Re: Are *observed* SR effects real?
- From: mluttgens@xxxxxxxxxx
- Date: Thu, 21 Aug 2008 07:12:58 -0700 (PDT)
On Jul 24, 2:36 pm, PD <TheDraperFam...@xxxxxxxxx> wrote:
On Jul 24, 6:19 am, mluttg...@xxxxxxxxxx wrote:
On Jul 23, 6:31 pm, PD <TheDraperFam...@xxxxxxxxx> wrote:
On Jul 23, 11:08 am, mluttg...@xxxxxxxxxx wrote:
On Jul 23, 5:06 pm, PD <TheDraperFam...@xxxxxxxxx> wrote:
On Jul 23, 8:48 am, mluttg...@xxxxxxxxxx wrote:
On Jul 23, 1:36 pm, PD <TheDraperFam...@xxxxxxxxx> wrote:
On Jul 23, 6:19 am, mluttg...@xxxxxxxxxx wrote:
You have been contradicting yourself!
You agreed that the domain of applicability of SR is limited
to 'inertial' frames.
Please pay attention to what I actually said. What I said is that
there are many frames that are not *absolutely* inertial, but in which
the non-inertial effects are much smaller than the effect being
measured and are therefore negligible (where "negligible" literally
means "can be neglected").
Iow, you agree with what I wote:
"Claiming that nothing changes physically when the Earth moves
wrt the plane is wrong, because the Earth is gravitationally
linked with the Sun (neglecting the Galaxy, and even the whole
Universe), and you should know that SR cannot be applied
in gravitational fields."
<No, I don't agree with it. Please read what I wrote about the
equivalence principle, which is one of the underlying bases of GR..
I wrote: "you should know that SR cannot be applied
in gravitational fields", and suddenly, you jump
to GR! Does that imply that SR also applies (nothing
coming from SRists can surprise me, even bad faith)!
Please pay attention. I told you where to re-read. Since you are
incapable of doing that, I will repeat myself.
One of the backbone principles of GR is that any sufficiently small
laboratory in free-fall (that is, IN A GRAVITATIONAL FIELD) is
indistinguishable from an inertial frame of reference. So, yes,
special relativity can be applied even where there is a gravitational
field as long as the tidal effects due to gravity are much smaller
than the other effects (including ones predicted by special
relativity) being measured. Furthermore, you made the earlier
incorrect statement that special relativity cannot be used where there
is acceleration. That is also incorrect.
Where did I claim that SR can't be used where frames are
accelerating?
My point is that SRists too often forget physical reality:
Here are a few examples:
- The Earth is rushing toward cosmic muons (Paul B. Andersen)
This is physically nonsensical, because the Earth is
gravitationally linked to the Sun, etc...
You misunderstand apparently. The suggestion is not that the Earth is
rushing toward cosmic ray muons and leaving the Sun behind. The
suggestion is that the Earth *and* the Sun *and* the galaxy the Sun is
gravitationally linked to is rushing toward the muon. There is nothing
wrong with that statement. As a reminder of this, observationally *and
physically* other galaxies are in general receding from our own (see
Hubble and what he's most famous for). Now, in what sense can you pick
out whether it is the others that are receding from ours or ours that
is receding from the others, and more importantly, is there any
*physical* distinction that is important?
- One cannot tell from 600 mph relative motion between
the Earth and a plane, whether it is the plane that's moving
or the Earth that's moving (PD)
The Earth is rotating, for instance at 600 mph at some
latitude. At such latitude, a plane whose ground speed is
zero has an 'air' speed of 600 mph, as any pilot would
confirm.
Well, actually no. If the air is still with respect to the ground, the
air and ground speed would be both 600 mph. But the speed of the plane
with respect to a line through the centers of the Sun and the Earth
could well be zero.
- It is not possible to know if a train is moving, without
'looking' outside the train.
This is false, as a train follows the curvature of the Earth,
and is consequently subject to an acceleration a = v^2/R,
where R is the Earth radius. When v is small, 'a' can be
neglected, and SR approximately applied.
But when v is a not negligible fraction of c, like is many
SR thought experiments, 'a' becomes enourmous.
For instance, with v = 0.1 c, 'a' is about 1.5*10^10 cm/s^2!
Using such big velocities in a SR thought experiment is
physically nonsensical.
And no such huge speed was implied. As I already mentioned to you, H&K
performed their experiments at speeds much, much lower than even
0.00001c.
PD
- Etc, etc, etc ...
Marcel Luttgens
Let's settle this first before continuing
About your hypothesis that the Earth *and* the Sun
*and* the galaxy are rushing toward muons:
Introduction, see
http://en.wikipedia.org/wiki/Introduction_to_special_relativity
"There is a class of reference frames, all
moving at uniform velocity with respect to
each other. They are called inertial
reference frames. SR only applies in such
frames.
Some major predictions of special relativity
are time dilation (under which a moving clock
ticks more slowly than when it is at rest
with respect to the observer) and length
contraction (under which a moving rod may
be found to be shorter than when it is at
rest with respect to the observer)."
Notice that those effects of length contraction
and time dilation are *reciprocal*:
If a clock B is moving at v relative to
a clock A, clock B ticks slower than clock
A according to tB = tA * sqrt(1-v^2/c^2).
But, as clock A is moving at -v relative to
clock B, one has also tA = tB * sqrt(1-v^2/c^2).
A specific example from
http://en.wikipedia.org/wiki/Twin_paradox :
"Consider a space ship traveling from Earth to
the nearest star system outside of our solar
system: a distance d = 4.45 light years away,
at a speed v = 0.866c (i.e., 86.6 percent of
the speed of light, relative to the Earth).
The Earth-based mission control reasons about
the journey this way (for convenience in this
thought experiment the ship is assumed to
immediately attain its full speed upon
departure): the round trip will take
t = 2d / v = 10.28 years in Earth time
(i.e. everybody on earth will be 10.28 years
older when the ship returns). The flow of
time on the ship and aging of the travelers
during their trip will be slowed by the factor
epsilon = sqrt(1 - V^2/c^2), the reciprocal
of the Lorentz factor. In this case, epsilon
= 0.5, and the travelers will have aged only
0.500 × 10.28 = 5.14 years when they return.
The ship's crew members also calculate the
particulars of their trip from their
perspective. *They know that the distant star
system and the Earth are moving relative to
the ship at speed v during the trip*. In their
rest frame the distance between the Earth
and the star system is epsilon * d = 0.5d
= 2.23 light years (length contraction),
for both the outward and return journeys.
Each half of the journey takes 2.23 / v
= 2.57 years, and the round trip takes
2×2.57 = 5.14 years. Their calculations
show that they will arrive home having
aged 5.14 years. The travelers' final
calculation is in complete agreement with
the calculations of those on Earth, though
they experience the trip quite differently."
Notice: "The ship's crew members know that
the distant star system and the Earth are
moving relative to the ship at speed v
during the trip".
This view is false, because it is physically
impossible that the distant star system
and the Earth move at v relative to the ship.
If both frames were inertial, one could apply
the above relations tB = tA * sqrt(1-v^2/c^2)
and tA = tB * sqrt(1-v^2/c^2).
Then, tB/tA = tA/tB, tB^2=tA^2 and tB=tA,
which is only valid when v = 0.
In the scenario, as the spaceship B moves at
a big velocity v <> 0 relative to the Earth A,
one can rightly infer that tB = tA * sqrt(1-v^2/c^2)
= 0.500 × 10.28 years = 5.14 years.
But, in fact, the spaceship B moves at v
relative to an Earth that is almost "rest" in
the Universe (cf. its velocity wrt the CMBR).
Iow, the spaceship moves approximately at v
in the Universe, and this is the reason why its
clock reads tB = tU * sqrt(1-v^2/c^2), where
tU, the time marked by a clock almost at rest
in the Universe, is very close to tA.
On the other hand, as the Earth A can be considered
at rest in the Universe, i.e. vEarth =~ 0 wrt the
Universe, one gets tA =~ tU from tA =
tU * sqrt(1-vEarth^2/c^2).
So, in the so-called twin paradox", one is left with
tB =~ tA * sqrt(1-v^2/c^2) =~ 5.14 years
and tA = 10.28 years, meaning that when the twins
born on the day the ship leaves meet again, the
traveler is 5.14 years old and the stay-at-home
twin is 10.28 years old.
There is no paradox at all!
SRists make the same mistake when they claim
that the Earth (and the distant star system (sic)!)
moves relative to cosmic muons, or that the
length of vacuum pipes where pions are accelerated
appears to be contracted, because of their velocity
relative to the pions. They forget that the pipes are
at rest in the lab, that the lab is situated on Earth,
and that the Earth itself is almost at rest in the Universe,
irrespective of SRists' imaginary world.
Marcel Luttgens
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