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A constant is mathematical abstraction. There is no mathematics outside people's minds. There are no numbers outside mind of an observer, no time, no space. Wh

A constant is mathematical abstraction. There is no mathematics outside people's minds. There are no numbers outside mind of an observer, no time, no space. Which abstractions are good enough approximations of laws of the Universe, and which are mere creations of the mind is an open question since the first human language has been established.) Upanishads and the Buddha have tried to clarify the mess a bit, but... According to the finest human philosophy, nothing is permanent, hence, nothing is constant. Atoms - the basic building blocks, are "stable" as long as they has been made inside a star, but they are not permanent or constant (they might end up in another star). Their weights, electrical properties are stable ("constant" is not applicable here, being from another domain of pure abstractions which we call mathematics). Mathematical ratios could be computed, of course, given that measurements are accurate enough, but they does not exist either. These are rarest concepts of the mind which reflect some aspects of reality as it is.

tremon 11y ago
I think the article is talking about physical properties, like c, h, or G, that we measure to be the same every time. You seem to be talking about numerical representations.
- hansen 11y ago
  c and ℏ don’t encode any physics, they just fix measuring units. Actually it’s common to choose units s.t. ℏ = c = 1.
  - simonh 11y ago
    So the same constants can have different numerical representations. Isn't that what tremon just said?
    - hansen 11y ago
      Maybe I haven’t understood him right, but he said: > […] physical properties, like c, h […] which is false, c and ℏ aren’t “physical properties”. The numerical values we attach to them are merely a convention. In SI units c isn’t even something that is measured. The second is defined via a measurement, c has a fixed defined value (no measurement involved), and the meter is defined via the second and c. In natural units this is even simpler: ℏ = c = 1. The fine structure constant is another thing. It caries no dimension and encodes the strength of EM coupling. But as an interesting site note: These coupling constant are pretty complicated things, they actually depend on the energy/length scale of your experiment. The numbers you find in text books are just the low energy limits.
      - tremon 11y ago
        Well, I did mean the physical properties behind the symbols, i.e. speed of light, energy quantum, gravitational constant. I understand that the numerical quantities we assign to those constants are arbitrary, but even though they're not dimensionless, the physical properties they represent are still considered constant, am I right?
        hansen 11y ago
        > the physical properties behind the symbols Maybe my interpretation is a bit mathematical and a physicist would disagree but I wouldn’t call the speed of light or the Planck constant a “physical property”. In case of the speed of light the actually geometric thing, that exists w/o resorting to some arbitrary choice of units, is causality. In the case of the Planck constant there are different equivalent properties that I would call “physical”, but it all boils down to representations of symmetries. The gravitational constant is more complicated and I’m not quite sure what to make of it. Setting it to 1 too means that we get rid of all units and we measure length in multiples of the Planck length. But so far there is no experimental evidence that the Planck unit is something special that could be interpreted as some purely geometric property. I wouldn’t call it something “physical” with what we know today.
        tremon 11y ago
        the actually geometric thing, that exists w/o resorting to some arbitrary choice of units, is causality I can agree with that in principle, but continuing in that line of reasoning: what remains is that the effects of an event ripple outward at a certain speed (ignoring quantum entanglement for a moment). It is my impression that c represents the upper limit of event propagation speed, and as such I would classify it a physical property. I'm a bit hazy about the exact physical implications of h-bar, but I thought it represented the absolute lower bound of energy quantization. Whether that is a real fundamental property or a consequence of underlying structure is yet to be determined, I believe.
        hansen 11y ago
  - xvedejas 11y ago
    That's true because these values have units attached to them. Look at the fine structure constant for a counterexample though -- it is a unitless ratio of measured values which is not quite exactly 137; this is true regardless of what units you use to measure it.

tremon 11y ago

I think the article is talking about physical properties, like c, h, or G, that we measure to be the same every time. You seem to be talking about numerical representations.

hansen 11y ago
c and ℏ don’t encode any physics, they just fix measuring units. Actually it’s common to choose units s.t. ℏ = c = 1.
- simonh 11y ago
  So the same constants can have different numerical representations. Isn't that what tremon just said?
  - hansen 11y ago
    Maybe I haven’t understood him right, but he said: > […] physical properties, like c, h […] which is false, c and ℏ aren’t “physical properties”. The numerical values we attach to them are merely a convention. In SI units c isn’t even something that is measured. The second is defined via a measurement, c has a fixed defined value (no measurement involved), and the meter is defined via the second and c. In natural units this is even simpler: ℏ = c = 1. The fine structure constant is another thing. It caries no dimension and encodes the strength of EM coupling. But as an interesting site note: These coupling constant are pretty complicated things, they actually depend on the energy/length scale of your experiment. The numbers you find in text books are just the low energy limits.
    - tremon 11y ago
      Well, I did mean the physical properties behind the symbols, i.e. speed of light, energy quantum, gravitational constant. I understand that the numerical quantities we assign to those constants are arbitrary, but even though they're not dimensionless, the physical properties they represent are still considered constant, am I right?
      - hansen 11y ago
        > the physical properties behind the symbols Maybe my interpretation is a bit mathematical and a physicist would disagree but I wouldn’t call the speed of light or the Planck constant a “physical property”. In case of the speed of light the actually geometric thing, that exists w/o resorting to some arbitrary choice of units, is causality. In the case of the Planck constant there are different equivalent properties that I would call “physical”, but it all boils down to representations of symmetries. The gravitational constant is more complicated and I’m not quite sure what to make of it. Setting it to 1 too means that we get rid of all units and we measure length in multiples of the Planck length. But so far there is no experimental evidence that the Planck unit is something special that could be interpreted as some purely geometric property. I wouldn’t call it something “physical” with what we know today.
        tremon 11y ago
        the actually geometric thing, that exists w/o resorting to some arbitrary choice of units, is causality I can agree with that in principle, but continuing in that line of reasoning: what remains is that the effects of an event ripple outward at a certain speed (ignoring quantum entanglement for a moment). It is my impression that c represents the upper limit of event propagation speed, and as such I would classify it a physical property. I'm a bit hazy about the exact physical implications of h-bar, but I thought it represented the absolute lower bound of energy quantization. Whether that is a real fundamental property or a consequence of underlying structure is yet to be determined, I believe.
        hansen 11y ago
- xvedejas 11y ago
  That's true because these values have units attached to them. Look at the fine structure constant for a counterexample though -- it is a unitless ratio of measured values which is not quite exactly 137; this is true regardless of what units you use to measure it.