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To compare the strength of e.g. the electromagnetic force and the gravitational force one should not simply compare the difference of strength for a specific particle, because there are too many (electron, proton, myon, etc.) and all these comparisons would yield a different number. Instead let's compare gravity and EM force using a scale given by fundamental constants. For gravity this means, we choose the gravitational force between two particles of Planck mass $m_P=\sqrt{\hbar c/G}$ and for the EM force we compute the force between two particles of Planck charge $q_P=\sqrt{4\pi\epsilon_0 \hbar c}$. If we compute the forces for these two cases respectively we get $$ F_g = G \frac{\hbar c/G}{r^2} = \frac{\hbar c}{r^2}\\ F_{EM} = \frac{1}{4\pi\epsilon_0} \frac{4\pi\epsilon_0 \hbar c }{r^2} = \frac{\hbar c}{r^2} $$ So we see the gravitational force and the electromagnetic force are actually of equal strength and range when they are compared at their natural scale.

In this sense gravity is not the weakest force. Instead the puzzle here can be rephrased to: Why is the mass of the known particles so low compared to the Planck mass, or why is the charge of the known particles so high compared to the Planck charge?

For example the ratio between planck mass and electron mass is $$ \frac{m_P}{m_e} = 2.389 \cdot 10^{22} $$ whereas the ratio between planck charge and the charge of the electron is $$ \frac{q_P}{q_e} = 11.706 $$ The ratio of these ratios is $2.040 \cdot 10^{21}$ and why this is such a high number is the real puzzle, and I don't know any theory which could explain this number.

It should be noted that the so called Mass-to-charge ratio for an electron is of order $10^{11}$, for a hypothetical particle with a Planck charge and a Planck mass it is accordingly of order $10^{-11}$ $$ \frac{q_e}{m_e} = 1.759 \cdot 10^{11} \frac{C}{kg} ,\ \frac{q_P}{m_P} = 8.617 \cdot 10^{-11} \frac{C}{kg} = \sqrt{\frac{4\pi\epsilon_0}{G}} $$ which I think is a quite remarkable "symmetry".

UPDATE: The numbers shown here might not be familiar. But I want to note that the fine-structure constant is $$ \alpha^{-1} = \left(\frac{q_P}{q_e}\right)^2 = 11.706^2 = 137.036 $$ and the gravitational fine structure constant is $$ \alpha_G^{-1} = \left(\frac{m_P}{m_e}\right)^2 = (2.389 \cdot 10^{22})^2 = 5.709 \cdot 10^{44} $$

To compare the strength of e.g. the electromagnetic force and the gravitational force one should not simply compare the difference of strength for a specific particle, because there are too many (electron, proton, myon, etc.) and all these comparisons would yield a different number. Instead let's compare gravity and EM force using a scale given by fundamental constants. For gravity this means, we choose the gravitational force between two particles of Planck mass $m_P=\sqrt{\hbar c/G}$ and for the EM force we compute the force between two particles of Planck charge $q_P=\sqrt{4\pi\epsilon_0 \hbar c}$. If we compute the forces for these two cases respectively we get $$ F_g = G \frac{\hbar c/G}{r^2} = \frac{\hbar c}{r^2}\\ F_{EM} = \frac{1}{4\pi\epsilon_0} \frac{4\pi\epsilon_0 \hbar c }{r^2} = \frac{\hbar c}{r^2} $$ So we see the gravitational force and the electromagnetic force are actually of equal strength and range when they are compared at their natural scale.

In this sense gravity is not the weakest force. Instead the puzzle here can be rephrased to: Why is the mass of the known particles so low compared to the Planck mass, or why is the charge of the known particles so high compared to the Planck charge?

For example the ratio between planck mass and electron mass (the proton mass should not be used for comparison, because a proton is not a point particle and it's mass is made complicated by effects of QCD) is $$ \frac{m_P}{m_e} = 2.389 \cdot 10^{22} $$ whereas the ratio between planck charge and the charge of the electron is $$ \frac{q_P}{q_e} = 11.706 $$ The ratio of these ratios is $2.040 \cdot 10^{21}$ and why this is such a high number is the real puzzle, and I don't know any theory which could explain this number.

It should be noted that the so called Mass-to-charge ratio for an electron is of order $10^{11}$, for a hypothetical particle with a Planck charge and a Planck mass it is accordingly of order $10^{-11}$ $$ \frac{q_e}{m_e} = 1.759 \cdot 10^{11} \frac{C}{kg} ,\ \frac{q_P}{m_P} = 8.617 \cdot 10^{-11} \frac{C}{kg} = \sqrt{\frac{4\pi\epsilon_0}{G}} $$ which I think is a quite remarkable "symmetry".

UPDATE: The numbers shown here might not be familiar. But I want to note that the fine-structure constant is $$ \alpha^{-1} = \left(\frac{q_P}{q_e}\right)^2 = 11.706^2 = 137.036 $$ and the gravitational fine structure constant is $$ \alpha_G^{-1} = \left(\frac{m_P}{m_e}\right)^2 = (2.389 \cdot 10^{22})^2 = 5.709 \cdot 10^{44} $$

To compare the strength of e.g. the electromagnetic force and the gravitational force one should not simply compare the difference of strength for a specific particle, because there are too many (electron, proton, myon, etc.) and all these comparisons would yield a different number. Instead let's compare gravity and EM force using a scale given by fundamental constants. For gravity this means, we choose the gravitational force between two particles of Planck mass $m_P=\sqrt{\hbar c/G}$ and for the EM force we compute the force between two particles of Planck charge $q_P=\sqrt{4\pi\epsilon_0 \hbar c}$. If we compute the forces for these two cases respectively we get $$ F_g = G \frac{\hbar c/G}{r^2} = \frac{\hbar c}{r^2}\\ F_{EM} = \frac{1}{4\pi\epsilon_0} \frac{4\pi\epsilon_0 \hbar c }{r^2} = \frac{\hbar c}{r^2} $$ So we see the gravitational force and the electromagnetic force are actually of equal strength and range when they are compared at their natural scale.

In this sense gravity is not the weakest force. Instead the puzzle here can be rephrased to: Why is the mass of the known particles so low compared to the Planck mass, or why is the charge of the known particles so high compared to the Planck charge?

For example the ratio between planck mass and electron mass is $$ \frac{m_P}{m_e} = 2.389 \cdot 10^{22} $$ whereas the ratio between planck charge and the charge of the electron is $$ \frac{q_P}{q_e} = 11.706 $$ The ratio of these ratios is $2.040 \cdot 10^{21}$ and why this is such a high number is the real puzzle, and I don't know any theory which could explain this number.

It should be noted that the so called Mass-to-charge ratio for an electron is of order $10^{11}$, for a hypothetical particle with a Planck charge and a Planck mass it is accordingly of order $10^{-11}$ $$ \frac{q_e}{m_e} = 1.759 \cdot 10^{11} \frac{C}{kg} ,\ \frac{q_P}{m_P} = 8.617 \cdot 10^{-11} \frac{C}{kg} = \sqrt{\frac{4\pi\epsilon_0}{G}} $$ which I think is a quite remarkable "symmetry".

To compare the strength of e.g. the electromagnetic force and the gravitational force one should not simply compare the difference of strength for a specific particle, because there are too many (electron, proton, myon, etc.) and all these comparisons would yield a different number. Instead let's compare gravity and EM force using a scale given by fundamental constants. For gravity this means, we choose the gravitational force between two particles of Planck mass $m_P=\sqrt{\hbar c/G}$ and for the EM force we compute the force between two particles of Planck charge $q_P=\sqrt{4\pi\epsilon_0 \hbar c}$. If we compute the forces for these two cases respectively we get $$ F_g = G \frac{\hbar c/G}{r^2} = \frac{\hbar c}{r^2}\\ F_{EM} = \frac{1}{4\pi\epsilon_0} \frac{4\pi\epsilon_0 \hbar c }{r^2} = \frac{\hbar c}{r^2} $$ So we see the gravitational force and the electromagnetic force are actually of equal strength and range when they are compared at their natural scale.

In this sense gravity is not the weakest force. Instead the puzzle here can be rephrased to: Why is the mass of the known particles so low compared to the Planck mass, or why is the charge of the known particles so high compared to the Planck charge?

For example the ratio between planck mass and electron mass is $$ \frac{m_P}{m_e} = 2.389 \cdot 10^{22} $$ whereas the ratio between planck charge and the charge of the electron is $$ \frac{q_P}{q_e} = 11.706 $$ The ratio of these ratios is $2.040 \cdot 10^{21}$ and why this is such a high number is the real puzzle, and I don't know any theory which could explain this number.

It should be noted that the so called Mass-to-charge ratio for an electron is of order $10^{11}$, for a hypothetical particle with a Planck charge and a Planck mass it is accordingly of order $10^{-11}$ $$ \frac{q_e}{m_e} = 1.759 \cdot 10^{11} \frac{C}{kg} ,\ \frac{q_P}{m_P} = 8.617 \cdot 10^{-11} \frac{C}{kg} = \sqrt{\frac{4\pi\epsilon_0}{G}} $$ which I think is a quite remarkable "symmetry".

UPDATE: The numbers shown here might not be familiar. But I want to note that the fine-structure constant is $$ \alpha^{-1} = \left(\frac{q_P}{q_e}\right)^2 = 11.706^2 = 137.036 $$ and the gravitational fine structure constant is $$ \alpha_G^{-1} = \left(\frac{m_P}{m_e}\right)^2 = (2.389 \cdot 10^{22})^2 = 5.709 \cdot 10^{44} $$

To compare the strength of e.g. the electromagnetic force and the gravitational force one should not simply compare the difference of strength for a specific particle, because there are too many (electron, proton, myon, etc.) and all these comparisons would yield a different number. Instead let's compare gravity and EM force using a scale given by fundamental constants. For gravity this means, we choose the gravitational force between two particles of Planck mass $m_P=\sqrt{\hbar c/G}$ and for the EM force we compute the force between two particles of Planck charge $q_P=\sqrt{4\pi\epsilon_0 \hbar c}$. If we compute the forces for these two cases respectively we get $$ F_g = G \frac{\hbar c/G}{r^2} = \frac{\hbar c}{r^2}\\ F_{EM} = \frac{1}{4\pi\epsilon_0} \frac{4\pi\epsilon_0 \hbar c }{r^2} = \frac{\hbar c}{r^2} $$ So we see the gravitational force and the electromagnetic force are actually of equal strength and range when they are compared at their natural scale.

In this sense gravity is not the weakest force. Instead the puzzle here can be rephrased to: Why is the mass of the known particles so low compared to the Planck mass, or why is the charge of the known particles so high compared to the Planck charge?

For example the ratio between planck mass and electron mass is $$ \frac{m_P}{m_e} = 2.389 \cdot 10^{22} $$ whereas the ratio between planck charge and the charge of the electron is $$ \frac{q_P}{q_e} = 11.706 $$ The ratio of these ratios is $2.040 \cdot 10^{21}$ and why this is such a high number is the real puzzle, and I don't know any theory which could explain this number.

It should be noted however that the so called Mass-to-charge ratio for an electron is of the same order of magnitude than for a hypothetical particle with a Planck charge and a Planck mass. $$ \frac{q_e}{m_e} = 1.759 \cdot 10^{11} \frac{C}{kg} ,\ \frac{q_P}{m_P} = 8.617 \cdot 10^{11} \frac{C}{kg} = \sqrt{\frac{4\pi\epsilon_0}{G}} $$ which I think is quite a remarkable coincidence.

To compare the strength of e.g. the electromagnetic force and the gravitational force one should not simply compare the difference of strength for a specific particle, because there are too many (electron, proton, myon, etc.) and all these comparisons would yield a different number. Instead let's compare gravity and EM force using a scale given by fundamental constants. For gravity this means, we choose the gravitational force between two particles of Planck mass $m_P=\sqrt{\hbar c/G}$ and for the EM force we compute the force between two particles of Planck charge $q_P=\sqrt{4\pi\epsilon_0 \hbar c}$. If we compute the forces for these two cases respectively we get $$ F_g = G \frac{\hbar c/G}{r^2} = \frac{\hbar c}{r^2}\\ F_{EM} = \frac{1}{4\pi\epsilon_0} \frac{4\pi\epsilon_0 \hbar c }{r^2} = \frac{\hbar c}{r^2} $$ So we see the gravitational force and the electromagnetic force are actually of equal strength and range when they are compared at their natural scale.

In this sense gravity is not the weakest force. Instead the puzzle here can be rephrased to: Why is the mass of the known particles so low compared to the Planck mass, or why is the charge of the known particles so high compared to the Planck charge?

For example the ratio between planck mass and electron mass is $$ \frac{m_P}{m_e} = 2.389 \cdot 10^{22} $$ whereas the ratio between planck charge and the charge of the electron is $$ \frac{q_P}{q_e} = 11.706 $$ The ratio of these ratios is $2.040 \cdot 10^{21}$ and why this is such a high number is the real puzzle, and I don't know any theory which could explain this number.

It should be noted that the so called Mass-to-charge ratio for an electron is of order $10^{11}$, for a hypothetical particle with a Planck charge and a Planck mass it is accordingly of order $10^{-11}$ $$ \frac{q_e}{m_e} = 1.759 \cdot 10^{11} \frac{C}{kg} ,\ \frac{q_P}{m_P} = 8.617 \cdot 10^{-11} \frac{C}{kg} = \sqrt{\frac{4\pi\epsilon_0}{G}} $$ which I think is a quite remarkable "symmetry".