# Just how 'big' is a photon?

1. Nov 30, 2011

### sophiecentaur

Most people seem to think of photons as little bullets and this is often OK, when you are considering light (amongst the whole em spectrum). When challenged about the 'extent' of a photon, they will say "It's a wavelength long / wide / big" or some such arm waving statement. Because the wavelength of visible em is so short, it is possible to gloss over the details and, indeed, to visualise little bullets ('corpuscles', as they used to be called).

Of course, there is an instant objection to the notion of a photon being just one wavelength long, on the grounds that a single cycle of a sinusoid (which is what you'd have if just one such photon were to be travelling through space in isolation) would have an infinitely wide spectrum, full of harmonics that would be detectable. We don't see these - ever, for photons of any wavelength.

BUT, what about when we are dealing with low Radio Frequency em? Consider a photon with an 'extent' of just one wavelength. For a 200kHz transmission, that represents a wavelength of 1500m. Now take a very simple transmitter with, say, the collector of a transistor connected to a short wire. Take an equally simple receiver, with a short wire connected to the base of transistor. Separate them by 10m. The receiver will receive photons that the transmitter is sending it. These photons, if they were to have the proposed extent would have to extend from the transmitter to a region that is 100 times as far away as the receiver input or, they would somehow need to extend ('coiled up?' somehow) from within the transmitter to somewhere within the nearby receiver. This just has to be a nonsense model. In fact you just can't allow a photon to have any extent al all or there will be some circumstance like the above that spoils the model.

The 'energy burst' model is also a problem if you consider the mechanism that generated any particular photon. All photons of a particular energy are assumed to be identical (there is only one parameter with which to describe them). That would imply that the systems that generated these little identical bursts of energy would all need to have identical characteristics. There will be a range of charge systems that can generate em of any given frequency but they would all need to generate a burst of em with the identical pulse shape. In the classical sense, that would mean that the resonances within any system would all need to have the same Q and to make the transition within exactly the same time interval. This is asking a lot, for all 2.23900000000eV transitions to be identical, whether they were the result of a single, discrete, atomic gas transition or a transition within a continuous energy band in a solid. The only way round this is for the transition time to be irrelevant and for the 'arrival' or 'departure' of a photon to be in the form of an impulse. Hence the spatial and temporal extent of a photon must be considered as zero.

These 'little bullets' all have to be infinitely small. But that's the least of our problems with QM, when we try to force it to lie within our conventional ideas.

2. Nov 30, 2011

### Bill_K

The electromagnetic field is a quantum field, and the photon is a single quantum excitation of that field. Just as for all particles in quantum mechanics, a photon does not have a unique shape, rather it is a wave packet with a finite size and frequency spread. Even a 'pure' frequency photon such as Hydrogen alpha has a certain line width and a certain spatial extent, related by the uncertainty principle. The size and shape of a photon depends on the circumstances which created it.

No, the size of a photon is not one wavelength. The size corresponds to the lifetime of the atomic state that emitted it. For example if the lifetime is roughly a nanosecond, then the size of the photon is about 30 cm. How does this avoid a contradiction? You'd think for a photon that large you might be able to detect just part of it. No, because just as for all other quantum particles, the amplitude of the photon is a probability amplitude - it's the probability of detecting the photon at that point. Photons, like all quantum particles, interact at a single point, regardless of how big their wavepacket is.

3. Nov 30, 2011

### sophiecentaur

I have a problem with the fact that nearly everyone restricts the discussion of photons to those involved in optical / atomic transitions. Once a beam of light / radio waves has been launched, how can anyone 'know' where it originated? By that I mean how would a "pure" frequency photon from a Hydrogen atom be distinguished from one which came from an LED? In what way could it be different? What other parameters are used to characterise photons other than their energy?
Would a Hydrogen atom be 'blind' to photons produced from an LED. I don't think so.

4. Nov 30, 2011

### Bill_K

Their spread in energy. We are so used to writing down plane waves that we forget that in real life everything is a superposition. There are two equivalent ways of looking at a wave packet: a) it's a single photon with a finite size and a spread in frequency. b) it's a probabilistic superposition of photons, each one a plane wave with completely sharp frequency and infinite extent. Which description you use amounts to a choice of basis. Plane waves are mathematically clean, but being infinite they make it difficult to ask "how big is it", and "where and when was it created"?

5. Nov 30, 2011

### sophiecentaur

That is to do with the statistics of a lot of photons and what you say confirms that there really is confusion about this. The question I ask is the nature of an individual photon. That is, after all, what interacts with a charge system when it is released or absorbed.

There is a catch 22 situation here. A single photon, if one insists that it actually 'exists' in the em wave and travels anywhere, needs to have infinite extent. I have no problem with this - it makes eminent sense, as it explains diffraction, for a start. So why do people insist on it as having a very limited (little bullet) extent?
It seems to me that, in the rest of your post, you are giving more of a description of the effect of a large number of photons than a description of an individual photon. I can't see how your model 'a' can really hold because it would have to imply that different photons would need to interact differently with a given system. Don't they have to be identical?
Also, if there needs to be a 'probabilistic superposition' (as in b) then, for a very low intensity source, turned on for a very short while, how could a small number of photons turn up in an identifiable interference pattern before the others had even been emitted from the source? How do they 'know'?

This is why I feel happier with a wave treatment, with the photon just being there and identifiable at the actual time of interaction with the systems at each end. It's all a bit abstract because you only know they're there when the do actually interact. Hummm.

6. Nov 30, 2011

### Q-reeus

Maybe because of photoelectric effect - one always gets just pinprick spots on the screen.

In #2 Bill K writes: "The electromagnetic field is a quantum field, and the photon is a single quantum excitation of that field... just as for all other quantum particles, the amplitude of the photon is a probability amplitude - it's the probability of detecting the photon at that point. Photons, like all quantum particles, interact at a single point, regardless of how big their wavepacket is." This leaves me somewhat confused. Is the field itself taken to be a continuous E, B, field, so the photon is 'comprised' of such? Or do we take 'field' to mean an abstract probability amplitude space, the photon itself considered as a point particle? Otherwise, if the interaction is truly always at a point, would this not imply instantaneous collapse of an extended wavepacket 'field' that could be light years in spatial extent?

7. Nov 30, 2011

### Cthugha

Ehm, this is not true unless we are purely discussing theory here. Sometimes a monochromatic mode of the em-field is termed photon and that would indeed have infinite extent as it also has a perfectly defined energy. However, this is a pathological case that never occurs in reality.

Real single photons are defined by a state with fixed photon number of one. This state does not necessarily have to (and in fact will never) be monochromatic, but will be spectrally broadened at least due to the finite duration of the emission process. This is already the case at the single photon level.

8. Nov 30, 2011

### Ken G

The point is well taken, that's what the photon is in our theory for talking about it, but note the deeper problem here if we are to interpret the "photon" concept ontologically-- we are defining the thing by its state! That's why I would prefer to say there is no such thing as a "real single photon", it is entirely a conceptual language, an element of a theory, which borrows its ontology from mathematics (like all physical notions that sound ontological) but which never transcends or exits that mathematical source. There's no such thing as a real photon, and this is also made clear by the basic indistinguishability of photons. We can distinguish their states, but not the things that have these states, so the "things" themselves are largely indeterminate. We must not confuse our language about things for the things themselves, or we get all worried about "what is a photon really." A photon is really whatever we choose to say it is, we made it up and it does not even have to be viewed as a thing with a unique definition, it can be a set of definitions useful in different contexts but related in some important way. This is all perfectly normal in physics, we do it all the time even though we often don't realize it.

The relevance to the OP question is that once we recognize that the ontology of the photon is entirely contextual, then we can see that "how big it is" is also a contextual issue. For the purposes of diffraction, the deBroglie wavelength is what matters, for interference, it is the coherence length (related to the size of the wave function, as some pointed to above). These are both also true of electrons, but electrons have (at least) two other relevant "sizes"-- the absence of internal structure gets the electron defined to be a point object, and light interacts with free electrons as if they had a "Thomson cross section" related to the "classical radius of the electron." The same object can come in many shapes and sizes, so we are best recognizing that it has no unique ontology at all.

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9. Nov 30, 2011

### sophiecentaur

I can go along with most of that.
SO why is it that the Photon is treated by all and sundry as something with the same sort of 'reality' as a cannon ball? It seems to me that it only serves to confuse. Isn't it time to make it more plain to the World that photons are not like that at all?
How many times do we read that the Photoelectric Effect 'proves' that photons are particles?
Q reeus made the comment a few posts ago. All the photoelectric effect shows is that E =hf and that energy interactions with em waves are Quantised. Can't we, as the relatively well-informed, do the World a favour and start putting things a bit more accurately?

10. Nov 30, 2011

### Cthugha

The terminology of real photon was used to distinguish between the concept of single modes of the em field which is in no way assignable to experimental studies and the concept of photon number states which can be assigned to experimental studies. There is no ontological implication in that wording, just a distinction between two different concepts which happen to share the same name for historical reasons. You can go ahead and call one experimental photon instead or whatever if you find the terminology appropriate.

"How big is a photon" is simply an ill-defined question as the concept of size itself cannot be extrapolated to photons without clarifying its meaning.

This is rather a problem of the term particle. The usage in QM and the everyday usage of that word are very different. Any qm particle is different from a cannon ball.

1) Having quantized interactions IS a large portion of the meaning of having a particle in qm. The coincidence that the term particle is used for something rather different in classical physics is a rather unfortunate historical development. However, I do not think it is possible to have people use other terms instead.

2) In fact, it is a common misconception that the photoelectric effect demonstrates quantization. In fact it does not and could be explained without quantized interaction. One needs to demonstrate antibunching instead.

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11. Nov 30, 2011

### sophiecentaur

Haha. It may be an ill-defined question but it keeps getting asked. I have a feeling that we are a bit stuck with that one - rather in the same way that electrical current is described as electrons moving down a wore at high speed.

Common (mis?)use of words seems to be a problem all through Science.

12. Nov 30, 2011

### Q-reeus

you mean 'without quantized field' surely - there has to be some quantization going on - e.g. electron energy levels in detector surface. A.Neumaier argued just that some time back in a long thread. Problem I had with that is when it gets down to infrequent single photon emission hitting a distant small screen. If the screen area is very small relative to wavefront area (assuming spherically expanding wave past slit in 2-slit experiment)[let's make that single slit experiment - no complications with interference fringes], probability of ejecting a single photoelectron surely is infinitesimal, as only a tiny fraction of a single photon's energy impinges on the screen. With point particle viewpoint, ejection probability is simply always proportion to screen area.

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13. Nov 30, 2011

### f95toli

Whereas you can't assign a "size" to a photon it IS possible to sometimes find a connection with classical EM in that the wavelength matters even for a single photon number state.
A good example is cavity QED where the cavities are entirely "classical" in that they are designed using conventional EM even thouugh they are used in the QM regime.
Specifically, if you have a lamda/2 microwave cavity/resonator with a single photon in it and you want that photon to interact with another system (say an atom with a suitable transistion, or a qubit of some sort) the coupling strength has its maximum value in the centre of the cavity where -classically- you would expect the E field to have its maxumum value.
Hence, in cases where photons are confined in a certain space (which tends to be a pretty common situation experimentally) they have a "size" related to their (classical) wavenlength.

I should perhaps point out that it IS possible to quantize everything (the cavity, transmission lines etc) and use QM even in the design, but it is usually pretty pointless since the results agree with classical EM,

14. Nov 30, 2011

### sophiecentaur

That's an interesting way of looking at it and it's like the 'electron in a box' model. But I think it's just semantics to say the photon is 'that size' rather than its probability function - which is how the electron in a box model is treated.

I have a feeling that I am falling into the trap of trying to keep a foot in both camps though.

15. Nov 30, 2011

### A. Neumaier

But tiny probabilities are indeed appropriate here.

Note that many real life situations that actually happen have in fact extremely tiny probabilities.

For example, the probability that a given book unknown to you contains exactly the characters it contains in exactly that arrangement is incredibly small, far smaller than the ratio of surface area of the smallest and the largest things currently known to exist.

16. Nov 30, 2011

### edguy99

You are going from the collector of a transistor connected directly to the base of another transistor. Is this really a "transmission" of a photon?

17. Nov 30, 2011

### sophiecentaur

Well, the transmission is using em and can you avoid using photons? What else would you suggest?

18. Nov 30, 2011

### Ken G

In my view, the whole issue is resolved by noticing what the phrase "photons are particles" actually should mean to a scientist. It should mean nothing other than "in many contexts, we find it useful to imagine that a photon is a particle. This means, we borrow the ontological element 'particle' from a geometric/mathematical idealization that gives meaning to the concept, and apply the ontological concept to help us picture and understand observational outcomes via some particular theory that can manipulate the particle concept, often involving wave mechanics along the way." Now, that is rather long-winded, so we end up saving time and saying "a photon is a particle", but we really should mean the long-winded version. The only real problem appears when we forget that we should mean that, which does in fact happen all the time!

19. Nov 30, 2011

### edguy99

A density of electrons that varies on a regular basis over time (called the frequency). By default, this includes a density of electrons that varies from more dense to less dense, on a regular basis over space (called the wavelength).

20. Nov 30, 2011

### Ken G

Yes, that resolves the problem. My pointing to the ontological issues was to show where the question "how big is a photon" comes from, which is an overdependence on the reliance of ontological thinking (in the sense that anything that is physically real should have a unique physical size associated with it).
Yes, that is certainly the crux of the issue. So why do people imagine that "how big is a photon" is a well defined question? Ontological thinking. But if the "size" of a photon is contextual, then perhaps the whole notion of a photon is also contextual, and if that's true of our dearest friend the photon, perhaps it is true of all forms of scientific ontology.
Quite so, yet the re-use of the term is not coincidental. The "particle" ontology has certain attributes, yet the cannon ball and the photon borrow different ones. The confusion is resolved when we recognize that all these attributes exist only in the conceptual structure, not the real versions that are borrowing elements from that structure.
I often use "quantum" instead of "particle" for just that reason. Still, we must recognize that any word that gets used must not be confused with some kind of true ontology, they are all just going to label a set of borrowed ontologies.
That sounds like it's worth a thread of its own.