# What is Size of Photon?

Is there any size of photon if so what is it?

And also which particle had smallest size / radius / volume considering all of the matter.

• Elementary particles do not have sizes in the conventional sense. They have a wave length corresponding to their energy but one can consider them point-like in the sense, that they do not seem to have any inner structure, that becomes visible at high energy scattering. One can assign sizes in a meaningful manner to composite particles like hadrons, atoms, molecules because they have a stationary wave function and therefore probability distribution of the constituents. – Sebastian Riese Sep 13 '15 at 12:04
• More on size of photon. – Qmechanic Sep 13 '15 at 12:22

A photon is a unit ("quantum") of excitation of the quantum electromagnetic field. Thinking roughly of the quantum field as a vast collection of quantum harmonic oscillators, each oscillator corresponding to a mode of vibration of the field, we specify the quantum field's state by stating how many quantums above the QHO ground state each mode oscillator is in (recall that a quantum harmonic oscillator has equispaced energy levels of even energy spacing $h\,\nu$ with ground state energy $\frac{1}{2}\,h\,\nu$). The one and only physical entity in this picture is the quantum field, the "photons" are just units used to name the state of mode oscillators, just as Euros or Dollars or Rupees or Yens might be used to name the state of your bank account. The field doesn't even have to have a certain number of photons in each oscillator: being a quantum object, it can be in a linear quantum superposition of states with definite photon numbers (superposition of Fock states).

So one can no more ask what the physical extent of a photon is any more than one can ask what the physical extent of the integer $1$ is. I would commend the Physics SE question "Which is more fundamental, Fields or Particles?" and user DanielSank's answer in particular to find out more about these ideas.

However, one can meaningfully ask for characteristic sizes of regions significantly influenced by the electromagnetic field in a pure one-photon state. As with the electron field, we can delocalize the disturbance arbitrarily: a one photon state that is a momentum eigenstate is theoretically delocalized over all space. In general, one photon states are extremely hard to confine to regions smaller than about a wavelength. The electromagnetic field can in special circumstances be confined to smaller regions, but it then becomes evanescent and in any case this doesn't happen in freespace: interaction with matter is needed so that we aren't really talking about pure photons anymore, but rather superpositions of EM and matter excitations.

• Excellent answer. Just to emphasize what is said in the first paragraph: "Classical" states with a well defined electrical/magnetic field always have indefinite photon number (especially coherent classical radiation, which can be understood as photons in a coherent state). – Sebastian Riese Sep 13 '15 at 12:10
• @SebastianRiese So my physical intuition, regarding say if a certain particle has a certain mass, implying (in the classical world only) that a certain physical size is required to accommodate that mass, is completely misguided? I ask just to confirm this as a complete self study person. No textbook that I have ever come across has explicitly said this, although imo, frequent reminders to forget classical ideas and intuition, would be helpful, as it is so ingrained. – user81619 Sep 13 '15 at 15:54
• @AcidJazz I don't see how this is related with my comment, but yes. Especially as the fundamental fermions are massless in the vacuum, where the Higgs symmetry is not broken and they only acquire mass due to the interaction with the Higgs field in the vacuum where the symmetry is spontaneously broken. – Sebastian Riese Sep 13 '15 at 16:17
• @SebastianRiese Sincere apologies for that, I mean to address WSA (Rod), not yourself and I was using a small phone with large fingers. Thanks and sorry for my mistake. – user81619 Sep 13 '15 at 16:22
• Hi. I personally disagree with this interpretation. Yes, it's not meaningful to ask what is the size of a "quantum" of an excitation, but I believe the question is to be interpreted as "What is the physical size of the quantum electromagnetic field when it is excited by one unit?". The answer then is that if E is the energy of the excitation, then the relevant length is the Compton wavelength $\lambda=h/E$. Acid Jazz's intuition then is also correct: Anything with a certain mass, has a certain energy and a certain wavelength associated with it. – Heterotic Sep 14 '15 at 9:39

Is there any size of photon if so what is it?

The photon is an elementary particle among the others which form a basis for the standard model of particle physics.

The Standard Model of elementary particles (more schematic depiction), with the three generations of matter, gauge bosons in the fourth column, and the Higgs boson in the fifth.

The model encapsulates all the experimental data very successfully, and the size of these particles is considered zero, they are point particles.

And also which particle had smallest size / radius / volume considering all of the matter.

A composite particle, like a proton which is made up from three quarks and their dynamic exchanges, has a definite size, given the energy of the probing interaction.

Elementary particles are point particles.

String theory which is trying to extend the standard model and unify it with gravitation hypothesizes that elementary particles are vibrations on a one dimensional string, whose dimension is of order of the planck length, 16x10^-36meters, a very small length not measurable experimentally.

• Elementary particles are point particles.. What does this statement actually mean? It means that you consider them to be points in your original (pre-quantized) equations. Quantization, however, spoils everything. When you quantize the theory, particles acquire effective sizes (wavelengths / wavefunction localizations / etc), just like mentioned in the other answer. – Prof. Legolasov Sep 13 '15 at 13:23
• @Hindsight The standard model is a quantized model. The particles entered in the calculations of crossections are considered zero point. In field theoretical terms it means that the creation and annihilation operators act on a point. String theory aims to extend this to one dimensional string but is yet to be successful in a workable model. – anna v Sep 13 '15 at 13:26
• Anna, I understand what you are saying and I agree with you. But, IMHO, OP's question was more real-life-connected. In real life, particles can never-ever-ever be considered points (and I am sure you also agree with this). – Prof. Legolasov Sep 13 '15 at 13:29
• My point is that OP hasn't asked "What is our mathematical description of photon", but "Is there ANY size of a photon?" – Prof. Legolasov Sep 13 '15 at 13:31
• @Hindsight As an experimentalist, I consider them points within experimental errors. I think it is very confusing to the questioners to introduce field theory as an answer to naive questions, without also stretching in this case that the fields are fields over zero dimensional points – anna v Sep 13 '15 at 13:32