# What is a Field?

A shorter post today to break up what have been quite a series of length editions. So we’re about to talk about a concept fundamental to the subject of Physics and explain what it is – the field.

Fields were first conceptualised by Michael Faraday in the 19th Century and later immortalised into mathematical equations by James Clerk Maxwell. Faraday’s thoughts regarding fields were provoked by his tinkering with glass rods, needles, pins and magnets which repel and attract. Before Faraday the forces between objects such as a pin and a magnet or the moon and the earth were thought of as spooky ‘action at a distance’ – there was clearly some interaction between these objects but being separated by space it was unclear exactly how or rather what was mediating that interaction. This mediator was Faraday’s conceptual leap, the existence of a entity in the space between bodies which is distorted by electric and magnetic bodies and itself acts upon the bodies. This is the field.

The field is visualised as being composed of lines, ‘field lines’ which fill the space between objects. to use Rovelli’s metaphor, fields are like ‘a gigantic cobwebs filling everything around us.’ The lines (electromagnetic ones in this case) are distorted by electric or magnetic objects and in turn transmit the electric and magnetic forces from one object to another through this distortion. Therefore, it is not the objects that attract or repel each other directly it is the effect they have on their surrounding field lines which is then transmitted through the medium of the field lines themselves from one to the other- no more spooky ‘action at a distance’. The field lines can wobble and fluctuate, just like waves on the surface of a choppy sea.

You can see an example of the distortion in the field lines produced by two electrical charges below. When the charges are two of the same, +,+ the field lines are seen to diverge away from each other which is what we would expect from knowing that like charges repel each other (put two north poles of a magnetic together and feel the outward push). When the two charges are opposite, -,+ the field lines are seen to converge which again is what we expect knowing that opposite charges attract. (Maybe this is the cause for the saying opposites attract, although this might be true with particles I personally don’t find it the case with people..) When mathematically modelling the field we can assign value and direction to every point in space, which can be visually represented by the size and direction of the field line. Any particle susceptible to the field will then experience a force with corresponding strength and direction.

The next great stroke of genius came in the realisation that speed at which these field lines move is the same as the speed of light! James Clerk Maxwell realised that light itself is just a product of the fluctuations of Faraday’s field lines! Light and colours are simply oscillations of lines of the electromagnetic field at a particular frequency. Moreover other oscillations of the field lines at lower frequencies produce different types of electromagnetic waves such a radio waves or infrared waves – 20th century technology is born. (Quick note: we do not see the field lines themselves, only the vibrations/oscillations of the lines.)

But, it doesn’t stop here with the electromagnetic field, oh no all of the fundamental interactions have a field associated with them to mediate their dynamics. Electricity and magnetism – the electromagnetic field, gravity – the gravitational field, the strong force – the strong field, the weak force – the weak field. The fundamental interactions are also characterised by their particular fundamental particle, whose general term is a gauge boson. More specifically these are, photons for electromagnetic, gravitons for gravitational, gluons for strong and W and Z bosons for weak. In fact in 2012 a pivotal discovery at CERN was made of a new fundamental particle – the Higgs Boson. This particle is the particle that is suspected to give mass to other particles – Joseph is about to do a post on it imminently so I won’t tread on his toes but it also has an associated field – the Higgs field. The Higgs field is an energy field that is thought to exist everywhere in the universe and be responsible for giving mass to the other gauge bosons (apart from the photon which doesn’t interact with it, hence is massless!). So there we have it all the fundamental fields which mediate all the fundamental forces in nature. But there is just one more revolutionary step to be mentioned.

Up till now the universe consisted of space, fields and particles. The stroke of genius came from Einstein (of course it did) in 1915 with his theory of General Relativity. Einstein realised that the gravitational field was not just another one of the fields, the gravitational field was so much more, the gravitational field was space itself. There was no longer this mysterious nothingness of space ‘between’ field lines, the gravitational field line was the space. Just as with other field lines the gravitational field lines respond, move and bend in the presence of matter. So our everyday word ‘space’ does too as they are the same thing. Though I doubt we’ll all drop our colloquial convention and starting calling space the gravitational field, bit of a mouth full. Anyway, we have seen this idea with the visual depiction of space ‘bending’ in presence of heavy masses.

There we have it, space is no longer a separate entity, space is a field and the universe now consists of fields and particles alone. We are not trapped in rigid container filled with material but a malleable, flexible shell which curves and distorts in the presence of matter. Such was the powerful and revolutionary introduction of the field which not only allowed us to invent the lightbulb and create the radio but drastically changed our understanding of the fundamental constitutions of the universe and the nature of space itself.

## 46 responses to “What is a Field?”

1. Thank you. I have read a lot of science, but did not study physics in school. I’m finding your blog posts very helpful.

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• Thank you very much, comments like these always encourage me to write more!

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2. Thanks so much for this, I even took notes!!

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3. Aside from the structure of fields indicating line patterns of forces that have various effects on different materials I wonder exactly how the different types of fields manipulate space. Science has discarded the concept of an ether but is it really gone or have we simply renamed it as space? Experiment has indicated that certain materials such as iron and a few other element react to a magnetic field and others such as cellulose or water do not. What makes the difference? Everything reacts to a gravity field and nothing like H.G.Wells’ Cavourite or Buck Roger’s neutronium blocks gravity. Why is this so and is it impossible? Since photons have no mass but must travel through gravity distorted space they obviously react to gravity. But do electric and magnetic fields also distort space? I wonder.

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• The idea of our this mysterious notion of ‘space’ or ether is what is precisely overturned by Einstein’s general relativity. We must not continue to think of the space between field lines any longer as the gravitational field is space itself. The electric and magnetic fields themselves do not distort space, yet all particles/matter distort the gravitational field lines in their vicinity – therefore the electrically charged particle are what distort the gravitational field lines. The effect is reciprocal as their movement is susceptible to the distorted lines, producing the familiar effect of gravity on objects.

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4. Great post. No need for particles though, if we want to be ultra reductionist we can say “the universe now consists of fields alone” 😉

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• An interesting point! I assume you mean the fact that one might consider the universe to be reducible to nothing more than quantum fields. Quantum field theory is the area of science which pushes my buttons like no other. It is virtually impossible to express non-mathematical terms the emergence of a particle from a quantum field but suffice it to say it happens. The conceptual leap to state that the world is comprised of nothing more than quantum fields raises a number of deep questions; but is it right to label fields as fundamental? I don’t know the answer to this question; but my opinion is that it is not. There appears to be underlying rules and structure to fields that hint towards a more fundamental understanding. I believe this is the most interesting area of modern Physics.

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• Hi Joseph, that’s exactly what I was referring to and I agree it’s a fascinating area. Are fields fundamental? Like you I have no idea of the truth there, but I’m really not a rabid reductionist anyway – like David Deutsch I believe there can be fundamental principles at various “levels” of explanation. Of course there’s nothing wrong with seeking ever more fundamental levels in the reductionist sense, indeed it’s a wonderful and exciting program of research, we just need to make sure we know what it is we’re doing when we do that….

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• The question of the most fundamental level is indeed the most pressing and interesting question to face the human race. Understanding the world on this level is in the most literal sense understanding everything; greed is acceptable when the greed is for knowledge. There does of course however come a point where you can find yourself in a debate about the definition of the world fundamental itself!

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• I think we could probably find ourselves in a debate about more than the definition of the word fundamental ;). That would be a good thing though – debate is constructive (and really the primary process driving knowledge-acquisition, if you take a broad view of “debate”).

I completely agree that greed for knowledge is not only acceptable, but essential. Re: “understanding everything” though – hypothetically, if fields were indeed fundamental, would you believe that the Schrödinger equation could yield a complete understanding of the reasons Trump won the election?

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5. You have a way of explaining complicated matters in a clear and straightforward way, which I really like.

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6. I well remember the iron filings and the magnet from school they looked just like lines around the poles. We must not forget that the intuitive genius of Faraday gave us the electric motor and the generator without which we would literally be in the dark ages.
Why can we have magnetism without electricity but wherever there is electricity we have a magnetic field? Why is it that among the elements only iron cobalt and nickel exhibit magnetism? What is so special about iron ? What is the difference between electricity in a copper wire and electric waves or should I say electromagnetic waves in space? Lastly but not least where does the energy come from when a magnet picks up a piece of iron? Is it stored in the magnet ? and if so how did it get there?
My last remarkable fact may not be relevant but every hemoglobin molecule has an iron atom at its centre is this anything to do with magnetism ?

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• Hi Kertsen, some interesting questions!

1. It is actually a moving electric field that creates the magnetic field, and likewise a moving magnetic field will induce an electric field. The relationship is two way between them.
2. The ability of a metal to possess magnetic qualities is the result of free electrons. Each electron has its own sort of magnetic field which in most metals is totally paired off (it isn’t exactly like this but imagine there are 1 million N electrons and 1 million S electrons so no overall charge). The magnetic metals just don’t pair off in full which means there is a resultant magnetism.
3. There is a fundamental difference between the flow of electrons in a copper wire between a + and a – terminal. Some electric currents may emit electromagnetic waves; but they are not the same thing. Remember electric flows can be slowed or sped up. Electromagnetic waves are excitations in orthogonal electric and magnetic fields.
4. There is actually no force/energy to hold two magnetically charged objects together. There is a force required, a potential energy to hold then apart. As soon as something is in the field it has the potential energy – much in the same way that you have gravitational potential energy until you leave Earth’s gravitational field.
5. I don’t think blood has anything to do with ordinary magnetism, or I think if you were in a strong magnetic field it would be game over. I think there is a more biological answer in respect to weak magnetism and blood but I am not qualified to give this!

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7. I appreciate the answer but why is a field exposed with those iron filing lines? What do those lines signify? Does the field only exist along those lines and not between them? Or is a field somehow a folding of space into creases which form the lines?I am curious about the shape of space and its texture.

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• The answer is actually far less exciting than you might have hoped – so I am sorry to let you down! There are no field lines and the space between field lines does not exist by virtue of the fact that they don’t exist. They are a way of visualizing a field which leads to common misconceptions – not helped by dam iron fillings! The lines we draw have no physical meaning; the mathematical conception of a field is that it assigns some value, be it vector or scalar to every point in space in the field; clearly this breaks if it is only on the lines, you would float between gravitational field lines! If you kept penciling in more and more lines not touching between the lines you would eventually get a smooth vector or scalar function. This is more accurate, but near on impossible to see the direction or understand – hence we do not draw this for visualization purposes. Returning to the iron filings, when each filing is within a field it is magnetic also – so they clump up. Each filing will go to the closest clump which gives the illusion of lines, but it the filing-filing interaction rather than the existence of lines as a property of nature producing this. Does that make any sense?

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• Through the Google Images sites I have had a closer look at the iron filings patterns and agree that the lines formed by the filings are an illusion of the random clumping of the filings but the images are two dimensional and I would be fascinated by some way to see the field patterns in three dimensions. Perhaps a cloud of a suspension of very fine iron filings in air or water influenced by a magnetic or electromagnetic field would be revealing. It might also by interesting as in instrument for making a video of a variable field.

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8. I have to apologize for these childish questions but I never had the opportunity to speak to a polished chrome plated shiny physicist before and I am a bit excited that a scientist really cares to explain things. I worked as a display designer at the small Museum of Atomic Energy in Oak Ridge Tennessee and all the scientists there wanted to talk about was baseball so I had to invent the exhibits myself. When common phenomena are explained as waves or twists in space, as a visual minded artist I always wanted to see what they looked like and transverse electromagnetic waves never made simple sense in 3D space. When I was learning to be a radar technician in the US Army Airforce in Boca Raton Florida back in 1945 and was working with antennas I could understand the transverse waves moving up and down horizontally but when I tried to visualize what happened over the top of the antenna the ups and the downs never seemed to work out. This is the same type of necessity to kind of run my hand over space and feel the textures of a magnetic or electric field. What would space look like if I could see it? I guess it’s childish but I never found much use in growing up and at my age it seems unlikely and, considering what grown ups are doing to the world, not particularly attractive. Sort of like Einstein’s wild ride on a light beam.

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9. Hmmm, I wonder if there are ‘fields’ at work in the properties of attraction between strangers. Sometimes I wonder about this phenomenon (which does not happen regularly, I hasten to add) 🙃

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• I think that might be the action of a hormonal field!

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10. Ok. I’ll admit I haven’t read yet because you two are too deep to read on the fly. Maybe you already answered this, but I saw the display picture on the post and a question occurred to me. The magnetic lines between the two poles appear to be joining or merging or drawing together. I was wondering if we know if there’s something specific the outward lines are drawing toward and if so, what?

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• Hm I would not say so, if you look at image of the two opposite electric charges in the post itself, the lines still tend to curve round to draw together but the image itself doesn’t have the scale to accommodate this. The curvature of the field lines does get weaker the further away from the charged particle itself so the effect isn’t as obvious. Thanks for dropping by!

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• Thank you for your answer. Trying to wrap my mind around what these fields actually are. And for the record, I did go back and read the article.

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11. Thanks for those explanations just one puzzling fact iron may not be a magnet so when it becomes a magnet we somehow create free electrons inside the iron? I must admit it all seems somewhat strange but it all seems to work. Am I correct in thinking atoms are electrically neutral with a positive nucleus and negative electrons? Please ignore me if I ask too many questions I know you are pretty busy.

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• Not at all Kertsen – metals have free electrons; these are electrons which are not tightly bound to one specific atom but are still part of the overall structure of the metal. This is why metals conduct electricity – it is the flow of these free electrons which creates the current. The difference is with iron, for example, that when you pair up the free electrons you are left with an overall magnetism which is why iron can feel a force when placed in an electric field and yet other metals do not. Think of it as magnetic pairing of free electrons much like pairing of electrons and protons to give electrical neutrality. So yes – you are correct that an atom has a positively charged nucleus, with protons and neutrons (no charge) with electrons. The charge of an electron and a proton is equal and opposite. Thank you for reading!

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12. Wonderful thank you for this I have been looking for just such an explanation. You guys are the best.
When you say that space is now better understood as fields two questions arise.
1. Is “space” simply information?
2. Can and do different fields i.e. Gravitational fields and electrical fields or any other examples, ever interact with each other to produce interesting events?

Thank you so much have an amazing day!

QP

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13. it is really interesting topic , i am reading this topic again and again
really work hard by a writer .

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• i am mechlogy and i will come again and again your blog

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14. A rookie question but is the particle/wave identity field-related?

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• Not a rookie one, actually a very advanced one. Particles and fields are intimately related, the gauge bosons I mentioned above are actually the ‘quanta’ of their respective fields. This however is the realm of quantum field theory which is way over my head at the minute so I dare not try to explain! I shall try re-approach the topic in the future when I have a more solid understanding myself. Thanks for your insightful question!

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15. I can never stop saying it but I am a big fan of this blog.. very clear and well explained as usual. I wonder if you can write something about the anti-matter and black energy, to explain to people like me the beauty of our universe. thank you

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• Thank you very much! Yes thanks for the suggestion I was actually wondering what to write on next – I’m going to add antimatter and dark energy to my upcoming list.

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16. Wow, a lot of things that I did not know. Better start reading your post 3 or 4 times before going to the next. Thank you for sharing

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17. This really reminds me of the pandora myth, where all evils are set loose and hope barricaded in that box. Its as almost parallel to the field which you fluently wrote. The concept is that, when a certain molecule is thrown in any matter it will always adapt,adopt and assess its own situation.

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18. Pingback: Physics is massive·

19. Great post Mekhi. I wrote about Michael Faraday in Brian Clegg and my book “10 physicists who transformed our understanding of reality” – see