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> Nature and the universe is all about continuous quantities One could argue that nature always deals in discrete quantities and we have models that accurately

> Nature and the universe is all about continuous quantities One could argue that nature always deals in discrete quantities and we have models that accurately predict these quantities. Then we use math that humans clearly created (limits) to produce similar models, except they imagine continuous inputs.

adrian_b 1y ago
The quantity of matter and the quantity of electricity are discrete, but work, time and space are continuous, like also any quantities derived from them. There have been attempts to create discrete models of time and space, but nothing useful has resulted from those attempts. Most quantities encountered in nature include some dependency on work/energy, time or space, so nature deals mostly in continuous quantities, or more precisely the models that we can use to predict what happens in nature are still based mostly on continuous quantities, despite the fact that about a century and a half have passed since the discreteness of matter and electricity has been confirmed.
- gpm 1y ago
  > but work, time and space are continuous I'm under the impression that all our theories of time and space (and thus work) break down at the scale of 1 plank unit and smaller. Which isn't proof that they aren't continuous, but I don't see how you could assert that they are either.
  - dhosek 1y ago
    Matter and energy are discrete. The continuity or discreteness of time and space are unknown. There are arguments for both cases, but nobody really knows for sure. It’s fairly easy to go from integers to many subsets of the reals (rationals are straightforward, constructible numbers not too hard, algebraic numbers more of a challenge), but the idea that the reals are, well real, depends on a continuity of spacetime that we can’t prove exists.
    - adrian_b 1y ago
      Energy is continuous, not discrete. Because energy is action per time, it inherits the continuity of time. Action is also continuous, though its nature is much less well understood. (Many people make confusions between action and angular momentum, speaking about a "quantum of action". There is no such thing as a quantum of action, because action is a quantity that increases monotonically in time for any physical system, so it cannot have constant values, much less quantized values. Angular momentum, which is the ratio of action per phase in a rotation motion, is frequently a constant quantity and a quantized quantity. In more than 99% of the cases when people write Planck's constant, they mean an angular momentum, but there are also a few cases when people write Planck's constant meaning an action, typically in relation with some magnetic fluxes, e.g. in the formula of the magnetic flux quantum.) Perhaps when you said that energy is discrete you thought about light being discrete, but light is not energy. Energy is a property of light, like also momentum, frequency, wavenumber and others. Moreover, the nature of the photon is still debated. Some people are not convinced yet that light travels in discrete packets, instead of the alternative where only the exchange of energy and momentum between light and electrons or other leptons and quarks is quantized. There are certain stationary systems, like isolated atoms or molecules, which may have a discrete set of states, where each state has a certain energy. Unlike for a discrete quantity like the electric charge, such sets of energy values can contain arbitrary values of energy and between the sets of different systems there are no rational relationships between the energy values. Moreover, all such systems have not only discrete energy values but also continuous intervals of possible energies, usually towards higher energies, e.g. corresponding to high temperatures or to the ionization of atoms or molecules.
      - deleted 1y ago
        [deleted]
  - adrian_b 1y ago
    The Planck units are bogus units that do not have any significance. Perhaps our theories of time and space would break down at some extremely small scale, but for now there is no evidence about this and nobody has any idea which that scale may be. In the 19th century, both George Johnstone Stoney and Max Planck have made the same mistake. Each of them has computed for the first time some universal constants, Stoney has computed the elementary electric charge in 1874 and Planck has computed the 2 constants that are now named "Boltzmann's constant" and "Planck's constant", in several variants, in 1899, 1900 and 1901. (Ludwig Boltzmann had predicted the existence of the constant that bears his name, but he never used it for anything and he did not compute its value.) Both of them have realized that new universal constants allow the use of additional natural units in the system of fundamental units of measurement and they have attempted to exploit their findings for this purpose. However both have bet on the wrong horse. Before them, James Clerk Maxwell had proposed two alternatives for choosing a good unit of mass. The first was to choose as the unit of mass the mass of some molecule. The second was to give an exact value to the Newtonian constant of gravity. The first Maxwell proposal was good and when analyzed at the revision of SI from 2018 it was only very slightly worse than the final choice (which preferred to use two properties of the photons, instead of choosing an arbitrary molecule besides using one property of the photons). The second Maxwell proposal was extremely bad, though to be fair it was difficult for Maxwell to predict that during the next century the precision of measuring many quantities will increase by many orders of magnitude, while the precision of measuring the Newtonian constant of gravity will be improved only barely, in comparison with the others. Both Stoney and Planck have chosen to base their proposals for systems of fundamental units on the second Maxwell variant, and this mistake made their systems completely impractical. The value of Newton's constant has a huge uncertainty in comparison with the other universal constants. Declaring its value as exact does not make that uncertainty disappear, but it moves the uncertainty into the values of almost all other physical quantities. The consequence is that if using the systems of fundamental units of George Johnstone Stoney or of Max Planck, almost no absolute value of any quantity can be known accurately. Only the ratios between two quantities of the same kind and the velocities can be known accurately. Thus the Max Planck system of units is a historical curiosity that is irrelevant for practice. The right way to use Planck's constant in a system of units has become possible only 60 years later, when the Josephson effect was predicted in 1962, and SI has been modified to use it only after other 60 years, in 2019. The units of measurement that are chosen to be fundamental do not matter in any way upon the validity of physical laws at different scales. Even if the Planck units were practical, that would give no information about the structure of space and time. The definition of the Planck units is based on continuous models for time, space and forces. Every now and then there are texts in the popular literature that mention the Planck units as they would have some special meaning. All such texts are based on hearsay, repeating affirmations from sources who have no idea about how the Planck units have been defined in 1899 and about how systems of fundamental units of measurement are defined and what they mean. Apparently the only reason why the Planck units have been picked for this purpose is that in this system the unit of length happens to be much smaller than an atom or than its nucleus, so people imagine that if the current model of space breaks at some scale, that scale might be this small.
  - deleted 1y ago
    [deleted]
- dudinax 1y ago
  We do not know whether work time and space are continuous
  - adrian_b 1y ago
    What we know is that we use mathematical models based on the continuity of work, time and space (and on the discreteness of matter and electricity) and until now we have not seen any experiment where a discrepancy between predicted and measured values could be attributed to the falseness of the supposition that work, time and space are continuous. Obviously this does not exclude the possibility that in the future some experiments where much higher energies per particle are used, allowing the testing of what happens at much smaller distances, might show evidence that there exists a discrete structure of time and space, like we know for matter. However, that has not happened yet and there are no reasons to believe that it will happen soon. The theory about the existence of atoms is more than 2 millennia old, then it has been abandoned for lack of evidence, then it was revived at the beginning of the 19th century, due to accumulated evidence from chemistry, and it was eventually confirmed beyond doubt in 1865, when Johann Josef Loschmidt became the first who could count atoms and molecules, after determining their masses. So the discreteness of matter had a very long history of accumulating evidence in favor of it. Nothing similar applies to the discreteness of time and space, for which there has never been any kind of evidence. The only reason of the speculations about this is the analogy made with the fact that matter and electricity had been believed to be continuous, but eventually it has been discovered that they are discrete. Such an analogy must make us keep an open mind about the possibility of work, time and space being discrete, but we should not waste time speculating about this when there are huge problems in physics that do not have a solution yet. In modern physics there are a huge amount of quantities that should be computable by theory, but in fact they cannot be computed and they must be measured experimentally. Therefore the existing theories are clearly not good enough.
    - AIorNot 1y ago
      Umm SpaceTime is likely NOT to be fundamental or continuous https://youtu.be/GL77oOnrPzY?si=nllkY_E8WotARwUM https://youtu.be/GL77oOnrPzY?si=nllkY_E8WotARwUM Also Bells Therom implies no locality or non realism which to me furthers the nail on the coffin of spacetime

adrian_b 1y ago

The quantity of matter and the quantity of electricity are discrete, but work, time and space are continuous, like also any quantities derived from them. There have been attempts to create discrete models of time and space, but nothing useful has resulted from those attempts. Most quantities encountered in nature include some dependency on work/energy, time or space, so nature deals mostly in continuous quantities, or more precisely the models that we can use to predict what happens in nature are still based mostly on continuous quantities, despite the fact that about a century and a half have passed since the discreteness of matter and electricity has been confirmed.

gpm 1y ago
> but work, time and space are continuous I'm under the impression that all our theories of time and space (and thus work) break down at the scale of 1 plank unit and smaller. Which isn't proof that they aren't continuous, but I don't see how you could assert that they are either.
- dhosek 1y ago
  Matter and energy are discrete. The continuity or discreteness of time and space are unknown. There are arguments for both cases, but nobody really knows for sure. It’s fairly easy to go from integers to many subsets of the reals (rationals are straightforward, constructible numbers not too hard, algebraic numbers more of a challenge), but the idea that the reals are, well real, depends on a continuity of spacetime that we can’t prove exists.
  - adrian_b 1y ago
    Energy is continuous, not discrete. Because energy is action per time, it inherits the continuity of time. Action is also continuous, though its nature is much less well understood. (Many people make confusions between action and angular momentum, speaking about a "quantum of action". There is no such thing as a quantum of action, because action is a quantity that increases monotonically in time for any physical system, so it cannot have constant values, much less quantized values. Angular momentum, which is the ratio of action per phase in a rotation motion, is frequently a constant quantity and a quantized quantity. In more than 99% of the cases when people write Planck's constant, they mean an angular momentum, but there are also a few cases when people write Planck's constant meaning an action, typically in relation with some magnetic fluxes, e.g. in the formula of the magnetic flux quantum.) Perhaps when you said that energy is discrete you thought about light being discrete, but light is not energy. Energy is a property of light, like also momentum, frequency, wavenumber and others. Moreover, the nature of the photon is still debated. Some people are not convinced yet that light travels in discrete packets, instead of the alternative where only the exchange of energy and momentum between light and electrons or other leptons and quarks is quantized. There are certain stationary systems, like isolated atoms or molecules, which may have a discrete set of states, where each state has a certain energy. Unlike for a discrete quantity like the electric charge, such sets of energy values can contain arbitrary values of energy and between the sets of different systems there are no rational relationships between the energy values. Moreover, all such systems have not only discrete energy values but also continuous intervals of possible energies, usually towards higher energies, e.g. corresponding to high temperatures or to the ionization of atoms or molecules.
    - deleted 1y ago
      [deleted]
- adrian_b 1y ago
  The Planck units are bogus units that do not have any significance. Perhaps our theories of time and space would break down at some extremely small scale, but for now there is no evidence about this and nobody has any idea which that scale may be. In the 19th century, both George Johnstone Stoney and Max Planck have made the same mistake. Each of them has computed for the first time some universal constants, Stoney has computed the elementary electric charge in 1874 and Planck has computed the 2 constants that are now named "Boltzmann's constant" and "Planck's constant", in several variants, in 1899, 1900 and 1901. (Ludwig Boltzmann had predicted the existence of the constant that bears his name, but he never used it for anything and he did not compute its value.) Both of them have realized that new universal constants allow the use of additional natural units in the system of fundamental units of measurement and they have attempted to exploit their findings for this purpose. However both have bet on the wrong horse. Before them, James Clerk Maxwell had proposed two alternatives for choosing a good unit of mass. The first was to choose as the unit of mass the mass of some molecule. The second was to give an exact value to the Newtonian constant of gravity. The first Maxwell proposal was good and when analyzed at the revision of SI from 2018 it was only very slightly worse than the final choice (which preferred to use two properties of the photons, instead of choosing an arbitrary molecule besides using one property of the photons). The second Maxwell proposal was extremely bad, though to be fair it was difficult for Maxwell to predict that during the next century the precision of measuring many quantities will increase by many orders of magnitude, while the precision of measuring the Newtonian constant of gravity will be improved only barely, in comparison with the others. Both Stoney and Planck have chosen to base their proposals for systems of fundamental units on the second Maxwell variant, and this mistake made their systems completely impractical. The value of Newton's constant has a huge uncertainty in comparison with the other universal constants. Declaring its value as exact does not make that uncertainty disappear, but it moves the uncertainty into the values of almost all other physical quantities. The consequence is that if using the systems of fundamental units of George Johnstone Stoney or of Max Planck, almost no absolute value of any quantity can be known accurately. Only the ratios between two quantities of the same kind and the velocities can be known accurately. Thus the Max Planck system of units is a historical curiosity that is irrelevant for practice. The right way to use Planck's constant in a system of units has become possible only 60 years later, when the Josephson effect was predicted in 1962, and SI has been modified to use it only after other 60 years, in 2019. The units of measurement that are chosen to be fundamental do not matter in any way upon the validity of physical laws at different scales. Even if the Planck units were practical, that would give no information about the structure of space and time. The definition of the Planck units is based on continuous models for time, space and forces. Every now and then there are texts in the popular literature that mention the Planck units as they would have some special meaning. All such texts are based on hearsay, repeating affirmations from sources who have no idea about how the Planck units have been defined in 1899 and about how systems of fundamental units of measurement are defined and what they mean. Apparently the only reason why the Planck units have been picked for this purpose is that in this system the unit of length happens to be much smaller than an atom or than its nucleus, so people imagine that if the current model of space breaks at some scale, that scale might be this small.
- deleted 1y ago
  [deleted]
dudinax 1y ago
We do not know whether work time and space are continuous
- adrian_b 1y ago
  What we know is that we use mathematical models based on the continuity of work, time and space (and on the discreteness of matter and electricity) and until now we have not seen any experiment where a discrepancy between predicted and measured values could be attributed to the falseness of the supposition that work, time and space are continuous. Obviously this does not exclude the possibility that in the future some experiments where much higher energies per particle are used, allowing the testing of what happens at much smaller distances, might show evidence that there exists a discrete structure of time and space, like we know for matter. However, that has not happened yet and there are no reasons to believe that it will happen soon. The theory about the existence of atoms is more than 2 millennia old, then it has been abandoned for lack of evidence, then it was revived at the beginning of the 19th century, due to accumulated evidence from chemistry, and it was eventually confirmed beyond doubt in 1865, when Johann Josef Loschmidt became the first who could count atoms and molecules, after determining their masses. So the discreteness of matter had a very long history of accumulating evidence in favor of it. Nothing similar applies to the discreteness of time and space, for which there has never been any kind of evidence. The only reason of the speculations about this is the analogy made with the fact that matter and electricity had been believed to be continuous, but eventually it has been discovered that they are discrete. Such an analogy must make us keep an open mind about the possibility of work, time and space being discrete, but we should not waste time speculating about this when there are huge problems in physics that do not have a solution yet. In modern physics there are a huge amount of quantities that should be computable by theory, but in fact they cannot be computed and they must be measured experimentally. Therefore the existing theories are clearly not good enough.
  - AIorNot 1y ago
    Umm SpaceTime is likely NOT to be fundamental or continuous https://youtu.be/GL77oOnrPzY?si=nllkY_E8WotARwUM https://youtu.be/GL77oOnrPzY?si=nllkY_E8WotARwUM Also Bells Therom implies no locality or non realism which to me furthers the nail on the coffin of spacetime