Wave Functions

[steve_bank]

Demystifying QM.

This in the text I sed in a class.

https://web.pdx.edu/~pmoeck/books/Tipler_Llewellyn.pdf

A wave function is a solution to the wave equation. An easy example to visualize is the wave function for a particle in a square indite poetical well, a model for a glass laser tube.

The solution is sines and cosines. When the wavelength of a photon in a laser tube is an integer multiple of the length of the tube resonance occurs and there is sinusoidal standing EM wave in the tube or box. The wave in a laser the is physically measurable.

The wave function for an infinite poetical well represents the probability of a particle(photon) being in a volume as dy*dx*dz -> 0. Hence the term probability wave.

https://web.iitd.ac.in/~nkurur/2013-14/Isem/cyl100/pib_sa.pdf

Particle in a box - Wikipedia

en.wikipedia.org

When a measurement is made the wave function 'collapses' into one state.

Wave function collapse - Wikipedia

en.wikipedia.org

When the wave function collapses there is no debris, loud boom, or bright flash....

 

[Jarhyn]

So, dumb question... Let's say that I have a photon, and there is some minimum distance related to the fine structure constant that defines the speed of light with reference to all other constants being used as a base of their units such that those constants become 1.

Let's say that this photon is 1 of that minimum distance.

Is it possible to for a photon to actually have more energy than that?

 

[steve_bank]

I have no idea of what you are talking about.

Energy is an SI unit of measure just like meters and kilograms.. EM radiation energy and power are measured . One of the first methods to measure EM power was to measure the rise in temperature of a resistance.

Connect an antenna recurring EM radiation to a resistor. The temperature of the resistor rises above ambient. Measure the temperature.

Tale the resister and put a DC voltage V across across it. Then increase the voltage until the temperature of the resistor equals that caused by the EM signal.

The power of the EM signal is then equal to V^2/R in watts, thermal equivalent work. In SI units heat, work, and energy have the same unit, Joules.

Power in watts is energy in Joules per second, W = J/s. Calculate energy in Joules and divide by number of photons, Joules per photon.

Bolometer - Wikipedia

en.wikipedia.org

A bolometer is a device for measuring radiant heat by means of a material having a temperature-dependent electrical resistance.[1][2] It was invented in 1878 by the American astronomer Samuel Pierpont Langley.

So, if a photon can have more than theoretical energy then it should be mensurable, assuming it can be measured above noise. See the noise thread....

It would show up somewhere.

 

[Jarhyn]

I have no idea of what you are talking about.

Energy is an SI unit of measure just like meters and kilograms.. EM radiation energy and power are measured . One of the first methods to measure EM power was to measure the rise in temperature of a resistance.

Connect an antenna recurring EM radiation to a resistor. The temperature of the resistor rises above ambient. Measure the temperature.

Tale the resister and put a DC voltage V across across it. Then increase the voltage until the temperature of the resistor equals that caused by the EM signal.

The power of the EM signal is then equal to V^2/R in watts, thermal equivalent work. In SI units heat, work, and energy have the same unit, Joules.

Power in watts is energy in Joules per second, W = J/s. Calculate energy in Joules and divide by number of photons, Joules per photon.

Bolometer - Wikipedia

en.wikipedia.org

A bolometer is a device for measuring radiant heat by means of a material having a temperature-dependent electrical resistance.[1][2] It was invented in 1878 by the American astronomer Samuel Pierpont Langley.

So, if a photon can have more than theoretical energy then it should be mensurable, assuming it can be measured above noise. See the noise thread....

It would show up somewhere.

The energy of a photon is a function of its wavelength, ya? Like an X-ray is more energetic because the period of the sine wave is really short so the photon moves more energetically to meet it's requirement to move forward at the speed of light.

But, if there are limits to how meaningfully "small" things are in the universe, this would mean there is a limit to how meaningfully energetic a photon can be, ya?

If we are looking at the physical limits of "fine structure" this should be an easily calculated number.

 

[Bomb#20]

So, dumb question... Let's say that I have a photon, and there is some minimum distance related to the fine structure constant that defines the speed of light with reference to all other constants being used as a base of their units such that those constants become 1.

Let's say that this photon is 1 of that minimum distance.

Is it possible to for a photon to actually have more energy than that?

There are a variety of natural unit systems that try to make physical constants 1; the basic unit of distance depends on which system you pick. For instance, it's about 10^-35 m in Planck units and 10^-16 m in Strong units. The highest energy photon ever measured had a wavelength of about 10^-22 m, for what it's worth. But units are arbitrary and physical reality doesn't care about them -- there's no reason to expect any of these units to correspond to a minimum distance. There is no minimum distance at all in the standard model -- the universe is infinitely continuous as far as we know. Some attempts at going beyond known physics to a Theory of Everything such as string theory imply there's a minimum distance, but based on constraints from astronomical observation, if a minimum distance exists at all it must be smaller than 10^-48 m. As far as we know there's nothing about photon physics ruling out photons with a wavelength of 10^-48 m, or 10^-148 m for that matter, but there are no known physical processes that could create photons that energetic, or even as energetic as the Planck scale.

 

[steve_bank]

Yes, E = h*frequency of a photon. It is imagined as an oscillator.

One of the things that led to QM was trying to predict blackbody radiation using classical mechanics. It led to infinite energy. That dean that light was quantized with a photon energy proportional to wavelength was part of the solution, as I recall.

AE made his reputation for the Photoelectric Effect. He experimentally demonstrated that light was quantized.

https://physics.bu.edu/~duffy/EssentialPhysics/chapter27/section27dash2.pdf

Photoelectric effect - Wikipedia

en.wikipedia.org

https://astro1.panet.utoledo.edu/~ljc/PE_eng.pdf

You can look up Plank time and length. That would be another thread.

Intuitively. Everything at the lowest level appears quantized to us. Energy can only be transferred in discrete steps. So moving an object may have a minimum distance represented by quantized energy needed to move it.

 

[Jarhyn]

But like, this runs up against the Hartree unit stuff. Essentially, selections where all the fundamental constants, at their smallest quantized levels, are treated as the basic unit.

This leads to the fine structure constant being expressed purely in that one waveform equation I'm too stoned to remember the name of right now and too stoned to care to look up right now.

Wouldn't this imply a theoretical upper bound of energy of a single photon?

I mean this is just a high thought, but like, if the "fine structure" of the universe only gets so fine, then at some point there's no structure which could support the photon, right?

I'm just curious as to whether there's a theoretical upper bound as to how fast the fields can switch due to how "grainy" the fields themselves are in their finest structure.

This would imply a theoretical lower bound on wavelength, ya?

 

[bilby]

Energy is an SI unit of measure just like meters and kilograms

You are confusing the dimensions with the units of measure.

If I said "Distance is an imperial unit of measure like ounces and horsepower", you would be wise to guess that I had no idea what distance actually was.

Energy isn't a unit of measure, it is a dimension; And SI is just a collection of units of measure.

 

[Bomb#20]

AE made his reputation for the Photoelectric Effect. He experimentally demonstrated that light was quantized.
...
Intuitively. Everything at the lowest level appears quantized to us. Energy can only be transferred in discrete steps. So moving an object may have a minimum distance represented by quantized energy needed to move it.

That's not how it works. Light transfers energy one photon at a time, sure, but a photon can have any amount of energy because it can have any wavelength. In fact a photon has every wavelength, since the same photon has different wavelengths in different reference frames. As far as we know there's no minimum distance and no minimum energy, and even constructing a theory for how there could be is hard to reconcile with Special Relativity. What's actually quantized, in the sense of coming only in integer multiples of a basic unit, isn't everything. It's a few specific things, like charge, baryon number, and angular momentum and "action", i.e., momentum times distance.

 

[pood]

Not sure what is being demystified here about the wave function. As far as I know its calculational value is on solid foundation. But that is epistemology. They “mystery” comes in when and if we consider its ontology.

But then, that is philosophy, so …

 

[Bomb#20]

But like, this runs up against the Hartree unit stuff. Essentially, selections where all the fundamental constants, at their smallest quantized levels, are treated as the basic unit.

This leads to the fine structure constant being expressed purely in that one waveform equation I'm too stoned to remember the name of right now and too stoned to care to look up right now.

Wouldn't this imply a theoretical upper bound of energy of a single photon?

I mean this is just a high thought, but like, if the "fine structure" of the universe only gets so fine, then at some point there's no structure which could support the photon, right?

I'm just curious as to whether there's a theoretical upper bound as to how fast the fields can switch due to how "grainy" the fields themselves are in their finest structure.

This would imply a theoretical lower bound on wavelength, ya?

I think you're being misled by the name "fine structure constant". It's a historical name from the phenomenon where it was first discovered. The name refers to the fine structure of the light and dark bands in the spectrum of hydrogen, not to the fine structure of the universe. And the Hartree unit is just like an electron volt, huge compared to any possible graininess of the universe and tiny compared to any possible upper bound. A one-Hartree photon is smack dab in the ultraviolet.

 

[steve_bank]

AE made his reputation for the Photoelectric Effect. He experimentally demonstrated that light was quantized.
...
Intuitively. Everything at the lowest level appears quantized to us. Energy can only be transferred in discrete steps. So moving an object may have a minimum distance represented by quantized energy needed to move it.

That's not how it works. Light transfers energy one photon at a time, sure, but a photon can have any amount of energy because it can have any wavelength. In fact a photon has every wavelength, since the same photon has different wavelengths in different reference frames. As far as we know there's no minimum distance and no minimum energy, and even constructing a theory for how there could be is hard to reconcile with Special Relativity. What's actually quantized, in the sense of coming only in integer multiples of a basic unit, isn't everything. It's a few specific things, like charge, baryon number, and angular momentum and "action", i.e., momentum times distance.

A photon is an abstraction used to model and explain experiment and requirements measurement. It is assigned attributes and portieres.

Energyandf matter are quntized. Matter is quntzed by discrete atoms. The amo8nt of mergy that can be put in in a car gasoline tank is the number of gasoline molecules that will fit. The energy in moving air or water is quantzed by the number of gas and waterr mo;molecules.

For a solid state photo detector when the energy of the photon equals the band gap voltage of the detector molecule absorption occurs and free electrons are created. I look at it as a form of romancer, when the photon cossetting at a frequency matches the resonant frequency of atom adsorption occ8rs. An analogy to mechanical and electrical resonance. The energyb tr5asfer to a detector is quantized.

The flip side is a sold state photo diode. Put a current through it and the atoms in the laser emit photons at a wavelength dtetermi9jned by the atoms. Current is quantized.

The energy stored in a capacitor is E(joules) = .5 * capacitance(farads) * voltage^2. At the everyday macro scale the number of electrons stored on a capacitor are so high that computationally wen treat energy as infinity divisible. But the energy is quantized by the discrete electron.

Whether a phonon actually exists, who knows. We know the models work. When propagating EM is treated like a wave when t interacts with matter is is treated like a particle.

Theories are deigned to work together without conflict.

There can not be infinite energy in a photon.

 

[Loren Pechtel]

It sounds to me like the question might be whether you can have a photon with a wavelength less thank the Plank length.

 

[bilby]

It sounds to me like the question might be whether you can have a photon with a wavelength less thank the Plank length.

I suspect that you can; Wavelength isn't real. Photons have frequency; The 'wavelength' is just a derived distance that represents the maximum distance they could theoretically travel per cycle if moving at c, it doesn't have to actually be travelled by anything.

 

[Bomb#20]

It sounds to me like the question might be whether you can have a photon with a wavelength less thank the Plank length.

You can. Every photon has a wavelength less than the Planck length in some inertial reference frame moving in the opposite direction at so close to c that the photon is blue-shifted down to below the Planck length.

 

[Bomb#20]

Energyandf matter are quntized. Matter is quntzed by discrete atoms. ...The energy in moving air or water is quantzed by the number of gas and waterr mo;molecules.

No. The energy in moving air or water is in Joules, and number of gas and water molecules is not in Joules. The kinetic energy is 1/2mv^2, and you can quantize the mass all you please in integer multiples of the mass of an H2O or N2 or O2 molecule but that can't quantize the energy, because v is not quantized.

There can not be infinite energy in a photon.

True, but that's not the point in dispute. The argument is about whether there's some finite energy that a photon can't have.

 

[barbos]

It sounds to me like the question might be whether you can have a photon with a wavelength less thank the Plank length.

You can. Every photon has a wavelength less than the Planck length in some inertial reference frame moving in the opposite direction at so close to c that the photon is blue-shifted down to below the Planck length.

Both Special and General Relativity break down at such speeds and do not apply. So no, you can't.
SR/GR are less fundamental than QM.

 

[Bomb#20]

It sounds to me like the question might be whether you can have a photon with a wavelength less thank the Plank length.

You can. Every photon has a wavelength less than the Planck length in some inertial reference frame moving in the opposite direction at so close to c that the photon is blue-shifted down to below the Planck length.

Both Special and General Relativity break down at such speeds and do not apply.

At such speeds relative to what frame of reference?

 

[barbos]

It sounds to me like the question might be whether you can have a photon with a wavelength less thank the Plank length.

You can. Every photon has a wavelength less than the Planck length in some inertial reference frame moving in the opposite direction at so close to c that the photon is blue-shifted down to below the Planck length.

Both Special and General Relativity break down at such speeds and do not apply.

At such speeds relative to what frame of reference?

Relative to CMB.

 

[steve_bank]

Energy in gasoline is quantized by molecules Energy in an EM wave is quantized by photons. Electrical current is quantized by electrons. Generally the quantization is well below a measurement threshold and we take it as infinity divisible. Quantization of energy is not controversial.

Energy is transferred to the photon when created. If you go by QM energy has a minimum that can be transferred to a photon. So in turn frequency is then quantized.