Understanding Virtual Particles: Excitations of Quantum Fields

[eightsquare]

I did some research on Wikipedia, and I quote from the write up on Real Particles:
"The term(Virtual Particles) is somewhat loose and vaguely defined, in that it refers to the view that the world is made up of "real particles": it is not; rather, "real particles" are better understood to be excitations of the underlying quantum fields. Virtual particles are also excitations of the underlying fields, but are "temporary" in the sense that they appear in calculations of interactions, but never as asymptotic states or indices to the scattering matrix."

What I wanted to ask was, what is the meaning of "excitation of the underlying fields"? What quantum field are they talking about? I always thought that in quantum mechanics fields were basically made up of particles. But that brings me back in a loop.

 

[eightsquare]

Why do particles move when force is applied?

According to Wikipedia, a particle is nothing but an excitation of the underlying quantum field. So how exactly are forces defined in quantum mechanics and why does the 'excitation' tend to move when we apply a force to it?

 

[wotanub]

Welcome to PF, 8². I'm not sure what level of physics you have, I think a "mid-level" understanding of quantum mechanics is needed to answer this question. At least the quantum harmonic oscillator and some classical field theory.

I know about this in terms of very basic QFT. Do some research on quantizing the EM field. One can write down the Hamiltonian for an EM field, and find it has a form like the harmonic oscillator. The eigenstates of the corresponding number operator are called Fock states. When the raising operator is applied to the Fock state it increases the quanta of the field by one. The quanta is called a photon and the raising operator is re-termed the creation operator since it creates a qunata. Similarly, the lowering operator is called the annihilation operator. I imagine the approach is similar for whatever kind of field you would like to quantize.

Here's a good lecture video that explains it very clearly.
And the Wikipedia article. http://en.wikipedia.org/wiki/Quantization_of_the_electromagnetic_field

In QM, we really don't discuss forces per se, we prefer to talk about energy. Particles experience force because they have potential energy, and they move because they have momentum, and the force can change momentum, just like in classical mechanics. You can always write down the force, equations of motion, or what have you from the Hamiltonian (energy), but equations of motion really take a back seat in quantum mechanics.

 

[Maui]

Particles somewhat in the future.
For a more detailed response see:

https://en.wikipedia.org/wiki/Quantum_field_theory

and any of the books often recommended here.

 

[mattt]

Quantum Fields are some mathematical objects that appear in some mathematical structures used to produce predictions of the outcomes of some experiments.

 

[The_Duck]

According to Wikipedia, a particle is nothing but an excitation of the underlying quantum field. So how exactly are forces defined in quantum mechanics and why does the 'excitation' tend to move when we apply a force to it?

You can think of a field as the surface of a pond and "excitations" as traveling waves on the surface. Forces appear when different parts of the water have different properties (different "potential energy"), which can cause the waves to bend (toward regions of lower potential energy) instead of propagating in straight lines.

 

[No-where-man]

You can think of a field as the surface of a pond and "excitations" as traveling waves on the surface. Forces appear when different parts of the water have different properties (different "potential energy"), which can cause the waves to bend (toward regions of lower potential energy) instead of propagating in straight lines.

This is very interesting. But is entire universe (well at least this visible observable part of the universe) made of one quantum field or more quantum fields that are directly connected and full of interactions?

 

[eightsquare]

@No-where-Man- I'm pretty sure more than one field. Every elementary particle is considered to be a quanta of their respective fields, and as there are many elementary particles, I'd say there are many fields full of interactions.

To everyone- The vacuum fluctuation model of the beginning of the universe imply that these fields exist even in a vacuum, even when there is no real particle affecting the space around it. Maybe this is a fallout of the Heisenberg uncertainty principle, but does it mean that even the existence of fields is uncertain on the most fundamental level and that even nothing can have fluctuations due to uncertainty?

 

[mpv_plate]

... does it mean that even the existence of fields is uncertain on the most fundamental level and that even nothing can have fluctuations due to uncertainty?

Yes. The fields cannot have definite zero value and definite zero conjugate momentum everywhere all the time because of the canonical commutation relations. Even if there are no particles in the fields.

 

[No-where-man]

Yes. The fields cannot have definite zero value and definite zero conjugate momentum everywhere all the time because of the canonical commutation relations. Even if there are no particles in the fields.

I'm still confused with the answer, I read a lot about Heiseneberg's uncertainity principle, and I'm still not sure if I understand it.
Why wouldn't fields have 0 value and definite zero conjugate momentum everywhere all the time (whatever that means), just because you cannot 100% know both position and momentum at the same time?
I don't understand why would this be a case?

I'm not questioning Heisenberg's uncertainty principle at all, I just don't understand it.

 

[The_Duck]

I'm still confused with the answer, I read a lot about Heiseneberg's uncertainity principle, and I'm still not sure if I understand it.
Why wouldn't fields have 0 value and definite zero conjugate momentum everywhere all the time (whatever that means), just because you cannot 100% know both position and momentum at the same time?
I don't understand why would this be a case?

The uncertainty principle is more general than the one between position and momentum of particles. In field theory, we have an uncertainty relation between the value of a field at a point, and its time rate of change at that point. (Partly to make an analogy to the more familiar position-momentum uncertainty relation, we sometimes call the time rate of change of the field its "conjugate momentum." This is jargon: "momentum" here has nothing to do with the momentum of particles or anything like that).

The position-momentum relation for particles implies that if you confine a particle to some region, its momentum becomes uncertain. We might poetically think of this uncertainty as a result of constant unobserved fluctuations in the position and momentum of the particle. The uncertainty relation described above for fields has a similar result. If a field, for example the electromagnetic field, is "naturally" zero in vacuum, it cannot be exactly zero all the time because of the uncertainty relation between the value of the field and its time rate of change: if we know that the field has a value close to zero, then there is some uncertainty in its time rate of change. Again we can poetically think of this as a result of constant unobserved "vacuum flucuations" of the field, which consist of the value of the field fluctuating in some region around zero.

 

[hilbert2]

In field theory, we have an uncertainty relation between the value of a field at a point, and its time rate of change at that point. (Partly to make an analogy to the more familiar position-momentum uncertainty relation, we sometimes call the time rate of change of the field its "conjugate momentum." This is jargon: "momentum" here has nothing to do with the momentum of particles or anything like that).

A question about this... The generalized uncertainty principle relates the combined uncertainty of two observables to their commutator (two commuting observables can be measured accurately at the same time, a noncommuting observable pair can not). Do the field strength and its conjugate momentum of a fermionic field obey a commutation or an anticommutation relation? With the creation and annihilation operators of fermion fields there seem to be anticommutation rules.

 

[No-where-man]

The uncertainty principle is more general than the one between position and momentum of particles. In field theory, we have an uncertainty relation between the value of a field at a point, and its time rate of change at that point. (Partly to make an analogy to the more familiar position-momentum uncertainty relation, we sometimes call the time rate of change of the field its "conjugate momentum." This is jargon: "momentum" here has nothing to do with the momentum of particles or anything like that).

The position-momentum relation for particles implies that if you confine a particle to some region, its momentum becomes uncertain. We might poetically think of this uncertainty as a result of constant unobserved fluctuations in the position and momentum of the particle. The uncertainty relation described above for fields has a similar result. If a field, for example the electromagnetic field, is "naturally" zero in vacuum, it cannot be exactly zero all the time because of the uncertainty relation between the value of the field and its time rate of change: if we know that the field has a value close to zero, then there is some uncertainty in its time rate of change. Again we can poetically think of this as a result of constant unobserved "vacuum flucuations" of the field, which consist of the value of the field fluctuating in some region around zero.

But wouldn't be possible to actually detect energy value of the field, if you know at least one of properties (either position or momentum)?
I mean can the non-zero energy be detected?
And please read this and tell me what you think:
http://www.sciencedaily.com/releases/2013/03/130303154958.htm

Thanks.

 

[mpv_plate]

Why wouldn't fields have 0 value and definite zero conjugate momentum everywhere all the time (whatever that means), just because you cannot 100% know both position and momentum at the same time?

You can actually know both of them simultaneously (technical remark: quentum fields are not observable, so I'm talking here figuratively), but due to the commutation relations there is a non-zero probability that the values of the fields or their momenta will differ from zero when you next "measure" them.

Heisenberg uncertainty is not saying that you cannot know the non-commuting quantities simultaneously. The uncertainty is only defining the statistical features of repeatedly measured values. But during one measurement you can measure both non-commuting quantities to arbitrary precision simultaneously.

Some details about the vacuum state of quantum fields are http://www.quantumfieldtheory.info/website_Chap03.pdf. Go to page 55, paragraph 3.4.3 Zero Point (Vacuum) Energy.

 

[No-where-man]

You can actually know both of them simultaneously (technical remark: quentum fields are not observable, so I'm talking here figuratively), but due to the commutation relations there is a non-zero probability that the values of the fields or their momenta will differ from zero when you next "measure" them.

Heisenberg uncertainty is not saying that you cannot know the non-commuting quantities simultaneously. The uncertainty is only defining the statistical features of repeatedly measured values. But during one measurement you can measure both non-commuting quantities to arbitrary precision simultaneously.

Some details about the vacuum state of quantum fields are http://www.quantumfieldtheory.info/website_Chap03.pdf. Go to page 55, paragraph 3.4.3 Zero Point (Vacuum) Energy.

Ok, thanks, I thought about zero-point energy but I actually thought this was a crackpot hypothesis not made by true physics, I was wrong:
Can you just comment this link I found:
http://www.sciencedaily.com/releases/2013/03/130303154958.htm

 

[The_Duck]

Do the field strength and its conjugate momentum of a fermionic field obey a commutation or an anticommutation relation?

An anticommutation relation. Also my statement above that the conjugate momentum is the time rate of change of the field isn't true for fermionic fields.

can the non-zero energy be detected?

Yes. One way of thinking about the Casimir effect is in terms of the "zero-point energy" due to these "vacuum fluctuations."

There's a caveat, though: we can't detect the *absolute* energy density due to vacuum fluctuations. In the Casimir effect, for instance, we can only detect the *change* in vacuum energy density produced by the presence of a pair of conducting plates.

 

[Maui]

Can you just comment this link I found:
http://www.sciencedaily.com/releases/2013/03/130303154958.htm

Their experiment highlights a property of quantum systems - that their behavior is dependent on what can be known. You still need a 'strong' measurement for any real reading, the weak measurements are only revealing what the system is doing mostly(this would be classically impossible so interpret as you deem fit). The bottom line is this - they are not really getting aroung the Heisenberg uncertainty principle. They are getting more data than 'usual'(about the first property) but it's as ambiguous as Heisenberg postulated close to a century ago.

 

[eightsquare]

Why are there only a finite number of fields? And do we know why they interact with each other the way they do?

 

[No-where-man]

Why are there only a finite number of fields? And do we know why they interact with each other the way they do?

I will bet that there is a truly infinite number of fields.

 

[ZapperZ]

Why are there only a finite number of fields?

Where do you get such a thing?

Zz.

 

[eightsquare]

@ZapperZ: So is it that only some fields can be quantized and most of them don't interact with each other? Otherwise we'd keep seeing new particles every day.

 

[Bill_K]

Why are there only a finite number of fields? And do we know why they interact with each other the way they do?

There is one field for each type of elementary particle, no more, no less. In the Standard Model, there are (depending on how you count them) 29 different particles. So: 29 fields. (EDIT:Sorry, 36.)

 

[eightsquare]

There is one field for each type of elementary particle, no more, no less. In the Standard Model, there are (depending on how you count them) 29 different particles. So: 29 fields.

So what does Zapper's message mean?

 

[ZapperZ]

@ZapperZ: So is it that only some fields can be quantized and most of them don't interact with each other? Otherwise we'd keep seeing new particles every day.

So what does Zapper's message mean?

You seem to think that when I asked where you get such things, that my question implies such-and-such. I'm trying to figure out WHERE you got the information that allows you to make such a conclusion, so that I know in what context you are asking. I have to know what you know before I actually understand the origin of the question! After all, this thread started with you asking what "quantum fields" are! I have no idea if you've understood what it is and whether you have any understanding of how they relate to the elementary particles.

Zz.

 

[eightsquare]

From what I've read, all fields in quantum mechanics can be quantized. And since we have only a finite number of elementary particles, I concluded that there are only a finite number of fields.

 

[Naty1]

eightsquare...

And since we have only a finite number of elementary particles, I concluded that there are only a finite number of fields.

So far that fits what we know. All electrons are supposedly identical because they are all excitations of same electromagnetic vacuum field [wave] . Nobody knows exactly what an electron 'really' is. All we know is that when it interacts its seems to do so at a point ...like an infinitesimally small particle... but exactly how small that 'point' is remains for the time being smaller than we can detect...but likely bigger than Planck size...


After numerous discussions in these forums, [a couple links to discussions are listed below] the best [relatively non computational] descriptions I have seen include these:

If you are familiar with complex imaginary numbers, like a +bi, this is one way to approach 'particles':

[ The "operators" referred to are mathematical entities [expressions] that make others appear [creation operators] and disappear [annihilation operators. They create and destroy 'particles mathematically.]

...complex imaginary numbers and their operators are associated with virtual particles, which cannot be detected, while complex real numbers and their operators are associated with real [detectable] particles.

There is not a definite line differentiating virtual particles from real particles — the equations of physics just describe particles (which includes both equally). The amplitude that a virtual particle exists interferes with the amplitude for its non-existence; whereas for a real particle the cases of existence and non-existence cease to be coherent with each other and do not interfere any more. In the quantum field theory view, "real particles" are viewed as being detectable excitations of underlying quantum fields. ...

Two other descriptions I like:

Tomstoer

Particles appear in rare situations, namely when they are registered.

Marcus:

The trouble with the particle concept is that one cannot attribute a permanent existence; It only exists at the moment it is detected. The rest of the time there is a kind of spread out thing---a cloud---a wave---a field---something that is less "particular", something that cannot be detected.

Lots more here:

What is a particle:
https://www.physicsforums.com/showthread.php?t=386051

 

[eightsquare]

Thanks.

 

[No-where-man]

eightsquare...So far that fits what we know. All electrons are supposedly identical because they are all excitations of same electromagnetic vacuum field [wave] . Nobody knows exactly what an electron 'really' is. All we know is that when it interacts its seems to do so at a point ...like an infinitesimally small particle... but exactly how small that 'point' is remains for the time being smaller than we can detect...but likely bigger than Planck size...After numerous discussions in these forums, [a couple links to discussions are listed below] the best [relatively non computational] descriptions I have seen include these:

If you are familiar with complex imaginary numbers, like a +bi, this is one way to approach 'particles':

[ The "operators" referred to are mathematical entities [expressions] that make others appear [creation operators] and disappear [annihilation operators. They create and destroy 'particles mathematically.]

Two other descriptions I like:

TomstoerMarcus: Lots more here:

What is a particle:
https://www.physicsforums.com/showthread.php?t=386051

I disagree with Marcus and you, if there were no fields all the phenomena that physics have "seen" so far in the experiments would never be possible in the first place.
If you talk about interaction, no interaction would be possible if these quantum fields did not exist in the first place, because can't interact with the empty void/nothingness.

Interaction would never be possible if fields, regardless if we're watching them or not, did not exist in the first place!
Quantum fields are more than just pure models, they are experimentally, irrefutably proven.

 

[Maui]

Interaction would never be possible if fields, regardless if we're watching them or not, did not exist in the first place!
Quantum fields are more than just pure models, they are experimentally, irrefutably proven.

I agree, I think this is entirely correct and I am willing to take it a step further and say that obviously the MWI can not be entirely wrong and neither can the orthodox CI. The CI needs the MWI for the real wavefunctions and the MWI needs the CI for the preferred basis problem. The preferred basis problem can be 'solved' if we accept that brains cannot observe quantumness (the hup and some experiments link knowledge and behavior of quantum particles) and probably brains single out the single reality that we observe because that is the only possible way to make sense of reality(and brains are about making sense of things). When brains go wrong due to schizophrenia or LSD or even in dreams during sleep, their neurons probably could not get the right pattern for making complete sense of the reality of fields/possibilities. This(the idea that brains could be interface between the fields and single classical-like reality) allows the world to be completely quantum and yet experienced as completely classical and comprehensible with the utilization of quantum computing while providing some clues into the nature of human experience, the nature of dreams and sheds some light on what is out there (quantum fields).

I can see no contradiction or conflict with known experiments and it's compatible with locality, realism and known science that rests on them both while both the mwi and the ci when taken separately struggle to explain adequately the outside world of observations. Even decoherence makes sense as the classical world happens at the time of information becoming available about quantum systems and in this framework the role of decoherence appears natural.

 

[No-where-man]

I agree, I think this is entirely correct and I am willing to take it a step further and say that obviously the MWI can not be entirely wrong and neither can the orthodox CI. The CI needs the MWI for the real wavefunctions and the MWI needs the CI for the preferred basis problem. The preferred basis problem can be 'solved' if we accept that brains cannot observe quantumness (the hup and some experiments link knowledge and behavior of quantum particles) and probably brains single out the single reality that we observe because that is the only possible way to make sense of reality(and brains are about making sense of things). When brains go wrong due to schizophrenia or LSD or even in dreams during sleep, their neurons probably could not get the right pattern for making complete sense of the reality of fields/possibilities. This(the idea that brains could be interface between the fields and single classical-like reality) allows the world to be completely quantum and yet experienced as completely classical and comprehensible with the utilization of quantum computing while providing some clues into the nature of human experience, the nature of dreams and sheds some light on what is out there (quantum fields).

I can see no contradiction or conflict with known experiments and it's compatible with locality, realism and known science that rests on them both while both the mwi and the ci when taken separately struggle to explain adequately the outside world of observations. Even decoherence makes sense as the classical world happens at the time of information becoming available about quantum systems and in this framework the role of decoherence appears natural.

Finally someone sees what I'm saying, thanks for the support.
Yes, if fields do not exist, how do you make interaction with something that does not exist (regardless, if you don't observe/watch or have any effect on these fields)?
Answer is: you don't, because it does not exist, so yes, fields do definitely 100% exist independently outside of all of our interactions with fields (energy fields, force fields, quantum fields and similar), otherwise there would never be any interaction with anything ever.