Why can't we go faster than light?

[ajb]

So, write down the Dirac equation with a Yukawa coupling, maybe it is enough to consider the scalar field as a background, I don't know, and show me what you are trying to tell me.

[Schneibster]

I'm no physicist. Can't you do that?

 

I note you avoided my question.

 

I'll try each point in turn instead.

 

Do you deny that the Higgs field determines the rest mass that is an input to the Dirac field equations of the fermion field, through Yukawa coupling of the two fields?

Edited April 7, 2014 by Schneibster

[ajb]

I'm no physicist. Can't you do that?

No, as I don't know what your claim is and so I don't know what I am trying to show exactly. The coupling depends on acceleration, but of what?

 

I note you avoided my question.

Sorry, ask your question again.

 

Do you deny that the Higgs field determines the rest mass that is an input to the Dirac field equations of the fermion field, through Yukawa coupling of the two fields?

More or less that is what I have been saying. The Higgs via a Yukawa coupling and also due to the non-navishing VEV produces the mass of fermions in a gauge invariant way.

 

You then said something about the acceleration, which is what I don't undertsand.

[Schneibster]

I asked it twice in post 75.

 

What "claim" are you talking about?

More or less that is what I have been saying.

 

OK, now we're getting somewhere.

 

Do you deny that the Dirac field is explicitly Lorentz symmetric, i.e. incorporates special relativity?

Edited April 7, 2014 by Schneibster

[davidivad]

just to note, i just broke the light speed barrier in my basement tomorrow.

 

i knew einstein was right!

wait a minute, i thought it was the other way around.

Edited April 7, 2014 by davidivad

[ajb]

I asked it twice in post 75.

Are we good so far? No, not really.

 

What "claim" are you talking about?

Something to do with the Yukawa coupling depending on acceleration, that is your claim and I have asked for some clarification.

 

Do you deny that the Dirac field is explicitly Lorentz symmetric, i.e. incorporates special relativity?

Not the field, that has a transformation rule under the Lorentz group, but the Dirac action is Lorentz invariant yes. And I have not said otherwise.

[Schneibster]

So you deny something from that post?

 

Could you be explicit about what you disagree with, please? I'm unclear from what you've said what the problem is. All of those propositions look fine to me and you're in the process of agreeing with each one piecemeal. So far you're getting impatient with me trying to figure out what you think is wrong. Maybe if you'd say something other than "your conclusion" and start discussing why the conversation might be productive more quickly. That conclusion, I'll point out, was not mentioned in that post, so actually you still haven't answered my question.

 

Meanwhile, fine, so you admit mass comes into the Dirac equations for fermions through the Yukawa interaction with the Higgs scalar field, and you admit that the Dirac field defined by those equations is explicitly specially relativistic. Right?

 

Now, do you deny that the rest mass that the Lorentz transform acts upon is the rest mass determined by the Yukawa interaction with the Higgs field?

 

BTW, not sure what the claim that the Dirac field, i.e. the fermion field, is not Lorentz symmetric, is based upon. In fact the anticommutation of the half-integer spin fermions is determined explicitly due to Lorentz symmetry; it is therefore responsible for Pauli Exclusion and their other obedience to the Fermi-Dirac statistics. I have no idea what claiming the Dirac field is not Lorentz symmetric means.

Edited April 7, 2014 by Schneibster

[Schneibster]

Sorry but if you won't answer questions I can't figure out where you've made your mistake.

[ajb]

Could you be explicit about what you disagree with, please?

I don't know if I can say this any clearer. Please explain to me what you mean, carefully, by the Yukawa coupling's dependence on acceleration. That is what I am unclear about.

 

Meanwhile, fine, so you admit mass comes into the Dirac equations for fermions through the Yukawa interaction with the Higgs scalar field, and you admit that the Dirac field defined by those equations is explicitly specially relativistic. Right?

Right, but the Dirac field is not Lorentz invariant itself, it transforms as a spinor.

 

Now, do you deny that the rest mass that the Lorentz transform acts upon is the rest mass determined by the Yukawa interaction with the Higgs field?

It correct that the rest mass of fermions in the standard model is understood as being generated via a Yukawa coupling with the Higgs field.

 

 

BTW, not sure what the claim that the Dirac field, i.e. the fermion field, is not Lorentz symmetric, is based upon.

The fact that the Dirac field transforms under a spinor representation. (Text book stuff now)

 

 

In fact the anticommutation of the half-integer spin fermions is determined explicitly due to Lorentz symmetry; it is therefore responsible for Pauli Exclusion and their other obedience to the Fermi-Dirac statistics.

It is determined by certain representations of the Lorentz group.

 

I have no idea what claiming the Dirac field is not Lorentz symmetric means.

Look, this is very basic quantum field theory now. The Dirac field transforms as a spinor and the action you build is Lorentz invariant. The fields that build up the action need not be Lorentz invariant and indeed they usually are not, unless you have just the scalar field.

 

As you don't know about this I cannot trust anything else you have said in this post. I must therefore disregard your statements about the Yukawa coupling and acceleration, unless you can make it clear.

[Schneibster]

You're still not answering my question. I started to do what you ask ("please explain"), and you didn't agree with me on the basics in post #77, and you won't tell me what you disagree with. You keep bringing up extraneous material. I'm sorry, I don't intend to let go of this until you've answered it.

 

I don't build houses on foundations of air. Until you agree with the basics I don't see how you can object to their results unless you say what basic you don't agree with.

 

Which one of the basics in post #77 do you disagree with?

 

I am becoming impatient myself, now. If you think can show me something wrong with my reasoning, then show me something wrong with my reasoning; so far you can't.

 

Oh, and incidentally I made another mistake; I should have said Einstein tensor, not Ricci tensor. It's actually mostly the Ricci tensor but we should be rigorous. It does not, however, make any difference to my point.

 

And I do not intend to move on to your other points until this is cleared up. Sorry but if you're going to tell me I'm wrong you're darn well going to tell me how.

Edited April 8, 2014 by Schneibster

[ajb]

You're still not answering my question.

I am now confused. In post 77 you say

 

"I'm no physicist. Can't you do that?"

 

I said, no as I am not sure what I would be trying to show.

 

 

"I note you avoided my question."

 

Okay, I apologise for this.

 

 

 

"Do you deny that the Higgs field determines the rest mass that is an input to the Dirac field equations of the fermion field, through Yukawa coupling of the two fields?"

 

And I said somewhere that I agree, the rest mass of the fermions in the standard model is attributed to the Yukawa coupling of the fermions with the Higgs. You then need to break the symmetry and see the mass as being due to the non-vanishing VEV of the Higgs field.

 

I started to do what you ask ("please explain"), and you didn't agree with me on the basics in post #77, and you won't tell me what you disagree with.

Nowhere have I said that the basics of post 77 are incorrect. See above.

 

You keep bringing up extraneous material.

All I have asked, more than once is a proper explanation of your statement about the Yukawa coupling being dependent on acceleration.

 

I don't build houses on foundations of air.

Your clear misunderstanding of what a Dirac field is suggests otherwise, sorry.

 

Until you agree with the basics I don't see how you can object to their results unless you say what basic you don't agree with.

So again, just to be clear. Can you explain what you mean by the Yukawa coupling being dependent on acceleration. You said that in post 69.

 

Which one of the basics in post #77 do you disagree with?

Again, just to be clear. What you wrote in post 77 is okay.

 

I am becoming impatient myself, now. If you think can show me something wrong with my reasoning, then show me something wrong with my reasoning; so far you can't.

You have not made any real attempt to explain your statement in post 69!

 

 

And I do not intend to move on to your other points until this is cleared up. Sorry but if you're going to tell me I'm wrong you're darn well going to tell me how.

Post 79 has a mistake, or you have not phrased it well "...the Dirac field is explicitly Lorentz symmetric, i.e. incorporates special relativity?" Same in post 82 "BTW, not sure what the claim that the Dirac field, i.e. the fermion field, is not Lorentz symmetric, is based upon."

 

If by symmetric you mean transforms as a scalar then you are wrong. If you mean it transforms under some representation of the Lorentz group, then you are right. It transforms as a spinor.

[Schneibster]

My mistake, post 75.

 

Since you've mentioned the Dirac field at the end of your last two posts, and still appear to feel that the Dirac field is not Lorentz symmetric, I will remind you that spin is based on the Lorentz symmetry, and for the Dirac field to be non-relativistic, it must, therefore, according to you, not have a spin. I don't think you've thought this all the way through.

 

Edited to add, for the benefit of observers: spin is due to the fact that you cannot replace two successive Lorentz boosts with a single one; if you do, you must add a rotation. This is a consequence of the Lorentz symmetry. And that rotation is spin angular momentum. Since the very definition of the Dirac field is that it has spin 1/2, as opposed to the boson or Bose-Einstein field which has unitary spin, special relativity enters firmly into both the Fermi-Dirac and Bose-Einstein fields at their very most basic definition. It is not escapable by any trickery at all.

Edited April 9, 2014 by Schneibster

[ajb]

Since you've mentioned the Dirac field at the end of your last two posts, and still appear to feel that the Dirac field is not Lorentz symmetric,

Okay, then can you just define a little more carefully what you mean by symmetric? Do you mean

 

i) Lorentz invariant in the sense that it transforms as a scalar under the Lorentz group?

 

ii) Transforms in some other way, for example under a tensor or spinor representation of the Lorentz group? (Hint, it transforms as a spinor)

 

Or do you mean something else?

 

You may mean that the action for the Dirac field is Lorentz invariant, that I will agree with totally.

 

I will remind you that spin is based on the Lorentz symmetry, and for the Dirac field to be non-relativistic, it must, therefore, according to you, not have a spin. I don't think you've thought this all the way through.

This sounds different, more like taking the non-relativistic limit somewhere. Doing so would probably mean that like all non-relativistic theories we need to include spin "by hand" due to phenomenological reasons.

Edited April 9, 2014 by ajb

[Schneibster]

You're talking about the math. The derivation of the mathematics is not the definition of the physical behavior.

 

I'm talking about the field. And I'm talking about relativity and spin. You can't have a spin 1/2 particle/field without defining spin, and you can't have spin without relativity. Simple as that.

 

And I'm still waiting for what's wrong with post 75. (Sorry for my mistake.)

Edited April 9, 2014 by Schneibster

[ajb]

You're talking about the math. The derivation of the mathematics is not the definition of the physical behavior.

True, but the wonderful and amazing thing is that the two are not completely separate. If they were, then we would not have theoretical physics at all!

 

I'm talking about the field.

Okay, then just make it clear to me how you think that transforms? It is important and the reason why fermions carry spin 1/2.

 

 

And I'm talking about relativity and spin. You can't have a spin 1/2 particle/field without defining spin, and you can't have spin without relativity. Simple as that.

Right, the real nature of spin is hidden in the structure of the Lorentz group and its representations, absolutely right. I don't recall saying otherwise.

 

That said, before the nature of spin was really understood it was simply bolted on for phenomenological reasons. This is how it is how it is treated in non-relativistic quantum mechanic as standard.

 

Anyway, back to my question. Please explain your statement on the Yukawa coupling depending on acceleration?

 

(I am not implying you are wrong or right, just I am interested to see if there is any physics in that statement.)

Edited April 9, 2014 by ajb

[Schneibster]

Post 75, please?

[ajb]

Higgs field ->

Scalar field

Extremely simple has only one interaction besides self-interactions

couples through Yukawa interaction with

Dirac field ->

Yukawa interaction with Higgs field provides "rest mass"

Dirac field is more complex, provides many attributes

 

That sounds okay, but of course no details here.

 

 

Dirac field is explicitly relativistic, incorporates Lorentz symmetry

Lorentz symmetry acts on "rest mass" (see above)

 

Okay, but maybe not worded great. The Dirac carries a representation of the Lorentz group which is (part of) the group to do with special relativity.

 

mass ->

more properly mass/energy or stress-energy tensor

 

Okay, for a test particle we can think of mass as the "conserved charge" related to energy-momentum conservation.

 

 

 

 

Acts upon all three both of

Ricci tensor

metric tensor

cosmological constant

And is in turn acted upon by them.

 

So energy-momentum acts as a source for gravity okay.

 

Are we good so far?

And the above tells us that the Yukawa coupling depends on acceleration?

[Schneibster]

That sounds okay, but of course no details here.

 

 

Okay, but maybe not worded great. The Dirac carries a representation of the Lorentz group which is (part of) the group to do with special relativity.

 

 

Okay, for a test particle we can think of mass as the "conserved charge" related to energy-momentum conservation.

 

 

 

 

So energy-momentum acts as a source for gravity okay.

 

 

And the above tells us that the Yukawa coupling depends on acceleration?

 

No. That's the preliminaries. We've never talked deeply about this stuff before so I don't know how to gauge your experience. I think we agree as far as that, remembering my mistake confusing the Ricci and Einstein tensors, and that you'll agree to what you see there so far.

 

Except for the part about relativity and the Dirac field; I think we need to thrash that out first. Maybe I've made a mistake there. If so there's no point in going on; that's the mistake, I learned something, and since my assertion is based on it, obviously my assertion was wrong. This is why I'm being so finicky.

[ajb]

We've never talked deeply about this stuff before so I don't know how to gauge your experience.

You can assume I have the knowledge of GR and QFT upto the standard of a first year grad student(after the first year) for sure, a bit more than that on certian aspects. Neither is exactly what I am working on at the moment, so I accept my knowedge will be "rusty" in places. In part that is why I wanted to tease out any physics in your statements.

 

Except for the part about relativity and the Dirac field; I think we need to thrash that out first. Maybe I've made a mistake there. If so there's no point in going on; that's the mistake, I learned something, and since my assertion is based on it, obviously my assertion was wrong. This is why I'm being so finicky.

Okay, I am glad you have learned something. That is what this site is all about really.

[Schneibster]

Well, I haven't learned anything yet. At least not anything that I was wrong about.

 

The Dirac field is the spin 1/2 Fermi-Dirac particles, or fermions, correct?

 

And there are only two spin moieties, half-spin and integer-spin, correct?

 

And the integer spin particles are the bosons, which are in the other moiety from the fermion field we are discussing, correct?

 

And this means that the most important difference between the two biggest moieties of particles, one of which represents classical "matter" and the other of which represents classical "energy," is spin, correct?

 

And spin is, not merely affected by but entirely due to Lorentz symmetry, correct?

 

So how can you claim the Dirac field is not relativistic when its most basic character, its spin is determined by the symmetry of special relativity, the Lorentz symmetry?

[ajb]

And spin is, not merely affected by but entirely due to Lorentz symmetry, correct?

Yes, it is something to do with the Lorentz group.

 

So how can you claim the Dirac field is not relativistic when its most basic character, its spin is determined by the symmetry of special relativity, the Lorentz symmetry?

First, I have not claimed that the Dirac field is not relativistic, in the sense that it carries a representation of the Lorentz group. The Dirac field transforms as a spinor.

 

It is the word symmetry that is coursing the trouble. The Dirac field is not Lorentz symmetric in the sence that it does not change under a Lorentz transformation. It most certianly does have a non-trivial transformation law.

 

Unless you actually want me to write out the transformation law, you can look it up easily enough.

[Schneibster]

Well, then you're using "Lorentz symmetric" in a completely different manner than I'm used to.

 

So you're saying that "Lorentz symmetric" is something that can only be said about a scalar? It's not something a complex field inherits from the scalars that make it up?

 

And also, several parts of the Dirac field do transform. So I'm not sure what you mean when you say it "does not change under a Lorentz transformation."

 

I suspect the problem is deeper; that your definition of "Dirac field" is different than I'm used to.

Edited April 9, 2014 by Schneibster

[ajb]

So you're saying that "Lorentz symmetric" is something that can only be said about a scalar? It's not something a complex field inherits from the scalars that make it up?

If what you end up with is also a genuine scalar, then okay.

 

And also, several parts of the Dirac field do transform.

Right, so we now both agree that the Dirac field has a non-trivial transformation law under the Lorentz group.

 

http://en.wikipedia.org/wiki/Bispinor

 

Importantly, the mass term in the Dirac Lagrangian is a Lorentz scalar, that is invariant under the Lorentz group; [math]m \bar{\psi}\psi[/math], while the spinor itself has a non-trivial transformation law.

 

Maybe by Lorentz symmetric you mean Lorentz covariant, that is has some well defined transformation rule under the Lorentz group.

Edited April 10, 2014 by ajb

[Schneibster]

I was right. You are confusing the Dirac Lagrangian with the Dirac field.

[ajb]

I was right. You are confusing the Dirac Lagrangian with the Dirac field.

Or as I see it you were wrong and confusing the Dirac Lagrangian with the Dirac field!

 

You kept saying the Dirac field and I kept saying I suspect you mean the action (or equivalently in this case the Lagrangian).

 

Okay, moving on... back to your statement that the Yukawa coupling depends on velocity.

Edited April 11, 2014 by ajb