Hi folks,
As you know ,there are four fundamental known forces (and... recently they are talking about the 5th one),
gravitational, electromagnetic, strong nuclear, weak nuclear and ???
so,I googled about electromagnetic force and found a useful table called "electromagnetic frequency spectrum":

And there was lots of amazing formulas,functions and devices in any range of frequency for this known FORCE.
so,the main questions is ....
"Is there any possible table for 3 other known forces ,in order to categorize them over frequncy spectrum?"

 

Hi folks,
As you know ,there are four fundamental known forces (and... recently they are talking about the 5th one),
gravitational, electromagnetic, strong nuclear, weak nuclear and ???
so,I googled about electromagnetic force and found a useful table called "electromagnetic frequency spectrum":

And there was lots of amazing formulas,functions and devices in any range of frequency for this known FORCE.
so,the main questions is ....
"Is there any possible table for 3 other known forces ,in order to categorize them over frequncy spectrum?"

Not that I know of. I'm not sure that frequency is even a relevant concept in terms of the other forces. What I can tell you is that there are actual particles that mediate the strong force (gluons) and the weak force (W and Z bosons). I've heard of gravitational waves but I'm not aware of a particle associated with gravity.

https://en.wikipedia.org/wiki/Gravitational_wave
A quote from the article:
In principle, gravitational waves could exist at any frequency. However, very low frequency waves would be impossible to detect and there is no credible source for detectable waves of very high frequency. Stephen Hawking and Werner Israel list different frequency bands for gravitational waves that could plausibly be detected, ranging from 10^−7 Hz up to 10^11 Hz.[23]

Apparently there is a hypothetical particle called a graviton.
https://en.wikipedia.org/wiki/Graviton

 

You might have found a site about a phenomenon called "Wave / Particle Duality" which describes the force exerted by the momentum of a photon (commonly known as one wave length of a given frequency of light). The momentum of a photon increases with increasing frequency of the light wave in accordance with the formula P = Planck's Constant / Wave Length.

 

thanks for useful replies,
This is all of my thought about this subject by considering your answers,

I think, if all of the 4 kinds of force are independent from each other,they must have independent behaviour over frequency spectrum,
so,if one day we could find out any coherence between these spectrums,it may have proved the possible theories like "unity of forces" somehow.

As an assumption,Frequency is a the most important and independent feature of both mass and energy that makes them show various properties and distinguished behaviours,
indeed, it descibes how compact/densed is packet of energy (or even mass).
as for matter,it could be even equivalent to "Density",as we have 4 forms of solid,liquid,gas,plasma depends on frequency of their molcule's fluctuation or so called "density".as the higher fluctuating matters have the lower density.
other parameters like energy,momentum,etc colud be a subsequent measurements of the frequency parameter.
even in social relations we say : people have the same wavelength (frequency),that means they have the same personalities .

BTW that the quantum theories imply that there are independent quantum features along with frequency in mass/energy world,that should be considered and described in models and calculations.

well,It's pleasured to know any about wrong or right part of my thought.
thanks

 

A while back I was doing some amateur research into the whole thing and just happen to stumble upon the fact that the Planck charge seems to be precisely equal to the square root of Plank mass times Planck length (taking into account a certain scaling factor that is).

From there I was able to come up with a plausible generic (point-like) equation for all of the possible forces. F(0) and F(1) describe the electromagnetic and gravitational forces, respectively. F(2) produces an equation that requires three "particles" (quarks?) so I'm assuming that's the strong nuclear force (hard to test since the exact equation for that force is not currently known). I didn't look at any higher dimensional forces but now that scientists are looking at new candidate (the so-called X17 particle) whose strength has actually been measured, I just might dive back into it.

As for the weak nuclear force, I don't really agree that it should be called an actual force per se. More like a complex interaction of forces governed by the probabilities of stochastic processes.

Anyway, if I am actually on the right track then that would seem to imply that all of the forces of nature issue are intrinsically connected.

Just a theory of course.

 

I think, if all of the 4 kinds of force are independent from each other,they must have independent behaviour over frequency spectrum,
so,if one day we could find out any coherence between these spectrums,it may have proved the possible theories like "unity of forces" somehow.

First, consider that 'force' -- in the context of fundamental physics -- is an old-fashioned notion. Modern physicists describe the universe in terms of mathematical fields, with equations of motion that characterize how these fields interact with each other, if at all. As of now, physicists know these characterizations to be effective field theories, valid only in certain regimes and energy scales. All the big, fundamental theories you've heard of, such as general relativity and the standard model, are effective field theories. There are enormous, domain-specific challenges to unifying these theories, and it is entirely possible that we never manage to do it.

Second, consider that frequency is simply the reciprocal of time: any phenomenon that can be quantified in time can be equivalently quantified in frequency. And while it's true that sometimes we, as humans, gain insight by transforming a problem from one domain to another, rest assured that physicists have been well-aware of this trick for hundreds of years. Indeed, they've gone much further. Emmy Noether showed us that conservation of energy is the result of time invariance (or, more succinctly, energy is the charge of time), and so physicists talk about the ultra-violet (high frequency/small wavelength) regime for high-energy physics, and the infrared (low frequency, long wavelength) regime for the low-energy physics of typical human scales.

In short, countless numbers of really smart people have dedicated their lives to the quest of trying to unify everything that we know about physics. You are most welcome to join their ranks, though you should, at minimum, try to learn what they've had to say about the issue. I'm not saying this applies to you, but there is a romantic idea that a non-expert, armed only with cleverness and "out of the box" thinking, can revolutionize physics. This is a farce, with literally zero chance of occurring. Anyone who wants to revolutionize physics will, necessarily, have to learn physics first.

 

A while back I was doing some amateur research into the whole thing and just happen to stumble upon the fact that the Planck charge seems to be precisely equal to the square root of Plank mass times Planck length (taking into account a certain scaling factor that is).

Rather than representing a fundamental insight, I'd say this is just a consequence of how Planck units are constructed. In other words, if you build a system of units from a set of physical constants, each of which has its own base dimension (i.e., length, mass, time, charge), then it's tautological -- an algebraic fact -- that the units can be expressed in terms of each other.

 

As an assumption,Frequency is a the most important and independent feature of both mass and energy that makes them show various properties and distinguished behaviours,

Quite an assumption, considering that neither mass nor energy has a frequency.

Nor does force. (What is the frequency the gravitational force that keeps you on the surface of the earth?)

Frequency is a property of repeating change in a quantity. It is not fundsmental.

Bob

 

What is the frequency the gravitational force that keeps you on the surface of the earth?

Maybe, but when I hear about newly detected gravitational "waves" I immediately think of frequency. Furthermore, if I understand even remotely, which I don't, supposedly "string theory" states something like everything is a vibrating string. (Again this leads to frequency.) Last I heard string theory isn't proven or even can't be, but still when I hear vibration I think frequency. But this is probably my complete lack of comprehension of the related subjects.

 

Rather than representing a fundamental insight, I'd say this is just a consequence of how Planck units are constructed. In other words, if you build a system of units from a set of physical constants, each of which has its own base dimension (i.e., length, mass, time, charge), then it's tautological -- an algebraic fact -- that the units can be expressed in terms of each other.

Right but the way things are currently formulated, the electric field is described in terms of charge, length, and time, whereas gravity by mass, length, and time. No one as far as I know has ever claimed that either mass or charge is fundamental - but not both. I chose the former, given that when looking at K^2 = ML vs. M = K^2L^(-1) it seems most likely that mass (M) is fundamental and charge (K) is not. In support of this, pretty much every single equation I've ever seen involving the Planck charge utilizes not K but K^2!

Looking at things from that perspective allowed me to create a derivation that just magically spit out what appears to be the quark field. Again, there is no way to verify that until all of the parameters of the strong force are actually nailed down by the scientific community (which is precisely why I abandoned that little area of study at the time). So until then I guess I'll just have to sit back and wonder...

 

Right but the way things are currently formulated, the electric field is described in terms of charge, length, and time, whereas gravity by mass, length, and time. No one as far as I know has ever claimed that either mass or charge is fundamental - but not both.

Both (rest) mass and (electric) charge are fundamental physical properties. We know this because they're invariant: their values stay the same in all reference frames. That is the physical perspective. In the context of units, however, we're free to define things in terms of other things. For example, we can think of the physical constant c (the vacuum speed of light) as the conversion factor between length and time, and thus define time in terms of length. In this way, we can say that one second is equal to 300 million meters of time. This is precisely what physicists do when they use dimensionless units such as c = 1, which only works out if you've defined time in terms of length (or vice versa).

Using physical constants, you can play this game with any of the "fundamental" dimensions. Planck units are just one possible choice that happens to be convenient for certain types of physicists.

Looking at things from that perspective allowed me to create a derivation that just magically spit out what appears to be the quark field.

Do you mean the gluon field? Interestingly, the quark model was actually developed by considering pure mathematics, specifically the eight representations of rotations in a particular group (SU(3)), which Murray Gell-Mann called the "eightfold-way".

 

Both (rest) mass and (electric) charge are fundamental physical properties. We know this because they're invariant: their values stay the same in all reference frames. That is the physical perspective. In the context of units, however, we're free to define things in terms of other things. For example, we can think of the physical constant c (the vacuum speed of light) as the conversion factor between length and time, and thus define time in terms of length. In this way, we can say that one second is equal to 300 million meters of time. This is precisely what physicists do when they use dimensionless units such as c = 1, which only works out if you've defined time in terms of length (or vice versa).

Using physical constants, you can play this game with any of the "fundamental" dimensions. Planck units are just one possible choice that happens to be convenient for certain types of physicists.

You've missed the point. Just try to describe gravity in terms of charge and electric potential in terms of mass. You can't! Because each supposedly contains a "dimension" that the other doesn't. Unless, that is, we can in fact define one of those dimensions in terms of the others. Eliminate and simplify and you get a very curious set of equations.

Do you mean the gluon field? Interestingly, the quark model was actually developed by considering pure mathematics, specifically the eight representations of rotations in a particular group (SU(3)), which Murray Gell-Mann called the "eightfold-way".

Interesting! See, even the symmetry groups seem to support my theory. SU(1) = F(0) = electric, SU(2) = F(1) = gravity, and SU(3) = F(2) = strong force.

 

well,all of your comments pointed respectful and useful facts/informations for me,especially about string theory.
IMO ,when we have stucked between many unapproved puzzling assumptions,the best way is using "induction".
so,maybe my thought ,as an induction was to say , if changing frequency is giving different behaviour and personality to electromagnetic domain,It could be have the same effect to other independent domains( if it is to be).and we can consider it as an important and independent feature for these domains.besides we know that many concepts in mass/energy world have their own intrinsic resonant frequency that is their nature,not manipulated.
I think ,all the thing is happening in nowadays modern physic labs, is the same process,that is finding " Independent" reactions features and behaviours during mass to energy conversions (or vice versa) to find new particles or forms of energy.
And ...by not mixing up the definitions of " Invariancy" vs "Independency" and... other screwy concepts .
thanks

 

You've missed the point. Just try to describe gravity in terms of charge and electric potential in terms of mass. You can't! Because each supposedly contains a "dimension" that the other doesn't. Unless, that is, we can in fact define one of those dimensions in terms of the others. Eliminate and simplify and you get a very curious set of equations.

But that was precisely my point: using physical constants, we can define the "fundamental" dimensions in terms of each other. In SI units, electric charge is a base dimension, but in other units it's not (i.e., it's defined in terms of mass, length, time). How we "dimension things" is a matter of convention and convenience. Trying to find fundamental insights by manipulating Planck units is akin to choosing the base-10 number system and marveling that 1/3 has an infinite decimal expansion. The things that fall out of Planck units (or number representations) are quirks of the chosen units (or number representations), not fundamental aspect of physics (or numbers).

Interesting! See, even the symmetry groups seem to support my theory. SU(1) = F(0) = electric, SU(2) = F(1) = gravity, and SU(3) = F(2) = strong force.

As I understand it, the symmetries of electromagnetism are the representations of U(1) (rotations and reflections), not SU(1) (just rotations). Perhaps that was a typo, as indeed the symmetries of electroweak interactions are the representations of SU(2), and strong interactions are the representations of SU(3). Thus, the standard model is the gauge group \( U(1) \times SU(2) \times SU(3) \). I don't know nearly enough differential geometry to understand the symmetry group of GR, but I'm fairly certain you can't squeeze the isometries of GR (with respect to a continuously-variable metric) in SU(2). Even still, I'm genuinely curious how you derived \( U(1) \times SU(2) \times SU(3) \) solely by manipulating Planck units.

 

But that was precisely my point: using physical constants, we can define the "fundamental" dimensions in terms of each other. In SI units, electric charge is a base dimension, but in other units it's not (i.e., it's defined in terms of mass, length, time). How we "dimension things" is a matter of convention and convenience. Trying to find fundamental insights by manipulating Planck units is akin to choosing the base-10 number system and marveling that 1/3 has an infinite decimal expansion. The things that fall out of Planck units (or number representations) are quirks of the chosen units (or number representations), not fundamental aspect of physics (or numbers).

I know what you're saying. Like V=IR, I=V/R, R=V/I. But aren't charge and mass incompatible dimensions? I've personally never seen them expressed together in one equation anyway.

As I understand it, the symmetries of electromagnetism are the representations of U(1) (rotations and reflections), not SU(1) (just rotations). Perhaps that was a typo, as indeed the symmetries of electroweak interactions are the representations of SU(2), and strong interactions are the representations of SU(3). Thus, the standard model is the gauge group \( U(1) \times SU(2) \times SU(3) \). I don't know nearly enough differential geometry to understand the symmetry group of GR, but I'm fairly certain you can't squeeze the isometries of GR (with respect to a continuously-variable metric) in SU(2).

You're right I was totally confused about that. It's so strange how symmetry groups govern that aspect of physics. Almost seems like black magic!

Even still, I'm genuinely curious how you derived \( U(1) \times SU(2) \times SU(3) \) solely by manipulating Planck units.

Obliged. You could probably make better sense of it than I've been able to. I'll post back later once I've rounded everything up.

 

I know what you're saying. Like V=IR, I=V/R, R=V/I. But aren't charge and mass incompatible dimensions? I've personally never seen them expressed together in one equation anyway.

It's even more "symbolic" than rearranging the terms in Ohm's law. The physical quantities that we associate with charge and mass are fundamental properties, i.e., they're physically distinct aspects of matter and so -- as properties -- cannot be defined in terms of each other. But consider what happens when we ascribe these properties with units, such as when we take a measurement: we're actually describing the thing in terms of something else; it's an abstraction.

Every measurement is relative to some reference, the choice of which fixes the base unit. Typically, we choose a reference that has the same "natural dimensions", like length, as the thing being measured and we don't give it much thought. (In fact, we do this so often that it's easy to forget that units are an abstraction, not the thing itself, much like we forget that the numeral '5' is not the number five.) But units are arbitrary -- we can always change them and still be talking about the same thing -- and they fix a scale, which can be inconvenient in different contexts (we don't use miles to describe font sizes).

Because they are abstractions, our units don't have to have the same "natural dimension" as the thing we're describing. We still need a reference, however, and the universe provides a bunch of these in the form of physical constants, like the vacuum speed of light and the gravitational constant. These are handy for unit-making because as physical constants, they're universal -- i.e., they're not an arbitrary human choice -- and the "natural dimensions" of these constants span the gamut. By picking a physical constant with suitable dimensions, we can create "unnaturaly dimensioned" units with nothing more than algebraic manipulation.

For example, c is the physical constant that we associate with the vacuum speed of light. As a speed, it has "natural dimensions" of length per time. In SI units, it's approximately 300E6 meters per second. Now, if you're a physicist that deals with a bunch of equations that each have multiple factors of c, it's convenient to use units for which c is just a dimensionless value of 1. To do that, we have to "re-dimension" time as a distance (or vice-versa):
\[ c = 300 \times 10^6 \; \frac{\text{m}}{\text{s}} = 1 \qquad \Rightarrow \qquad 1 \text{ s} = 300 \times 10^6 \text{ m} \]
And while it seems weird to express a time in terms of a distance, that is precisely what we do with the light-year. (The reciprocal notion -- expressing a distance in terms of time -- is common, too, as in: "My house is 5 minutes from the gas station.")

The short of it is that by leveraging physical constants as conversion factors we can express our units in terms of pretty much anything we want. In the particular case of Planck units, they've used five physical constants as conversion factors, including both the gravitational and Coulomb constants, so it's not at all surprising that charge and mass algebraically fall out of any equations expressed in Planck units.

You're right I was totally confused about that. It's so strange how symmetry groups govern that aspect of physics. Almost seems like black magic!

Indeed! Symmetries (in both math and physics) represent invariants, aspects that don't change under certain transformations. I can't tell if the connection between math and physics is deeply profound or tautologically trivial, although if it's the latter, that in itself may be a deeply profound fact.

Obliged. You could probably make better sense of it than I've been able to. I'll post back later once I've rounded everything up.

Cool, thanks.

 

I'll just demonstrate the basic gist of things with a simple program:

*** Planck units (2019 NIST CODATA values) ***

Planck length: 1.61626e-35 m

Planck time: 5.39125e-44 s

Planck mass: 2.17643e-08 kg

Planck charge: 1.87555e-18 C

*** Related constants ***

Speed of light: 2.99792e+08 m s^-1

Speed of light squared: 8.98755e+16 m^2 s^-2

Length over mass constant: 7.42616e-28 m kg^-1

Length-mass constant: 3.51767e-43 m kg

Planck force: 1.21026e+44 N

Planck energy: 1.95608e+09 m^2 kg s^-2

Reduced planck's constant: 1.05457e-34 m^2 kg s^-1

Planck's constant: 6.62607e-34 m^2 kg s^-1

*** Possible force field constants ***

Field(0) [electromagnetic]: 8.98755e+16 m^2 s^-2

Field(0) variables: 1.34659e+27 m^-1 kg

Field(1) [gravitational]: 6.6743e-11 m^3 kg^-1 s^-2

Field(1) variables: 1.81331e+54 m^-2 kg^2

Field(2) [strong force?]: 4.95644e-38 m^4 kg^-2 s^-2

Field(2) variables: 2.44178e+81 m^-3 kg^3

Field(3) [X17 particle?]: 3.68073e-65 m^5 kg^-3 s^-2

Field(3) variables: 3.28808e+108 m^-4 kg^4

*** Connection between charge and length-mass? ***

Planck charge squared: 3.51768e-36 s^2 A^2

Length-mass with scaling removed: 3.51767e-36 m kg

All of the above dimensions are generated at compile-time so not much chance of incorrect results there. You can run it yourself if you like (download here).

The rest is up to interpretation. As you can see this so-called "generalized point-like force field constant equation" raises some serious questions. For one, it implies that electric charge does not involve mass at all but only has the dimensions of the speed of light. I'm not sure what that could mean. Also with only one additional known force to compare with (gravity) it's kind of hard to accept without seeing at least one more example. Two is compelling but three is about my lowest threshold to be fairly convinced.

Symmetries (in both math and physics) represent invariants, aspects that don't change under certain transformations. I can't tell if the connection between math and physics is deeply profound or tautologically trivial, although if it's the latter, that in itself may be a deeply profound fact.

Sorry, mere mortal here...what exactly does "tautologically trivial" mean anyway? Like that they're really one and the same or something?

 

Also notice that all of the above output was calculated using just three of the base Planck units.

Another thing...if charge really is just composed of length-mass then that would mean that the current Planck charge is about seven orders of magnitude off and would obviously have to change all of the other units involving electromagnetism (eg: the ampere, etc).

I forgot to clarify that only the dimensions of the field(N) variables are important here. (That is, you can ignore the numeric portion of the expression for now). They represent the variables that are multiplied with a given force-field constant to yield the resultant force. (Which is why I simply divide the Planck force by each constant to generate the dimensions of these variables).

*** EDIT ***

One last thing: the "scaling factor" might have something to with how the ampere was defined. The force between two wires one meter apart passing one ampere of current produces 2e-7 newtons of force. The scaling factor is exactly half of that although I'm not sure if that actually means they are indeed connected.

 

As you can see this so-called "generalized point-like force field constant equation" raises some serious questions. For one, it implies that electric charge does not involve mass at all but only has the dimensions of the speed of light.

I don't understand what the field constants are supposed to represent. They can't be coupling constants, as those are dimensionless. You derive them from the product of the square of the speed of light with successive powers of what you call the "length over mass constant". But the units don't make sense. For example, what you associate with the gravitational field has units \( \text{m}^3 \cdot \text{kg}^{-1} \cdot \text{s}^{-2} \), but the gravitational field has dimensions of force per unit mass:
\[ \frac{[\text{F}]}{[\text{M}]} = \frac{\text{kg} \cdot \text{m} \cdot \text{s}^{-2}}{\text{kg}} = \text{m} \cdot \text{s}^{-2} \]
Likewise, what does it mean for the EM field to have units of square meter per square second?

Sorry, mere mortal here...what exactly does "tautologically trivial" mean anyway? Like that they're really one and the same or something?

I mean that it may be the case that the reason we keep finding such deep connections between physics and math may simply be an artifact of how our brains are wired -- to a hammer, everything looks like a nail. The less trivial (but more tautological, as it were) case is if math and physics are indeed the same thing: the universe is a mathematical object. Max Tegmark is probably the most famous proponent of this view.

 

I don't understand what the field constants are supposed to represent. They can't be coupling constants, as those are dimensionless.

Coupling constants aren't dimensionless. If they were their place in the equation would have no effect on the dimensions of the resulting force.

You derive them from the product of the square of the speed of light with successive powers of what you call the "length over mass constant". But the units don't make sense. For example, what you associate with the gravitational field has units \( \text{m}^3 \cdot \text{kg}^{-1} \cdot \text{s}^{-2} \), but the gravitational field has dimensions of force per unit mass:

\[ \frac{[\text{F}]}{[\text{M}]} = \frac{\text{kg} \cdot \text{m}\cdot \text{s}^{-2}}{\text{kg}} = \text{m} \cdot \text{s}^{-2} \]

F = MA = MLT^-2

For two pointlike bodies in space F = G * (M1 * M2) / (Lr * Lr). So G = (F = MLT^-2) / (M^2L^-2) = (MLT^-2) * (M^-2L^2) = M^-1L^3T^-2.

What you've expressed is simply the second derivative of a body's position within said field.

Likewise, what does it mean for the EM field to have units of square meter per square second?

I know it's very paradoxical isn't it? I don't get it either. And how can the field variables have dimension M/L? That implies only one particle is involved. Umm yeahhh...

Again, I have yet to look at things from the other way around. Could be that charge is fundamental and mass is just an equivalence effect of the interplay of just charge, length, and time. Maybe then it would yield more sensible looking equations...

I mean that it may be the case that the reason we keep finding such deep connections between physics and math may simply be an artifact of how our brains are wired -- to a hammer, everything looks like a nail. The less trivial (but more tautological, as it were) case is if math and physics are indeed the same thing: the universe is a mathematical object. Max Tegmark is probably the most famous proponent of this view.

Interesting perspective. Or perhaps even more specifically the universe is basically just some kind of mathematical automatation...a program!