Re: Does gravity address fermions and bosons differently?
- From: PD <TheDraperFamily@xxxxxxxxx>
- Date: Sun, 10 Feb 2008 12:10:05 -0800 (PST)
On Feb 10, 6:30 am, Albertito <albertito1...@xxxxxxxxx> wrote:
On 10 feb, 11:39, Eric Gisse <jowr...@xxxxxxxxx> wrote:
On Feb 10, 2:16 am, Albertito <albertito1...@xxxxxxxxx> wrote:
On 10 feb, 03:15, Eric Gisse <jowr...@xxxxxxxxx> wrote:
On Feb 9, 5:24 am, Albertito <albertito1...@xxxxxxxxx> wrote:
On 9 feb, 02:35, Eric Gisse <jowr...@xxxxxxxxx> wrote:
On Feb 8, 9:21 am, Albertito <albertito1...@xxxxxxxxx> wrote:
On 7 feb, 17:56, Albertito <albertito1...@xxxxxxxxx> wrote:
Hi all,
I have an interesting question for you. Since it is often
claimed that newtonian gravity predicts half the correct
deflection angle for a photon, and GR can predict the
correct one, that argument is used to show that GR
is the correct theory of gravitation and newtonian
gravity is just an approximation. But, what if newtonian
gravity could predict the correct deflection angle, too?.
A photon is a boson of spin 1 and is massless.
Bulk neutral matter is fermionic (mainly spin 1/2).
Is the spin of a particle the key to see how it should be
deflected by gravity?. In the case of fermions the deflection
is just their orbital motions.
We are interested in see how a photon can be deflected
in newtonian gravity. The usual method is to fake that
photon.We assume that photon should behave like a
fermion with kinetic energy E = mc^2/2. But, that's unphysical.
The general formula for a particle, with spin s, travelling at
speed v should be
E = s mv^2.
So, under newtonian gravity, for a photon, it would yield
E = mc^2,
as s=1, and v=c.
With that assumption, we can predict the correct deflection
angle in newtonian gravity, for a photon. So, it seems
the spin of the particle must be taken into account. After all,
a photon can't be faked to behave as a fermion. Its spin must
be taken into account when we deal with its angular momentum.
Sorry, I made a mistake of appreciation in my
first post :-) Let me explain the details of the
correction.
Computation of the deflection angle in newtonian
gravity:
I wonder where you tried to copy this from.
Consider a hyperbolic trajectory for a particle,
Why does the trajectory have to be hyperbolic? You have four orbital
choices [why four? where do they come from?] - elliptical, circular,
hyperbolic, and parabolic.
regarded as the deflected trajectory by a massive
body with mass M. The angle of intersection of the
asymptotes of that hyperbola is alpha, such that
tan(alpha/2) = a/b,
where a is the transverse and b the conjugate
semiaxis.
Ah, and what are the transverse and conjugate "semiaxis" ?
Sounds a lot like the semimajor and major axes of an orbit, but who
can tell?
According to newtonian mechanic, we know that
a = GM/2E ,
Wrong. a = | K / 2E | where K is the kinetic energy of a particle.
where E is total energy of that particle (E expressed in
energy per unit of mass). So, we get
tan(alpha/2) = GM/2Eb.
This is a severe butchering of the equation for scattering in
hyperbolic orbits, where alpha is the asymptote angle. Otherwise it
makes no sense whatsoever.
If GM/2E is meaningfully larger than b, then we can
attain the approximation
alpha = GM/Eb.
Uh, no.
tan(x) = sin(x) / cos(x)
For x << 1, you can expand sin(x) and cos(x) in a power series and
only keep the first term. sin(x) ~= x, and cos(x) ~= 1.
So if GM/2E >> b, tan(alpha/2) >> 1 and you can't make that
approximation. Knowing some calculus sure would be handy right about
now, wouldn't it?
Under newtonian gravity, we get a deflection angle
alpha = 2GM/c^2b,
and b denotes the periastron distance
(turning point).
Wrong. There is no c in Newtonian gravity, and you totally butchered
the mathematics.
So, under newtonian gravity, total energy E of that
particles travelling at c is
E = c^2/2.
Wrong. Particles have mass.
GR predicts a deflection angle of
alpha = 4GM/c^2b,
So, under GR, that means total energy E of that particles
is
E' = c^2/4
Simply wrong.
How can we solve the discrepancy E = 2E' ?.
I wonder, do your teachers try to correct your constant simultaneous
usage of a period and question mark? Do you always ignore them because
you think you know better?
Sorry for the orthographic faults and typos.
That's because English is not my native
language, but Spanish :-)
Oh, and you are trying to compare two different theories. You are
wrong by definition.
No, I'm not trying to compare two different
theories. The discrepancy E' = 2E, refers
to the predicted angle E under newtonian
E is an ENERGY not an angle.
Ok ok, I meant angles. I wrote E' = 2E
(the observed angle E' doubles the predicted
one E). That's my fault, I should have written
alpha' = 2alpha. Anyway, the hypothesis still
remains: is alpha'>alpha because energy E'< E?
Obviously, your answer is the laconic NO.
Open a textbook and gain some understanding. I will not take the time
to teach you both general relativity and classical mechanics, and the
understanding required to use both. If you actually care, open a
textbook.
Are you sure textbooks will tell me the truth?
What textbooks will tell you is how to determine the truth, and in
particular how scientists determine the truth. Physics books, you will
find, are not long series of assertions, but discussions of *how* we
know what we know.
In particular, you will also find that imagination and creativity are
NOT sufficient for physical insight. If you were hoping that an agile
mind and a blinding insight are sufficient for making significant
progress in science, then I have a brutal reality check to offer you.
You will find that essentially any practicing scientist will be quick
to dispel you of that misapprehension. This may not be what you want
to hear. But on the other hand, it will save you years of misguided
aspirations based on naive notions of how science works. If you don't
want to do the grunt work and toil required to make your agile mind
and blinding insights worthwhile, then you are chasing the wrong
field.
What about imagination and creativity?
Is a well-educated guy smarter and more
creative than a non so well-educated one?
Around 16th century textbooks taught the
geocentric model (i.e. Ptolemaic system),
so in that epoch, any well-educated guy
believed that the Sun was orbiting around
the Earth, that the Earth was the center of
the universe. Is that the kind of truth I
must learn? I have a fine rule saying that
there are no true theories. A theory is a
model, and in physics, mathematics are the
tools for contructing and testing models
(theories), along with engineering. Can a
non well-educated painter paint a brilliant
painting?. The paintings of a painter who
assisted to Ars School are all performed in
an academic fashion, the mainstream fashion.
Most of those academic paintings are boring,
ugly and lacking of originality.
.
- References:
- Does gravity address fermions and bosons differently?
- From: Albertito
- Re: Does gravity address fermions and bosons differently?
- From: Albertito
- Re: Does gravity address fermions and bosons differently?
- From: Eric Gisse
- Re: Does gravity address fermions and bosons differently?
- From: Albertito
- Re: Does gravity address fermions and bosons differently?
- From: Eric Gisse
- Re: Does gravity address fermions and bosons differently?
- From: Albertito
- Re: Does gravity address fermions and bosons differently?
- From: Eric Gisse
- Re: Does gravity address fermions and bosons differently?
- From: Albertito
- Does gravity address fermions and bosons differently?
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