Natural Order and Science

[little_monkey]

Says the guy, YOU, who can't understand a basic definition that even a 5-year old would. Get a reality check.

You have such a compulsive need to display your superiority that you wouldn't recognize knowledge if it hit you in the head with a 4x4. It is literally impossible to discuss the subject with you because the only mode of communication your ego seems to allow is lecturing to an adoring audience. I don't even remember anymore what I asked you about your concept of virtual particles, but it doesn't matter because you keep saying the same three lines over and over again anyways.

you mean the same three lines you still don't understand, LOL. Ok smart guy, how do you embed particles into fields considering that a particle transforms under an irreducible unitary representations of the Poincare group, taking into account that for m=0, you have two states, and for m>0, there are 2J+1 states, where m is mass and J is spin? (hint: you get to learn that in the first few chapters of any QFT textbook, so it shouldn't be so hard for you to get to the answer). I await your response...

[Alex K]

Ok, I correct myself, you have lecturing as well as issuing random exams, if the latter can be called a form of communication. You are really one of the most obsessively overbearing people I have ever "discussed" physics with, and not with the best reading comprehension either as I noticed in the other thread. Why do I feel like I'm in 5th grade again arguing whose action figure has the better superpower during recess?

Should I indulge you? Fine.

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So first of all, your question is not worded very clearly, and one could get the impression that you are labouring under the misconception that there are always two states in the massless case. If you think that, you shouldn't go round giving exams.

There are two issues here, one is how to "embed particles in fields" in the sense of quantizing the classical field theory, and the other, how particles of different spin are represented as fields. Now, you seem to be mainly alluding to the latter, although there are related subtleties in the former.
First of all, in the massless case, one is interested in transverse states, so instead of considering the full Poincaré group, one analyses the corresponding representations of the little group and resulting helicity states. Now, in the case of J=0, there is nothing much to analyse, one has a singlet under the little group as well as parity, and there is one state, not two. Now, so far we haven't seen a massless helicity 0 particle in nature, but the picture of course doesn't change in the massive case when going to the full Poincaré group. The representation is still trivial, still no spin. Going to massless higher spins, most famously photons or gravitons, the little group will have a single representation again, but this time with nonvanishing helicity. Applying parity then flips the helicity, and we get the two states one is used to corresponding to circular polarizations in the case of the photon, and the usual left- and righthanded rotating strain solutions of linearized gravity. Once again, going to the massive case, we switch to the full Poincaré group with, accordingly, larger irreducible representations.

All this is a purely group theoretic analysis of spin, and the situation in quantized field theory is a bit more involved because we have to explicitly say how and why the states in the massless case are reduced to representations of the little group. In the case of photons, the connection is as follows - they are massless because everything is in a linear representation of the gauged U(1), and it is precisely the same gauged U(1) which allows us to eliminate the additional longitudinal state, for example via GB or BRST. For spin-2, a similar but more involved construction is possible, as here we have the "gauge transformations" as relics of the diffeomorphism invariance of the full theory.

When masses are forbidden by such linearly realized symmetries, they arise via an explicit or spontaneous breaking of said symmetry. This then leads to extended conditions for the physical states involving the Goldstone or Stückelberg fields if you're doing GB.

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Is there anything you would like to add, oh ye pompous one? Ok, now I feel dirty. One should talk about the science for science's sake, to improve one's knowledge, and with a bit of humility. You treat science as if you were a baboon and physics your red swollen ass, a display unbecoming to its dignity.

[little_monkey]

Ok, I correct myself, you have lecturing as well as issuing random exams, if the latter can be called a form of communication. You are really one of the most obsessively overbearing people I have ever "discussed" physics with, and not with the best reading comprehension either as I noticed in the other thread. Why do I feel like I'm in 5th grade again arguing whose action figure has the better superpower during recess?

Should I indulge you? Fine.

---

So first of all, your question is not worded very clearly, and one could get the impression that you are labouring under the misconception that there are always two states in the massless case. If you think that, you shouldn't go round giving exams.

There are two issues here, one is how to "embed particles in fields" in the sense of quantizing the classical field theory, and the other, how particles of different spin are represented as fields. Now, you seem to be mainly alluding to the latter, although there are related subtleties in the former.
First of all, in the massless case, one is interested in transverse states, so instead of considering the full Poincaré group, one analyses the corresponding representations of the little group and resulting helicity states. Now, in the case of J=0, there is nothing much to analyse, one has a singlet under the little group as well as parity, and there is one state, not two. Now, so far we haven't seen a massless helicity 0 particle in nature, but the picture of course doesn't change in the massive case when going to the full Poincaré group. The representation is still trivial, still no spin. Going to massless higher spins, most famously photons or gravitons, the little group will have a single representation again, but this time with nonvanishing helicity. Applying parity then flips the helicity, and we get the two states one is used to corresponding to circular polarizations in the case of the photon, and the usual left- and righthanded rotating strain solutions of linearized gravity. Once again, going to the massive case, we switch to the full Poincaré group with, accordingly, larger irreducible representations.

All this is a purely group theoretic analysis of spin, and the situation in quantized field theory is a bit more involved because we have to explicitly say how and why the states in the massless case are reduced to representations of the little group. In the case of photons, the connection is as follows - they are massless because everything is in a linear representation of the gauged U(1), and it is precisely the same gauged U(1) which allows us to eliminate the additional longitudinal state, for example via GB or BRST. For spin-2, a similar but more involved construction is possible, as here we have the "gauge transformations" as relics of the diffeomorphism invariance of the full theory.

When masses are forbidden by such linearly realized symmetries, they arise via an explicit or spontaneous breaking of said symmetry. This then leads to extended conditions for the physical states involving the Goldstone or Stückelberg fields if you're doing GB.

---

Is there anything you would like to add, oh ye pompous one?  Ok, now I feel dirty. One should talk about the science for science's sake, to improve one's knowledge, and with a bit of humility. You treat science as if you were a baboon and physics your red swollen ass, a display unbecoming to its dignity.

The pompous side of me wants to add that it was Wigner who classified the state for m=0, you get two states, and for m>0, you get 2j+1 states, that the Poincare group has no finite-dimensional representation, but you get the infinite ones by embedding a polarization vector which is momentum dependent, making the basis vector infinite-dimensionally. Yes to your post about removing certain degrees of freedom, yes to your post to point out the connection to gauge theory. You should have mentioned the Ward identities, but I'll forgive you. Ok, I misjudged you, but that was because of how you behaved towards me. My initially post was not addressed to you, but you took the liberty to jump him, and belittled me. I didn't know if you were deliberately obstinate in refusing to see my point about a simple definition. Also, I put into one of my posts a word that anyone in QFT would have reacted but you didn't, so I concluded that you were an impostor. But this post corrects this impression you had given me so far - an impression all on your doings. So, yes I'm a professor who taught this stuff for 25 years, so I know it like the back of my hand. I'm also retired with lots more time on my hand, and I guess I will be spending more time on this forum. If I threw some dirt on you it's because YOU started it. Most likely we will cross path again on this forum. I'll leave it up to you if you want to restart afresh or continue this hostility.

[I_am_not_mafia]

PHYSICS FIGHT!

[Alex K]

Most likely we will cross path again on this forum. I'll leave it up to you if you want to restart afresh or continue this hostility.

Sure, no problem. I'm not the vindictive type.

Anyway, about your definition of virtual particles
Now that I know that you know this stuff well on a technical level, I can word my earlier question/remark more precisely.
Basically all the QFT lit I know treats the concept of "virtuality" of stable particles as the distance of the four momentum from the mass shell. I don't recall encountering a distinction between "real" and "virtual" particles based solely on whether they interact with an detector (which to me smells like mixing interpretations of QM, especially the arbitrary definition in copenhagen where the classical detector starts, and categories in QFT - something I am not used to), and if you could give me a reference i.e. to a textbook that does that, I would be grateful because it would be a new approach to the concept to me. I should have most of the known ones, but would be grateful if I didn't have to leaf through all of them searching for the right bits.

Don't you agree that even objects that in usual parlance would be called "real photons" - because they are emitted, have pretty much lightlike momentum and are registered at macroscopic distances from the source - can be described as a propagator between e.g. an electron in the source and an electron in the detector? (I think even Weinberg does that when talking about cluster decomposition, but I might confuse it with another book). This propagator interpreted as a Fourier transform to position space will contain momentum space propagators with all manner of off-shell four-momenta. Why do you still get a perfectly onshell photon in the S-Matrix element even if no photon ever registered is *purely and exactly* onshell? Precisely because we do a somewhat "unphysical" approximation by going to asymptotic times, right?

This lack of a sharp distinction and the somewhat artificial nature of the "real" in and out states was what I was trying to get at in order to dispel Harris' idea that there is this fundamental philosophical difference between real and virtual particles where one type really exists and the other is just a figment of theorists' imaginations.

Do you disagree?

p.s.
we are not even talking about loops here, which would open a whole new can of worms if we were to map the related physics to simple binary language like "real" and "virtual". But also here I think that the need to cancel soft real emission photons with loop corrections in Bloch-Nordsieck underlines the lack of a sharp philosophical ontological distinction between real and virtual particles. We are also not talking about unstable particles where the difference between on- and offshell is even muddier.

You should have mentioned the Ward identities, but I'll forgive you.

I have mentioned gauge invariance and Gupta Bleuler conditions, that totes counts as a substitute for Ward identities! I have implicitly even mentioned Slavnov Taylor

[Angrboda]

And then my eyes glazed back over....

[little_monkey]

Anyway, about your definition of virtual particles

I don't remember exactly where I got this notion but I believe it was in Anthony Zee' s QFT IN A NUTSHELL, where he makes the following suggestion - I have put it in one of my earlier post, maybe not to you. He says you can look at the interaction between two electrons from afar,and what you conclude is an electrical repulsive force, or from QFT, it's an exchange of virtual particles. Then he asked, what about when you have opposite charges, do you get an attraction? So in redoing the calculation for the Feynman propagator, he gets an opposite sign, suggesting as in classical physics, you have an attractive force. I think that it was in that book he makes the plead that virtual are just as real as the ones that would hit your eyes. But I went through that book a long time ago. So maybe my thinking about these things have evolved since then. And so my thinking is a hodge-podge of all my readings and my own reflections. Regardless, I made that claim in one of my blogs (http://soi.blogspot.ca/2015/09/superposi...tates.html).

NOTE: Now my blogs have been designed to answer specific questions I often had from students, former students and acquaintances of students/former students. So they are not in any order, some are more elaborate than others, done at different levels of who I had in mind. They are pedagogical tools, not me bragging about my skills...;-)

[Alex K]

Zee's book is interesting, unconventional and full of anecdotes and inside information. I had it on my desk not too long ago, but had ro return it before I could really look at it in detail. I plan to get it though.

[Harris]

All that said, I am firm on my argument that virtual particles are not particles at all.

Did you actually make an argument yourself somewhere in there?

Although, I have made my point clear but unfortunately because of my little carelessness you dudes had a chance to mess things up. Anyway, that would not stop me from writing the truth which some people are twisting on purpose to support their pleasure seeking behaviour.

In my following argument I will totally avoid any technical term such as abstract mathematical ideas like real/complex vector spaces, bra-ket, conjugates, Hermitian operators, Hamiltonian, Eigen etc. so the folks who do not have any idea of what quantum physics is can also follow this discussion.

Let us assume that we have two metal balls which are detectable because of their physical properties. If force applied on these balls they can move and interact. This is our first observation.

In case we move the metal balls closer and they start influencing each other without even interacting physically that gives us an understanding that these balls also have some indiscernible properties. When these balls start attracting or repelling each other this behaviour leads us to our knowledge of magnetism. This is our second observation which is indirect in nature.

Conclusion: Metal balls are directly detectable due to their physical properties. However, magnetic fields are detectable only when those fields start influencing other objects.

In today’s world it is a common knowledge that atoms are not the fundamental particles and they are also made of even smaller particles.

Atoms are made of nanoscopic balls called Fermions and the force those fermions carry are known as Bosons. When force fields (bosons) interact they can influence fermions to behave in certain ways. Fermions are detectable due their physical properties and bosons are detectable indirectly by the way fermions behave during their interactions.

By the word particle the first idea which may occur in mind is about something that is solid and that has detectable physical properties such as colour, shape, mass, etc. The force field on the other hand is not detectable until it interacts with something. However, scientists decided to put both fermions and bosons (force fields) under the same category of particles in quantum physics. Both fermions and bosons are called particles and that is the point when things start getting fuzzy for a person who is not well educated in science.

When two electrons approach each other, their charges create a disturbance. This disturbance pushes them apart and their paths bent outwards. In case of electron and positron the disturbance is similar in type but different in details so oppositely charged electron and positron attract each other and their paths are bent inwards. In other words, when two fermions interact their force fields mediates a force that changes their momentum and path of motion.

Many scientists push the idea that when two force fields interact together there is an exchange of undetectable particles (the Virtual Particles or Photons) that cause the attraction or repulsion among interacting fermions which carry those force fields. As if force fields are made of invisible particles which push or attract each other when they come near to each other. But this is just a Jargon because force fields are not detectable directly and nobody knows what exactly is happening inside those interacting fields. Scientists call those interactions of force fields “Exchange of Virtual Particles.” They call these particles “Virtual” because:

They are not detectable directly
They would never be found on their own
They do not have energy to become a well formed ripple moving through space and
They decay as soon as their causes are gone.

This is what a “Virtual Particle” and some people are twisting this idea to spread a false concept that at quantum level “Virtual Particles (as if REAL PARTICLES)” can appear out of nowhere.

This concept is wrong for one more reason. In modern physics there is no such thing as empty space. Fields pervade space. They are conditions and properties of space. The vacuum is filled with electromagnetic fields which are active and dynamic and within these fields always some activities are happening at nanoscopic levels. These fields are not smooth and fluctuations may cause energy-mass-energy conversions at small levels. In no way one can claim that energy-mass-energy conversions happen out of nothing because an unfathomable ocean of fluctuating fields provide a good solid base for such activities.

Saying that “Virtual Particles” can come into existence from nothing is a deliberate abuse of science. To me it seems that people who resist the idea of God are putting another effort to spin layman’s head with a false concept. Just like they did it by spreading the idea of Natural Selection without giving intelligible mechanism for Natural Selection.

[Harris]

Your post illustrates perfectly what I was implying: since you have no way to differentiate between what is true or false, then your proposal "our beings encompass a huge amount of data stored in our conscience, a gift of nature, blah,blah...' is just another statement that has no validity. The question you should be asking: how can one differentiate a crackpot theory from the real thing? If you have no test to differentiate these two, then your theory is no more and no less valid than any other crackpot theory. So you can advance the idea that "our beings encompass a huge amount of data stored in our conscience, a gift of nature, blah, blah..."but it is no different than any other crackpot theory.

Are you saying that you can differentiate all truths of nature because you have handful knowledge about the physical world?

Has your scientific knowledge brought you any jackpot theory about your own life?

Are you saying you have followed strictly laws of physics in making all your emotional decisions in your life?

If you are saying all that then I do not believe you.