I assume you mean fundamental particles since atoms are bound states of particles and we have certainly observed atoms.

We never observe particles. We observe quanta of energy, momentum, angular momentum and charges. While this combination of physical properties is conventionally called "a particle", it's not an object. It's merely the transfer of energy, momentum, angular momentum and charge from one system to another.

@JohnRennie I added "fundamental" to the title. My question relates to the issue that many people seem to feel that the electron field somehow describes another entity that is a small hard lump. This is the focus of the question. And in that sense, an atom is not a particle.

@FlatterMann more or less my position. But, do we have some kind of reference that would clearly state this as an orthodox position. My motivation is to be able to respond compactly in discussions on the matter.

The only reference that you need in science is nature. Having said that, Einstein had this figured out in his 1905 paper on the photoelectric effect. The only mistake he made in that paper was to assign a location property to photons, which was a remnant of Newton's corpuscular theory of light. Since energy was known to be a system property, that was a fairly trivial mistake. In any case, if people doubt you, point to a solar panel, explain that it converts 10^22 photons per second into electrical energy and ask them where the collected photon particles are supposed to come out?

What does it mean for a particle to "actually exist"? Is the discrete blips a cathode ray produces on a screen enough evidence of existence for you?

@ACuriousMind What you are seeing there are not particles. They are flashes of light that are being caused by the localized conversion of energy. Why that conversion is localized has been theoretically explained by Mott in 1929. His paper is one of the most overlooked fundamental insights in physics, as far as I can tell.

@FlatterMann The point of my comment was to get OP to clarify their question (since presumably they have already discarded things like cathode rays as sufficient evidence), not to solicit other opinions. Please remember that comments are for criticizing and clarifying the post they're commenting on, not for general discussion.

@ACuriousMind Agreed. I apologize for my "zeal". This is one of the few topics that gets me going.

@ACuriousMind I have added what I hope will clarify. I am using the word observe and exist informally. And I am not even slightly saying "particles don't exist change my mind". I am asking for experiments that people think have to be interpreted in terms of hard lumpish particles. Maybe this should be moved to a chat session. If you are interested. But, my question is not really philosophical.

I'm questioning your term "observed", what it means to you ? Observed with a naked eye ? Observed with an optical microscope, electron scanning microscope, other means ? Some particles so weakly interacts with fields, including electromagnetic radiation, that it's an achievement to capture traces even a few of them (consider neutrino particle). And particle chamber is an observation to you or not ? "Observation" is very vague term. Humanity has passed naked eye observation barrier some time ago and will not return back.

Even looking through the glasses, - is not a naked eye observation :-D Otherwise, if any evidence of particles collected within some measuring devices is okay to you,- there are gazillion of ways to notice particle behavior.

@FlatterMann Well it’s obvious that nothing is solid and particles are just systems of smaller particles.

@BillAlsept Given the definition of "particle" in physics as the approximation of the motion of an extended classical body by the motion of its center of mass that is very unlikely.

@BillAlsept In classical mechanics? Yes. Can we prove that photons are nothing but field energy? Absolutely. That's the reason why there is no tap on solar panels. We never have to drain them of the excess photons they are collecting.

@FlatterMann while my views appear to be mostly aligned with yours here, I feel that the argument is incorrect or at least incomplete. Solar panels get hot and radiate photons. So, one could say they are self draining. Also, the total number of photons does not have to be conserved even if we assume they exist as lumpish particles - as we have the principle that they can be created and destroyed. Having said that - I am currently engaged in several arguments in which I am supporting the idea that photons are nothing but fields.

@FlatterMann Field energy is not an answer because you’re not describing what it is or where it comes from. We know it’s made of individual photons. I mean just saying field energy is no different than saying inspiration or spiritual energy etc. I’m not saying there’s no such thing as fields because there are photon fields. What are you saying your field is??

@BillAlsept okay, I know you seem to be talking to Flattermann and not noticing me, but I just wanted to say that for me the field is the field. It is otherwise undefined it is made of itself. So, I agree with you that it is not made of field energy. It may have associated energy (as does an electric field) but that does not mean it is made of energy. However, I would also feel that we do not know that it is made of individual photons. A photon is a certain pattern in the field, the field does not have to be described as a collection of photons.

@PonderStibbons Saying that a field is a field with it it’s made of its self it’s still no answer. There’s something there or there’s not. Photons create the field, not the other way around. Photons can be described, Fulton fields can be described, and with a photon model you can derive any light phenomena. Just saying a field is the field doesn’t answer anything.

@PonderStibbons Yes, the field is the field. It's the subject in our sentences. The important aspect about energy is that it is not a subject but has the function of an adjective. It is a property of the field. So while "the nature of the field" may not be satisfactorily explained or even explainable at all, the nature of energy as a property of the field is extremely well defined (at least locally, at the level of general relativity even that seems to run into considerable technical problems). Physics is therefor all about the properties of "stuff" and not "the stuff" itself.

@BillAlsept Energy, momentum, angular momentum and charges are what physicists actually care about. That was already so in classical mechanics and it hasn't changed all the way to quantum field theory. I agree that we don't teach it that way, especially at the high school level, but we should. Focusing on the important properties takes the philosophical nonsense about "the nature of things" off the table. If you don't believe that this is a winning strategy, then look at mathematics. Mathematicians don't care about objects, they only care about the consequences of their abstract properties.

@PonderStibbons A photon is the amount of energy that gets transferred between the electromagnetic field and an external system during an irreversible process (emission or absorption). It is not a thing and we can never find a photon outside of such irreversible processes. It is therefor not useful to talk about photons as if they were objects. They are not objects, they don't have any "properties" themselves because they are a property of physical processes already. No, photons don't create the field. They are a property of the field for certain interactions.

@FlatterMann your first and fourth sentence get it right. And energy, momentum, angular momentum and charges are what physicist should care about. Focusing on those important properties is important. Just saying a field is a field gets you nowhere. I think a winning strategy is to know what that field actually is. What if we treated everything the way you’re treating fields? What if we didn’t care what protons or neutrons or molecules or atoms or anything was and all we had to do was say a proton is a proton or an atom is an atom and that’s all the answer we need.

@FlatterMann not quite sure why you mentioned most of what you just addressed to me - as I never said anything in contradiction to it. But, I would disagree about what a photon is. That is - I know what a photon field is, but I think that photon is just an adjective. And I expect you are incorrect about requiring a photon to be associated with an irreversible process. Non linear, perhaps, but irreversible. Not sure why you went that way.

@FlatterMann I strongly suspect that a lot of this comes down to differences in the linguistic aspects of the terms. Having spoken to plenty of people on this topic over the years, I feel that people take a lot of it in different ways from each other and often in arguments pick up on some element of the usage of the word which was not fundamental to the intention.

@BillAlsept to be more precise - if we say that some things are built out of other things then at some point we have to stop or we have an infinite descent. Fundamental fields are called that because they are fundamental. That is - not made of anything. They just are. If you came up with a new theory where the current fundamental fields (photon, electron, etc) were fields in an effective field theory, then you would just create a new set of fundamental fields that are not made from anything.

@BillAlsept Unless you want to invoke particle democracy.

@BillAlsept and energy is a property of the field, not what it is made from. Eg, in Schroedinger theory, essentially the temporal partial derivative.

@BillAlsept Pondering the nature of a field is useless. An electric field is simply the description of the forces between charges. It is that by definition. It tells you absolutely nothing about "what a charge is". It only tells you how a charge behaves because that is how it was defined by humans.

@PonderStibbons I, or better machines that I have designed and partly built with my own hands, have measured trillions of photons. Every single time an irreversible energy exchange took place. Not once in my life have I ever seen or measured a photon without such a process. I have never met a single physicist who could show me how one can measure a photon without one. If you know, this would be the time to tell me.

If you can't (and I know that you can't), then I will simply reject your claim as easily as I reject claims about perpetual motion.