 |
|
| Science Forum Index » Physics - Relativity Forum » Chapter: The mechanisms behind Non-Simultaneity... |
|
Page 1 of 2 Goto page 1, 2 Next |
|
| Author |
Message |
| Hans de Vries... |
 Posted: Thu Nov 05, 2009 11:35 pm |
|
|
|
Guest
|
I recently finished the introductory chapter on the
mechanisms behind non-simultaneity.
http://physics-quest.org/Book_Chapter_Non_Simultaneity.pdf
4.1 Changing reference frames and non-simultaneity . . . . . . 2
4.2 Lorentz invariance of the wave equation. . . . . . . . . . . . 3
4.3 Observed simultaneity and Derived simultaneity. . . . . . . 5
4.4 Everybody sees the same light-cone frame . . . . . . . . . . 6
4.5 Passengers in rows and atoms in rows . . . . . . . . . . . . . 8
4.6 The velocity dependent viewing angle . . . . . . . . . . . . . 9
4.7 Simultaneity and the invariance of size . . . . . . . . . . . . 10
4.8 The relative versus the absolute viewing angle . . . . . . . 12
4.9 The ellipsoids of
simultaneity . . . . . . . . . . . . . . . . . . . 16
4.10 From ellipsoids to spheres of simultaneity . . . . . . . . . . 20
4.11 Step 1: From absolute to relative positions . . . . . . . . . 24
4.12 Step 2: Viewing while Lorentz contracted. . . . . . . . . . 26
4.13 Simultaneity from the Spherical Mirror clock . . . . . . . . 28
4.14 Reversal of Lorentz contraction . . . . . . . . . . . . . . . .
32
4.15 Reversal of Time
dilation. . . . . . . . . . . . . . . . . . . . . 34
4.16 Simultaneity from Huygens principle . . . . . . . . . . . . . 38
4.17 Simultaneity and the light wavefront direction . . . . . . 39
4.18 The wavefront rotation of matter waves . . . . . . . . . . 42
4.19 Negative energy waves and wavefront rotation. . . . . . 44
The subject is maybe a bit elementary for a QFT book but a
substantial effort is made to visualize why exactly we experience
different simultaneities in different reference frames and why we
experience our world as invariant under boosts.
It is done so in a pedestrian step by step mode with lots of
visualizations. The most pedestrian path would start at 4.3 and
end at 4.12
Some feedback would be welcome.
Regards, Hans
__________________
http://www.physics-quest.org |
|
|
| Back to top |
|
|
|
| Hans de Vries... |
| Posted: Thu Nov 05, 2009 11:44 pm |
|
|
|
Guest
|
with improved formatting:
http://physics-quest.org/Book_Chapter_Non_Simultaneity.pdf
4.1 Changing reference frames and non-simultaneity . . . . 2
4.2 Lorentz invariance of the wave equation. . . . . . . . 3
4.3 Observed simultaneity and Derived simultaneity . . . . 5
4.4 Everybody sees the same light-cone frame . . . . . . . 6
4.5 Passengers in rows and atoms in rows . . . . . . . . . 8
4.6 The velocity dependent viewing angle . . . . . . . . . 9
4.7 Simultaneity and the invariance of size . . . . . . . 10
4.8 The relative versus the absolute viewing angle. . . . 12
4.9 The ellipsoids of simultaneity . . . . . . . . . . . 16
4.10 From ellipsoids to spheres of simultaneity . . . . . 20
4.11 Step 1: From absolute to relative positions. . . . . 24
4.12 Step 2: Viewing while Lorentz contracted . . . . . . 26
4.13 Simultaneity from the Spherical Mirror clock . . . . 28
4.14 Reversal of Lorentz contraction. . . . . . . . . . . 32
4.15 Reversal of Time dilation. . . . . . . . . . . . . . 34
4.16 Simultaneity from Huygens principle. . . . . . . . . 38
4.17 Simultaneity and the light wavefront direction . . . 39
4.18 The wavefront rotation of matter waves . . . . . . . 42
4.19 Negative energy waves and wavefront rotation . . . . 44
Regards, Hans
_____________________________
http://www.physics-quest.org |
|
|
| Back to top |
|
|
|
| glird... |
| Posted: Fri Nov 06, 2009 8:55 am |
|
|
|
Guest
|
On Nov 6, 4:35 am, Hans de Vries wrote:
[quote]
I recently finished the introductory chapter on the mechanisms behind non-simultaneity.
http://physics-quest.org[/quote]
/Book_Chapter_Non_Simultaneity.pdf
Some feedback would be welcome. >
1. The following sentence appears on page 13:
"The crossings of the x-axis and x'-axis mark the events from which
the light rays reach the observer in the middle at the same time."
In the figure, x and x' are not on or parallel to each
other.therefore this is a wheelerian thesis rather than an STR one.
2. Given that X is thera horizontal axis of system A (x,y,z) and that
cs B (x',y',z') moves along it at v, if X' is NOT on or parallel to X
an affine rotation is to be performed - as stipulated by Minkowski in
his 1907 paper "Space and Time" - in order to make it so. Once X and
X' ARE on or parallel to each other, there is no reason for any
"boost" or "rotation" to change the angle as per your wheelerian
figure.
3. If we have 3 or more systems each moving at a different speed than
the others, WHY does each X' or X" etc axis rotate by exactly the
amount needed for your wheelerian "explanation" of the reason that
lengths "appear" contracted "even though they aren't")!
glird |
|
|
| Back to top |
|
|
|
| Hans de Vries... |
| Posted: Sat Nov 07, 2009 6:46 am |
|
|
|
Guest
|
On Nov 6, 7:55 pm, glird <gl... at (no spam) aol.com> wrote:
Hi Glird, thank you for reading and providing feedback.
[quote]
1. The following sentence appears on page 13:
"The crossings of the x-axis and x'-axis mark the events from which
the light rays reach the observer in the middle at the same time."
In the figure, x and x' are not on or parallel to each
other.therefore this is a wheelerian thesis rather than an STR one.
2. Given that X is thera horizontal axis of system A (x,y,z) and that
cs B (x',y',z') moves along it at v, if X' is NOT on or parallel to X
an affine rotation is to be performed - as stipulated by Minkowski in
his 1907 paper "Space and Time" - in order to make it so. Once X and
X' ARE on or parallel to each other, there is no reason for any
"boost" or "rotation" to change the angle as per your wheelerian
figure.
[/quote]
What the figure on page 13 shows is how a "fast jetline passenger"
receives light, from the passenger behind him, which has traveled
longer as the light from the passenger in front of him.
It's this difference which defines the different simultaneity in
the moving reference frame.
(http://physics-quest.org/Book_Chapter_Non_Simultaneity.pdf)
[quote]3. If we have 3 or more systems each moving at a different speed than
the others, WHY does each X' or X" etc axis rotate by exactly the
amount needed for your wheelerian "explanation" of the reason that
lengths "appear" contracted "even though they aren't")!
glird
[/quote]
Real physical Lorentz contraction is shown by the moving stable
solutions of the wave equations for the EM potentatial field and
the matter fields (basically the Klein Gordon equation)
The potential field of a moving charge is Lorentz contracted.
See for instance the first section of:
http://physics-quest.org/Book_Chapter_EM_LorentzContr.pdf
The different simultaneities in different reference frames
reverse this physical effect of Lorentz contraction.
This can be seen by looking at figure 4.25 at page 33:
http://physics-quest.org/Book_Chapter_Non_Simultaneity.pdf
The physically Lorentz contracted moving train is LONGER by
a factor gamma on the x'-axis compared to the length of the
train at rest (measured on the x'-axis).
Regards, Hans
_______________________________
http://www.physics-quest.org/ |
|
|
| Back to top |
|
|
|
| Tom Roberts... |
| Posted: Sat Nov 07, 2009 5:50 pm |
|
|
|
Guest
|
Hans de Vries wrote:
[quote]Real physical Lorentz contraction is shown by the moving stable
solutions of the wave equations for the EM potentatial field and
the matter fields (basically the Klein Gordon equation)
[/quote]
If by "physical" you mean "what I measure", then this is correct. But
that is often NOT what people expect "physical" to mean. In particular,
for the case of a moving rod, most people expect "physical length
contraction" to mean "the rod itself gets shorter", and this most
definitely is NOT true. Experts will move on without being confused by
your phrasing, but non-experts usually do get confused by such
statements -- it happens all the time around here.
For a thing like a rod it is QUITE CLEAR that looking at it from a
moving frame does not affect the thing itself, so the object itself is
not physically affected by any observer's "length contraction". For
fields, which are not things (in the same sense that a rod is a thing,
anyway), it's clear that the field (qua function on the manifold) is not
affected by any coordinates whatsoever, "moving" or otherwise.
So I advise authors to avoid the term "physical" when discussing "length
contraction" or "time dilation", because it provides no added value, and
can easily cause confusion. Especially among people not already expert
in relativity (which is nearly everyone around here). Say "measured"
instead, because that is really what you mean.
Everything I said about "physical" also applies to "real" -- non-experts
have an even stronger expectation that a "real length contraction" of a
rod applies to the rod itself. Again, say "measured" instead, because
that's what you mean.
The underlying problem is that words like "physical" and "real" do not
have a single, well-defined meaning. Different people read different
connotations into them. While this can never be completely eliminated,
these particular words are especially prone to such misinterpretation,
and the results can be extremely confusing to non-experts.
Tom Roberts |
|
|
| Back to top |
|
|
|
| Inertial... |
| Posted: Sat Nov 07, 2009 7:09 pm |
|
|
|
Guest
|
"Tom Roberts" <tjroberts137 at (no spam) sbcglobal.net> wrote in message
news:H-2dnf4lgO1ZZGjX4p2dnAA at (no spam) giganews.com...
[quote]Hans de Vries wrote:
Real physical Lorentz contraction is shown by the moving stable
solutions of the wave equations for the EM potentatial field and
the matter fields (basically the Klein Gordon equation)
If by "physical" you mean "what I measure", then this is correct. But that
is often NOT what people expect "physical" to mean. In particular, for the
case of a moving rod, most people expect "physical length contraction" to
mean "the rod itself gets shorter", and this most definitely is NOT true.
Experts will move on without being confused by your phrasing, but
non-experts usually do get confused by such statements -- it happens all
the time around here.
For a thing like a rod it is QUITE CLEAR that looking at it from a moving
frame does not affect the thing itself, so the object itself is not
physically affected by any observer's "length contraction". For fields,
which are not things (in the same sense that a rod is a thing, anyway),
it's clear that the field (qua function on the manifold) is not affected
by any coordinates whatsoever, "moving" or otherwise.
So I advise authors to avoid the term "physical" when discussing "length
contraction" or "time dilation", because it provides no added value, and
can easily cause confusion. Especially among people not already expert in
relativity (which is nearly everyone around here). Say "measured" instead,
because that is really what you mean.
Everything I said about "physical" also applies to "real" -- non-experts
have an even stronger expectation that a "real length contraction" of a
rod applies to the rod itself. Again, say "measured" instead, because
that's what you mean.
The underlying problem is that words like "physical" and "real" do not
have a single, well-defined meaning. Different people read different
connotations into them. While this can never be completely eliminated,
these particular words are especially prone to such misinterpretation, and
the results can be extremely confusing to non-experts.
[/quote]
Nicely put .. a sizable proportion of arguments here could be averted by
taking that advice. Words like "physical" and "real" provides the ambiguity
crackpots need in their desperate attempts to construct some sort of
strawman argument. |
|
|
| Back to top |
|
|
|
| Hans de Vries... |
| Posted: Sun Nov 08, 2009 1:56 am |
|
|
|
Guest
|
On Nov 7, 11:50 pm, Tom Roberts <tjroberts... at (no spam) sbcglobal.net> wrote:
[quote]Hans de Vries wrote:
Real physical Lorentz contraction is shown by the moving stable
solutions of the wave equations for the EM potentatial field and
the matter fields (basically the Klein Gordon equation)
The underlying problem is that words like "physical" and "real" do not
have a single, well-defined meaning. Different people read different
connotations into them. While this can never be completely eliminated,
these particular words are especially prone to such misinterpretation,
and the results can be extremely confusing to non-experts.
Tom Roberts
[/quote]
Hi Tom,
I certainly do agree that words like "physical" and "real" do
not have a single, well-defined meaning, and can cause additional
confusion to already confused people. I also appreciate that you
want to reserve the word "real" for the proper, invariant, character-
ristics. I'll be more careful.
The use of the word physical however should to be seen in the
context of the book itself as a quantum field theory book.
All objects/observers are described as propagating according to
the relativistic wave equations.
The (linear) relativistic wave equations can be represented as the
continuum limit of simple discrete mass/spring systems. See for
example section 3.4 which contains an introductory discussion of
the Klein Gordon equation in the context of Time dilation:
http://physics-quest.org/Book_Chapter_Time_Dilation.pdf
The moving stable solutions of these systems exhibit both Lorentz
contraction and Time dilation (The latter already in the form of
the eigen frequency of a particle along its trajectory).
This (all within a single reference frame) without any knowledge
of the Lorentz transform itself and even though a mass/spring system
representation picks out a specific preferred reference frame.
The wave equations, being compatible with special relativity,
Give actually rise to Lorentz contraction and Time dilation which
Is not that surprisingly and they should be expected to do so.
See the two chapters on Lorentz contraction and Time dilation
from this perspective: (section 2.1 derives Lorentz contraction)
http://physics-quest.org/Book_Chapter_EM_LorentzContr.pdf
http://physics-quest.org/Book_Chapter_Time_Dilation.pdf
The chapter on simultaneity is written in the same context as
the two above, linking the wave equations to non-simultaneity.
http://physics-quest.org/Book_Chapter_Non_Simultaneity.pdf
Regards, Hans
__________________________________
http://www.physics-quest.org/ |
|
|
| Back to top |
|
|
|
| Hans de Vries... |
| Posted: Sun Nov 08, 2009 4:26 am |
|
|
|
Guest
|
On Nov 8, 1:28 pm, "Androcles" <Headmas... at (no spam) Hogwarts.physics_p> wrote:
[quote]
The underlying problem is that words like Lorentz "contraction"
and time "dilation" do not have a single, well-defined meaning.
Einstein dilates length, Lorentz contracts length.
Einstein:
xi = x'/sqrt(1-v^2/c^2) where x' = x-vt.
Lorentz:
L = L0 * sqrt(1-v^2/c^2)
The underlying problem is that some idiots don't know the
difference between "multiply" and "divide".
Be more careful.
[/quote]
Hi, Androcles
Both your expressions are equally well valid.
It should be noted that L and L0 do not contain the same set of
events so the formula only serves to determine the correct measured
length of a static non-changing object.
If the object changes over time then you need the first expression
to determine the correct length at a certain time t.
Regards, Hans
The second expression follows from the Lorentz transform:
---------------------------------------------------------
starting with....: x = gamma(x' + beta t')
inserting........: t' = gamma(t - beta x )
and setting......: t = 0
gives............: x = gamma(x'-beta^2 gamma^2 x)
and finally......: x = x'/gamma
--------------------------------------------------------- |
|
|
| Back to top |
|
|
|
| Bruce Richmond... |
| Posted: Sun Nov 08, 2009 6:24 am |
|
|
|
Guest
|
On Nov 7, 7:09 pm, "Inertial" <relativ... at (no spam) rest.com> wrote:
[quote]"Tom Roberts" <tjroberts... at (no spam) sbcglobal.net> wrote in message
news:H-2dnf4lgO1ZZGjX4p2dnAA at (no spam) giganews.com...
Hans de Vries wrote:
Real physical Lorentz contraction is shown by the moving stable
solutions of the wave equations for the EM potentatial field and
the matter fields (basically the Klein Gordon equation)
If by "physical" you mean "what I measure", then this is correct. But that
is often NOT what people expect "physical" to mean. In particular, for the
case of a moving rod, most people expect "physical length contraction" to
mean "the rod itself gets shorter", and this most definitely is NOT true.
Experts will move on without being confused by your phrasing, but
non-experts usually do get confused by such statements -- it happens all
the time around here.
For a thing like a rod it is QUITE CLEAR that looking at it from a moving
frame does not affect the thing itself, so the object itself is not
physically affected by any observer's "length contraction". For fields,
which are not things (in the same sense that a rod is a thing, anyway),
it's clear that the field (qua function on the manifold) is not affected
by any coordinates whatsoever, "moving" or otherwise.
So I advise authors to avoid the term "physical" when discussing "length
contraction" or "time dilation", because it provides no added value, and
can easily cause confusion. Especially among people not already expert in
relativity (which is nearly everyone around here). Say "measured" instead,
because that is really what you mean.
Everything I said about "physical" also applies to "real" -- non-experts
have an even stronger expectation that a "real length contraction" of a
rod applies to the rod itself. Again, say "measured" instead, because
that's what you mean.
The underlying problem is that words like "physical" and "real" do not
have a single, well-defined meaning. Different people read different
connotations into them. While this can never be completely eliminated,
these particular words are especially prone to such misinterpretation, and
the results can be extremely confusing to non-experts.
Nicely put .. a sizable proportion of arguments here could be averted by
taking that advice. Words like "physical" and "real" provides the ambiguity
crackpots need in their desperate attempts to construct some sort of
strawman argument.- Hide quoted text -
- Show quoted text -
[/quote]
Not only crackpots but anyone trying to get things straight in their
own mind. It is easy after we understand things to accept them as
being the proper explaination, but when seeing it presented for the
first time we are usually a bit sceptical and evaluate each step of
the process. In doing so we each form our own opinion of what is
"really" going on. If the explaination is solid and guides the
learner through every step of reasoning there should be no problem in
arriving at the correct conclusion. The problem with some around here
is that they took a wrong step early on and convinced themselves that
they got it right while everyone else went the wrong way. And every
time they travel down that path they wear the rut deeper in the
direction of the wrong path.
Anyway  I agree that should not be used at this point. It might be
worth discussing them seperately though. |
|
|
| Back to top |
|
|
|
| Androcles... |
| Posted: Sun Nov 08, 2009 7:28 am |
|
|
|
Guest
|
"Hans de Vries" <hans.de.vries.nl at (no spam) gmail.com> wrote in message
news:4a7c9a4a-56f0-43f5-8cef-c0448be3861f at (no spam) s15g2000yqs.googlegroups.com...
[quote]On Nov 7, 11:50 pm, Tom Roberts <tjroberts... at (no spam) sbcglobal.net> wrote:
Hans de Vries wrote:
Real physical Lorentz contraction is shown by the moving stable
solutions of the wave equations for the EM potentatial field and
the matter fields (basically the Klein Gordon equation)
The underlying problem is that words like "physical" and "real" do not
have a single, well-defined meaning. Different people read different
connotations into them. While this can never be completely eliminated,
these particular words are especially prone to such misinterpretation,
and the results can be extremely confusing to non-experts.
Tom Roberts
Hi Tom,
I certainly do agree that words like "physical" and "real" do
not have a single, well-defined meaning, and can cause additional
confusion to already confused people. I also appreciate that you
want to reserve the word "real" for the proper, invariant, character-
ristics. I'll be more careful.
The underlying problem is that words like Lorentz "contraction"[/quote]
and time "dilation" do not have a single, well-defined meaning.
Einstein dilates length, Lorentz contracts length.
Einstein:
xi = x'/sqrt(1-v^2/c^2) where x' = x-vt.
Lorentz:
L = L0 * sqrt(1-v^2/c^2)
The underlying problem is that some idiots don't know the
difference between "multiply" and "divide".
Be more careful. |
|
|
| Back to top |
|
|
|
| Hans de Vries... |
| Posted: Sun Nov 08, 2009 7:45 am |
|
|
|
Guest
|
On Nov 8, 6:33 pm, "Simple Simon" <pi.r.cubed-nos... at (no spam) gmail.com> wrote:
[quote]Hans de Vries wrote:
This should be:
x = gamma(x'-beta^2 gamma x)
[/quote]
Correct, Thanks for correcting the typo. At least somebody
who reads this seriously :^)
Regards, Hans
_____________________________________
http://www.physics-quest.org/ |
|
|
| Back to top |
|
|
|
| glird... |
| Posted: Sun Nov 08, 2009 8:24 am |
|
|
|
Guest
|
On Nov 7, 5:50 pm, Tom Roberts wrote:
[quote]In particular, for the case of a moving rod, most people expect "physical length contraction" to mean "the rod itself gets shorter", and this most definitely is NOT true. Experts will move on without being confused by your phrasing, but non-experts usually do get confused by such statements -- it happens all the time around here.
[/quote]
Thus sayeth a self-deluded amateurish expert.
[quote]For a thing like a rod it is QUITE CLEAR that looking at it from a moving frame does not affect the thing itself, so the object itself is not physically affected by any observer's "length contraction".
For fields, which are not things (in the same sense that a rod is a[/quote]
thing, anyway), it's clear that the field (qua function on the
manifold) is not affected by any coordinates whatsoever, "moving" or
otherwise.>
Correct.
[quote]So I advise authors to avoid the term "physical" when discussing "length contraction" or "time dilation", because it provides no added value, and can easily cause confusion. Especially among people not already expert in relativity (which is nearly everyone around here).
Say "measured" instead, because that is really what you mean.[/quote]
When "experts" say 'physical" THEY mean
"measured". In STR, which uses esynched clocks as measuring tools, the
difference in setings per successive clock of a given such esynched
system allows the measured 'length contraction" of a given system is a
function of that difference; and may not be physically real.
[quote]Everything I said about "physical" also applies to "real" -- non-experts have an even stronger expectation that a "real length contraction" of a rod applies to the rod itself.
[/quote]
It DOES. "Experts" think that the contractions "don't
really_waderdatmeens happen" but are only a figment "as measured by"
differently moving systems.
[quote]Again, say "measured" instead, because
[if you are an ex pert] that's what you mean.[/quote]
The underlying problem is that words like "physical" and "real" do
not have a single, well-defined meaning. Different people read
different connotations into them. While this can never be completely
eliminated, these particular words are especially prone to such
misinterpretation, and the results can be extremely confusing to non-
experts
[such as}
[quote]Tom Roberts
[/quote]
glird |
|
|
| Back to top |
|
|
|
| Androcles... |
| Posted: Sun Nov 08, 2009 10:22 am |
|
|
|
Guest
|
"Hans de Vries" <hans.de.vries.nl at (no spam) gmail.com> wrote in message
news:ad39ee44-042a-49eb-8ffa-3676650a7d61 at (no spam) b2g2000yqi.googlegroups.com...
On Nov 8, 1:28 pm, "Androcles" <Headmas... at (no spam) Hogwarts.physics_p> wrote:
[quote]
The underlying problem is that words like Lorentz "contraction"
and time "dilation" do not have a single, well-defined meaning.
Einstein dilates length, Lorentz contracts length.
Einstein:
xi = x'/sqrt(1-v^2/c^2) where x' = x-vt.
Lorentz:
L = L0 * sqrt(1-v^2/c^2)
The underlying problem is that some idiots don't know the
difference between "multiply" and "divide".
Be more careful.
[/quote]
Hi, Androcles
Both your expressions are equally well valid.
It should be noted that L and L0 do not contain the same set of
events so the formula only serves to determine the correct measured
length of a static non-changing object.
If the object changes over time then you need the first expression
to determine the correct length at a certain time t.
Regards, Hans
The second expression follows from the Lorentz transform:
---------------------------------------------------------
starting with....: x = gamma(x' + beta t')
inserting........: t' = gamma(t - beta x )
and setting......: t = 0
gives............: x = gamma(x'-beta^2 gamma^2 x)
and finally......: x = x'/gamma
---------------------------------------------------------
=============================================
Bwahahahahaha!
Which magic hat did you pull gamma and beta from?
http://tvtropes.org/pmwiki/pub/images/avernum4_rabbitinthehat.png
The underlying problem is that some idiots don't know the
difference between beta and gamma. Be more careful. |
|
|
| Back to top |
|
|
|
| Hans de Vries... |
| Posted: Sun Nov 08, 2009 11:21 am |
|
|
|
Guest
|
On Nov 8, 7:33 pm, "Androcles" <Headmas... at (no spam) Hogwarts.physics_p> wrote:
[quote]What hat did you pull your magic gamma from?
Androcles.
[/quote]
Well, if you're serious (?)
1-beta^2 beta^2 1
1 + beta^2 gamma^2 = -------- + -------- = -------- = gamma^2
1-beta^2 1-beta^2 1-beta^2
This is what turns your "multiply by gamma" into a "divide by gamma"
Regards, Hans
_________________________________
http://www.physics-quest.org/ |
|
|
| Back to top |
|
|
|
| Simple Simon... |
| Posted: Sun Nov 08, 2009 12:33 pm |
|
|
|
Guest
|
Hans de Vries wrote:
[quote]On Nov 8, 1:28 pm, "Androcles" <Headmas... at (no spam) Hogwarts.physics_p> wrote:
The underlying problem is that words like Lorentz "contraction"
and time "dilation" do not have a single, well-defined meaning.
Einstein dilates length, Lorentz contracts length.
Einstein:
xi = x'/sqrt(1-v^2/c^2) where x' = x-vt.
Lorentz:
L = L0 * sqrt(1-v^2/c^2)
The underlying problem is that some idiots don't know the
difference between "multiply" and "divide".
Be more careful.
Hi, Androcles
Both your expressions are equally well valid.
It should be noted that L and L0 do not contain the same set of
events so the formula only serves to determine the correct measured
length of a static non-changing object.
If the object changes over time then you need the first expression
to determine the correct length at a certain time t.
Regards, Hans
The second expression follows from the Lorentz transform:
---------------------------------------------------------
starting with....: x = gamma(x' + beta t')
inserting........: t' = gamma(t - beta x )
and setting......: t = 0
gives............: x = gamma(x'-beta^2 gamma^2 x)
[/quote]
This should be:
x = gamma(x'-beta^2 gamma x)
[quote]and finally......: x = x'/gamma
---------------------------------------------------------[/quote] |
|
|
| Back to top |
|
|
|
|
|
All times are GMT - 5 Hours
The time now is Fri Dec 04, 2009 6:03 am
|
|