Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: varsigma on 02/08/2022 00:32:22
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I've been having a stoush with someone recently, about a simple enough thing which is, how physical units are defined.
It seems that, at first we don't bother defining distance, other than in terms of a unit thereof. That is, we just assume that distances are somehow axiomatic. This is clearly not the case when we define units of time; currently defined accurately in terms of a single, 'central' frequency, and the constant speed of light.
But physics doesn't stop and ask, "what really is a unit of distance", or "what is a unit of time", etc. Physics just assumes that units can be defined in terms of each other--speed, in terms of time and distance e.g.--and doesn't bother with the philosophy.
Distance "is what it is"; you measure some and just get on with it. In fact humans measure distances all the time, walking or driving is a 'measurement' of distance; when you move any part of your body it 'moves through' a distance and this constitutes a measurement (of distance). Accurate measurements aren't a rule as such, but are assumed to be a requirement if a theory is being supported by experiments.
Or, why don't we have definitions of time and distance, etc, in other more fundamental terms?
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I'll add that there are also definitions of more abstract kinds of 'distance'; one obvious one is the distance between two primes in number theory.
Another kind is the distance of a path through a graph in graph theory, or the distance between two permutations of a permutation group in group theory. An affine distance is encountered sometimes in lectures on black holes and the like, but what is an affine distance? In any manifold distance is given by a metric; the surface of our planet qualifies as a manifold because it can be given coordinates, because it has distances 'built in' between different locations. It's just a fact of nature that planets have a finite volume and a finite surface, so finite distances are just a kind of trivial subset.
But a topological distance can be nontrivial, right?
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we just assume that distances are somehow axiomatic
A lot of people (most people?) are confused when they first run into concepts from Special Relativity whereby observers in different frames of reference will will come up with a different distance and time between the same same two events.
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Or, why don't we have definitions of time and distance, etc, in other more fundamental terms?
I'm not sure what your asking. Fundamentally, distance is "from here to there" and time is "from now to then". We developed tools (rulers and clocks) to accurately measure these dimensions. So what do you think is missing?
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Or, why don't we have definitions of time and distance, etc, in other more fundamental terms?
I think that we are just using the ancient greeks system when it comes to "measure" the "earth" things.
Geometry mean "the measurment of earth" (literaly).
When "we" invented science, so greek science, we initialy used the so called "philosophy".
Within the philosphy we had the "geometry" (this portion of philosphy ended up creating mathematic).
The principe was : I am a man, i try to investigate the relation (bigger or smaller and in some quantitativ way what is the relational mathematical proportion) between things "i" can measure ("i" is the one who measure, so "the man").
Therefore the fundamental terms are in some ways "anthropomorphic", so related to men, and if you want to be less human related, you can say "macroscopical" (this term is better accepted within modern science but it is the same).
Now, you can effectivly do some "other" (dimensional) definition of space (i will not speak of time, this is too complicated since you cant understand the simple space problem).
The second dimension is "who" is measuring the distance.
The first, primitiv way to quantitize distance is "greek related", so macroscopical.
The second is to add some dimension, saying : "For who" is the distance related ? (for who is the second dimension).
The "distance", so the proportion between your unit and your measure depends on what you are.
If your own scale (what you are) is around plancks lower limit (that exists for macroscopic things), the result of the distance is not the same as the distance for some other being at other scale.
Distance = f(scale).
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The second dimension is "who" is measuring the distance.
The first, primitiv way to quantitize distance is "greek related", so macroscopical.
The second is to add some dimension, saying : "For who" is the distance related ? (for who is the second dimension).
I don't believe that 'who' is a dimension by any scientific definition.
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I don't believe that 'who' is a dimension by any scientific definition.
Thats just because you never heard of the scale realtivity of Laurent Nottale.
https://luth.obspm.fr/~luthier/nottale/ukrechel.htm
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I don't believe that 'who' is a dimension by any scientific definition.
Thats just because you never heard of the scale realtivity of Laurent Nottale.
https://luth.obspm.fr/~luthier/nottale/ukrechel.htm
Even in the lunatic fringe, 'who' is not a dimension.
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Even in the lunatic fringe, 'who' is not a dimension.
No, "who" is the scale.
If you consider the length of ths some coast you can have :
1. The classical length (dimension 1).
2. The fractal length (dimension higher).
So the length is dependant of the scale resolution, length = f(scale).
Typicaly the scale of man is 1 m (the "who").
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It's sort-of true that if two people walked round the coastline of the UK counting their paces and then multiplied the number of paces by the length of their stride they would disagree on the length of the perimeter (and an ant would have a much longer trip).
But that's not a "who" thing, it's "a how long is their pace?" thing- that's a distance, for which the unit is the metre.
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counting their paces and then multiplied the number of paces by the length of their stride they would disagree on the length of the perimeter
Surely the disagreement would be of the order of (the uncertainly of stride length multiplied by the number of paces) plus (one average stride multiplied by the uncertainty of counting) for each participant. You can take the root sum of squares for your best prior estimate of the limit of disagreement.
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Typicaly the scale of man is 1 m (the "who").
That is where the French revolutionaries got it wrong. The Romans had sensible natural scales, that still persist in the last backward country - the USA.
Thumb - inch
Foot - foot (12 inches)
Arm - yard (36 inches thumb to nose)
Adult humans are mostly between 5 and 6 feet tall (1.5 - 1.8m)
Mile - milia passuum - 1000 paces (a Roman pace being together, left, right, together - like a proper dance script) - 1760 yards for the average soldier, who covered 4 - 6 miles per hour on a road (the Romans made the roads, and invented standard shoe sizes to keep the army marching efficiently on them)
Pound - 2 day's bread ration
Gallon - 10 pounds (2 days ration) of water
though the Yanks have screwed up the system by having a US pint equal a pound, and keeping 8 pints to the US gallon.
Defining the meter as a fraction of the earth's polar circumference through Paris was all very well politically, but not directly measurable. Navigators generally use the sexagesimal system with a nautical mile equalling one minute of latitude (directly measurable) and being adequately close to 1000 fathoms (hand-to-hand span when pulling up your sounding weight).
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counting their paces and then multiplied the number of paces by the length of their stride they would disagree on the length of the perimeter
Surely the disagreement would be of the order of (the uncertainly of stride length multiplied by the number of paces) plus (one average stride multiplied by the uncertainty of counting) for each participant. You can take the root sum of squares for your best prior estimate of the limit of disagreement.
Are you deliberately missing the point?
It's not about the inaccuracy involved; it's about teh effect of scale when measuring a fractal object.
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So it's about the interpretation of "round the coastline". The continuous smooth ovoid that just encloses Great Britain is almost certainly shorter than the high tide contour.
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Ok. So it looks like the uncertainty problem has come up. I suppose it's a rule of thumb that any measurement is uncertain.
And I've realised that the problem of 'fundamental' units is more or less resolved (depending on I also guess a realist or positivist stance) by the constant speed of light. So the metre and second are defined in terms of this constant plus a constant frequency of light. Nonetheless the measurement problem doesn't go away--in wave mechanics there is always a classical uncertainty when measuring frequencies or counting wavefronts. (It's in Modern Physics by Kenneth Krane too)
So if, axiomatically, the speed of light is constant in a vacuum, then there is a finite number of wavefronts in a unit distance, passing a fixed point, in a unit time. Uncertainty has to apply to this 'fixed' point, though.
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Just checking I'm on the same page as most people, when I try to define physical stuff like distance.
Or rather, why I assume distances exist and that measuring them isn't a problem with any special difficulty. Distance, area and volume are such a part of our experience that we don't ask, usually, about why distances, or why spaces, exist.
Beyond measurement and theory, there is philosophy. I guess the philosophy of distance isn't interesting.
I remember though, an interesting question about time in an electronics lecture; why is time a real number (of seconds) in formulas and equations? The answer given was pretty much "it just is".
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My best attempt at explaining what distance is, is that it turns out to be a kind of information.
Or at least it does when we introduce a unit of distance and use it to measure another distance.
So it's like an alphabet with one character if you choose units that evenly divide a physical distance--the information per se is then literally the length of a string. Is information physically real or just conceptual? Can I really think of a real distance in metres as having entropy?
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in wave mechanics there is always a classical uncertainty when measuring frequencies or counting wavefronts
As I recall, one earlier definition of the meter specified:
The metre is the length equal to 1,650,763.73 wavelengths in vacuum of the radiation corresponding to the transition between the levels 2p10 and 5d5 of the krypton 86 atom.
https://en.wikipedia.org/wiki/History_of_the_metre#Krypton_standard
So it's not like they are limited to measuring an integer number of wavelengths (here they measured 2 decimal places of a wavelength)...
There are fundamental limits to measurement due to Heisenberg uncertainty, but you can usually overcome these limits by taking the measurement over a very long time period, which allows reduced uncertainty in position or momentum.
You have to be very patient when making fundamental physical measurements...
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You have to be very patient when making fundamental physical measurements...
The UK National Physical Laboratory used to budget 20 person-years per decimal point. Turned out to be a remarkably good estimate as my team spent almost exactly that amount of time reducing the uncertainty in radiation dose measurement from 1% to 0.1%.
Pedant mode: Heisenberg described the inherent indeterminacy of a phenomenon, not the uncertainty of its measurement. Lots of people use the mistranslation because many textbooks use a hypothertical "reflected photon" measurement to derive the equation.
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Pedant mode: Heisenberg described the inherent indeterminacy of a phenomenon, not the uncertainty of its measurement.
It is possible to weight the odds in Heisenberg indeterminacy, by using squeezed quantum states. You reduce the uncertainty in one dimension (which you care about), and accept that it will be less certain in another dimension (that you don't care so much about).
- So if you were measuring a distance accurately (eg the length of the standard meter, or the length of a gravitational wave detector), you may care more about uncertainty in distance than you care about uncertainty in photon momentum.
- Both LIGO and VIRGO use squeezed quantum states to improve sensitivity in detection of gravitational wave events.
- They both use real reflected photons to make the measurement
See: https://en.wikipedia.org/wiki/Squeezed_states_of_light
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Still wearing my linguistic pedant hat, what you are actually doing with squeezed states is reducing the indeterminacy of one vector of a phenomenon in order to reduce the uncertainty of your measurement. It's remarkably like heterodyning.
Just thought of a macroscopic analogy. How do you count sheep? In a field, they are all milling about in various directions so you don't know if you've counted one twice, or missed out a few. So you can either take a photograph, which tells you how many were there at the time you took the photo (but you don't know where they are now) or you herd (squeeze) them through a gate and count them one at a time into separate pens. Well, it's no worse a model than the bouncing photon!
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These are not, by any means, the only physical units. For starters, you can change the units so that mass, space, time, and temperature are all the same (Planck units). The quantities chosen are not even fundamental (for example, charge is unquestionably more fundamental than current, and moles are essentially a conversion factor between AMUs (atomic mass units) and kilogrammes). And because Candelas are entirely human-based, they are not physically fundamental at all. Finally, these units omit nearly all of quantum mechanics' fundamental parameters.
The seven basic units are simply convenient choices for dealing with many classical physics equations (I believe it is easier to measure current than charge, for instance). Charge, mass, space, and time are the fundamental units for electromagnetism and gravity equations, and temperature is useful for thermodynamics (although you can actually calculate it in many cases from an average kinetic energy, which in turn is derived from the previous units). Moles convert microscopic to macroscopic quantities, and I'm not sure what candelas are doing there.
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I think the more fundamental thing isn't actually any physical units, but rather difference.
A distance "lies between" two different points; a voltage "exists between" two different amounts of charge.
Without fundamental differences, measurement isn't that well-defined, I would say.
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Mass is mass. No difference between anything. Likewise charge.
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Mass is mass. No difference between anything.
?? Not sure what that means; the mass of the earth and the mass of the moon are both masses. And yet, there's a difference between them; if I subtract one from the other, that's the difference, and it might be negative.
It might be the case that this difference has no physical significance (except that isn't true); it might be that the information the difference has in it, amounts to nothing useful. Except it does
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It might be the case that this difference has no physical significance (except that isn't true); it might be that the information the difference has in it, amounts to nothing useful. Except it does
There are two unsupported claims there.
Were you expecting us to "just believe you"?
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There are two unsupported claims there.
Were you expecting us to "just believe you"?
There are two unsupported claims? Surely the masses of the earth and moon being different isn't an unsupported claim?
Or perhaps I could weigh their masses and make sure, but how?
Is the other unsupported claim that the difference is useful information?
In physics, there are indeed things that you should 'just believe'. For instance, you should believe that distances exist and can be measured. That's actually what most people do believe, so physics teachers usually skip the definition of distance and measuring distance.
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The difference between the masses of the earth and the moon, or indeed any two bodies, does not constitute a fundamental physical quantity, unlike the spatial difference between point A and point B, which as you say defines "distance". Mass is defined without introducing a second object or point.
Measuring distance is (or at least used to be) one of the most important lessons in elementary physics.
The definitions are straightforward. Time is what prevents everything happening at once, and distance is what prevents everything being in the same place.
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Measuring distance is (or at least used to be) one of the most important lessons in elementary physics.
It still is. The concept of distance and it’s measurement is also a key feature of most elementary education.
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The difference between the masses of the earth and the moon, or indeed any two bodies, does not constitute a fundamental physical quantity,
So you say.
I say it does constitute something more fundamental than physical units, in this case units of mass. The mass difference is physically significant and it does contain information. I don't understand why that means it is or isn't a physical quantity; I don't understand the significance of the rest of your post.
I say that difference is more fundamental and you say the distance between two points is fundamental. Why aren't the two points more fundamental? Mass is defined without introducing a second object or point.
A point is defined without introducing a second point, but you need a second point to define a distance. You need a second distinct mass to define a mass difference likewise.
Like I said, difference is more fundamental than a choice of units.
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You seem not to understand the word "constitute" , nor the difference between a ratio and a difference.
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You seem not to understand the word "constitute" , nor the difference between a ratio and a difference.
You seem not to understand a rational argument. How to make one, that is.
Please explain your claim, so far just a bare statement, that the difference between two masses does not constitute a fundamental physical quantity.
I want you to explain all the terms you're using. Explain what a physical quantity is, then what a fundamental physical quantity is, with examples. I want it absolutely clear and irrefutable so that the difference between two masses is excluded from the set of fundamental physical quantities.