# Understanding forces in QFT [closed]

I recently came to know that any type of force is exerted by a particle on another with the help of gauge bosons/virtual particles which are in reality a mathematical aide and do not have actual existence.

Since, force fields are a result of force on particles having unit mass/charge etc. Cannot be a mediator for force as it derives its roots from force itself. Then how is force exerted between two particles/bodies?

• The ontology of quantum field theories isn't well understood : plato.stanford.edu/entries/quantum-field-theory/#Ont Oct 27, 2013 at 22:17
• Electro-magnetic fields can carry energy and momentum from one place to another. Anyone who tells you they are not "real" is (a) trying to sell you something, (b) living in a state of sin, or (c) a philosopher (which is far, far worth than either (a) or (b)). Oct 27, 2013 at 22:20
• @dmckee, your statement presupposes that energy and momentum are real. :) Oct 27, 2013 at 23:33
• @dmckee : I believe the link was related to electrostatic field and not electromagnetic field, what we have been told is that electrostatic field is the field which acts for mediating force between two charged particles placed at some distance, but the field itself is just force per unit charge so how can it be a force mediator ? Oct 28, 2013 at 2:13
• rijul, what is as real as real can be are the phenomena, the metaphysically given. As rational curious creatures, we define concepts and construct mathematical models to explain and predict the phenomena, improving or discarding them as time moves on. What should be pointed out is that, in the original version of your question, you accept the reality of "force" while questioning the reality of the electric field. But, the concept of force is, itself, an abstraction from observations of physical phenomena just as electric field, electric charge, energy, momentum, etc. are. Oct 28, 2013 at 13:23

Cannot be a mediator for force as it derives its roots from force itself I think you're confused because the electric field is usually defined as: $\vec E=\frac {\vec{F}} q$. But this a matter of convention, you could define $\vec F =q \vec E$. And the are strong reasons to think that fields are real, like momentum conservation, the fact that electromagnetic interaction has finite speed and simplicity (whatever that means). In fact, potential could be considered even more fundamental, as observed in the Aharonov-Bohm effect.

The quantum vaccum is another evidence of fields, but since I don't know any QFT I can't explain you why.

Anyway, this is more philosophy than physics (some one could argue the opposite). You could say that forces don't exist, because you just observe the movement of the particles, which may not be real either.

• I read the content of the link, but failed to completely understand the idea. I did understand that the phenomenon somehow proves the physical existence of electric potential, but I could not understand it as explaining physical existence of force fields. Please bear with me and explain, and if possible provide more related links. Also do you agree that force carrier/virtual particles are essentially non-existent ? Oct 28, 2013 at 10:57
• @rijulgupta wrt the Aharonov-Bohm effect, I tried to say that if vector potential is more fundamental than the magnetic field, it probably is even more fundamental than the magnetic force. About, virtual particles, I should wait at least four years until a have a minimum knowledge of QFT to answer that. But I think that they could be avoided (it would be interesting to know how is it explained from a string theory POV). Oct 28, 2013 at 11:03
• Thanks for the answer, so can we say that force fields are an actual thing and not just mathematical tools ? Oct 28, 2013 at 11:08
• @rijulgupta In MY opinion it is very difficult to distinguish between what's real ("real" is something not well defined) and mathematical tools. But since it's useful to consider fields as real, unless there is an equivalent forumulation of QFT which doesn't use fields, I would say they do exist (Ockham's razor). Oh, and note that there are formulations of Classical Mechanics (Langrage and Hamilton Mechanics) which don't use the concept of "force", but no one says that forces don't exist. Oct 28, 2013 at 11:17

Fundamental forces are mediated by fields like the electromagnetic field. An interaction mediated by such a field may be described quantum mechanically in terms of virtual particles, and while it's true you may regard virtual particles as purely mathematical aides that are not 'real', the fields themselves are. In particular, they need to carry energy and momentum if you want the corresponding conservation laws to hold.

• I believe charged particles interact via electrostatic fields which derive from electrostatic force, so how can it mediate force when it derives from force itself ? Oct 28, 2013 at 2:15
• @rijulgupta: the electromagnetic field causes the Lorentz force, which in turn causes charged particles to accelerate; as what we actually observe are the accelerations, existence of Lorentz force and electromagnetic field are inferred opposite to the direction of cause and effect; of course you can also build your model axiomatically if this makes you uncomfortable, but introducing the electromagnetic field as 'the thing that mediates the Lorentz force, measurable via test charges' is perfectly fine from a physicists point of view Oct 28, 2013 at 11:32
• Thabk you for the response, I just recently got comfortable with the fact that force fields can be physically interpreted, I was under the influence of wrongful thinking that force fields are non existent. But I know now that they can be physically interpreted. Oct 28, 2013 at 11:35
• I think many physicists would actually agree that force fields don't 'really' exists - they are just a way to describe what happens when coupling a physical field like the electromagnetic one to a charge Oct 28, 2013 at 11:46
• I got to this conclusion cia jinawee's answer and comments. If you coukd give some proof of its non existence, I would be really thankful Oct 28, 2013 at 11:48

It is true that the existence of these so called virtual particles is more of a philosophical question rather than scientific (at times, atleast). However, QFT has established a very sound explanation for force fields excluding gravity. It does involve virtual particles, though they cannot be strictly called 'mediators'. The real mediators are the gauge bosons, the existence of which have been confirmed by multiple experiments. Virtual particles are merely effective tools that allow us to use our knowledge of gauge bosons to understand the force fields. If you are already familiar with QFT and gauge bosons, then you must know that the distinction between a real particle and a virtual particle is a very frail, but useful one.

Now for a good explanation of how force is exerted you should thoroughly read this: http://math.ucr.edu/home/baez/physics/Quantum/virtual_particles.html (a rather large explanation, and the author does a better job than I can ever do, so there you go).

• Why does wikipedia say "Elementary particles, whose interactions are described by a gauge theory, interact with each other by the exchange of gauge bosons—usually as virtual particles" en.m.wikipedia.org/wiki/Gauge_boson Oct 28, 2013 at 1:53
• Gauge bosons help us understand the force fields, but its only through the 'virtual particle' phenomenon that we can factor them in the field mechanisms. But these virtual particles are basically elementary particles, existing as small fluctuations for a short period of time. For example, the Coloumb force is explained by the exchange of virtual photons. The photon is an elementary particle, and the force field is modeled by using its virtual counterpart. If you need more info, close this thread and open up a discussion in the chat room. I will be glad to explain more. Oct 28, 2013 at 2:15
• chat.stackexchange.com/rooms/11241/understanding-forces, please join the room Oct 28, 2013 at 4:15