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Wiki says that a photon of mass equivalent to $10^{-62}$ kg has been detected:

10×10−62 kg Mass equivalent of the energy of the lightest photon detected [citation needed]

This equates ($mc^2=E=hf=h\frac{c}{\lambda}$) to a wavelength of $\lambda=2.2\times 10^{20}$ m (roughly a million ly)! Can anyone provide a citation for this measurement? And how can such a large wavelength/low energy photon be detected?

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Apart from the quotation (true/false un/reliable un/documented ....), I'd like to learn about the lightest photon detected, or about the instrumental limit: what is the lower limit of energy that can be registerd by an intrument (or the greatest wavelength), and how it is done? For example, can you detect a radiowave of 1 Hz?

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  • $\begingroup$ "Ly" is for lightyears (please confirm)! If yes, that is awesome and should be mentioned in any school book. Meanwhile, you are able to give reference? Again, wavelenght is 1 million lightyears, correct? $\endgroup$
    – Peter Bernhard
    Oct 21, 2022 at 8:11

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Okay, so I am taking this question to mean what is the lowest-energy photon that can be individually detected. This is certainly an interesting technological question.

I can't give an authoritative answer, but the lowest energy detectors I am familiar with is at the CMB microwave background energy of ~ $3Kk_B$, which corresponds to a wavelength of about 5 mm, or a frequency of around 60 GHz. These are the transition edge sensing bolometers that are used in the Bicep 2 experiment and similar experiments.

The way that these work is that they use a superconducting material just below the superconducting transition temperature, which is heated up enough by absorption of one photon to transition to the normal temperature. This changes the resistance, which is ultimately read out as a slight increase in the amount of heat dissipated.

The limit to the lowest energy photon one can detect with these sensors is given most directly by the size of the superconducting bandgap. 3 K already corresponds to a ~0.25 meV gap, which is on the low end of materials as far as I know (compare for example with this chart). So I don't think one could use this to get a whole lot farther, certainly not down to radio wave scales. But I welcome any thoughts on this matter.

Edit 03/2019: A new result shows detection of photons at around 200 MHz (corresponding to a wavelength of 10 m) that are stored in a resonator, using coupling to a superconducting qubit similar to the systems mentioned by Daniel Sank in the comments. The natural frequency of the qubit is in the GHz, so they had to do some clever designing to make it sensitive to such a lower frequency.

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    $\begingroup$ We can go lower by about an order of magnitude :-) We can detect 5 GHz photons in superconducting circuits. Granted, those aren't free-space photons, but still we can detect them. $\endgroup$
    – DanielSank
    Dec 5, 2018 at 19:21
  • $\begingroup$ @DanielSank thanks! Do you also use transition edge sensors? And since you point out that it's not free space, are you in some strong coupling regime that increases your sensitivity? $\endgroup$
    – Rococo
    Dec 6, 2018 at 3:26
  • $\begingroup$ I work with superconducting quantum circuits (qubits etc.). Those systems support microwave frequency electromagnetic modes which can be occupied by integer amounts of energy (i.e. photons). $\endgroup$
    – DanielSank
    Dec 6, 2018 at 6:35
  • $\begingroup$ Considering that ultracold atoms can get gaps of at least 6 orders of magnitude smaller than superconducting gaps, I wonder if they are able to see much lower energy photons. $\endgroup$
    – KF Gauss
    Feb 19, 2019 at 7:03
  • $\begingroup$ @KFGauss that is an interesting question. For ultracold atoms in optical cavities, in particular, it does seem like there should be some hope of improving on this. But I am not aware of any developments in this direction. $\endgroup$
    – Rococo
    Feb 19, 2019 at 22:17
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The article says "Consequently, there can only ever be an experimental lower bound on the mass of a supposedly massless particle; in the case of the photon, this confirmed lower bound is of the order of $3×10^{−27} eV = 10^{−62} kg$." It is saying that the rest mass of the photon, if it exists, is less than $10^{−62} kg$ which is different to the frequency of the photon. Effectively it is making a comment on the range that the inverse square is accurate, which turns out to be $\frac{\hbar}{mc} \approx 10^{20}m$.

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  • $\begingroup$ In the box it is stated that the photon has been experimentally detected $\endgroup$
    – user104372
    Apr 5, 2016 at 8:30
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    $\begingroup$ Read the table. It says: "Mass equivalent of the energy of the lightest photon detected [citation needed]", that article is badly worded, but it doesn't talk about the photon rest mass, apparently. $\endgroup$
    – ACuriousMind ♦
    Apr 5, 2016 at 8:32
  • $\begingroup$ @ACuriousMind, it clearly refers to an experimental finding: Consequently, there can only ever be an experimental lower bound on the mass of a supposedly massless particle; in the case of the photon, this confirmed lower bound is of the order of 3×10−27 eV = 10−62 kg. $\endgroup$
    – user104372
    Apr 5, 2016 at 8:35
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    $\begingroup$ @user11374 Yes, it is (although since there is no citation, so who knows how reliable that is). I was talking to jim, who seems to have interpreted the article as talking about the rest mass. Well, the two sentences just don't fit together. The "mass equivalent" in the table doesn't mesh with the "lower bound on the mass of a massless particle". This may just be one of the cases where you shouldn't trust Wikipedia too much. $\endgroup$
    – ACuriousMind ♦
    Apr 5, 2016 at 8:42
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    $\begingroup$ Poor Wikipedia entry: no citation, ambiguous, seemingly incorrect as written. Caveat emptor. $\endgroup$
    – garyp
    Apr 5, 2016 at 11:48
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One should note what comes immediately after the text you are referring to - and, in fact, in the quotation you give:

[citation needed]

This means the quoted information was not cited to a reliable source by the person who put it there, and that means it could potentially be inaccurate. So this should immediately raise a red flag.

And, in fact, this information is inaccurate, or at least inaccurately reported: all photons, as far as we can tell, have zero mass. Thus, they are all the "lightest" photons ever detected. When an "energy" is cited for a photon, it is not a mass, but rather its kinetic energy: photons are purely kinetic objects and kinetic energy is the only kind of energy they possess.

So what is this $10^{-62}\ \mathrm{kg}$ figure that is cited? Well, first off, it cannot be a mislabeled kinetic energy, because if that were the case then the frequency, as given by

$$mc^2 = E = hf$$

would be around $1.4 \times 10^{-12}\ \mathrm{Hz}$, or $1.4\ \mathrm{pHz}$. That is a picohertz, or one cycle of vibration per terasecond (thus equivalently $1\ \mathrm{Ts}^{-1}$), so in the span of a terasecond only about one and a half wave cycles would be completed. But one terasecond, or 1000 gigaseconds, already surpasses the total span of complex human societies (about 175 gigaseconds, or 5,500 years), much less our astronomical observations. Moreover, the wavelength of such a photon is on the order of interstellar distances, and thus would require an antenna of similar size to absorb with any reasonable probability. Detection of such a photon would thus be entirely infeasible both with today's technology and with the current elapsed length of time of human civilization.

Instead, what this figure really means is given by the text in the orders-of-magnitude article just above the table:

Consequently, there can only ever be an experimental lower bound on the mass of a supposedly massless particle; in the case of the photon, this confirmed lower bound is of the order of $3×10^{−27}$ eV = $10^{−62}$ kg.

Actually, "lower bound" here should be "upper bound". The figure is indeed referencing the actual mass, and what it is saying is a photon cannot be more massive than $10^{-62}\ \mathrm{kg}$. But this is not a recorded mass, as in that someone saw a photon with confirmed positive mass at least this much, but rather it is a bound on mass as determined by experiments to detect if there is any non-zero mass to a photon. This figure thus represents the limit of experimental error in experiments seeking to determine the mass, and thus is highly consistent with an exact mass of zero for all photons.

tl;dr - Wikipedia is inaccurate.

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  • $\begingroup$ What wavelength would that mass correspond to? $\endgroup$
    – Peter Bernhard
    Oct 21, 2022 at 8:22
  • $\begingroup$ @Peter Bernhard : Since a cycle takes 1 Ts then with light travel speed of ~300 Mm/s = 300 Em/Ts it would be 300 Em long, which is of near-galactic dimensions (roughly 32,000 light years). $\endgroup$
    – The_Sympathizer
    Oct 21, 2022 at 16:50
  • $\begingroup$ So in the question quote "to a wavelength of λ=2.2×1020 m (roughly a million ly)" can plausibly be read as: wavelenth is one million light years. One million light years is a theoretical number, yours is empirical? The One million does not exist? $\endgroup$
    – Peter Bernhard
    Oct 21, 2022 at 17:00
  • $\begingroup$ @Peter Bernhard: No idea what you mean. Also just note a small correction: I read 1 Ts as the period, that's for 1 pHz, the actual frequency is 1.4 pHz so it's somewhat shorter wavelength and period - ~0.7 Ts and ~210 Em or 23,000 ly. Not sure where they get 1 Mly from. That $10^{-62}\ \mathrm{kg}$ indeed corresponds to $9 \times 10^{-46}\ \mathrm{J}$ and then to the order of magnitude given of frequency and wavelength. To get 1 Mly order of magnitude would need $10^{-64}\ \mathrm{kg}$. $\endgroup$
    – The_Sympathizer
    Oct 21, 2022 at 17:10
  • $\begingroup$ Me too, I must correct; you got me right, I feel understood, sorry.... "a photon of mass equivalent to 10−62 kg has been detected" - That is empirical. So, I guess it is: unbelievable. you say 1 million light years, that is beyond one galaxy I guess. $\endgroup$
    – Peter Bernhard
    Oct 21, 2022 at 19:18
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We can be certain radio astronomical observations of the 1,420mHz hydrogen line arises from many dispersed photons created in inter and intra galactic clouds of neutral hydrogen, caused by the hyperfine splitting of the ground state of the hydrogen atoms there. I would doubt though that anyone has been able to detect these photons individually as even in a receiver cooled to near 0K, the signal would likely be swamped by thermal noise.

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