| Topic: |
Science > Physics |
| User: |
"Mike Helland" |
| Date: |
12 Aug 2004 09:00:28 AM |
| Object: |
QFT Questions |
Can anyone clarify some basic things about quantum field theory for me?
Is it true the search for quantum gravity is based on QFT?
Is it true that in QFT every field is propogating at c?
Can you can model quantum mechanics without QFT?
Would that be non-relativistic quantum mechanics?
What experimental evidence exists for QFT that doesn't exist for
non-relativistic quantum mechanics?
Have attempts been made at quantum gravity without QFT, where the
graviton is travelling faster than c?
Thanks.
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| User: "Alfred Einstead" |
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| Title: Reconciling quantum theory & relativity (was: QFT Questions) |
14 Aug 2004 06:58:07 AM |
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(Mike Helland) wrote:
Can anyone clarify some basic things about quantum field theory for me?
Is it true the search for quantum gravity is based on QFT?
More generally, the search to reconcile Quantum Theory with Relativity
is focused on bringing the most developed parts of each (General
Relativity and Quantum Field Theory) onto a common foundation.
Is it true that in QFT every field is propogating at c?
The propagator of a massless field is a solution to the wave
equation with singular source:
d^2 u/dt^2 - c^2 del^2 u = k delta(x)
u(r,0) = du/dt (r,0) = 0
It's non-zero and singular on the light cone; which is the same
thing as saying that the field propagates at light speed.
The propagator for a massive field, a solution to the Klein
Gordon equation
d^2 u/dt^2 - c^2 del^2 u + m^2 u = k delta(x)
(I might have the signs reversed on the m's and delta's) has
the same singular part on the light cone, plus an additional
non-zero part within the light cone.
Can you can model quantum mechanics without QFT?
Would that be non-relativistic quantum mechanics?
More generally, there is no consistent relativistic concept of
a particle. The Heisenberg relations for particle trajectories
t |-> (x(t), y(t), z(t)):
[x(t), x'(t)] = [y(t), y'(t)] = [z(t), z'(t)] = i h-bar/m
[x(t),y(t)]=[y(t),z(t)]=[z(t),x(t)] = 0
[x'(t),y'(t)]=[y'(t),z'(t)]=[z'(t),x'(t)] = 0
[x(t),y'(t)]=[y(t),z'(t)]=[z(t),x'(t)] = 0
[y(t),x'(t)]=[z(t),y'(t)]=[x(t),z'(t)] = 0
don't generalize readily for worldlines in Relativity,
s |-> (t(s), x(s), y(s), z(s)).
More generally, it's not possible to represent particle worldlines
in a relativistic setting in a way compatible with quantum theory
without violating causality. This is a fairly well-known result
explained, for instance, in Ticciati (Quantum Field Theory For
Mathematicians; section 1.6 The Position Operator [and it's
impossibility]).
More generally still, even further than that, there is no concept
of a particle as a corpuscular entity in relativity in the first
place. E = m c^2 means matter can interconvert with energy. What
becomes of a corpuscle that converts, if you assumed that particles
were of this form? In QM, operators apply for all time. So, the
position operator (X(t), Y(t), Z(t)) implicitly assumes that the
thing is around forever in the past and forever into the future.
What experimental evidence exists for QFT that doesn't exist for
non-relativistic quantum mechanics?
(1) Particles don't have separate identity as individual corpuscules;
e.g., there is only 1 way to put two particles of the same type
into two boxes, one in each; not 2 ways.
In essence, that means all the electrons in the universe is actually
the same electron at different places at the same time. All the
photons is the same photon at different places at the same time.
They have no more identity as individual objects than waves on an
ocean do.
The difference in the way particles are counted affects the
determination of such empirical constants as the specific heats
of materials. And, this discrepancy has been known about since
the early to mid 19th century.
It should also be of interest to remember that in a general
context of spacetime (whether Newtonian or Relativistic, it
doesn't matter) "individual" people don't have existence as
separate individuals either. They don't have worldlines at
all. Rather their "worldlines" are actually strands on a
web-shaped structure that includes everybody on it, including
the food you eat... since you're related to your food. Your
strand is connected to your mother's at that point&time in
spacetime corresponding to where&when you were a fetus.
(2) Particle identity and number are not preserved; and particle
identity and number cannot be construed in any way that enables
one to infer that they are preserved.
Interactions like
nu_e + W- --> e
might be interpreted as a number-preserving interaction if one
adopted the fiction that the electron (e) is a bound state
of a neutrino (nu_e) and W-. But then, one also has interactions
like
W- --> anti-nu_e + e
[which is a prime example of the matter-energy conversion issue
raised above, since the W is a particle of energy] which ruin
that interpretation.
Then you also have interactions such as:
Z --> W+ + W-
W+ --> Z + W+
W+ + W- --> Z
etc.; which completely defy any attempt to categorize as a
number preserving interaction, even modulo any kind of
assumption about their being bound states. For instance,
one has the interaction:
Z --> W+ + W-
--> (Z + W+) + W- = Z + (W+ + W-)
--> Z + Z
which absolutely can never be construed as a particle number
preserving interaction of any kind under any interpretation of
any kind.
Have attempts been made at quantum gravity without QFT, where
the graviton is travelling faster than c?
The light cone, itself, is the root of the problem both (1)
in trying to reconcile GR and QFT and (2) in trying to even
formulate a consistent QFT, which is still an open problem.
Since the propagators are singular on the light cone, then
the fields are represented in terms of singular delta-like
functions. But the field equations are non-linear, which
means they involve non-linear combinations of singular
functions ... which is generally ill-defined and lies at
the root of all the problems with the infinities in
quantum fields (and even for classical fields).
String theory is supposed to ameliorate that issue by
modelling fields not in terms of point-like particles, but
in terms of line-like particles.
But that way of resolving (2) can never be anything more
than a workaround, since it doesn't even begin to address
the problem of (1).
The problem of (1) runs much deeper, isn't even recognized
(much less addressed) by either of the main approaches to
quantum gravity (loop QG or string theory) and entails a
resolution much more striking.
Quantum gravity is supposed to quantize the metric for
spacetime itself. That means that the coefficients in
the line element:
ds^2 = sum (g_{mn} dx^m dx^n: m,n=0,1,2,3)
are no longer even well-defined numbers, but instead have
values which are state-dependent and take on a dispersed
distribution about a "expectation" value.
The light cone, itself, is defined by
ds^2 = 0.
Likewise, the inside and outside of the light cone are
defined by ds^2 > 0 and ds^2 < 0.
But the defininition the various objects which enter into
quantum field theory requires one FIRST write down the
commutators
[A(x), B(x+dx)] = 0 if ds^2 < 0
which assumes that the light cone has ALREADY been defined.
So, in order to define the g_{mn}'s one needs to first have
a definition of ds^2. And in order to define ds^2, one
needs to first have a definition of the g_{mn}'s.
That's a catch-22 with no way out.
It means that the causality principle
[A(x), B(x+dx)] = 0 if ds^2 < 0
can't be consistently maintained.
At root of this problem is that the light cone, being defined
in terms of the g's (which are now smeared out with non-zero
dispersions), is smeared out and is no longer a sharply defined
object. The actual location of the light cone is state-dependent.
So, what looks like a causal interaction in one state may be
causality violating seen in another state.
The punchline, of course, is that states can combine by
superposition. So, you can have a superposition of states,
where the interaction is both causal and causality-violating.
This type of anomaly doesn't have a concept or name, so I
called it "Light Cone Tunnelling". Using the loophole provided
by the non-sharpness of the light cone in the context of a
quantized metric, you can actually tunnel out from under the
light cone.
There is a close analogue to this, however, that is already
well-known. The event horizon of a black hole is actually
part of the light cone. It's stationary because all along
the event horizon, the outward radial speed of light is 0.
In this case, light cone tunelling corresponds to energy
that comes out from the black hole. This is already known
as Hawking Radiation.
The way it is explained in more prosaic terms in terms of
ordinary QFT makes essential use of the ambiguity of the
vacuum state.
In general relativistic context, it is actually the case
that the distinction between:
(particle A present) <-> (anti-particle A absent)
(particle A absent) <-> (anti-particle A present)
is observer-dependent. Two observers in different states
of acceleration see things differently. This means,
among other things, that what counts as a vacuum in one
frame of reference is not so in the other, since the
absence of all A's in one frame will be seen as a
plenum of anti-A's in the other frame.
So, in a strong gravitational field, it's possible to
mine the vacuum and steal away a particle which, from
afar, looks like one is absorbing the absence of the
opposite particle (i.e., absorbing negative energy).
From afar, the black hole takes in negative energy, which
is just a fancy way of saying that it's spitting out positive
energy -- the Hawking radiation.
This is the mechanism by which energy tunnels through the
light cone, in this specific context.
In a more general context, this should also provide the
means by which energy can tunnel through light cones and
produce a faint shadow of causality violation.
So, the "striking" consequence I alluded to above is
causality violation, itself. The roadblock that keeps
quantum theory from being reconciled with relativity
is the unwillingness to drop the assumption of causality.
That's the root of all the problems of bringing the two
theories together.
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| User: "Very cryptic" |
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| Title: Re: Reconciling quantum theory & relativity (was: QFT Questions) |
17 Aug 2004 11:27:08 AM |
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(Alfred Einstead) wrote in message news:<e58d56ae.0408131343.4a606513@posting.google.com>...
More generally, there is no consistent relativistic concept of
a particle. The Heisenberg relations for particle trajectories
t |-> (x(t), y(t), z(t)):
[x(t), x'(t)] = [y(t), y'(t)] = [z(t), z'(t)] = i h-bar/m
[x(t),y(t)]=[y(t),z(t)]=[z(t),x(t)] = 0
[x'(t),y'(t)]=[y'(t),z'(t)]=[z'(t),x'(t)] = 0
[x(t),y'(t)]=[y(t),z'(t)]=[z(t),x'(t)] = 0
[y(t),x'(t)]=[z(t),y'(t)]=[x(t),z'(t)] = 0
don't generalize readily for worldlines in Relativity,
s |-> (t(s), x(s), y(s), z(s)).
More generally, it's not possible to represent particle worldlines
in a relativistic setting in a way compatible with quantum theory
without violating causality. This is a fairly well-known result
explained, for instance, in Ticciati (Quantum Field Theory For
Mathematicians; section 1.6 The Position Operator [and it's
impossibility]).
I'm not sure what the theorem actually states, but I do know there IS
a covariant canonical QM model of a single relativistic particle.
[x^mu,x^nu]=[p_mu,p_nu]=0
[x^mu,p_nu]=i hbar delta^mu_nu
has an irreducible rep. The trick is to impose the constraint
[(p-qA)^2-m^2]|psi>=0 for the physical states |psi> and only work with
"physical" operators which commute with [(p-qA)^2-m^2].
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| User: "Andy Y" |
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| Title: Re: Reconciling quantum theory & relativity (was: QFT Questions) |
18 Aug 2004 04:08:00 AM |
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(Very cryptic) wrote in message
whopkins@csd.uwm.edu (Alfred Einstead) wrote in message
This is a fairly well-known result
explained, for instance, in Ticciati (Quantum Field Theory For
Mathematicians; section 1.6 The Position Operator [and it's
impossibility]).
I'm not sure what the theorem actually states, but I do know there IS
a covariant canonical QM model of a single relativistic particle.
[x^mu,x^nu]=[p_mu,p_nu]=0
[x^mu,p_nu]=i hbar delta^mu_nu
has an irreducible rep. The trick is to impose the constraint
[(p-qA)^2-m^2]|psi>=0 for the physical states |psi> and only work with
"physical" operators which commute with [(p-qA)^2-m^2].
Please excuse the ignorance, but the position operator does or does
not commute with the aforementioned operator?
-Andy
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| User: "Igor" |
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| Title: Re: Reconciling quantum theory & relativity (was: QFT Questions) |
19 Aug 2004 04:51:08 AM |
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(Andy Y) wrote in message news:<c3214d0d.0408171546.7553eee6@posting.google.com>...
very_cryptic@hotmail.com (Very cryptic) wrote in message
whopkins@csd.uwm.edu (Alfred Einstead) wrote in message
This is a fairly well-known result
explained, for instance, in Ticciati (Quantum Field Theory For
Mathematicians; section 1.6 The Position Operator [and it's
impossibility]).
I'm not sure what the theorem actually states, but I do know there IS
a covariant canonical QM model of a single relativistic particle.
[x^mu,x^nu]=[p_mu,p_nu]=0
[x^mu,p_nu]=i hbar delta^mu_nu
has an irreducible rep. The trick is to impose the constraint
[(p-qA)^2-m^2]|psi>=0 for the physical states |psi> and only work with
"physical" operators which commute with [(p-qA)^2-m^2].
Please excuse the ignorance, but the position operator does or does
not commute with the aforementioned operator?
-Andy
Neither p nor x commute with p - qA in general, since A is a function of x.
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| User: "Arnold Neumaier" |
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| Title: Re: Reconciling quantum theory & relativity |
19 Aug 2004 12:39:12 PM |
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Very cryptic wrote:
whopkins@csd.uwm.edu (Alfred Einstead) wrote in message news:<e58d56ae.0408131343.4a606513@posting.google.com>...
More generally, it's not possible to represent particle worldlines
in a relativistic setting in a way compatible with quantum theory
without violating causality. This is a fairly well-known result
explained, for instance, in Ticciati (Quantum Field Theory For
Mathematicians; section 1.6 The Position Operator [and it's
impossibility]).
I'm not sure what the theorem actually states, but I do know there IS
a covariant canonical QM model of a single relativistic particle.
[x^mu,x^nu]=[p_mu,p_nu]=0
[x^mu,p_nu]=i hbar delta^mu_nu
has an irreducible rep. The trick is to impose the constraint
[(p-qA)^2-m^2]|psi>=0 for the physical states |psi> and only work with
"physical" operators which commute with [(p-qA)^2-m^2].
The theorem says that any multiparticle theory with well-defined
world-lines satisfying certain natural conditions necessarily describes
noninteracting particles only (a tenso product of what you described).
This is not intrinsically QM, but also valid in classical relativistic
mechanics.
Arnold Neumaier
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| User: "Bjoern Feuerbacher" |
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| Title: Re: Reconciling quantum theory & relativity |
19 Aug 2004 07:24:05 AM |
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Very cryptic wrote:
[snip]
I'm not sure what the theorem actually states, but I do know there IS
a covariant canonical QM model of a single relativistic particle.
[x^mu,x^nu]=[p_mu,p_nu]=0
[x^mu,p_nu]=i hbar delta^mu_nu
has an irreducible rep. The trick is to impose the constraint
[(p-qA)^2-m^2]|psi>=0 for the physical states |psi> and only work with
"physical" operators which commute with [(p-qA)^2-m^2].
Excuse me, but what is x^0? A time operator? What are its eigenvalues
and eigenstates?
Bye,
Bjoern
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| User: "Charles J. Quarra" |
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| Title: Re: Reconciling quantum theory & relativity (was: QFT Questions) |
16 Aug 2004 12:55:44 PM |
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(Alfred Einstead) wrote in message news:<e58d56ae.0408131343.4a606513@posting.google.com>...
So, the "striking" consequence I alluded to above is
causality violation, itself. The roadblock that keeps
quantum theory from being reconciled with relativity
is the unwillingness to drop the assumption of causality.
That's the root of all the problems of bringing the two
theories together.
well as i see it, uncertainty and conserved simultanenous quantities
is exclusive only according to conmutators. Intuitively i would say
that a measurement of a spacetime interval for a particle trajectory
would constrain any simultaneous measurements of the g_{mn} quantities
to guarantee that such trajectory satisfy ds^2 <=0, ie: i would expect
spacetime trajectories states to be quantum entangled with the g_{mn}
states such as satisfy causality.
Note that im not saying that is what "must happen" in physics
reality; im only asserting that this possibility is not excluded from
what i understand. In fact i would say that is natural to expect it
[Moderator's note: Huge amounts of quoted text deleted by moderator. Please quote
reasonably. See http://www-stud.uni-essen.de/~sb0264/HowToPost.html -usc]
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| User: "Arnold Neumaier" |
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| Title: Re: Reconciling quantum theory & relativity |
16 Aug 2004 01:01:16 PM |
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In essence, that means all the electrons in the universe is actually
the same electron at different places at the same time. All the
photons is the same photon at different places at the same time.
They have no more identity as individual objects than waves on an
ocean do.
I find this a misleading way of picturing indistinguishability.
It is nore like having a bumpy but materially uniform surface,
where one cannot label the local maxima in a 'distinguishable' way
except by their relative position, and where new maxima may appear
or old ones disappear). Exactly the same happens for electrons and
positrons, which are in QFT just excitations of the electron field.
The analogue to the quantum field is the scalar field defining the
height of the surface at each point.
Arnold Neumaier
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| User: "Gregory L. Hansen" |
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| Title: Re: QFT Questions |
12 Aug 2004 11:09:39 AM |
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In article <ad157aec.0408120600.a8a1aa@posting.google.com>,
Mike Helland <mhelland@techmocracy.net> wrote:
Can anyone clarify some basic things about quantum field theory for me?
Is it true the search for quantum gravity is based on QFT?
Fields are quantized. Gravity is a field, so it should be quantized, too.
That is, it should follow deBroglie's relation connecting energy and
frequency, and should be describable with a quantum wavefunction.
Is it true that in QFT every field is propogating at c?
Can you can model quantum mechanics without QFT?
The quantum mechanics typically taught to undergrads is semiclassical.
That is, you suppose something like an electron influenced by a classical,
unquantized electric field. That's only approximately correct, since the
field is quantized, too.
Would that be non-relativistic quantum mechanics?
You can do relativistic quantum mechanics without the field theory
approach. It will be relativistic quantum mechanics with semiclassical
fields, and particle number won't be conserved (e.g. near the nucleus of
an atom) which is awkwardly handled with wavefunctions, but it's been
done.
What experimental evidence exists for QFT that doesn't exist for
non-relativistic quantum mechanics?
Basically everything coming out of accelerator experiments, for one. The
Lamb shift, which is low energy spectroscopy.
Have attempts been made at quantum gravity without QFT, where the
graviton is travelling faster than c?
It wouldn't surprise me if it had.
--
"Then they placed the ark of the Lord on the cart; along with the box
containing the golden mice and the images of the hemorrhoids."
-- 1 Samuel 6:11
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| User: "Creighton Hogg" |
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| Title: Re: QFT Questions |
12 Aug 2004 12:03:57 PM |
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On Thu, 12 Aug 2004, Gregory L. Hansen wrote:
In article <ad157aec.0408120600.a8a1aa@posting.google.com>,
Mike Helland <mhelland@techmocracy.net> wrote:
Can anyone clarify some basic things about quantum field theory for me?
Is it true the search for quantum gravity is based on QFT?
Fields are quantized. Gravity is a field, so it should be quantized, too.
That is, it should follow deBroglie's relation connecting energy and
frequency, and should be describable with a quantum wavefunction.
Of course it's a little more complicated than that. The naive QFT that
you'd base off of GR crashes and burns. There's basically three options
after that
a) We keep quantum mechanics as is and try to find a theory that can
reduce to GR in some limit.
b) We keep GR as is and expand our concepts of quantization.
c) None of the above.
a is the path string theory has taken and b the path Loop Quantum Gravity
has taken.
I switch votes between a,b, and c several times a week.
It's a good thing nature doesn't care what I think.
Have attempts been made at quantum gravity without QFT, where the
graviton is travelling faster than c?
It wouldn't surprise me if it had.
I don't know of any, to be honest. Like you said, it wouldn't be
surprising if there were, but I just haven't ever heard of it. In string
theory the graviton is a massless spin-2 particle. I don't think there is
a well-defined graviton in loop quantum gravity yet.
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| User: "Gregory L. Hansen" |
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| Title: Re: QFT Questions |
12 Aug 2004 01:47:22 PM |
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In article <Pine.LNX.4.44.0408121155450.7455-100000@erodium.hep.wisc.edu>,
Creighton Hogg <wchogg@hep.wisc.edu> wrote:
On Thu, 12 Aug 2004, Gregory L. Hansen wrote:
In article <ad157aec.0408120600.a8a1aa@posting.google.com>,
Mike Helland <mhelland@techmocracy.net> wrote:
Can anyone clarify some basic things about quantum field theory for me?
Is it true the search for quantum gravity is based on QFT?
Fields are quantized. Gravity is a field, so it should be quantized, too.
That is, it should follow deBroglie's relation connecting energy and
frequency, and should be describable with a quantum wavefunction.
Of course it's a little more complicated than that. The naive QFT that
you'd base off of GR crashes and burns. There's basically three options
after that
a) We keep quantum mechanics as is and try to find a theory that can
reduce to GR in some limit.
b) We keep GR as is and expand our concepts of quantization.
c) None of the above.
a is the path string theory has taken and b the path Loop Quantum Gravity
has taken.
I switch votes between a,b, and c several times a week.
It's a good thing nature doesn't care what I think.
Sort of related to b, but more general, is DeBroglie's relation. We
assume, basically, that the amount of energy that a gravitational wave
carries is Nhf for N quanta. Quantum mechanics as we know it elaborates
on that hypothesis.
I admit that my ignorance of the subject is such that I might have
imagined QED with an interaction strength going as -G instead of +e (or
whatever alpha would work out to), and calling the job half done.
Maybe I'll take the time to educate myself on that subject when the real
world stops beating me in the face with a 2x4 with a nail in it.
Have attempts been made at quantum gravity without QFT, where the
graviton is travelling faster than c?
It wouldn't surprise me if it had.
I don't know of any, to be honest. Like you said, it wouldn't be
surprising if there were, but I just haven't ever heard of it. In string
theory the graviton is a massless spin-2 particle. I don't think there is
a well-defined graviton in loop quantum gravity yet.
I don't have any references on hand, but here and there in journals like
the Phys Revs, Foundations of Physics, and the arXives, every once in a
while I find what seems like the most bizarre ideas being explored, which
render any crank's accusations of straight-jacketed scientific thinking to
be an admission of ignorance and laziness.
There've been experimental tests of causality in nuclear matter. There's
always been an interest in measuring c+v^a for a moving source.
Discussions of aether theories as a general class of theories with special
relativity being a special case. And so on. It wouldn't surprise me if
some FTL gravity were included.
--
Irony: "Small businesses want relief from the flood of spam clogging their
in-boxes, but they fear a proposed national 'Do Not Spam' registry will
make it impossible to use e-mail as a marketing tool."
http://www.bizjournals.com/houston/stories/2003/11/10/newscolumn6.html
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| User: "Creighton Hogg" |
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| Title: Re: QFT Questions |
12 Aug 2004 02:12:07 PM |
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On Thu, 12 Aug 2004, Gregory L. Hansen wrote:
In article <Pine.LNX.4.44.0408121155450.7455-100000@erodium.hep.wisc.edu>,
Creighton Hogg <wchogg@hep.wisc.edu> wrote:
Of course it's a little more complicated than that. The naive QFT that
you'd base off of GR crashes and burns. There's basically three options
after that
a) We keep quantum mechanics as is and try to find a theory that can
reduce to GR in some limit.
b) We keep GR as is and expand our concepts of quantization.
c) None of the above.
a is the path string theory has taken and b the path Loop Quantum Gravity
has taken.
I switch votes between a,b, and c several times a week.
It's a good thing nature doesn't care what I think.
<>
I admit that my ignorance of the subject is such that I might have
imagined QED with an interaction strength going as -G instead of +e (or
whatever alpha would work out to), and calling the job half done.
Well the problem is that the interaction strength *isn't* just G. The
coupling constant for a graviton vertex isn't a dimensionless constant,
it's proportional to energy! That's very bad, from the standpoint of QFT.
Unless you impose an energy cutoff everything goes all to hell. (I have
this nagging feeling there are still problems even if you do impose an
energy cutoff, but don't take my word for that.)
Maybe I'll take the time to educate myself on that subject when the real
world stops beating me in the face with a 2x4 with a nail in it.
Geez, it sounds like you've been having a rough time lately. Is it your
research? Did you know that the word "research" comes from a Swahili
phrase meaning "won't work"? No really, it does.
I don't know of any, to be honest. Like you said, it wouldn't be
surprising if there were, but I just haven't ever heard of it. In string
theory the graviton is a massless spin-2 particle. I don't think there is
a well-defined graviton in loop quantum gravity yet.
I don't have any references on hand, but here and there in journals like
the Phys Revs, Foundations of Physics, and the arXives, every once in a
while I find what seems like the most bizarre ideas being explored, which
render any crank's accusations of straight-jacketed scientific thinking to
be an admission of ignorance and laziness.
There've been experimental tests of causality in nuclear matter. There's
always been an interest in measuring c+v^a for a moving source.
Discussions of aether theories as a general class of theories with special
relativity being a special case. And so on. It wouldn't surprise me if
some FTL gravity were included.
Oh I agree completely. The Twentieth Century was *the* century for
bizzare and crazy science. Relativity, quantum mechanics, nuclear
physics, qft, quantum computers, etc. There were alot of big advances
that were downright crazy ideas, but they worked. Cranks are full of it
when they say we don't accept new ideas!
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| User: "Gregory L. Hansen" |
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| Title: Re: QFT Questions |
12 Aug 2004 03:02:48 PM |
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In article <Pine.LNX.4.44.0408121359520.7455-100000@erodium.hep.wisc.edu>,
Creighton Hogg <wchogg@hep.wisc.edu> wrote:
On Thu, 12 Aug 2004, Gregory L. Hansen wrote:
In article <Pine.LNX.4.44.0408121155450.7455-100000@erodium.hep.wisc.edu>,
Creighton Hogg <wchogg@hep.wisc.edu> wrote:
Of course it's a little more complicated than that. The naive QFT that
you'd base off of GR crashes and burns. There's basically three options
after that
a) We keep quantum mechanics as is and try to find a theory that can
reduce to GR in some limit.
b) We keep GR as is and expand our concepts of quantization.
c) None of the above.
a is the path string theory has taken and b the path Loop Quantum Gravity
has taken.
I switch votes between a,b, and c several times a week.
It's a good thing nature doesn't care what I think.
<>
I admit that my ignorance of the subject is such that I might have
imagined QED with an interaction strength going as -G instead of +e (or
whatever alpha would work out to), and calling the job half done.
Well the problem is that the interaction strength *isn't* just G. The
coupling constant for a graviton vertex isn't a dimensionless constant,
it's proportional to energy! That's very bad, from the standpoint of QFT.
Unless you impose an energy cutoff everything goes all to hell. (I have
this nagging feeling there are still problems even if you do impose an
energy cutoff, but don't take my word for that.)
Well, maybe you could come up with a prediction in the Newtonian limit.
Maybe I'll take the time to educate myself on that subject when the real
world stops beating me in the face with a 2x4 with a nail in it.
Geez, it sounds like you've been having a rough time lately. Is it your
research?
Crunching to meet a hard deadline to defend my thesis; I haven't had a
weekend in more than a month. The equipment still doesn't work right.
Nobody's hiring physicists, I'm going to be hearing things like "Doctor
Hansen, there's a wet spill in front of Waldenbooks" when I graduate. I'm
starting to incoherently mutter things through my beard, like "You can't
commercialize the weak force", and "Why does everything have to be so
hard?" I'll wind up buying a cane just to wave at young people a few
years my junior, and hang around coffee shops near college campuses
telling students the value of an education.
Did you know that the word "research" comes from a Swahili
phrase meaning "won't work"? No really, it does.
If you're serious about that, I would post the etymology on my office
door. But it looks French.
I don't know of any, to be honest. Like you said, it wouldn't be
surprising if there were, but I just haven't ever heard of it. In string
theory the graviton is a massless spin-2 particle. I don't think there is
a well-defined graviton in loop quantum gravity yet.
I don't have any references on hand, but here and there in journals like
the Phys Revs, Foundations of Physics, and the arXives, every once in a
while I find what seems like the most bizarre ideas being explored, which
render any crank's accusations of straight-jacketed scientific thinking to
be an admission of ignorance and laziness.
There've been experimental tests of causality in nuclear matter. There's
always been an interest in measuring c+v^a for a moving source.
Discussions of aether theories as a general class of theories with special
relativity being a special case. And so on. It wouldn't surprise me if
some FTL gravity were included.
Oh I agree completely. The Twentieth Century was *the* century for
bizzare and crazy science. Relativity, quantum mechanics, nuclear
physics, qft, quantum computers, etc. There were alot of big advances
that were downright crazy ideas, but they worked. Cranks are full of it
when they say we don't accept new ideas!
I'm not even talking about the big crazy ideas that worked. Also things
like Woodward's thoughts on the origin of inertia, the special
relativistic Newtonian gravity that Biswas discussed, "Covariant Ether
Theories and Special Relativity" by Kholmetskii (Physica Scripta 67, 381),
an attempt to measure gravity shielding during an eclipse (actually taking
LeSage's hypothesis seriously, Phys Rev D 62, 041101(R)), "Quantum
coherence and closed timelike curves" by Hawking, Phys Rev D 52, 5681, to
list some things off the top of my head or within reach.
Cranks see the pop-sci and the newsgroups, they don't seem to have a good
idea of the breadth of things that are attempted without the measure of
success required to be conveyed to the general public. They only see what
works, and assume nothing else is ever attempted. Or some of them
complain because scientists like Hawking *do* explore ideas like time
travel, rather than because they don't, and still managed to accuse
scientists of a fear of novelty while wanting the world to go back to
19th century science.
--
"I'm giving you the chance to look fate in those pretty eyes of hers
and say, 'Step off, *****. This is my party and you're not invited.'"
-- Chris Shugart, _Testosterone Magazine_
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| User: "Bjoern Feuerbacher" |
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| Title: Re: QFT Questions |
12 Aug 2004 09:53:12 AM |
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Mike Helland wrote:
Can anyone clarify some basic things about quantum field theory for me?
Is it true the search for quantum gravity is based on QFT?
Approximately right. More accurate would be to see that the search
for quantum gravity is based on the realization that every physical
theory should agree with the laws of quantum theory (not necessarily
quantum *field* theory!).
Is it true that in QFT every field is propogating at c?
No, that is wrong. It even makes little sense to say that a field
propagates. Particles and waves are the things which can propagate.
Can you can model quantum mechanics without QFT?
Yes, definitely, since quantum mechanics is the application of
the postulates of quantum theory to mechanics, whereas QFT is the
application of those postulates to field theory.
This question can already be answered by looking at history:
quantum mechanics was essentially born in 1926, QFT only in the forties.
So obviously one can "model" QM without QFT.
Would that be non-relativistic quantum mechanics?
No, not necessarily. E.g. both the Klein-Gordon equation and the
Dirac equation are quantum mechanical equations, not equations of
QFT (well, QFT uses them also, but for different mathematical objects),
but both are relativistic.
What experimental evidence exists for QFT that doesn't exist for
non-relativistic quantum mechanics?
Sorry, I do not understand this question. Could you rephrase it, please?
Have attempts been made at quantum gravity without QFT,
Yes, I would say. E.g. attempts in string theory. I would not call
that using QFT (but I don't know much about string theory, so I could
be wrong).
where the graviton is travelling faster than c?
I know of no attempts to describe Quantum Gravity where this happens.
Bye,
Bjorn
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| User: "Gregory L. Hansen" |
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| Title: Re: QFT Questions |
13 Aug 2004 09:14:50 AM |
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In article <cfg08o$jl1$1@news.urz.uni-heidelberg.de>,
Bjoern Feuerbacher <bfeuerba@ix.urz.uni-heidelberg.de> wrote:
Mike Helland wrote:
Is it true that in QFT every field is propogating at c?
No, that is wrong. It even makes little sense to say that a field
propagates. Particles and waves are the things which can propagate.
Assume he asked whether every particle and wave is propagating at c.
It depends on what you put into the field theory, but in electroweak
theory I thought the leptons and bosons would all be massless except for
interactions with the Higgs field, although I think that had mass. I'm
fuzzy on the details.
--
"For every problem there is a solution which is simple, clean and wrong."
-- Henry Louis Mencken
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| User: "Bjoern Feuerbacher" |
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| Title: Re: QFT Questions |
13 Aug 2004 09:35:17 AM |
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Gregory L. Hansen wrote:
In article <cfg08o$jl1$1@news.urz.uni-heidelberg.de>,
Bjoern Feuerbacher <bfeuerba@ix.urz.uni-heidelberg.de> wrote:
Mike Helland wrote:
Is it true that in QFT every field is propogating at c?
No, that is wrong. It even makes little sense to say that a field
propagates. Particles and waves are the things which can propagate.
Assume he asked whether every particle and wave is propagating at c.
It depends on what you put into the field theory, but in electroweak
theory I thought the leptons and bosons would all be massless except for
interactions with the Higgs field,
Right. But since these interactions do indeed happen, the particles
have mass, and thus propagate at less than c.
although I think that had mass.
The Higgs has mass because it interacts with itself.
I'm fuzzy on the details.
Me too - although I studied this several times in detail... It's just
to complicated to remember every detail when one does not need it.
Bye,
Bjoern
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| User: "Alfred Einstead" |
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| Title: Re: QFT Questions |
13 Aug 2004 04:56:56 PM |
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Bjoern Feuerbacher <feuerbac@thphys.uni-heidelberg.de> wrote:
It depends on what you put into the field theory, but in electroweak
theory I thought the leptons and bosons would all be massless except for
interactions with the Higgs field,
Right. But since these interactions do indeed happen, the particles
have mass, and thus propagate at less than c.
although I think that had mass.
The Higgs has mass because it interacts with itself.
I'm fuzzy on the details.
Me too - although I studied this several times in detail...
There are two equivalent pictures in the Standard Model: pre
symmetry breaking, where everything is massless and the Higgs has
4 modes; and post-symmetry breaking, where the vacuum state is
redefined, everything has a mass proportional to what it
coupled with the Higgs with in the other picture, and the
Higgs has only 1 mode, which is massive.
In classical terms, the Higgs is like a thick soup where
everything, moving at light speed, zig-zags about and travels
along mean paths which look, from a distance, like the path
of a massive particle.
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| User: "Gregory L. Hansen" |
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| Title: Re: QFT Questions |
13 Aug 2004 11:24:51 AM |
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In article <cfijj4$aqc$1@news.urz.uni-heidelberg.de>,
Bjoern Feuerbacher <bfeuerba@ix.urz.uni-heidelberg.de> wrote:
Gregory L. Hansen wrote:
In article <cfg08o$jl1$1@news.urz.uni-heidelberg.de>,
Bjoern Feuerbacher <bfeuerba@ix.urz.uni-heidelberg.de> wrote:
Mike Helland wrote:
Is it true that in QFT every field is propogating at c?
No, that is wrong. It even makes little sense to say that a field
propagates. Particles and waves are the things which can propagate.
Assume he asked whether every particle and wave is propagating at c.
It depends on what you put into the field theory, but in electroweak
theory I thought the leptons and bosons would all be massless except for
interactions with the Higgs field,
Right. But since these interactions do indeed happen, the particles
have mass, and thus propagate at less than c.
although I think that had mass.
The Higgs has mass because it interacts with itself.
Or, as in a typical introduction to QED, you could just put an "m" in the
denominator of the propagator, and the particle has mass. Higgs et. al.
aren't fundamentally part of QFT, it's a physical model that QFT is
applied to. But if you get your leptons from gauge transformations they
don't have mass, but interaction with the Higgs gives them mass. Or at
least makes them act as if they had mass.
My thought processes were sort of continuing from another thread that I
think it's time to give up on, concerning the change in speed of light
when it enters and exits a medium, and why that's not a force causing an
acceleration. Wald stresses, in his book on QFT in curved spacetimes,
that quantum field theory is a theory of fields, not of particles; there's
a natural particle interpretation in asymptotically flat spacetimes, but
not in general. And as you've said above, it makes little sense to say
that a field propagates. As far as I've figured, one of the main
quantitative distinctions between a field and an aether is that an aether
has a rest frame while a field doesn't. Sources of a field might have a
rest frame until we're saying fields are the sources of other fields, a
wave can have a group velocity, but the field doesn't have a rest frame.
So if Dirac and other lepton fields get their mass-like behavior from
interactions with Higgs fields, it kind of looks like F=ma is itself a
macroscopic concept that arises from essentially optical microscopic
behavior. Not quite like finding an index of refraction as a limit of
diffractive optics, but a similar idea.
Well, that's my wide-eyed speculation for the day.
--
"Don't try to teach a pig how to sing. You'll waste your time and annoy
the pig."
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