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B Discrete definitions of Physics Standard Units

  1. Sep 8, 2016 #1
    Dear PF Forum,
    Perhaps it's not a question, just a light discussion.
    From this, we get the standard time
    https://en.wikipedia.org/wiki/Caesium_standard, it's 9,192,631,770 ticks per second.
    I think this number should be discreet. No need to tune it to some figures after decimal point.
    Is this right? Although it wouldn't match 1/86400 day length. But, then again, for a very big body like earth with all its dynamic changes (weather, ocean, tectonic movement) it can't be too precise.

    And from time, we get the standard length:
    Which is 9,192,631,770 / 299,792,458. And I think 299,792,458 is not discreet. Is this true? This is the law of nature, right?Or..., as in https://en.wikipedia.org/wiki/Rømer's_determination_of_the_speed_of_light
    We arbitrarily set the speed of light: 299,792,458 meter per second, (whatever "meters" means) and we define that length that time travels when Ca 133 ticks 299,792,458 (discreet?) times and call it 299,792,458 meters (discreet?)

    In junior high, we were taught that 1 kg is the mass of 1 litre (length already defined) water in 3.980C. https://en.wikipedia.org/wiki/Properties_of_water#Density_of_water_and_ice. But there is 1 catch. It's 3.980C in 1 bar atmospheric pressure. But we define pressure in N/m2. And 1 Newton is the force to accelerate 1 kg for 1 meter per second per second. And we meet mass (KG) again :headbang:.
    So since Avogadro had set that 1 mole is 6.022140857(74)×1023 . So can we safely say that 1 gram is the mass of 6.022140857(74)×1023 hydrogen atoms? (Without deuterium/tritium isotop impurity?)
    And I think the rest, energy, calorie, volt, etc are derived from this standard unit.

    Perhaps my questions are not physical, but rather historical.
    Are these numbers:
    9,192,631,770, time
    299,792,458, length
    6.022140857(74)×1023 , mass
    Just curious to know :smile:.
    Thank you very much
  2. jcsd
  3. Sep 8, 2016 #2


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    It can't be too precise? For whom?

    Your GPS had to take into account even the minute time dilation effects to keep its precision. How big of an error do you think you'll end up with if the time clock on your GPS is rounded off to the nearest second? Would you like to fly on an airplane with that kind of an error, especially when it is estimating where the ground is during landing?

  4. Sep 8, 2016 #3
    I mean Caesium clock is very, very precise, but it's the earth rotation that can't be too precise. It's a very big body. But I do believe that GPS is accurate. Or..., the earth rotation is very precise?
  5. Sep 8, 2016 #4


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    No. The 9192631770 oscillations per second is a definition. Just like the definition of the meter in terms of a standard stick is obsolete, so is the definition of the second as a fraction of a day.

    What do you mean by discrete? It is a single value and it is a definition.

    This is not the definition of the kilogram. It is a property of water.
  6. Sep 8, 2016 #5
    Thanks @Orodruin for your answer.
    First of all, English is not my first language. Perhaps I can't express myself clearly.
    I'll try the other way.
    So we arbitrarily define 1 second is 9192631770 oscillations of Ca 133, which is almost close to 1/86400 the length of day?
    I mean Discrete is Integer.
    Take hydrogen frequency (as I saw in Contact movie) for example.
    Hydrogen frequency is: 1,420,405,751.78 Hz
    After we define the length of 1 second is 9192631770 Hz (integer) of Ca 133, then it's very rarely in nature that Hydrogen frequency coincidently has an integer value for 1 second. So I mean, perhaps we arbitrarily define 1 second is 9192631770 (integer value) Hz of Ca 133 frequency and the other elements frequency follows this standard.

    Yes, it is. But I think long ago, people had to define kilogram, and they used this property of water.

    I know that PF Forum Guidelines strongly against personal theories. But if I may indulge myself...
    Supposed we have already had the standard for time definiton 9,192,631,770 Hz of Ca 133.
    How do we define length? I think we can define it by the distance the light takes when Ca 133 has ticked 9,192,631,770 times.
    Because we haven't had the accurate definition of length, right?
    And we have metres (1/40000 the circular of latitude lines of earth accross Paris). And perhaps now we arbitrarily (?) define 1 metres is 1/299,792,458 (integer number?) the distance the light takes when Ca 133 has ticked 9,192,631,770 (integer number) times. Which is almost close to the definition of 1/40000 the latitude of earth?
    Thanks for your respond.
  7. Sep 8, 2016 #6


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    No, it is not. The kilogram is currently defined by the IPK artefact, nothing else. It is likely this definition will be changed to one involving only natural constants in the future but this is the current definition.

    Then say integer. Discrete is something else.

    This is the definition of the length unit. One meter is the distance that light travels in 1/299 792 458 seconds by definition.
    again, this is not how the meter is defined today.
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