Planck's equation and upper and lower bounds on the energy of a photon

[PainterGuy]

Hi,

Planck's equation is written as E=hν where "E" is energy of a photon, "h" is Planck's constant having value 6.626 070 15 x 10-34 Js, and "ν", Greek letter nu, is frequency.

Violet color has frequency range between 790–666 THz (Tera =10^12). If a violet photon of frequency 7.5 x 10^14 Hz is considered, its energy is 5 x 10^-19 Joule.

Note that frequency and wavelength are inversely proportional, if frequency increases the wavelength decreases and vice versa.

To calculate the energy of 'n' photons of same frequency, the equation could be written as E=nhν.

In the equation above, 'n' is discrete, 'h' is a constant but 'ν' is a real number which means it can ideally take on any real value.

Question 1: Are there any lower or upper bounds on the energy of a photon? I don't think a photon could have energy of 0 J because it would mean frequency of 0 Hz and at the same time to have infinite energy the photon must have infinite energy.

Question 2: I've always thought of a photon as a tiny wiggly wavy packet. An EM wave with frequency 30 Hz has the corresponding wavelength of 10,000 km (longer than the radius of the Earth). Well, this is no longer tiny wiggly wavy packet. How do I visualize a photon in such a case?

Thanks in advanceHelpful links:
1: https://en.wikipedia.org/wiki/Planck_constant
2: https://simple.wikipedia.org/wiki/Planck_constant
3: /watch?v=8DjbCTjXRbg (add www.youtube.com in front)
4: https://physics.stackexchange.com/q...the-highest-possible-frequency-for-an-em-wave

 

[A.T.]

Question 1: Are there any lower or upper bounds on the energy of a photon?

You are basically asking about the upper bounds on energy.

Question 2: I've always thought of a photon as a tiny wiggly wavy packet. An EM wave with frequency 30 Hz has the corresponding wavelength of 10,000 km (longer than the radius of the Earth). Well, this is no longer tiny wiggly wavy packet. How do I visualize a photon in such a case?

Just skip the "tiny" bit.

 

[vanhees71]

Photons are not "tiny little balls". One should never think about photons in terms of particles but in terms of electromagnetic fields. Then all apparent inconsistencies are overcome.

 

[Lord Jestocost]

Question 2: I've always thought of a photon as a tiny wiggly wavy packet. An EM wave with frequency 30 Hz has the corresponding wavelength of 10,000 km (longer than the radius of the Earth). Well, this is no longer tiny wiggly wavy packet. How do I visualize a photon in such a case?

To yield a wave packet, one needs a superposition of traveling waves with an appropriate distribution of various frequencies.
http://hyperphysics.phy-astr.gsu.edu/hbase/Waves/wpack.html#c1

 

[Klystron]

As posts #2 and #3 answer your questions, this explanation of Extremely Low Frequency (ELF) technology may help visualize long wavelength electromagnetic fields.

The wikipedia article provides an ELF lower limit of 3hz but I understand research and technology has progressed to lower frequencies / longer wavelengths. From the article:

Difficulties of ELF communication

One of the difficulties posed when broadcasting in the ELF frequency range is antenna size, because the length of the antenna must be at least a substantial fraction of the length of the waves. Simply put, a 3 Hz (cycle per second) signal would have a wavelength equal to the distance EM waves travel through a given medium in one third of a second. When the refractive index of the medium is greater than one, ELF waves propagate slower than the speed of light in a vacuum. As used in military applications, the wavelength is 299,792 km (186,282 mi) per second divided by 50–85 Hz, which equals around 3,500 to 6,000 km (2,200 to 3,700 mi) long. This is comparable to the Earth's diameter of around 12,742 km (7,918 mi). Because of this huge size requirement, to transmit internationally using ELF frequencies, the Earth itself forms a significant part of the antenna, and extremely long leads are necessary into the ground.

 

[A.T.]

I've always thought of a photon as a tiny wiggly wavy packet.

Here are some macroscopic analogies to quantum mechanical particles, which share some of their properties:

 

[PainterGuy]

Here are some macroscopic analogies to quantum mechanical particles, which share some of their properties:

Thank you for sharing these interesting videos but I think these videos are based on pilot wave theory which isn't considered mainstream interpretation on quantum mechanics. These videos helps a lot with intuitive and basic understanding. Please correct me if I'm wrong. Thank you!

 

[A.T.]

These videos helps a lot with intuitive and basic understanding. Please correct me if I'm wrong.

Here are more, but I will leave the correcting to those with more expertise on quantum mechanics:

 

[PeterDonis]

Are there any lower or upper bounds on the energy of a photon?

Mathematically speaking, no: Planck's formula can describe a photon of any finite energy greater than zero.

Physically speaking, most physicists believe that at high enough energies, a "photon" description would no longer be valid because other physics would come into play beyond simple quantum electrodynamics.