumping on
someone or putting someone down for his/her question makes absolutely
no sense. Every question is valid, no matter how bizarre or far-out it
may seem. I, for one, do acknowledge and recognize BD's question as
legitimate and valid as any other question in Physics and I am willing
to state my opinion and read and comment on your opinions too. If I
don't agree with your opinion, fine. That's ok. If you don't agree with
mine, fine. That's ok, too. Why would I get upset about that? I
honestly don't care who is right and who is wrong. We are all here to
learn. As I said, I know for a fact that none of us have all the
answers. I was once here too and got severely badgered for posting my
theories and research. Why is that? Are you folks some kind of
know-it-all Universal Truth Machine? BD, my friend, I am with you on
this one and I am willing to discuss the subject in an open-minded
manner.
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| User: "BD" |
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| Title: Re: QUESTION - establishment of units of measurement |
09 Feb 2006 11:06:35 AM |
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BD, my friend, I am with you on this one and I am willing to discuss the subject in an open-minded manner.
I do appreciate it (and your time invested).
I need to take some time and mull over the thread before I say more. ;)
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| User: "BD" |
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| Title: Re: QUESTION - establishment of units of measurement |
09 Feb 2006 10:04:54 AM |
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Starting with assuming that everybody else got it wrong is offensive.
Please quote where in my post I suggested that.
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| User: "BD" |
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| Title: Re: QUESTION - establishment of units of measurement |
09 Feb 2006 12:38:56 AM |
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The level of ignorance required by a denizen of the modern world who
freely enjoys all the goods and amenities provided him courtesy of
theoretical physics and then asks "what relevance it does have to the
real world" is, frankly, mindboggling.
***** off. Either answer the question or don't; dont duck it and throw
grenades like a git.
I never suggested that it was not relevant; I used the word as a means
of trying to understand how a system based on admittedly arbitrary and
admittedly variable units of measure can be used to model a world where
units of measure are not variable.
Please try to keep up.
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| User: "Spaceman" |
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| Title: Re: QUESTION - establishment of units of measurement |
09 Feb 2006 11:16:57 AM |
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"BD" <bobby_dread@hotmail.com> wrote in message
news:1139467136.187047.244680@g44g2000cwa.googlegroups.com...
| I never suggested that it was not relevant; I used the word as a means
| of trying to understand how a system based on admittedly arbitrary and
| admittedly variable units of measure can be used to model a world where
| units of measure are not variable.
Dear BD.
you will find many that have a problem with the science of measurement
and actually need variable uints so they can "worship" thier certain theory.
Of course, anyone that knows basic science knows that
if a second actually changes rate in a clock, it is a clocks fault
and a true scientist/physicist would look for the reason why the
clock malfunctioned to begin with and would not just allow
a "time changed rate" supposed cause.
:)
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| User: "" |
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| Title: Re: QUESTION - establishment of units of measurement |
09 Feb 2006 01:47:10 AM |
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In article <1139467136.187047.244680@g44g2000cwa.googlegroups.com>, "BD" <bobby_dread@hotmail.com> writes:
The level of ignorance required by a denizen of the modern world who
freely enjoys all the goods and amenities provided him courtesy of
theoretical physics and then asks "what relevance it does have to the
real world" is, frankly, mindboggling.
***** off. Either answer the question or don't; dont duck it and throw
grenades like a git.
I never suggested that it was not relevant; I used the word as a means
of trying to understand how a system based on admittedly arbitrary and
admittedly variable units of measure can be used to model a world where
units of measure are not variable.
Please try to keep up.
That's it. Bye, bye.
Mati Meron | "When you argue with a fool,
meron@cars.uchicago.edu | chances are he is doing just the same"
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| User: "BD" |
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| Title: Re: QUESTION - establishment of units of measurement |
09 Feb 2006 11:02:38 AM |
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That's it. Bye, bye.
*swish* - nuthin' but net.
Thank you, thank you... please tip your server - try the shrimp salad!
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| User: "John C. Polasek" |
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| Title: Re: QUESTION - establishment of units of measurement |
09 Feb 2006 09:34:38 AM |
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On 8 Feb 2006 20:43:11 -0800, "BD" <bobby_dread@hotmail.com> wrote:
Exactly the same formulae would work using a completely
different set of sizes for the fundamental units, provided
that all the constants of proportionality were adjusted
accordingly.
So you accept that these 'sizes for the fundamental units' can vary and
still render formulae valid - I agree.
But the sizes of 'real-world' units cannot vary. A gram could have been
reckoned as the weight of 500 grains of rice... but what if it had been
700? or 100?
If the sizes of the fundamental units can vary in theoretical physics
without negating the validity of dependent formulae, then what
relevance does theoretical physics have to a 'real world', in which
sizes and measures do NOT vary???
Let me put in my 2 cents worth. Here is an aspect not often
considered.
Suppose L = 1 foot, then it's equally correct to say
L = 12 inches.
L = N*M
The right hand side has 2 components a number and a metric. Think of
them as extensity and intensity. Their product is called a scalar
product valid in any coordinate system.
What does that mean?
L is the physical longness expressed as the frequency N of units that
have a lengthness of M. Large N, small M and v.v.
Well, how to convert this longness L to meters "m"?
N_m = L/m = 12*inches/39.37inches/meter =(12/39.37) meters.
Valid formulas are valid in any system as long as you carry along the
units. Too much nonsense results from ignoring this.
John Polasek
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| User: "" |
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| Title: Re: QUESTION - establishment of units of measurement |
08 Feb 2006 09:50:12 PM |
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To clarify Mati and Greg's points with a very simple example:
L/t=3Dv or, in english:
(length of displacement)/(time taken to move) =3D speed
The above is true if L is in meters and t in seconds. Then v is in
meters per second (and these are the Syst=E8me International units,
based on definitions adopted and standardized during the French
revolution... http://en.wikipedia.org/wiki/Systeme_International)
But the equation is *also* true if L is in miles and t is in hours. In
this case v is in miles per hour.
Specifically the values of L, t and v change depending on the units you
choose, but as long as you are consistent in adopting your choice of
units, their relationship (L/t=3Dv) is **always** valid.
As Mati says above, this means that all theories and formulae in
physics do not depend on the choice of units but assume/require
consistency.
Hope this helps BD and physicsboy!
Gianguido
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| User: "BD" |
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| Title: Re: QUESTION - establishment of units of measurement |
08 Feb 2006 11:00:27 PM |
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all theories and formulae in physics do not depend on the choice of units but assume/require consistency.
I agree with you, if one of the variables in play is _derived_ from the
others - ie velocity, by definition, will always be distance over time
- regardless of the measured units - because that is the _definition_
of velocity.
Is it the case that e=mc^2 illustrates a 'function' of energy based on
mass and c, as the above example does? Or does it posit a
_relationship_ between these variables? If it is a function, then so be
it. But if it posits a relationship, I am baffled at the coincidence of
it all.
What if, for example, you are asserting the amount of energy required
to move a mass that is 10kg across a level plane, assuming known values
of friction etc... You could tell me, because it is at this point
easily calculable. But if currently agreed-upon measures for energy and
for mass were 'accepted' independently, then if a gram was accepted to
measure, say, 50 grains of rice instead of 100, then the formula
required to calculate energy to move a 10kg mass would be markedly
different.
Lemme ask it this way: assuming that c is calculated in terms of m/s,
what if a metre was actually 110 cm instead of 100? Would the equation
still work, in the context of the real physical world? Yes, it would
work in terms of internal consistency, formulae and 'referential
integrity', because a metre is still a metre regardless of how long
that metre is in the real world - but what about in terms of the real
world of metres measuring 100cm?
I fully accept that there is likely some principle here that will put
all this together - but do you see what I'm asking? Do I maybe just
need a wee slap in the head? ;)
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| User: "" |
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| Title: Re: QUESTION - establishment of units of measurement |
09 Feb 2006 01:26:37 AM |
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Wow BD! I think we're going in circles a little. Let me see if I can
explain better and address some of your points.
BD wrote:
I agree with you, if one of the variables in play is _derived_ from the
others - ie velocity, by definition, will always be distance over time
- regardless of the measured units - because that is the _definition_
of velocity.
Is it the case that e=mc^2 illustrates a 'function' of energy based on
mass and c, as the above example does? Or does it posit a
_relationship_ between these variables? If it is a function, then so be
it. But if it posits a relationship, I am baffled at the coincidence of
it all.
There is really no difference between v=L/t and E=mc^2. Sure you could
think of the former as a definition for v, that is the way it is taught
in school. But the official definition of a meter is actually the
distance light travels in 1/299 792 458 of a second. So you see,
scientists really define the length as a "consequence" of the speed of
light. They say L=v*t. and of course this is correct too. Similarly,
there is no base definition for a Joule (for energy). So yes, you could
think of Einstein's famous formula as a "definition" of energy.
I guess what I amtrying to say is that the equal sign is tobe taken
very seriously! E-Q-U-A-L! So it does not matter is I say E=mc^2 or
m=E/(c^2)...
What if, for example, you are asserting the amount of energy required
to move a mass that is 10kg across a level plane, assuming known values
of friction etc... You could tell me, because it is at this point
easily calculable. But if currently agreed-upon measures for energy and
for mass were 'accepted' independently, then if a gram was accepted to
measure, say, 50 grains of rice instead of 100, then the formula
required to calculate energy to move a 10kg mass would be markedly
different.
I give you a bucket with 1 litre of water and ask you to hold it out.
For 1 hour! With a straight arm! Do you think the amount of energy you
will spend is going to change depending on how I define the unit of
mass? If I tell you it's about 1 kilogram or if I say about 2.2
pounds... Of course not. the reality of what happens is independent of
what convention we decide to use. But there is a given amount of energy
you will waste trying this out.
Another way of thinking about it is if you weigh something on a good
scale (and read the mass in pounds, say) and then weight the same thing
on a bad, miscalibrated, scale that also uses pounds you will get two
different readings. But the amount of energy necessary to move it by 1
ft wil lbe the same either way.
Lemme ask it this way: assuming that c is calculated in terms of m/s,
what if a metre was actually 110 cm instead of 100? Would the equation
still work, in the context of the real physical world? Yes, it would
work in terms of internal consistency, formulae and 'referential
integrity', because a metre is still a metre regardless of how long
that metre is in the real world - but what about in terms of the real
world of metres measuring 100cm?
so let's say the real unit for length has a symbol m and your
"alternative" unit is M..
As you said, m=100cm but M=1.1m=110cm. Let's leave the second, s,
unchanged for simplicity.
now in real units we have, approximately, c = 2.9979e8 m/s and in
"alternative" units we have C = c/1.1 = 2.7253e8 M/s
So the numerical values are different. And a lot of numerical values of
alot of things would change if we changed the definition of a meter.
The POINT is that the actual speed, measured by some imaginary,
perfect, experiment would be the same. If you give two light beams for
one second and track them with the different units one will have
travelled 2.9e8 m and the other 2.7e8 M but both will have arrived at
the same spot at the same time...
I fully accept that there is likely some principle here that will put
all this together - but do you see what I'm asking? Do I maybe just
need a wee slap in the head? ;)
No slap in the head necessary :-) No new "principle that will put all
this together" is necessary either though. It's pretty simple: units
are convenient conventions and as long as they are self-consistent all
is fine. Changing the units won't affect physics nor will it affect
"reality". Clearly then, units are just a convenience and nothing
fundamental. think of them as nouns in a language. If we *all* started
calling apples 'bumbles' the apples wouldn't change, and we would all
still be able to talk about them.
few! this was longer than I thought. I hope it clarifies things a
little. Do NOT hesitate to ask for clarifications if you need to.
Gianguido
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| User: "BD" |
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| Title: Re: QUESTION - establishment of units of measurement |
09 Feb 2006 11:14:02 AM |
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Do NOT hesitate to ask for clarifications if you need to.
I will have to mull it over in terms of my initial question before
responding further. But I will follow up when I've let it all 'gel' for
awhile.
Thanks for taking the time!! Much appreciated.
BD
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| User: "PD" |
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| Title: Re: QUESTION - establishment of units of measurement |
09 Feb 2006 12:36:17 PM |
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BD wrote:
Hey, all.
I've been bothered by this for awhile - it's not so much a physics
question, but I think it's relevant to physics.
Many of the principles and 'truths' in physics have been compressed and
summarized with very succinct mathematical equations - best example I
can think of is e=mc^2.
Each variable in this equation is measured in units that the human race
discovered or invented. A metre is a certain measurement of length, a
joule is a certain measurement of energy, a gram is a measurement of
mass (or is it weight? whatever), etc.
But when these units of measurement were discovered/created/invented,
were they not done so 'arbitrarily'? Did some 'council' not agree at
some point that a metre would be 'this long' and a 'joule' would be
'this much energy?
Is it not _extremely_ serendipitous (or even unlikely) that a
mathematical equation such as e=mc^2 could actually 'work', given how
the units of measurement used therein originated? It strikes me as
incredibly lucky that all the units of measurement we use here could
fit together so 'cleanly' unless there was something - dare I say -
unified about their acceptance.
Or maybe 'metres' and 'joules' weren't arbitrary in their origins...
Any comments? Is there something obvious about all this that nullifies
my question? In a way, I hope there is... ;)
There is, but it's not obvious.
When you introduce conventions for the sizes of some units, there are
some constraints and in other cases no constraint was imposed. Where
you don't have constraints, a conversion constant is introduced. A
conversion constant is merely a number that connects two unconstrained
set of units.
As an example of a constrained set, a joule is *defined* so that
1 joule = 1 kilogram * (1 meter)^2 / (1 second)^2.
That is, there was a well-recognized connection between energy on the
left and the quantities on the right, and so the unit was *chosen* so
that the conversion factor was simple (1).
As an example of an unconstrained set, consider length and time. For
ages and ages, we thought the two were not connected and so the units
were not constrained to each other. We know now that this is not the
case. There is therefore a *conversion* factor, c, that converts our
units of time to units of units of distance and vice versa.
1 meter = (c) * 1 second
Another example is the unconstrained units for gravitational force and
mass. We know now (actually, since Newton) that there is a connection
and so there is a conversion factor, G, that stitches those units
together:
1 newton = (G) * (1 kilogram)^2 / (1 meter)^2.
It is perfectly acceptable to choose a different set of units so that
most, if not all, of these conversion factors disappear -- these are
often called "natural units". They are unfamiliar units for the
beginning student but the laws of physics are essentially the same
except for the absence of a lot of those extraneous conversion factors
like c.
PD
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| User: "BD" |
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| Title: Re: QUESTION - establishment of units of measurement |
09 Feb 2006 12:40:49 PM |
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As an example of a constrained set, a joule is *defined* so that 1 joule = 1 kilogram * (1 meter)^2 / (1 second)^2.
So it sounds as if units of measure were initially established with
reference to other, already accepted, units of measure... If that is
the case, then their origin is not as arbitrary as I'd thought, which
does address a good part of my question. Thanks!
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| User: "" |
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| Title: Re: QUESTION - establishment of units of measurement |
09 Feb 2006 12:58:30 PM |
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All the units except for metre, second, Amp=E8re, Kelvin, mole and
candela are derived from these.
That addresses part of your concerns.
BUT, those 6 units are arbitrarily defined. (There definitions infact
have slightly changed over the years, not because we simply changed our
minds but because we found increasignly reliable and precise ways of
measuring length, time etc...)
So you could still wonder, why did we pick *that* length as the
definition of a metre. And what I was trying to convey is that it does
not matter. We chose certain definitions, initially, for
historical/economical reasons. But we *could* have chosen other
definitions and both the laws of physics and the real world would not
have changed.
Changing the units in an equation is like changing the language of a
text. Do it to all the components (words) and you can still read and
make sense. The language is an arbitrary choice that does not affect
the essence of the message.
Gianguido
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| User: "arvee" |
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| Title: Re: QUESTION - establishment of units of measurement |
09 Feb 2006 12:58:40 PM |
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BD wrote:
Hey, all.
I've been bothered by this for awhile - it's not so much a physics
question, but I think it's relevant to physics.
Many of the principles and 'truths' in physics have been compressed and
summarized with very succinct mathematical equations - best example I
can think of is e=mc^2.
Each variable in this equation is measured in units that the human race
discovered or invented. A metre is a certain measurement of length, a
joule is a certain measurement of energy, a gram is a measurement of
mass (or is it weight? whatever), etc.
But when these units of measurement were discovered/created/invented,
were they not done so 'arbitrarily'? Did some 'council' not agree at
some point that a metre would be 'this long' and a 'joule' would be
'this much energy?
Yes, but think back to how these things arose. Take classical
mechanics, for example. We have F = ma and E = Fd. Here, the
acceleration 'a' is measured using some agreed-upon length and time
units, and the units of force F are chosen to be as simple as possible.
Of course, you COULD choose to measure F in different units, in which
case you would need to write F = k ma, where k is some conversion
factor. Now, the energy, E, is essentially defined as force times
distance, where distance, d, is measured in the same length units that
went into measuring 'a'. Again, you could have decided to measure
energy in some other units, in which case the kinetic energy formula
would be KE = 1/2 r m v^2, where r is a conversion factor of some kind.
Over the centuries, other kinds of energy were discovered, so their
contributions needed to be included in expressions of total energy.
However, the exact way they enter the expression depends on the units.
For example, when I first started learning electromagnetism the books I
read were written in cgs units, with charges in statcoulombs (if memory
serves). Later, everybody seemed to switch to the units you see today,
so there are now all kinds of 4 pi epsilon_0 terms floating around in
Maxwell's equations. The exact expression for the "electromagnetic
energy" terms depend on the units you choose to do both your mechanics
and your electromagnetism.
R.G. Vickson
Is it not _extremely_ serendipitous (or even unlikely) that a
mathematical equation such as e=mc^2 could actually 'work', given how
the units of measurement used therein originated? It strikes me as
incredibly lucky that all the units of measurement we use here could
fit together so 'cleanly' unless there was something - dare I say -
unified about their acceptance.
Or maybe 'metres' and 'joules' weren't arbitrary in their origins...
Any comments? Is there something obvious about all this that nullifies
my question? In a way, I hope there is... ;)
Cheers,
BD
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| User: "Gregory L. Hansen" |
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| Title: Re: QUESTION - establishment of units of measurement |
09 Feb 2006 02:22:23 PM |
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In article <1139437188.085922.99490@f14g2000cwb.googlegroups.com>,
BD <bobby_dread@hotmail.com> wrote:
Hey, all.
I've been bothered by this for awhile - it's not so much a physics
question, but I think it's relevant to physics.
Many of the principles and 'truths' in physics have been compressed and
summarized with very succinct mathematical equations - best example I
can think of is e=mc^2.
Each variable in this equation is measured in units that the human race
discovered or invented. A metre is a certain measurement of length, a
joule is a certain measurement of energy, a gram is a measurement of
mass (or is it weight? whatever), etc.
But when these units of measurement were discovered/created/invented,
were they not done so 'arbitrarily'? Did some 'council' not agree at
some point that a metre would be 'this long' and a 'joule' would be
'this much energy?
The units are arbitrary. But they must be used consistently to get a
meaningful result. For instance, if mass is in kilograms and speed in
meters per second, then energy will be in joules, which have the units of
kilograms*meters^2/seconds^2.
As you might suspect, the joule is not defined independently of the
kilogram, the meter, or the second. It's basically defined by the
equation for kinetic energy,
K = 1/2 m v^2
If you have a known m that moves at a given v, then that defines the
energy it has. If something can make it go that fast, then it can impart
that much energy to it.
If mass is in pounds and speed is in feet per second, then energy will
have units of pounds*feet^2/second^2.
If there is an independently defined unit of energy, like the greg, then
the equation must be expressed in a form like
E = kmc^2
where k is a factor that converts from joules to gregs, or from whatever
system you're using.
--
"We need to remember that when we are faced with an unstructured problem
it is we who create the model in the form of a quantitative metaphor;
there is no correct model waiting in the wings for us to call onstage." --
Thomas L. Saaty, "Mathematical Methods of Operations Research" (1988)
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| User: "physicsboy" |
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| Title: Re: QUESTION - establishment of units of measurement |
09 Feb 2006 03:02:07 PM |
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Units of measurements, as well as any physical law, must be described
in terms of our present understanding of reality. Like I said before,
units of measurements and physical laws are meaningless outside of our
reality. It takes consciousness to measure and to question the nature
of these laws so the consciousness factor must be present in order to
interpret. There is a non-quantitative aspect to these measurement
units and calculations, be it physical, mathematical, metaphysical,
etc. The "mind" factor must always be present in order for any of this
to even make sense. For all these reasons, there really is an arbitrary
component to the development of these units of measurements. What I
fail to understand, really, is why BD was attacked when he asked the
question. In my opinion, his question makes a lot of sense.
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| User: "BD" |
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| Title: Re: QUESTION - establishment of units of measurement |
09 Feb 2006 03:15:38 PM |
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What I fail to understand, really, is why BD was attacked when he asked the question.
I don't think it was my question that was the issue; rather, it was
Mati's attitude. Thus far, he's the only one who has swung a punch; the
remainder of you have been wonderfully accomodating, and surprisingly
interested in what I have to say.
Mati jumped immediately on the word 'relevance' in my one posting,
becoming defensive and aggressive without even trying to ask me once
whether I meant what he 'thought' I meant..... not pausing to consider
that the word might have been used to mean 'applicability', rather than
'usefulness'.
As well, he said "Starting with assuming that everybody else got it
wrong is offensive." I never made that assumption, nor said anything
close to that in any of my posts. I also asked him to point out where
I'd made such an assumption. He won't.
In short, I think that he proved himself to be a combative jackass the
instant he laid finger to keyboard. Which is why I chose to insult him
right back, and snicker as I did so. I will not throw the first punch,
but at the same time, I will not be misquoted nor have my words taken
so absurdly out of context, without fighting back.
In short, my view is that he likely just needs a nap.
BD
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| User: "physicsboy" |
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| Title: Re: QUESTION - establishment of units of measurement |
09 Feb 2006 03:46:42 PM |
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I have often found that folks tend to be way too fanatical here to the
point that one is insulted directly. It happened to me not long after I
first joined. One poster even attacked me personally and explicitely
wrote down that I was a fool without even properly examining the ideas
I was attempting to put forth. While I welcome almost any type of
criticism, I do ask that people be polite and discuss within the
context of the argument. That is very difficult here. People often tend
to get personal and very frequently insult you directly as a person,
such as your intelligence, your qualifications, your education, your
knowledge, etc. That is very, very worng. I will never act in that way.
Everyone's opinion counts, even if it comes from the most
physics-ingnorant person in the world. In my opnion, everyone has
something to offer and we can learn from everyone, it does not matter
who it is.
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