The Higgs field and Relativistic Mass

[StBean]

I've read that(in theory) mass is a result of motion of a particle in the Higgs Field(space). Is this increase in mass they are talking about the same as relativistic mass--the increase in mass due to motion?

[freeaction]

Originally Posted by StBean

I've read that(in theory) mass is a result of motion of a particle in the Higgs Field(space). Is this increase in mass they are talking about the same as relativistic mass--the increase in mass due to motion?

Good question mr. bean.

The mass of many force carrying particles like the W+, W- and Z_0 is theorized to have come from the Higg's field. Basically at a certain energy level the Higgs field sort of freezes and when it does it gives mass to those force carrying particles while leaving the photon massless. When I speak of mass I mean the rest mass. It is popular in introductory physics texts to quantify relativistic effects in terms of a velocity dependent mass, but this is not very common in more advanced literature. The mass of a particle means it's rest mass, otherwise its a very cumbersome idea. The mass the Higg's field contributes to is the rest mass. Its actually more complicated than this, before the Higgs interferes with the fields of Electroweak theory there is no photon, instead there are (all massless before the Higg's effect)

W+,W-,W,and B

The Higgs field acts to recombine the W and B fields together to make what we see as the massive nuetral current Z_0 and the massless photon. So the Higg's field doesn't just add mass it creates new kinds of particles from this view point.

[Mike Dubbeld]

Originally Posted by StBean

I've read that(in theory) mass is a result of motion of a particle in the Higgs Field(space). Is this increase in mass they are talking about the same as relativistic mass--the increase in mass due to motion?

That one is easy. Relativistic mass is associated with relativistic velocities. So that parses that one out. The Higgs field is everywhere - it is the ether all over again as the 'bestower of mass.' Before I forget it is not popular to talk about 'relativistic mass' anymore. Quarks zoom around inside protons and neutrons at such speeds that they give them significantly greater mass. (I have the quote if you want it from the web. It was hard to find but it came from a university.)

But I am on relativity again thanks to Ledermans poor writing in Symmetry and the Beautiful Universe. I could not even figure out he was talking about the gamma factor/Lorentz transformation - he put it so simply for non-technical readers and then refers to sloppy footnotes. Brian Greene does the same thing. So I find myself reading a lot of physic books.

Anyway,
I was trying to find out how time dilation was proved and that led to cosmic rays bombarding the atmosphere causeing the creation of muons that have 207 times the mass of an electron accelerating to near light speeds. The muon has a decay life of 2.2 micro seconds and so at the speed of light it only lasts 600 meters into the Earth's atmosphere. But since it is traveling at relativistic speeds its life is prolonged to a gamma factor of 7.1 at .99c allowing it to trvel 16 mircoseconds or 4800 meters deep into the atmosphere.

Right away I doubted this one but the other example was storing muons in a storage ring in CERN by accelerating them to close to the speed of light they can extend their 'shelf life' to be 30 times as long. So apparently time dilation is true. I don't like this whole idea. It may be that the speed of light is infinite and time is absolute like Newton said. But with a qualifier - that the Higgs, like any other translucent substance light travels through has an index of refraction that determines how fast it travels through space. It is by virtue of the Higgs that light travels at the speed it does. That is more precise than simply the speed of light in a vacuum. More like the speed of light in the Higgs with its unique index of refraction. It is the Higgs that is supposed to determine what particles have mass and how much. Light is massless. (Arguably! It stores energy in its electromagnetic field and has momentum as radiation pressure - like the solar wind and corola.)

Now what special treatment occurs in the Higgs to increase a particle's mass to infinity at the speed of light? If you were traveling at .99 percent the speed of light and you fired a light beam in front of you, how fast would it move away from you? It would move away at the speed of light. How can that be unless the Higgs is a dynamic index of refraction/not fixed? If the speed of light was infinite, this would explain some things but brings up more questions. It is as perplexing as black holes. It must be the curvature of spacetime warps space somehow to produce these weird results. That is why I thought of black holes.

Mike Dubbeld

[StBean]

Ok thanks guys....for confusing me more, Hah! No really, this is good. You opened a few doors for me that I didnt know were there. Time to do some more reading. I have alot more questions to ask.

[StBean]

Now about relativisitic mass, from my understanding there is no undergoing change of internal structure of mass object, but more of a change in reality(spacetime) in which the mass is contained? Could this be the cause of the increased energy/mass with regards to a slower moving reference frame, but if measured from within the reference frame it would still remain the same invariant mass? Would the same amount of mass/energy existing in a different spacetime geometry have an effect on relativistic mass...ARghh, I hope this doenst sound too strange. I'm trying the best to clearly ask this question.

[Mike Dubbeld]

Originally Posted by StBean

Now about relativisitic mass, from my understanding there is no undergoing change of internal structure of mass object, but more of a change in reality(spacetime) in which the mass is contained? Could this be the cause of the increased energy/mass with regards to a slower moving reference frame, but if measured from within the reference frame it would still remain the same invariant mass? Would the same amount of mass/energy existing in a different spacetime geometry have an effect on relativistic mass...ARghh, I hope this doenst sound too strange. I'm trying the best to clearly ask this question.

No it doesn’t sound strange at all. There appears to be a little war going on between Serway and Young/Freedman. The 2 big names in college physics. It is a matter of interpretation.

-------------------
Relativistic Mass

Serway (Jewett) Physics for Scientists and Engineers –

‘Pitfall Prevention’ 39.6 p1267 6’th Edition Copyright 2004 [brackets are my comments]

‘Watch out for Relativistic Mass’

Some older treatments of relativity maintained the conservation of momentum principle at high speeds by using a model in which the mass of a particle increases with speed. You might still encounter this notion of “relativistic mass” in your outside reading, especially in older books. Be aware that this notion is no longer widely accepted and mass is considered as invariant, independent of speed. The mass of an object in all frames is considered to be the mass as measured by an observer at rest with respect to the object.’

Then he goes off into deriving the relativistic energy equations/work function/kinetic energy –

‘The constant term mc squared in Equation 39.23 [Kinetic Energy = (gamma – 1) mc squared], which is independent of the speed of the particle, is called the rest energy of the particle: E = mc squared.’

‘The term (gamma)mc squared, which does depend on the particle speed, is therefore the sum of the kinetic and rest energies. We define (gamma)mc squared to be the total energy E:

Total energy = kinetic energy + rest energy E = K + mc squared

or

E = (mc squared)/sqrt(1 – u squared/c squared = (gamma)mc squared

The relationship E = mc squared shows that mass is a form of energy where c squared in the rest energy term is just a constant conversion factor.’

Then he goes into momentum and says –

‘Finally, note that because the mass m of a particle is independent of its motion, m must have the same value in all reference frames. For this reason, m is often called the invariant mass. On the other hand, because the total energy and linear momentum of a particle both depend on velocity, these quantities depend on the reference frame in which they are measured.’

So it may well be that mass is invariant but momentum is not is the message I get for his saying this.

When I turn to University Physics by Young and Freedman (Copyright 2004 11’th edition)–

‘Equation 37.27 [ p = mv/sqrt(1/v squared/c squared) relativistic momentum = p] for relativistic momentum is sometimes interpreted to mean that a rapidly moving particle undergoes an increase in mass. If the mass at zero velocity (the rest mass) is denoted by m, then the “relativistic mass” is given by relativistic mass = m/(1 – v squared/c squared)’

‘Indeed, when we consider the motion of a system of particles (such as rapidly moving ideal gas molecules in a stationary container), the total rest mass of the system is the sum of the relativistic masses of the particles, not the sum of their rest masses. Also with relativistic mass, the famous equation e = mc squared can be applied to all types of energy, not just most types.’

‘However, if blindly applied, the concept of relativistic mass has its pitfalls. As Equation 37.29 shows, the relativistic generalization of Newton’s second law is not F = (relativistic mass)(acceleration), and we will show in Section 37.8 that the relativistic kinetic energy of a particle is not K = ½ relativistic mass v squared. The use of relativistic mass has its supporters and detractors, some quite strong in their opinions.’ p1427 [As in Serway and gang no doubt]

End Relativistic Mass
------------------------

Quark Relativistic Speed - Virginia Edu How things work htm web 22 Mar 2005 ‘Ask a physics question/physicist.’

How does one find out the speed of a quark? Is it 7000 times the speed of light? – D

‘It seems that quarks are forever trapped inside the particles they comprise--no one has ever seen an isolated quark. But inside one of those particles, the quarks move at tremendous speeds. Their high speeds are a consequence of quantum mechanics and the uncertainty principle--whenever a particle (such as a quark) is confined to a small region of space (i.e. its location is relatively well defined), then its momentum must be extremely uncertain and its speed can be enormous. In fact, a substantial portion of the mass/energy of quark-based particles such as protons and neutrons comes from the kinetic energy of the fast-moving quarks inside them.'

'But despite these high speeds, the quarks never exceed the speed of light. As a massive particle such as a quark approaches the speed of light, its momentum and kinetic energy grow without bounds. For that reason, even if you gave all the energy in the world to a single quark, its speed would still remain just a hair less than the speed of light.’
http://howthingswork.virginia.edu/othertopics.html

Just like we are mostly empty space like all other atoms with electrons, protons and neutrons are mostly empty space with quarks. The orbit of an electron around the nucleus of a hydrogen atom is something like 50,000 times larger than the nucleus itself – leaving mostly empty space in between. If you consider a quark to be down around the size of a Planck length – you have a similar situation. But there are 3 of them buzzing around inside these protons and neutrons at relativistic speeds. When I say ‘inside’ I mean I believe the proton surface itself is none other than the orbits of these quarks??? Don’t ask me to fit the gluons in here!!! I don’t know!! I really need to lean more on particle physics instead of relativity but relativity bites you every time you turn around it seems in particle physics.

End Relativistic Quark Speed
---------------------------------

Index of refraction

I was saying how the Higgs may give space the property of limiting light to the speed of light in a ‘vacuum’. That may be but since the Higgs is an unknown it may be more appropriate to talk about the speed of light in a vacuum of space as having an index of 1.000.

Some index’s of refraction below

vacuum 1.00000
Air 1.00029 p53 Physics for Biology/Greenberg
Water 20 degrees Celsius 1.3330 A CRC has a complete list for translucent materials
Glass, dense crown 1.588
Diamond 2.417

‘In a medium, the speed is reduced by the quantity called the index of refraction u, and the speed of light is given by v = c/u.’ p87 College Physics for Biology Students and Pre Med Students by Greenberg.

All I am saying is that if you perhaps a better way of perceiving this vacuum is as any other medium through which light travels – science simply having selected the vacuum of space as the standard and happens to be the fastest. But by parsing it out the way I am suggesting you remove the sacredness of the speed of light in a vacuum. You attribute this speed to something more specific and highlight the fact that there may be OTHER mediums in which the speed of light is not restricted/constrained. Like other dimensions. Non-locality and quantum tunneling happen somehow.

End Index of Refraction
---------------------------

Mike Dubbeld

[freeaction]

Originally Posted by StBean

Now about relativisitic mass, from my understanding there is no undergoing change of internal structure of mass object, but more of a change in reality(spacetime) in which the mass is contained? Could this be the cause of the increased energy/mass with regards to a slower moving reference frame, but if measured from within the reference frame it would still remain the same invariant mass? Would the same amount of mass/energy existing in a different spacetime geometry have an effect on relativistic mass...ARghh, I hope this doenst sound too strange. I'm trying the best to clearly ask this question.

Special relativity is only weird when you compare frames of reference. Within a single frame of reference you get the conservation of

1. Energy (E)
2. Momentum (Px,Py,Pz)

Both of these are defined in terms of the invariant rest mass m and the factor
gamma = 1/Sqrt(1-Beta^2) where Beta= u/c. Here u is the velocity of some particle and c is the speed of light in vacuum.

E=gamma*mc^2
P=gamma*mv

For example if two particle one with momentum P1=(a,0,0) and another with momentum P2=(0,b,0) collide and stick together then the momentum of their composite must be precisely Pcomposite = P1+P2 = (a,b,0). This is all within a certain frame lets call it S={(ct,x,y,z)}. Now you would like to ask the question if I'm another observer does the composite particle have the same momentum? The answer is no, the momentum of the composite particle could be zero or lots of things in another frame. Lets call the other frame S' for the sake of discussion.

Question: what quantities are the same in all frames of reference?

That is given "F" some physical quantity, when is it the case that F(S')=F(S). To answer this question carefully we must delineate exactly how the coordinates in S relate to the coordinates in S'. The answer is that S and S' are related by a "Lorentz Transformation". Don't be to scared it's just a slight generalization of a rotation. A rotation mixes different spatial dimensions together while a Lorentz transformation mixes time and space. In fact every rotation is also a Lorentz transformation in a trivial way. Lets call the Lorentz transformation L, we can write S'=LS. In other words we get the frame of reference S' by doing the Lorentz transformation L on the frame S. So the condition that F be invariant becomes F(LS)=F(S). When this condition is met for all possible Lorentz transformations L we say that F is a "scalar". The terminology "scalar" just means it behaves like an ordinary number. Examples of scalars in special relativity are: mass, spin, the "square" of the 4-momentum,...
My last entry is very telling. It is the "square" of the 4-momentum that is invariant for all frames. The 4-momentum is simply the energy and 3-momentum put together into a 4 component obect: P=[E/c,Px,Py,Pz]. In relativity the energy and momentum must be joined to make an invariant object. What is meant by "square" is the relavitic generalization of dot product let me call it N(the metric). N takes in two 4-vectors and spits out a number.
For example if P=(a,b,c,d) and Q=(k,l,m,n) then their "square" is simply

N(P,Q)=(a,b,c,d)*(k,l,m,n) = -ak+bl+cm+dn

It is under this N we find that for the 4 momentum P=(E/c,Px,Py,Pz)

N(P,P) = -(E^2)/c^2 + (Px)^2 + (Py)^2 + (Pz)^2

Now since this is the same in all frames we just choose the rest frame where the 3-momentum is zero and E=mc^2

N(P,P) = -E^2/c^2 = -m

Here's the cool thing, since N(P,P)=N(LP,LP) for all possible lorentz transformations L we have just proven that N(P,P)=-m in ALL intertial frames.
This is why m should be thought of as a fixed number which characterizes the particle in special relativity.

Hope this helps some, Mike is right also, there is some disagreement in introductory texts, but most of what is written in introductory physics books is not quite true... in detail or interpretation...