What is the role of fields in Quantum Field Theory (QFT)?

[mysearch]

I'm surprised no one took you up on this interesting calculation.

See post #24

 

[mysearch]

I recognise that I now need to return to studying the evolution of quantum physics through its various developments, i.e. NRQM, RQM, QFT, in more detail. I suspect this is not an easy task even for post-graduates, let alone for somebody with only a general interest in the subject. Based on only a preliminarily review of the following sources, this is going to take some time:

• Hans de Vries: Understanding Relativistic Quantum Field Theory
• David McMahon: Quantum Field Theory Demystified
• Paul Teller: An Interpretative Introduction to QFT
• Robert Klauber: Pedagogic Aids to Quantum Field Theory
• David Tong: Lectures on Quantum Field Theory

Therefore, have appreciated the insights provided in this thread, which have tried to clarify some of the semantics and attributes of both fields and particles that can be confusing at the outset. By way of examples:

Fields are unobservable, by definition.
There are not quantum waves in QFT.

A field is unobservable, therefore in rigour you cannot attach "physical existence outside their mathematical description"…..
Effectively fields have associated such concepts as energy and momentum density, and you cannot measure globally energy and momentum densities but only locally where there are particles…..
The field is a mathematical abstraction.
Each field and its quanta has different properties as charge, spin, mass...
An electron with energy E traveling is transporting energy.
A photon transports energy as well, but a photon is a quantum particle.

Regarding fields they are modeled as a collection of harmonic oscillators. And if you ask what is oscillating? Then either you avoid to answer or you return to a particle concept. Moreover, the concept of field is only approximate. It is now generally accepted that QFT is only an effective theory that breaks down to higher energies. Field theory also breaks in other situations, and alternatives are under active research.

A field in QFT has just as much substance as a field in classical physics. Take the electromagnetic field. If you think it has substance or no substance in classical physics, then it is the same in QFT.

I suspect that the full implications of some of these statements may only become clearer as I read into the details. However, at the start, it is not always clear whether a given concept is being described within the scope of physical theory or a mathematical model, i.e. is it physically tangible or just a mathematical abstraction. It was in this context that I raised the issue of ‘substance’ and would like to comment of the following responses:

I continue without understand what you mean by «substance». This is not a scientific term neither in QM nor QFT (the term substance is defined in chemistry).

It was never meant as a scientifically rigorous term. As indicated above, it was only intended as a descriptive term to try to differentiate between physically tangible versus some mathematical abstraction that could not be directly observed.

An elementary particle is a microscopic non-composite object characterized by mass, spin, charge.

E=mc² is not valid in the general case. A particle is an object with determined properties assigned to it.. Energy and position are not properties that define what a particle is. Moreover a particle does not need to be confined in a small volume of space.

Maybe I should have asked: what is mass in QM-QFT, because I am not sure I understand the subsequent caveats. For example, if a particle is characterised by mass and mass is associated with energy, why is energy not a property of the particle? Equally, in what context is an elementary particle not confined to a relatively small volume of space. The following Wikipedia reference is only intended as a general description of matter being associated with mass and general use of the word ‘substance’.

http://en.wikipedia.org/wiki/Matter
Matter is a general term for the substance of which all physical objects consist. Typically, matter includes atoms and other particles which have mass. A common way of defining matter is anything that has mass and volume. Mass is the amount of matter in an object and volume is the amount of space occupied by an object. However, different fields use the term in different and sometimes incompatible ways; there is no single agreed scientific meaning of the word "matter".

The term «matter wave» is a misnomer for me.

I was referring to the term in the context of deBroglie’s original description, as per the following Wikipedia reference. While I understand that QFT takes a different approach, I didn’t think the idea of wave packets representing particles was a complete ‘misnomer’. However, I was also making reference to the dispersive nature of matter waves in terms of the time evolution of the Scrodinger equation, although this might now be irrelevant in QFT.

http://en.wikipedia.org/wiki/Matter_wave
In quantum mechanics, a matter wave reflects that a wavelength that is inversely proportional to the momentum of a particle. The frequency of matter waves is directly proportional to the particle's total energy.

As always, appreciate any help on offer. Thanks

 

[PhilDSP]

This is a bit mystifying. The 1/10 ounce figure seems to be right if you use a smaller diameter than the classical radius:

Earth Radius/Electron Radius * Electron Mass
= (6.3781*10^6)/(2.0*10^-21)*(9.1*10^-31) = 2.9*10^-3 kg

But I get an even higher density difference than you and intuitively it seems to be in the wrong direction (How can something with much higher density weigh much less?)

Electron Density=Electron Mass/Electron Volume
=(9.1*10^-31)/[4/3*pi*(2.0*10^-21)^3] = 2.72*10^31

Earth Density=Earth Mass/Earth Volume
=(5.9*10^24)/[4/3*pi*(6.3*10^6)^3] = 5.49*10^3

 

[juanrga]

Maybe I should have asked: what is mass in QM-QFT, because I am not sure I understand the subsequent caveats. For example, if a particle is characterised by mass and mass is associated with energy, why is energy not a property of the particle?

Energy is a property of the particle. It seems you have misinterpreted me. What I really said was:

Energy and position are not properties that define what a particle is.

This is a different claim.

An electron is not defined by its energy E, which can vary from zero up to several GeV and beyond. An electron is defined by mass=m_e, spin=1/2 and a charge=-e.

http://en.wikipedia.org/wiki/Matter
Matter is a general term for the substance of which all physical objects consist. Typically, matter includes atoms and other particles which have mass. A common way of defining matter is anything that has mass and volume. Mass is the amount of matter in an object and volume is the amount of space occupied by an object. However, different fields use the term in different and sometimes incompatible ways; there is no single agreed scientific meaning of the word "matter".

That wikipedia article is an excellent reason of why the concept «substance» is not used in QM or in QFT. Elementary particles (a form of matter) do not need to have mass and volume. A photon has zero mass, for instance.

 

[waterfall]

I think the damage has been done by Einstein when he proposed the photon was a particle. At that time Planck rightly stated that a field was not a collection of photons but something unique. Then came de Broglie which said the particle was objective encased in its pilot wave. This crystalized the opposing team determination which resulted in the Copenghagen Interpretation where any objective or realism was gotten rid of. If we assume quantum fields are primary, and there is no such thing as particles or wave duality and quantum objects are simply unique objects in that they are simply quantum fields. Then the whole quantum debate can be avoided. Instead of the man on the street fighting whether an electron is a particle or wave... we can state it is a quantum field objectively and the undulations or momentum and energy of the field just create the electrons. I think we must promote this idea rather than debating whether they are particles or waves. They are neither. They are simply quantum fields and these are unique entities without any correlate in physical science. So what if we can detect particles in scattering experiments. We don't have to confuse the public by saying there are really particles when they are just momentum and energy of some objective quantum fields. Who agree with me and who don't and why is that?

 

[Ken G]

Earth Radius/Electron Radius * Electron Mass
= (6.3781*10^6)/(2.0*10^-21)*(9.1*10^-31) = 2.9*10^-3 kg

I think the problem is you don't want the ratio of the radii, you want the ratio of the volumes, to get the right factor by which to "scale up" the electron mass-- unless you are creating a very long and skinny Earth!

 

[Ken G]

See post #24

I missed that somehow.

 

[PhilDSP]

Good point! The initial attempt was only a one dimensional expansion for the mass but the other two spatial dimensions need to be expanded also.

Earth Volume / Electron Volume * Electron Mass
= [4/3*pi*(6.3781*10^6)^3] / [4/3*pi*(2.8179*10^-15)^3] * [9.1093*10^-31] = 1.0562*10^34 kg

Earth Mass = 5.9742*10^24
Sun Mass = 1.9889*10^30

Which is many orders of magnitude heavier than the Earth - over a thousand times heavier than the sun even. Phew, that's hardly something without "substance"!

 

[mysearch]

Hi,
I glad you’ve sort out your original calculation set in post #22. However, I would question the purpose of framing the issue in terms of any ratio between the Earth and an electron for it seems that comparing the density tells you what you really want to know, e.g.

However, wouldn’t the density of the electron be more relevant here?
Electron Density=Electron Mass/Electron Volume
=(9.1*10^-31)/(9.36*10^-44)=9.72*10^12
Earth Density=Earth Mass/Earth Volume
=(5.97*10^24)/(1.09*10^21)=5.52*10^3

An issue of interest to me is how you describe this apparent density, i.e. is it energy or mass. For this reason, I am still not totally clear on Juanrga last response.

An electron is not defined by its energy E, which can vary from zero up to several GeV and beyond. An electron is defined by mass=m_e, spin=1/2 and a charge=-e…
Elementary particles (a form of matter) do not need to have mass and volume. A photon has zero mass, for instance.

Can an electron have zero energy, if you include its rest mass [m=E/c^2]? If we ignore the concept of the ‘kinetic mass’ of a photon, we seem to be left with Planck’s basic definition [E=hf], such that the photon has no tangible ‘substance’ in terms of mass and can presumably only be described as a quanta of energy. Equally, I am not sure how you transpose the idea of density, as discussed above, either in terms of energy density or mass density if you cannot quantify the volume.

By way of acknowledgment of ‘Waterfalls’ first post. He seems, at least to me, to be raising some valid philosophical and scientific concerns about the current language used to describe the quantum world. Of course, I accept that the language used by experts might have redefined the common understanding of certain words in the context of such a specialised subject as QFT.

For a not-too obscure discussion of what it all really means, Paul Teller's book is quite useful.

Based on the recommendation above, I have just started to read Teller’s books. Here are two quotes taken from the first chapter, which re-assured me that some of my confusion was not necessarily confined to me, although I am not certain of this:

“Current views of quantum field theory do acknowledge an essential particle aspect. But I believe that they get this particle aspect wrong, and consequently they do not show clearly how the particle and field aspects fit together. Expositions of the particle aspect go wrong when they fail to make clear how the relevant notion of particle has evolved from the perhaps vague pre-quantum notions.”

“Interpreters of quantum theories almost never address the idea that particles, as material objects, are thought as substantial. Many of us, in our pre-quantum thinking, think of particles as composed of bits of substance, vaguely thought of as ‘stuff’. “​

However, Paul Teller is ‘only’ the Professor Emeritus of Philosophy at the University of California, such that the 'Sheldon Cooper’s' of theoretical physics might snort at this. Only joking.

 

[mysearch]

Hi,
By way of a quick cross-reference, Waterfall raised an issue in post #35, which he then followed up on in this thread. However, he has now moved this discussion to a separate thread, which may be of some further interest to people: Quantum Field as Physical Entity?

 

[PhilDSP]

Hi,
I glad you’ve sort out your original calculation set in post #22. However, I would question the purpose of framing the issue in terms of any ratio between the Earth and an electron for it seems that comparing the density tells you what you really want to know, e.g.

Well, my mind is not particularly good at imagining raw densities. Stuffing a large sun into the size of the Earth is nearly something that can be visualized. Even though visualization seems to be discouraged or at least unappreciated in these circles, it seems associating some "substance" to the math, even as an analog, sometimes allows you to put it to work where you wouldn't necessarily think of putting it to work otherwise.

 

[juanrga]

Can an electron have zero energy, if you include its rest mass [m=E/c^2]?

You can move the zero of the scale of energy by adding/substracting a constant. If you eliminate mc² you obtain that energy goes to zero as in Newtonian theory.

If you maintain mc² then the minimum of energy, in that scale, is not zero.

A similar change in scale is done in QFT for fields, where the term E₀ (vacuum) is often eliminated from the scale.