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

[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.