# What is the difference between a wave and a field?

Kenneth Boon Faker
I've been reading about Quantum Field Theory. It strikes me that since the 1920's, physicists have changed the name "wave" to "field". I can't tell the difference between today's "fields" and what was described a "wave" in quantum theory in the early 1900's.

So in quantum physics, is there a difference between a wave and a field, (and if so, what is the difference), or are the two words interchangeable? (Would it be possible to answer in layman's terms please).

Many thanks

Gold Member
2021 Award
A field is static and a wave oscillates with time. To take two extreme examples, if you have a rogue planet out in intergalactic space, its distortion of space-time creates a gravitational field around it. When two black holes merge, that creates a gravitational wave.

OOPS .. I see you've asked about QM waves/fields. Not sure if what I said is valid for that although I don't see why field and wave would be defined differently in QM.

Kenneth Boon Faker
Staff Emeritus

The etiquette here on PF is to never make a statement like that without saying exactly what you have been reading. A hyperlink is the best way. The reason is that readers often misinterpret what they read, so they say that the source says something it does not.

I don't understand why you connect waves with fields in your mind. Think of everyday life.

We have temperature fields; meaning a value of temperature at every point in 3D space, and in time. Temperature is a scalar field.

We have wind fields with a magnitude and direction of wind at every point in 3D space and in time. Wind is a vector field because it has both magnitude and direction.

How would those fields be like waves?

It is the phrase wave-function in QFT that confuses you?

Kenneth Boon Faker and sophiecentaur
Mentor
A field is a function whose input is a position (in space or spacetime) and whose output is some mathematical object, like a number or a vector. An example of a field whose output is a number might be the temperature in a room; it has some numerical value at every point in the room. An example of a field whose output is a vector would be the electrical field within that room; it is the force experienced by a charged test particle at a given point in the room.

A wave is any phenomenon whose behavior is described by some form of a particular differential equation, the "wave equation". Informally, that means "things that oscillate".

The two words are not even slightly interchangeable. Unfortunately I don't know any good "layman' terms, please" way of getting from the wave function of elementary quantum mechanics to quantum field theory; they are basically different formulations of the theory.

Monsterboy, Kenneth Boon Faker and russ_watters
Staff Emeritus
2021 Award
It strikes me that since the 1920's, physicists have changed the name "wave" to "field".

You're going to have to give specific examples. Otherwise, it's just the feeling of someone who doesn't understand what either one means. And given that waves and fields had definitions long before the 1920's, what you are claiming is immediately rather suspect.

Kenneth Boon Faker
A field is static and a wave oscillates with time.
No, that's not right at all.

Nugatory has a right answer, but I will add that waves exist within a field. A wave is a particular time-dependent pattern within a field which follows the mathematics of the wave equation, and the field is the medium. For example, an electromagnetic wave is a pattern (usually oscillatory in space and time) in the electromagnetic field. You can have patterns in a field which aren't waves -- e.g. the electromagnetic field where matter is present.

davenn and Kenneth Boon Faker
Kenneth Boon Faker
The etiquette here on PF is to never make a statement like that without saying exactly what you have been reading. A hyperlink is the best way. The reason is that readers often misinterpret what they read, so they say that the source says something it does not.

ou're going to have to give specific examples

I've gathered that subatomic particles have a wave-particle nature, (http://hyperphysics.phy-astr.gsu.edu/hbase/debrog.html#c1). The wave aspect of a particle it is not like a physical wave, but rather a probability wave, (i.e. a wave of information about where the particle is probably located etc.).

According to quantum field theory (), the fundamental buildings of the universe are not solid physical objects, but rather fields. These fields tend to ripple, which give rise to packets of energy. These packets of energy manifest as particles - electrons, neutrons, protons etc. (So even particles themselves are not solid objects rattling around.)

The fields in quantum field theory are not unlike the waves in traditional quantum theory, in the sense that they do not consist of any particular physical material. They are more like carriers of information and mathematics.

So to me, when today's physicists describe the "quantum fields", (which contain the maths and probabilities of the appearance of ripples), they are describing the same "waves" which Schrödinger, Heisenberg, Planck and Bohr described back in early 1900's.

Staff Emeritus
". I can't tell the difference between today's "fields" and what was described a "wave" in quantum theory in the early 1900's.

But you can tell the difference between the ocean and a wave on the surface of the ocean, right?

DaveC426913 and Kenneth Boon Faker
Kenneth Boon Faker
But you can tell the difference between the ocean and a wave on the surface of the ocean, right?

That's a good analogy, which, if you think about it, also demonstrates that it's one and the same thing.

Staff Emeritus
That's a good analogy, which, if you think about it, also demonstrates that it's one and the same thing.

How can you say that? There are not always waves on the ocean. Ocean and wave are not synonyms.

Kenneth Boon Faker
How can you say that? There are not always waves on the ocean. Ocean and wave are not synonyms.

They're made of the same 'substance', which was my original point to the thread. The difference between the ocean and quantum fields, however, is that quantum fields and quantum waves are not made of any material substance at all. They are more of an ethereal substance - the carriers of information and mathematical principles. (Dare I say it, quantum fields, which form the root and base of everything in the universe, reveal attributes more of mind and consciousness than anything physical).

Mentor
That's a good analogy, which, if you think about it, also demonstrates that it's one and the same thing.
That's like saying that elephants and running are the same thing because elephants sometimes run.

I would buy the analogies: wave is to field as ocean wave is to ocean water and as running is to running elephant.

Kenneth Boon Faker
That's like saying that elephants and running are the same thing because elephants sometimes run.

Oceans and ocean waves are made up of water molecules. They are made of the same substance. But the same can't be said of elephants and running. Quantum fields and quantum waves are also made of the same 'substance', that's the point I've been trying to make

Mentor
Oceans and ocean waves are made up of water molecules.
You will continue to confuse yourself if you continue to think of a wave as a moving something rather than a form of motion. To be fair however, confusion of this sort is very hard to avoid when trying to describe the concepts in natural language and by analogy instead of precisely and in the language of mathematics. If you set up and solve a few different wave problems (taut string, water wave, electromagnetic wave, ...) this entire wave vs. field problem will resolve itself - it will become clear that the wave and the thing waving are completely different things.

anorlunda and Kenneth Boon Faker
Gold Member
I can’t help thinking that the OP is looking for something that just isn’t there. The two terms are perfectly well defined in the Classical context and I can’t see that anything is different in Modern Physics. Waves all involve variations of some quantity in space and time but fields have a fixed value at any location and time.

Gold Member
2021 Award
Waves all involve variations of some quantity in space and time but fields have a fixed value at any location and time.
Which is exactly what I told him in post #2, only to be contradicted in post #6

Staff Emeritus
Which is exactly what I told him in post #2, only to be contradicted in post #6

It is splitting hairs, but you said fields are static. That's not the same as "fixed value at any location and time."

Gold Member
2021 Award
It is splitting hairs, but you said fields are static. That's not the same as "fixed value at any location and time."
Ouch. My hairs feel split.

CalcNerd and sysprog
nasu
What does it mean to have a fixed value at "any location and time"? This seems like true for anything, field or no field.
I mean, how else can be that value than "fixed"? It cannot vary in time or space because they are both fixed by specifying a certain location and time.

Gold Member
What does it mean to have a fixed value at "any location and time"? This seems like true for anything, field or no field.
I mean, how else can be that value than "fixed"? It cannot vary in time or space because they are both fixed by specifying a certain location and time.

Perhaps I could rephrase and say the value of a field doesn’t involve knowing its value somewhere else or at a different time: it is not expressed as a function of position or time.

nasu
I don't think that the second part of your statement is meaningful.
The concept of time dependent fields is used in many texts The magnetic field in the magnetic core of a transformer depends on both position and time. I don't think that the time variation is a good feature to distinguish fields from waves.

Gold Member
Fair enough. Replace “or” with “and”?

Monsterboy
Oceans and ocean waves are made up of water molecules. They are made of the same substance.

Consider some sound waves travelling through the air. Air is a medium made of gaseous molecules.

Can you claim that sound is "made" of air ? If that is so what happens when the sounds hits a water surface ?

You will see waves travelling on the surface, correct ?

Now, all of a sudden, sound waves "made" of air became sound waves "made" of water ? That doesn't make sense. If something is made of air, it cannot suddenly be made of water, isn't that right ?

Conclusion: Sound waves are not made of air or any substance, they are disturbances in a medium.

Waves are disturbances that propagate in a field.

Gold Member
I really don’t see the point in wasting more time on this. You could have the same argument about any pattern that’s created with a medium. A letter “B” is not usually thought of as Ink, Paint or LCD Pixels. The important quality of “B” is how it makes up words and carries information. I can’t imagine a long, fruitless discussion about “B”, along the lines of this “wave” discussion.
(That is unless the protagonists happened to be Philosophers with loads of time to spare.) [emoji6]

Monsterboy
I really don’t see the point in wasting more time on this. You could have the same argument about any pattern that’s created with a medium. A letter “B” is not usually thought of as Ink, Paint or LCD Pixels. The important quality of “B” is how it makes up words and carries information. I can’t imagine a long, fruitless discussion about “B”, along the lines of this “wave” discussion.
(That is unless the protagonists happened to be Philosophers with loads of time to spare.) [emoji6]
I just made the relationship between a wave and the medium (or field ?) clear to understand without any mathematics. The OP suggested that they are one and the same thing, I just gave an example to show that they are not.

In QM a particle is just an "excitation" in a field right ? Is that analogous to "disturbances" in my above example ?

Last edited:
Gold Member
I just made the relationship between a wave and the medium (or field ?) clear to understand without any mathematics. The OP suggested that they are one and the same thing, I just gave an example to show that they are not.

In QM a particle is just an "excitation" in a field right ? Is that analogous to "disturbances" in my above example ?

The trouble is if you want a rigorous and definitive answer to the question, you need to include all facets. You can not avoid Maths if you want that.
What you have written can be enough for a ‘chat’ but how far is this thread supposed to take us?
You pays yer money and you takes yer pick in a question like this.
There is no all embracing answer, I think.

Monsterboy
The trouble is if you want a rigorous and definitive answer to the question, you need to include all facets. You can not avoid Maths if you want that.
What you have written can be enough for a ‘chat’ but how far is this thread supposed to take us?
Well, looking at the OP and his arguments it was clear he was not into the math of the topic, so I gave a high school level answer, I don't know if your ink and letters analogy was directed at my post, did you find anything that didn't sound right ?

Rigorousness of answers should match the level of education of the OP, (but it's not always possible to know that before a few posts) or else he might be driven away....just my opinion.

Gold Member
“Rigorousness” should be appropriate, as you say. But where rigour is missing I always feel that there should be strong caveats. Popular Science tends to be lacking in those and that degrades the perceived level of understanding involved.

fleetwoodPC
“There are not always waves on the ocean.”

Is that true? It seems to me that every point on an ocean surface oscillates because, unlike a pool, the edges are too far for any particular wave to dampen by hitting an edge.

Gold Member
I can't think of a situation in which there are no waves in a part of the ocean (except, perhaps the frozen bits). There is always Energy flow over the Earth and that involves wind and other thermal transfer.

Is this thread really worth while resurrecting, though?

Gold Member
I can't think of a situation in which there are no waves in a part of the ocean (except, perhaps the frozen bits). There is always Energy flow over the Earth and that involves wind and other thermal transfer.
I can tell you that when the wind dies, the lake is like glass.

The field (water surface) remains, whether or not it is manifesting wavelike properties (er, waves).

Is this thread really worth while resurrecting, though?
Heh. No. But when has that stopped us?

davenn and sophiecentaur
fleetwoodPC
No.
Is this thread really worth while resurrecting, though?
No.
I read the messages and now understand that a field is a collection of measurements – a map of values.

Examples of those measurements are scalers (1D) and vectors (2D). (Could that measurement be another field if we're talking about, for example, a quantum field associated with a 'newtonian' point?

sysprog
“There are not always waves on the ocean.”

Is that true? It seems to me that every point on an ocean surface oscillates because, unlike a pool, the edges are too far for any particular wave to dampen by hitting an edge.
Well, anything composed of molecules that has a temperature above 'absolute zero' can be (not wrongly) said to 'oscillate' (exhibit more than zero motion at a molecular level), but a becalmed sailboat on the ocean doesn't normally encounter what a sailor would ordinarily think of as significant waves, right?

Staff Emeritus
“There are not always waves on the ocean.”

Is that true? It seems to me that every point on an ocean surface oscillates because, unlike a pool, the edges are too far for any particular wave to dampen by hitting an edge.
There's room for disagreement. In the picture below, would you say there are waves or no waves? The reflection of the mast in the water has ripples. It is not as smooth as a glass mirror.

berkeman and sysprog
sysprog
anorlunda said:
It is not as smooth as a glass mirror.
. . . and even a glass mirror has very tiny waves . . .