For example, energy, as photons, have both wavelength and frequency. Photons are expressions of distance; space, and time that are connected. Time alone will not product energy, since all you would have is frequency, but no wavelength.
That’s a little wonky.
I don’t think you quite understand what energy is and what photon is.
Energy is frequently misunderstood, because you have “energy” defined in sciences, and those “energy” that are more loosely described in non-science philosophies, and worse, in religions.
But since you have brought up photons and waves with energy, let leave out religions and philosophies, and stick with physical sciences (excluding Social Sciences, eg psychology, sociology, anthropology, economics, political science, etc), as in, staying with physics.
I think we should look at the system, first, before we go explore energy’s connection with a system.
In sciences, we have tendency to define a PHYSICAL SYSTEM with all sorts of observations, meaning these “observations” include MEASUREMENTS, for instances we can measure the spatial dimensions of a physical system, like length, width, height, surface areas, volume, and we can also measure the system’s mass, density and the list go on and on.
But there are also other observations we can make, such as its physical state (eg solid, liquid, gas, plasma), and we can break everything down a large physical system to multiple smaller physical systems, eg molecules, atoms, and even more smaller systems, composite particles like protons and neutrons, elementary particles like quarks, electrons, neutrinos, and yes, photons too.
So yes, you can treat a photon or photons as physical system.
You can treat a molecule, atom or particle as a “system” on its own.
Some of the physical systems I have left out, are fields and waves (EM waves or radiations). Fields and waves can be treated as physical systems too.
Now, whether the systems are large or small (down to quantum level), or that of fields and waves, in physics, there are physical properties of systems that we can observed and measurements that be observed.
One of those measurements and those properties that I have left out, is “energy”.
So what is “energy”?
In physics, energy is a measurement of the ability of a physical system to do “work”.
So essentially energy is like mass, they are both properties of the physical system, and in many case, mass and energy are intrinsically link to each other.
For instance, energy can be stored in the physical object, thus potential energy. Kinetic energy is when the object is doing work.
And when object doing work, some of those energies are loss, energy radiated or energy dissipated what we know as “heat” (radiated energy).
In classical mechanics, these energy and “work” are defined in unit known as “Joule” (J). And in heat, units are in Celsius, Fahrenheit and Kelvin.
While Joule and Kelvin are still being used, in modern physics, electroVolt (eV) is been more commonly used in number of different physics fields, eg particle physics, quantum physics, astrophysics, etc.
Now, while photon has zero rest mass, photon do have energy. Energy is a property that exist in photon.
Since Einstein’s paper on Photoelectric Effect in 1905, light is treated as both wave (EM wave) and particle (photon), hence the wave-particle duality.
The wave-particle duality is Einstein’s important contribution to quantum mechanics.
Anyway, electromagnetic waves and photons should be explored together, so photon should be seen as quanta of electromagnetism. As I said, because photon is massless, the EM field generated the EM forces that keep photons in motions. And since force exist (eg EM force), then there are energy.
I think keep forgetting that energy don’t exist on its own.
Now, this...
Time alone will not product energy, since all you would have is frequency, but no wavelength.
...this is not quite right.
You need to be reminded that energy is measurement of system’s ability to do work. And work require “forces” of some kinds, either moving on it own, or external forces being applied to the system.
For any system to do the “work”, it require force (eg potential-kinetic energy, EM forces). Forces required “time” - remember that acceleration require both distance and time. So without time, there can be no force, and without force there can be no energy to do the work.
And frequency cannot exist without time. Frequency require both time and wavelength, and electromagnetic wave cannot do without both wavelength and frequency. Without time there can be no frequency.