Science > Physics > Attraction vs repulsion - why does it depend on spin?
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Science > Physics |
| User: |
"" |
| Date: |
27 Feb 2005 01:59:13 PM |
| Object: |
Attraction vs repulsion - why does it depend on spin? |
Two identical electrons attract each other
gravitationally,
but repel each other electrically.
Both interactions are due to exchange
of virtual particles; for gravity they have
spin 2, for electromagnetism spin 1.
Is there a way to understand why
the difference in spin leads to attraction in one
case and to repulsion in the other?
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| User: "Uncle Al" |
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| Title: Re: Attraction vs repulsion - why does it depend on spin? |
27 Feb 2005 05:00:57 PM |
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wrote:
Two identical electrons attract each other
gravitationally,
but repel each other electrically.
Gravitational repulsion does not exist.
Both interactions are due to exchange
of virtual particles; for gravity they have
spin 2, for electromagnetism spin 1.
Gravitons have never been boosted into reality. They are a
mathematical result. There is no evidence at all that gravitation is
quantized.
Is there a way to understand why
the difference in spin leads to attraction in one
case and to repulsion in the other?
Why does spin have anything to do with it?
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf
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| User: "Bjoern Feuerbacher" |
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| Title: Re: Attraction vs repulsion - why does it depend on spin? |
03 Mar 2005 04:11:40 AM |
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Uncle Al wrote:
francoisbelfort@yahoo.fr wrote:
Two identical electrons attract each other
gravitationally,
but repel each other electrically.
Gravitational repulsion does not exist.
Both interactions are due to exchange
of virtual particles; for gravity they have
spin 2, for electromagnetism spin 1.
Gravitons have never been boosted into reality. They are a
mathematical result. There is no evidence at all that gravitation is
quantized.
Is there a way to understand why
the difference in spin leads to attraction in one
case and to repulsion in the other?
Why does spin have anything to do with it?
Spin has a lot to do with it. Look it up in Peskin&Schroeder,
"Introduction to QFT", table at the end of section 4.8.
Bye,
Bjoern
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| User: "tadchem" |
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| Title: Re: Attraction vs repulsion - why does it depend on spin? |
01 Mar 2005 09:59:04 AM |
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wrote:
Two identical electrons attract each other
gravitationally,
....based on their mass, not their spin...
but repel each other electrically.
....based on their charge, not their spin...
In a ground state helium atom the electrons are both electrostatically
attracted to the same nucleus, they repel each other electrostatically,
and the 'spin' (+1/2 for one, -1/2 for the other) produces a magnetic
moment for each that results in an attraction between the two
electrons. Toss in a spin 1 particle with the right amount of energy (a
photon) and you will energize one of the electrons into a state where
it is less strongly attracted to the nucleus and less strongly repelled
electrostatically by the other electron, but the magnetic interaction
becomes repulsive rather than attractive - both electrons end up with
the same spin. The spin for the photon has now become the spin for the
entire atom.
The electron-electron interactions are:
electrostatic = repulsive
gravitational = attractive
magnetic = either <depending on the alignment of the spins>
Gravitational effects are many orders of magnitude weaker than the
other effects.
Both interactions are due to exchange
of virtual particles; for gravity they have
spin 2, for electromagnetism spin 1.
If that's what you want to believe. 'Virtual' particles are a
convenience of representing interactions in terms of particle exchanges
rather than in terms of field effects. A spin of 2 is assigned to the
'graviton' simply for bookkeeping purposes.
Is there a way to understand why
the difference in spin leads to attraction in one
case and to repulsion in the other?
If you want to represent these interactions as the exchange of
particles and you look at conserved quantities like 'spin', then you
have to look at the spin of the entire system, not just that of the
particles that you toss into the pot.
It helps to think of spin like angular momentum - the earth has angular
momentum because it rotates on its own axis (it spins around itself),
but it also has angular momentum because it revolves around the sun (it
spins around something else).
In the final analysis, the matter of whether the interaction is
attractive or repulsive depends not on the *spin* of the particles or
of the system, but on the *nature* of the interaction itself.
Tom Davidson
Richmond, VA
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| User: "Guy Gordon" |
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| Title: Re: Attraction vs repulsion - why does it depend on spin? |
28 Feb 2005 03:14:00 AM |
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wrote:
Two identical electrons attract each other
gravitationally, but repel each other electrically.
Both interactions are due to exchange
of virtual particles; for gravity they have
spin 2, for electromagnetism spin 1.
Is there a way to understand why
the difference in spin leads to attraction in one
case and to repulsion in the other?
No. A positron and electron attract via spin 1 bosons.
The assumption in your last paragraph is wrong.
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| User: "" |
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| Title: Re: Attraction vs repulsion - why does it depend on spin? |
28 Feb 2005 01:59:32 PM |
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An outline as to why spin is involved in determining whether a force
between two like charges is attractive or repulsive may be found in
part I of Zee's, "Quantum Field Theory in a nutshell." The full reason
lies in the abstract algebra (group theory) of special relativity and
SU(N) groups. Wigner published a paper on this in the 1930s.
AA
PS--Uncle Al, an experiment was conducted in France a few years back
showing that gravity is quantized. I suppose this pushes the
theoretical gravition a bit closer to reality. Here is the report:
QUANTUM GRAVITATIONAL STATES have been observed for the first time. An
experiment with ultracold neutrons shows that their vertical motion in
Earth's gravitational field come in discrete sizes. Quantum properties
such as the quantization of energies, wavelike dynamics including
interference, and an irreducible uncertainty in the simultaneous
measurement of position and momentum usually emerge only at the atomic
level or under special circumstances (e.g., low temperatures) wherein a
particle is trapped in a potential well by a controlling force.
Observing such properties in phenomena governed by the electromagnetic
or the weak and strong nuclear forces is common enough, but the
strength of gravity, many orders of magnitude weaker than the other
forces, has not previously been strong enough to enforce the kind of
confinement needed to make quantum reality manifest. Such an effect has
now been seen. Physicists at the Institute Laue-Langevin reactor in
Grenoble, France employ a beam of ultracold neutrons. Moving at a pace
of 8 m/sec (compared to 300 m/sec for an oxygen molecule at room
temperature), the neutrons are sent on a gently parabolic trajectory
through a baffle and onto a horizontal plate. Because the neutrons
bounce at such a grazing angle, the plate is essentially a mirror for
the neutrons, which are reflected back upwards until gravity saps their
ascent; then the neutrons start falling again, eventually to be
captured by a detector. In effect the neutrons are caught in a vertical
potential well: gravity pulls down, while atoms in the surface of the
mirror push up. The researchers report seeing a minimum (quantum)
energy of 1.4 picoelectron volts (1.4 x 10^-12 eV), which corresponds
to a vertical velocity of 1.7 cm/sec. A comparison of this energy level
to the minimum energy for an electron trapped inside a hydrogen atom,
-13.6 eV, demonstrates why this kind of detection has not been made
before. The experiment provides also preliminary evidence for higher
quantized motion states as well. In the horizontal direction there is
no confinement and therefore no quantum effect. (By the way,
neutron-interferometry experiments, in which neutron waves are split
apart, moved around separate paths, and then brought back together in
order to produce an interference pattern, have been influenced by
gravity, but these neutron waves were not quantum states owing to the
gravitational field. By contrast, the Laue-Langevin experiment is the
first to observe quantum states of matter (neutrons) in Earth's
gravitational field.) The next step is to use a more intense beam and
an enclosure mirrored on all sides (the energy resolution improves the
longer the neutrons spend in the device). An energy resolution as sharp
as 10^-18 eV is expected, which would allow one to test such basic
propositions as the equivalence principle, according to which the
neutron's gravitational mass (as measured by its free fall in gravity)
is the same as its inertial mass (as prescribed by Newton's second law,
F=ma, where F is a generic force and a the acceleration imparted).
(Nesvizhevsky et al., Nature, 17 Jan 2002.)
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| User: "" |
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| Title: Re: Attraction vs repulsion - why does it depend on spin? |
28 Feb 2005 03:18:14 PM |
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wrote:
An outline as to why spin is involved in determining whether a force
between two like charges is attractive or repulsive may be found in
part I of Zee's, "Quantum Field Theory in a nutshell." The full
reason
lies in the abstract algebra (group theory) of special relativity and
SU(N) groups. Wigner published a paper on this in the 1930s.
AA
Hm, ok, but is there a simple way to understand it? This
text is probably out of my reach.
(Spin 2 is already a classical property of gravity (waves) -
independently whether gravitons exist or not.
And spin 2 forces are always attractive, whereas spin 1 mediated forces
can be either attractive or repulsive.)
And is there a reference for the Wigner paper? I'd like to read it ...
FB
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| User: "Franz Heymann" |
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| Title: Re: Attraction vs repulsion - why does it depend on spin? |
01 Mar 2005 12:36:20 AM |
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<francoisbelfort@yahoo.fr> wrote in message
news:1109625494.936187.216000@l41g2000cwc.googlegroups.com...
akalaniz@hotmail.com wrote:
An outline as to why spin is involved in determining whether a
force
between two like charges is attractive or repulsive may be found
in
part I of Zee's, "Quantum Field Theory in a nutshell." The full
reason
lies in the abstract algebra (group theory) of special relativity
and
SU(N) groups. Wigner published a paper on this in the 1930s.
AA
Hm, ok, but is there a simple way to understand it? This
text is probably out of my reach.
(Spin 2 is already a classical property of gravity (waves) -
independently whether gravitons exist or not.
That last assertion cannot conceivably be true. Classically, a
gravitational wave is a continuous process. How big a piece of it
would you have to snip out on which to assign an angular momentum 2h?
And via which route did Planck's constant enter into a classical
equation?
{:-((
--
Franz
"The great tragedy of science -- the slaying of a beautiful hypothesis
by an ugly fact."
T.H. Huxley
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| User: "Ben Rudiak-Gould" |
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| Title: Re: Attraction vs repulsion - why does it depend on spin? |
01 Mar 2005 07:23:08 AM |
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Franz Heymann wrote:
<francoisbelfort@yahoo.fr> wrote in message
news:1109625494.936187.216000@l41g2000cwc.googlegroups.com...
(Spin 2 is already a classical property of gravity (waves) -
independently whether gravitons exist or not.
That last assertion cannot conceivably be true. Classically, a
gravitational wave is a continuous process. How big a piece of it
would you have to snip out on which to assign an angular momentum 2h?
And via which route did Planck's constant enter into a classical
equation?
Well, spin-N bosons are associated with rank-N tensor fields, and gravity is
a rank-2 tensor field. And rank 2 tensors have a kind of 180 degree symmetry
to them.
I don't know the answer to the OP's question, though.
-- Ben
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| User: "Franz Heymann" |
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| Title: Re: Attraction vs repulsion - why does it depend on spin? |
01 Mar 2005 09:40:46 AM |
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"Ben Rudiak-Gould" <br276deleteme@cam.ac.uk> wrote in message
news:d01qbq$8ib$1@gemini.csx.cam.ac.uk...
Franz Heymann wrote:
<francoisbelfort@yahoo.fr> wrote in message
news:1109625494.936187.216000@l41g2000cwc.googlegroups.com...
(Spin 2 is already a classical property of gravity (waves) -
independently whether gravitons exist or not.
That last assertion cannot conceivably be true. Classically, a
gravitational wave is a continuous process. How big a piece of it
would you have to snip out on which to assign an angular momentum
2h?
And via which route did Planck's constant enter into a classical
equation?
Well, spin-N bosons are associated with rank-N tensor fields, and
gravity is
a rank-2 tensor field. And rank 2 tensors have a kind of 180 degree
symmetry
to them.
Yes.
However, the OP specifically said "whether gravitons exist or not"
If they don't exist, there is no object which could carry off the
angular momenta in the amounts he implied.
I don't know the answer to the OP's question, though.
The expression "*****" is an appropriate mode of expression, but
today is my day for being polite.
--
Franz
"The great tragedy of science -- the slaying of a beautiful hypothesis
by an ugly fact."
T.H. Huxley
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| User: "" |
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| Title: Re: Attraction vs repulsion - why does it depend on spin? |
01 Mar 2005 11:00:30 AM |
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Franz Heymann wrote:
"Ben Rudiak-Gould" <br276deleteme@cam.ac.uk> wrote in message
news:d01qbq$8ib$1@gemini.csx.cam.ac.uk...
Franz Heymann wrote:
<francoisbelfort@yahoo.fr> wrote in message
news:1109625494.936187.216000@l41g2000cwc.googlegroups.com...
(Spin 2 is already a classical property of gravity (waves) -
independently whether gravitons exist or not.
That last assertion cannot conceivably be true. Classically, a
gravitational wave is a continuous process. How big a piece of
it
would you have to snip out on which to assign an angular momentum
2h?
And via which route did Planck's constant enter into a classical
equation?
Well, spin-N bosons are associated with rank-N tensor fields, and
gravity is
a rank-2 tensor field. And rank 2 tensors have a kind of 180 degree
symmetry
to them.
Yes.
However, the OP specifically said "whether gravitons exist or not"
If they don't exist, there is no object which could carry off the
angular momenta in the amounts he implied.
Well, let us approach it this way:
A quantum of electromagnetic field has energy E=h*nu and spin h.
It follows that a quantity of electromagnetic radiation with energy E
carries angular momentum L=E/nu INDEPENDENTLY of what the actual value
of h is. It cancels out. Of course, there is a possibility of an
electromagnetic radiation carrying no angular momentum, it is linearly
polarized and can be viewed as sum of opposite circularly polarized
waves.
Is it possible to use the pure Maxwell equations, without ANY recourse
to photon or quantization, to prove that an electromagnetic wave
carries an angular momentum up to L=+-E/nu?
As for gravitations - if you analyze the pure General Relativity
description of gravity waves without assumption of graviton, does it
show that those waves carry up to L=+-2E/nu of angular momentum?
Furthermore, is it possible to prove, classically, that all fields that
either cannot carry angular momentum at all or carry angular momentum
up to 2E/nu, 4E/nu et cetera must be purely attractive? And is it
possible to prove that fields which carry angular momentum up to E/nu,
3E/nu et cetere have to be repulsive as well as attractive? And is it
possible to show that there cannot be any fields capable of carrying up
to and no more than some fractional amount of E/nu of angular momentum?
I don't know the answer to the OP's question, though.
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| User: "Franz Heymann" |
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| Title: Re: Attraction vs repulsion - why does it depend on spin? |
01 Mar 2005 02:48:03 PM |
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<chornedsnorkack@hushmail.com> wrote in message
news:1109696430.737458.37250@o13g2000cwo.googlegroups.com...
Franz Heymann wrote:
"Ben Rudiak-Gould" <br276deleteme@cam.ac.uk> wrote in message
news:d01qbq$8ib$1@gemini.csx.cam.ac.uk...
Franz Heymann wrote:
<francoisbelfort@yahoo.fr> wrote in message
news:1109625494.936187.216000@l41g2000cwc.googlegroups.com...
(Spin 2 is already a classical property of gravity (waves) -
independently whether gravitons exist or not.
That last assertion cannot conceivably be true. Classically,
a
gravitational wave is a continuous process. How big a piece
of
it
would you have to snip out on which to assign an angular
momentum
2h?
And via which route did Planck's constant enter into a
classical
equation?
Well, spin-N bosons are associated with rank-N tensor fields,
and
gravity is
a rank-2 tensor field. And rank 2 tensors have a kind of 180
degree
symmetry
to them.
Yes.
However, the OP specifically said "whether gravitons exist or
not"
If they don't exist, there is no object which could carry off the
angular momenta in the amounts he implied.
Well, let us approach it this way:
A quantum of electromagnetic field has energy E=h*nu and spin h.
It follows that a quantity of electromagnetic radiation with energy
E
carries angular momentum L=E/nu
You serve no purpose whatever by using creative editing to hide
Planck's constant.
I notice in retrospect that you have chosen play this juvenile trick
throughout in your screed.
It is childish.
INDEPENDENTLY of what the actual value
of h is. It cancels out. Of course, there is a possibility of an
electromagnetic radiation carrying no angular momentum, it is
linearly
polarized and can be viewed as sum of opposite circularly polarized
waves.
Is it possible to use the pure Maxwell equations, without ANY
recourse
to photon or quantization, to prove that an electromagnetic wave
carries an angular momentum up to L=+-E/nu?
Most certainly not. Planck's constant simply does not exist as far as
classical physics is concerned.
As a matter of fact, Maxwell's equations were propounded even before
it was known that there were physical entities which carried
electrical charge in quantised units. The equations refer throughout
to continuous charge distributions.
As for gravitations - if you analyze the pure General Relativity
description of gravity waves without assumption of graviton, does it
show that those waves carry up to L=+-2E/nu of angular momentum?
No. For the same reason. Classical General Relativity makes no
contact whatsoever with Quantum theory.
Furthermore, is it possible to prove, classically, that all fields
that
either cannot carry angular momentum at all or carry angular
momentum
up to 2E/nu, 4E/nu et cetera must be purely attractive?
No. The attractive/repulsive details of interactions are derivable
from the vector/tensor characteristics of a field purely by the use
of a very heavy dose of quantum field theory.
And is it
possible to prove that fields which carry angular momentum up to
E/nu,
3E/nu et cetere have to be repulsive as well as attractive? And is
it
possible to show that there cannot be any fields capable of carrying
up
to and no more than some fractional amount of E/nu of angular
momentum?
No. The attractive/repulsive nature of interactions are derivable
from the vector/tensor characteristics of a field purely by the use of
a very heavy dose of quantum field theory.
--
Franz
"The great tragedy of science -- the slaying of a beautiful hypothesis
by an ugly fact."
T.H. Huxley
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| User: "" |
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| Title: Re: Attraction vs repulsion - why does it depend on spin? |
01 Mar 2005 11:16:03 AM |
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Chapter 5 of Foster and Nightingale, "A Short Course In General
Relativity" contains a brief discussion on why (non-quantized)
gravitational radiation should be associated with a spin 2 particle in
terms of quadrupole radiation fields. More than once I've tried to
understand the nature of attraction/repulsion and spin via classical
arguments, and have never really succeeded. Zee's book together with
S. Weinberg's paper and the recent Chinese physics articles provide,
via quantum field theory and group theory, provide a much more
satisfactory account.
Alex
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| User: "Franz Heymann" |
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| Title: Re: Attraction vs repulsion - why does it depend on spin? |
01 Mar 2005 02:48:03 PM |
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<akalaniz@hotmail.com> wrote in message
news:1109697362.968620.37010@o13g2000cwo.googlegroups.com...
Chapter 5 of Foster and Nightingale, "A Short Course In General
Relativity" contains a brief discussion on why (non-quantized)
gravitational radiation should be associated with a spin 2 particle
in
terms of quadrupole radiation fields.
But that association is valid only when the field has been quantised.
So far this has proved to be impossible in the case of gravity.
More than once I've tried to
understand the nature of attraction/repulsion and spin via classical
arguments, and have never really succeeded.
You never will, because what you are talking about are purely quantum
effects.
Zee's book together with
S. Weinberg's paper and the recent Chinese physics articles provide,
via quantum field theory and group theory, provide a much more
satisfactory account.
--
Franz
"The great tragedy of science -- the slaying of a beautiful hypothesis
by an ugly fact."
T.H. Huxley
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| User: "" |
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| Title: Re: Attraction vs repulsion - why does it depend on spin? |
01 Mar 2005 03:19:04 PM |
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Yes, L = E/ omega for em fields - you can find this in Jackson's
Classical electrodynamics.
(In my edition it is on page 350, as an exercise. The calculation is
fully classical)
People who posted that this is impossible should eat their words.
For gravity it is also possible to derive
L = E/2 omega , but I have no reference at hand.
Francois
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| User: "Franz Heymann" |
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| Title: Re: Attraction vs repulsion - why does it depend on spin? |
02 Mar 2005 11:51:50 AM |
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<francoisbelfort@yahoo.fr> wrote in message
news:1109711944.280491.63170@z14g2000cwz.googlegroups.com...
Yes, L = E/ omega for em fields - you can find this in Jackson's
Classical electrodynamics.
(In my edition it is on page 350, as an exercise. The calculation is
fully classical)
People who posted that this is impossible should eat their words.
For gravity it is also possible to derive
L = E/2 omega , but I have no reference at hand.
If you had not removed all the headers and all the context, we might
have known what you are talking about.
--
Franz
"A first-rate laboratory is one in which mediocre scientists can
produce outstanding work"
P.M.S. Blackett
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| User: "" |
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| Title: Re: Attraction vs repulsion - why does it depend on spin? |
02 Mar 2005 01:42:29 PM |
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(1) Learn to use the threading view of Google.
(2) The answer was about a guy who had at least one physics error
in every post on this topic - like saying that L= E/ omega is
impossible
to prove without quantum theory - and who made up by adding
an unfriendly remark in each post. First study phyics, then understand
it,
then think and then only - post.
FB
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| User: "Franz Heymann" |
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| Title: Re: Attraction vs repulsion - why does it depend on spin? |
02 Mar 2005 04:25:33 PM |
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<francoisbelfort@yahoo.fr> wrote in message
news:1109792549.173842.232520@f14g2000cwb.googlegroups.com...
(1) Learn to use the threading view of Google.
This is not a google group. It is a usenet group which existed two
decades before google.
Subscribe directly to it if you want to play ball.
[snip]
--
Franz
"A first-rate laboratory is one in which mediocre scientists can
produce outstanding work"
P.M.S. Blackett
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| User: "George Jones" |
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| Title: Re: Attraction vs repulsion - why does it depend on spin? |
01 Mar 2005 07:18:55 AM |
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wrote:
akalaniz@hotmail.com wrote:
An outline as to why spin is involved in determining whether a force
between two like charges is attractive or repulsive may be found in
part I of Zee's, "Quantum Field Theory in a nutshell." The full
reason lies in the abstract algebra (group theory) of special relativity
and SU(N) groups. Wigner published a paper on this in the 1930s.
AA
Hm, ok, but is there a simple way to understand it? This
text is probably out of my reach.
(Spin 2 is already a classical property of gravity (waves) -
independently whether gravitons exist or not.
And spin 2 forces are always attractive, whereas spin 1 mediated forces
can be either attractive or repulsive.)
And is there a reference for the Wigner paper? I'd like to read it ...
The reference is
E.P. Wigner, On the representations of the inhomogeneous Lorentz group,
Ann. of Math. v40, 149-204 (1939).
Also relevant is
E. Wigner and V. Bargmann, group theoretical discussions of relativistic
wave equations, Proc. Nat. Acad. Sci. V34, 211-223, (1948).
Wigner's 1939 paper is *much* more difficult to read than Zee's text.
This classic paper, which treats the fundamental heart of the marriage
of quantum theory and special relativity, is one of the few examples of
a post 1900 paper that simultaneously made fundamental advances in
physics and mathematics by the standards of each.
However, for reasons I will give in a reply to AA, the paper has almost
*nothing* to say about the SU(N) groups.
I encourage you to get hold of a copy of Zee's book. The whole text is
informal, with part I being particularly informal. As AA says, Zee
gives the answer to your question. Chapter I.5, which starts on page 30,
is titled Coulomb and Newton: Repulsion and Attraction.
Like Franz, I don't see how spin 2 falls out classically. When
general relativity is linearized, a relativistic wave equation can be
derived. This wave equation is for spin 2, but the reasons come from
quantum theory.
Regards,
George
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| User: "" |
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| Title: Re: Attraction vs repulsion - why does it depend on spin? |
01 Mar 2005 10:59:43 AM |
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In going back to my pile of literature, you are correct about the
Wigner paper I cited having relatively little to say about the
connection between spin and the sign of propagator. That connection is
really laid out in S. Weinberg's paper and the two Chinese papers, and,
in my opinion, rather weakly so in Zee's book.
Regarding Wigner's work, I believe that Ryder's Quantum Field Theory
text does an descent job of discussing the algebra of the Lorentz and
Poincare groups.
Alex
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| User: "" |
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| Title: Re: Attraction vs repulsion - why does it depend on spin? |
28 Feb 2005 05:22:04 PM |
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What the "French" experiment shows is that if you treat the earth's
gravity field with Schrodinger's equation, you get discrete energy
states. The simple calculation was actually done years back in,
"Problems And Solutions In Quantum Chemistry And Physics," Charles S.
Johnson Jr. and Lee G. Pedersen, Dover, 1986, ISBN: 0-486-65236-X
Problem number 4.14 page118-119.
Papers that directly treat the question of how spin affects attraction
or repulsion between like "charges" (be these like electrical charges
for electric charge, or other more general charges) are:
Steven Weinberg, "Feynman Rules for any spin," Physical Review, Vol.
133, No. 5B, 9 March 1964
Huang Shi-Zhong et. al, "Projection Operator and Propagator for an
Arbitrary Integral Spin," Chin. Phys. Lett. Vol. 19, No. 12, 2002, p.
1767
Huang Shi-Zhong et. al., "Feynman Propagator for an arbitrary
half-integral spin," Chinese Physics, Vol. 12, No. 7, July 2003
The Wigner paper, one of the most cited papers in physics, is,
E. Wigner, "On Unitary Representations of the Inhomogeneous Lorentz
Group," The Annals of Mathematics, 2nd Ser., Vol 40, No. 1 (Jan. 1939),
p. 149-204.
This paper develops a lot of the mathematics required to do quantum
field theor with respect to group theory.
If you understand the quantum mechanics of angular momentum and
addition of angular momentum in terms of Jx, Jy, Jz, J^2, J+ and J-
operators, their eigenvalues and the matrix elements they generate,
then H. F. Jones, "Groups, Representations and Physics," 2nd. ed.,
chapter 8 will allow you to calculate particle spectra such as
3X3X3=10+8+8+1 for baryons (3 quarks) and 3X3*=6+3 for mesons (1 quark,
1 anti quark). J. J. Sakurai, "Modern Quantum Mechanics" does a great
job of explaining the use of the Young Tableau to simply calculating
particle spectra.
Again, Zee, "Quantum Field Theory in a nutshell," somewhere in the
first part of the book, shows what a particle of spin to acts and
smells like a graviton.
From a classical point of view, one may expand an electromagnetic field
in terms of multipoles (spherical harmonics). The spherical harmonics
have an l and m index which, when solving for the hydrogen atom,
represent the orbital angular momentum eigenvalues, and the z-axis
(arbitrarily chosen axis) eigenvalues. A positve and and negative
charge separated by a finite distance define a dipole, hence, with this
kind of classical argument we can say a photon (creator of
electromagnetic fields) has spin 1. That is l=1. One, however, cannot
make a gravity dipole as we don't seem to have antigravitating mass.
The next best thing we can do is build a quadrupole, hence l=2, hence
spin 2 particle. To be honest, I don't really like these "artificial"
classical arguments, but they may help to clear give one a picture.
Recall the hydrogen atom solved by Schrodinger's equation. It is
desribed by 3 quantum numbers: n = energy level, l = orbital angular
momentum and mz=-l, -l+1,...,0,...,l-1,l. The electron spin quantum
number, if there are no external magentic fields, and if we ignore the
interaction of the electron spin with the proton spin, can be ignored
as negligible. Whenever such a simple hydrogen atom radiates, changing
n, l and mz, the photons must, by energy conservation, be carrying
these quantum numbers.
Cheers,
AA
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| User: "George Jones" |
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| Title: Re: Attraction vs repulsion - why does it depend on spin? |
01 Mar 2005 07:49:09 AM |
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wrote:
An outline as to why spin is involved in determining whether a force
between two like charges is attractive or repulsive may be found in
part I of Zee's, "Quantum Field Theory in a nutshell." The full reason
lies in the abstract algebra (group theory) of special relativity and
SU(N) groups. Wigner published a paper on this in the 1930s.
Wigner's paper is on the inhomogeneous Lorentz group, i.e., the Poincare
group, which is the semi-direct product of the commutative group of
spacetime translations with the Lorentz group, and has nothing to do
with SU(n). In particular, Wigner's paper gives a detailed treatment of
the irreducible representations of the universal cover of the restricted
Poincare group (isomorphic to the semi-direct product of R^4 with
SL(2,C)). Unlike SU(n), this group is not compact, so finding its irreps
is more difficult.
However, SU(2) does come into play as (being isomorphic to) the little
group for any timelike vector.
[snip report of nice experiment]
Your reply notwithstanding, I agree with Greg.
Regards,
George
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| User: "Gregory L. Hansen" |
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| Title: Re: Attraction vs repulsion - why does it depend on spin? |
28 Feb 2005 02:30:06 PM |
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In article <1109620772.662553.268930@l41g2000cwc.googlegroups.com>,
<akalaniz@hotmail.com> wrote:
An outline as to why spin is involved in determining whether a force
between two like charges is attractive or repulsive may be found in
part I of Zee's, "Quantum Field Theory in a nutshell." The full reason
lies in the abstract algebra (group theory) of special relativity and
SU(N) groups. Wigner published a paper on this in the 1930s.
AA
PS--Uncle Al, an experiment was conducted in France a few years back
showing that gravity is quantized. I suppose this pushes the
theoretical gravition a bit closer to reality. Here is the report:
QUANTUM GRAVITATIONAL STATES have been observed for the first time. An
experiment with ultracold neutrons shows that their vertical motion in
Earth's gravitational field come in discrete sizes. Quantum properties
such as the quantization of energies, wavelike dynamics including
interference, and an irreducible uncertainty in the simultaneous
That's not quantum gravity, that's self-interference of neutrons in a
gravitational potential. Quantized particles in a classical field. It's
the neutrons that display the quantum behavior in this experiment, not
gravity.
--
"'No user-serviceable parts inside.' I'll be the judge of that!"
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| User: "G=EMC^2 Glazier" |
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| Title: Re: Attraction vs repulsion - why does it depend on spin? |
01 Mar 2005 03:31:21 PM |
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Franco Two spinning tops when spinning in a mutual direction(towards
each other) don't jump away but will circle each other after touching.
Both spinning in opposite directions will jump away from each other lose
lots of energy(wobble away) Spin is an intrinsic feature of all
particles,and gives important information(transfer) and can do it from a
distance(no need for them to touch. Bert
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| User: "" |
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| Title: Re: Attraction vs repulsion - why does it depend on spin? |
01 Mar 2005 11:36:52 AM |
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In sci.physics wrote:
Two identical electrons attract each other
gravitationally, but repel each other electrically.
Both interactions are due to exchange
of virtual particles; for gravity they have
spin 2, for electromagnetism spin 1.
Is there a way to understand why
the difference in spin leads to attraction in one
case and to repulsion in the other?
Look at S. Deser, http://arxiv.org/abs/gr-qc/0411026,
"How Special Relativity Determines the Signs of the
Nonrelativistic, Coulomb and Newtonian, Forces"
Abstract: We show that the empirical signs of the
fundamental {\it static} Coulomb/Newton forces are
dictated by the seemingly unrelated requirement that
the photons/gravitons in the respective underlying
Maxwell/Einstein physics be stable. This linkage,
which is imposed by special relativity, is manifested
upon decomposing the corresponding fields and sources
in a gauge-invariant way, and without appeal to static
limits. The signs of these free field excitation energies
determine those of the instantaneous forces between
sources; opposite Coulomb/Newton signs are direct
consequences of the Maxwell/Einstein free excitations'
odd/even spins.
Steve Carlip
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| User: "" |
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| Title: Re: Attraction vs repulsion - why does it depend on spin? |
01 Mar 2005 02:53:33 PM |
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(slight edit added)
Thanks...on first perusal of the "ancient lore" things seem to make
sense. In your paper, however, the spin 1 (Coloumb repulsion) and spin
2 (graviton attraction) particles, and higher spin particles, are
correlated to the number of indices of tensor fields of various rank in
a rather non-intuitive way. In section 3, for example, you show what
the sign must be for "Maxwell" fields without ever mentioning spin 1
photons. Dito for gravitons in section 4. Then in section 5 you talk
about spins being correlated to "corresponding static force signs".
Tacit in this is that photons are spin 1 animals and gravitons are spin
2 animals. The guy who started this post would thus liekly still be
scratching his head about why the photon is assigned spin 1 and the
graviton spin 2, and so on to higher spins. A review of how Cartesian
tensors may be expressed in terms of sperical tensors may help (J. J.
Sakurai, "Modern Quantum Mecanics" (1995), section 3.10".
Briefly, recall that spherical harmonics have an l and m index. When
used to describe the hydrogen atom, say, the value of l yields the
orbital angular momentum eigenvalues and mz yields the z-component of l
for the orbiting electron; the spatial distribution (electron cloud) is
given by the spherical harmonic Y(l,m; theta, phi). A Cartesian 3-D
vector has 3 independent components. We thus associate with vectors
spin 1 since the z-component (mz) then has three possible eigenstates:
-1, 0, 1. (Two states for a massless photon actually). Essentially,
since the electromagnetic field is a vector field, photons are assigned
spin 1.
Now for a quickie talk about spin 2. Let U and V be 3D Cartesian
vectors. Then
T = 1/2(UiVj+UjVi) - (1/3)U.V delta(ij), where i,j=1,2,3 (from
Sakurai 3.10.13 p. 234)
has five independent components, hence that tensor is assigned to a
spherical tensor with spin = 2 so that mz has five possible
eigenstates, namely {-2, -1, 0, 1, 2}. Thus, essentially, since the
gravity field is described by a symmetric 2 index tensor field (with
other constraints), the graviton is assigned spin 2. Thus, avoiding
deeper QFT and group theory, Section 3.10 of
Sakurai (1995) together with your paper should be enough to connect
spin with repulsive or attractive forces.
Zee's book and your paper (or Weinberg's and the cited other papers I
cited) then go on to show in different ways why/how the spin determines
whether a force is attractive or repulsive.
Alex
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| User: "Franz Heymann" |
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| Title: Re: Attraction vs repulsion - why does it depend on spin? |
01 Mar 2005 05:13:41 PM |
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<akalaniz@hotmail.com> wrote in message
news:1109710413.029524.193450@l41g2000cwc.googlegroups.com...
(slight edit added)
Please be a kind fellow and leave the headers and context intact,
otherwise we don't know why you are responding to whom.
--
Franz
"The great tragedy of science -- the slaying of a beautiful hypothesis
by an ugly fact."
T.H. Huxley
Thanks...on first perusal of the "ancient lore" things seem to make
sense. In your paper, however, the spin 1 (Coloumb repulsion) and
spin
2 (graviton attraction) particles, and higher spin particles, are
correlated to the number of indices of tensor fields of various rank
in
a rather non-intuitive way. In section 3, for example, you show
what
the sign must be for "Maxwell" fields without ever mentioning spin 1
photons. Dito for gravitons in section 4. Then in section 5 you
talk
about spins being correlated to "corresponding static force signs".
Tacit in this is that photons are spin 1 animals and gravitons are
spin
2 animals. The guy who started this post would thus liekly still be
scratching his head about why the photon is assigned spin 1 and the
graviton spin 2, and so on to higher spins. A review of how
Cartesian
tensors may be expressed in terms of sperical tensors may help (J.
J.
Sakurai, "Modern Quantum Mecanics" (1995), section 3.10".
Briefly, recall that spherical harmonics have an l and m index.
When
used to describe the hydrogen atom, say, the value of l yields the
orbital angular momentum eigenvalues and mz yields the z-component
of l
for the orbiting electron; the spatial distribution (electron cloud)
is
given by the spherical harmonic Y(l,m; theta, phi). A Cartesian 3-D
vector has 3 independent components. We thus associate with vectors
spin 1 since the z-component (mz) then has three possible
eigenstates:
-1, 0, 1. (Two states for a massless photon actually).
Essentially,
since the electromagnetic field is a vector field, photons are
assigned
spin 1.
Now for a quickie talk about spin 2. Let U and V be 3D Cartesian
vectors. Then
T = 1/2(UiVj+UjVi) - (1/3)U.V delta(ij), where i,j=1,2,3 (from
Sakurai 3.10.13 p. 234)
has five independent components, hence that tensor is assigned to a
spherical tensor with spin = 2 so that mz has five possible
eigenstates, namely {-2, -1, 0, 1, 2}. Thus, essentially, since the
gravity field is described by a symmetric 2 index tensor field (with
other constraints), the graviton is assigned spin 2. Thus, avoiding
deeper QFT and group theory, Section 3.10 of
Sakurai (1995) together with your paper should be enough to connect
spin with repulsive or attractive forces.
Zee's book and your paper (or Weinberg's and the cited other papers
I
cited) then go on to show in different ways why/how the spin
determines
whether a force is attractive or repulsive.
Alex
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| User: "" |
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| Title: Re: Attraction vs repulsion - why does it depend on spin? |
01 Mar 2005 03:08:54 PM |
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wrote:
Look at S. Deser, http://arxiv.org/abs/gr-qc/0411026,
"How Special Relativity Determines the Signs of the
Nonrelativistic, Coulomb and Newtonian, Forces"
Great, this at least clarifies many issues.
It is well written and long overdue, as some of
the posts show :-)
But I'd like to continue in more detail.
The paper shows that spin 2 is always attractive.
This is well "explained" in the famous (2-dimensional)
analogy of two masses that lie on a horizontal cloth under tension.
The two craters they create always attract each other.
Is a there an equally simple analogy that pictures why
two equal electric charges always
repel? The loop gravity people always say that electrodynamics is
based on anular structures. Can one find a visualization
of Maxwell's equations (or at least of the Coulomb field), maybe
using these rings, that shows why two like charges repel?
The next question would be even more demanding:
I am not sure that rings are a good description of spin 1
radiation, and a cloth is surely not a good description of
spin 2 radiation, but anyway - the issue I am after is this:
Can one find analogies for the two systems that somehow incorporate the
spins, or better, the symmetry of the exchanged radiation?
(spin 2: same after 180 degree rotation; spin 1 = same after 360
degrees)
Francois
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| User: "" |
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| Title: Re: Attraction vs repulsion - why does it depend on spin? |
01 Mar 2005 02:39:53 PM |
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Thanks...on first perusal of the "ancient lore" things seem to make
sense. In your paper, however, the spin 1 (Coloumb repulsion) and spin
2 (graviton attraction) particles, and higher spin particles, are
correlated to the number of indices of tensor fields of various rank in
a rather non-intuitive way. In section 3, for example, you show what
the sign must be for "Maxwell" fields without ever mentioning spin 1
photons. Dito for gravitons in section 4. Then in section 5 you talk
about spins being correlated to "corresponding static force signs".
Tacit in this is that photons are spin 1 animals and gravitons are spin
2 animals. The guy who started this post would thus liekly still be
scratching his head about why the photon is assigned spin 1 and the
graviton spin 2, and so on to higher spins. A review of how Cartesian
tensors may be expressed in terms of sperical tensors may help (J. J.
Sakurai, "Modern Quantum Mecanics" (1995), section 3.10".
Briefly, recall that spherical harmonics have an l and m index. When
used to describe the hydrogen atom, say, the value of l yields the
orbital angular momentum eigenvalues and mz yields the z-component of l
for the orbiting electron; the spatial distribution (electron cloud) is
given by the spherical harmonic Y(l,m; theta, phi). A Cartesian 3-D
vector has 3 independent components. We thus associate with vectors
spin 1 since the z-component (mz) then has three possible eigenstates:
-1, 0, 1. (Two states for a massless photon actually). Essentially,
since the electromagnetic field is a vector field, photons are assigned
spin 1.
Now for a quickie talk about spin 2. Let U and V be 3D Cartesian
vectors. Then
T = 1/2(UiVj+UjVi) - (1/3)U.V delta(ij), where i,j=1,2,3 (from
Sakurai 3.10.13 p. 234)
has five independent components, hence that tensor is assigned spin = 2
so that mz has five possible eigenstates, namely {-2, -1, 0, 1, 2}.
Thus, essentially, since the gravity field is described by a symmetric
2 index tensor field (with other constraints), the graviton is assigned
spin 2. Thus, avoiding deeper QFT and group theory, Section 3.10 of
Sakurai (1995) together with your paper should be enough to connect
spin with repulsive or attractive forces.
Zee's book and your paper (or Weinberg's and the cited other papers I
cited) then go on to show in different ways why/how the spin determines
whether a force is attractive or repulsive.
Alex
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