Effects of relativistic length contraction and time dilation
Peri of Pera
An observer monitors an object in space. It is a rod 1000m (L) long and
at rest.
The rod accelerates to a speed of 300000m/sec. The length of the rod
has contracted to 999.9995m (L'). The original second is dilated to
1.0000005. Both numbers are measured by the observer and confirmed by
the relativity formulas L'=L*sqrt(1-vv/cc) and T'=T/sqrt(1-vv/cc),
using a value c of 300000000m/sec. The observer calculates that a light
beam to cover distance L' in 1.0000005 seconds has a speed of
299999700m/sec.
The rod accelerates to 600000m/sec. The length is now 999.998m (L") and
the second has further dilated to 1.000002. The observer calculates
that a light beam to cover distance L" in 1.000002 seconds has now a
speed of 299998800m/sec.
The observer concludes that the theory of relativity proves that the
speed of light is not constant. If at rest c is 300000km/sec, at
300km/sec it is 299999km/sec and at 600km/sec it is 299998km/sec being
subject to both the effects of contraction and dilation.
Peter Riedt
nero
that you must consider that also the distance must be considered
contracted ..and so the ligth speed remain the same ...
can i have your opinion about
http://groups.google.com/group/clock-in-washmachine
rot...@gmail.com
>An observer monitors an object in space. It is a rod 1000m (L) long and
>at rest.
The observer notes (measures) the spped of the rod to be 0 m/s. The
observer measures the lenght of this resting rod to be 1000m
>The rod accelerates to a speed of 300000m/sec. The length of the rod
>has contracted to 999.9995m (L').
IF the observer measures the lenght of the moving rod, he will obtain a
measured length
of 999.9995m.
>The original second is dilated to 1.0000005.
?? One second in the oberver's frame remains one second in his own
frame.
You seem to be misinterpreting the time dilation formula. The 1.0000005
s has nothing to do with the problem.
Time is not dilated/contracted in the observer's frame. Time is
dilated/contracted in OTHER frames, according
to the observer. You have no need of time dilation in your problem
since all measurements are done in the observer's frame.
dlzc1 D:cox T:net@nospam.com N:dlzc D:aol T:com (dlzc)
"Peri of Pera" <rie...@yahoo.co.uk> wrote in message
news:1143352473....@z34g2000cwc.googlegroups.com...
> Effects of relativistic length contraction and time dilation
>
> An observer monitors an object in space. It is a rod
> 1000m (L) long and at rest.
> The rod accelerates to a speed of 300000m/sec. The
> length of the rod has contracted to 999.9995m (L').
> The original second is dilated to 1.0000005. Both
> numbers are measured by the observer and
> confirmed by the relativity formulas L'=L*sqrt(1-vv/cc)
> and T'=T/sqrt(1-vv/cc), using a value c of
> 300000000m/sec. The observer calculates that a light
> beam to cover distance L' in 1.0000005 seconds has
> a speed of 299999700m/sec.
Frame jump. The observer measures length_contracted /
observer_time *in his frame*.
David A. Smith
Dirk Van de moortel
"Peri of Pera" <rie...@yahoo.co.uk> wrote in message news:1143352473....@z34g2000cwc.googlegroups.com...
>
> An observer monitors an object in space. It is a rod 1000m (L) long and
> at rest.
> The rod accelerates to a speed of 300000m/sec. The length of the rod
> has contracted to 999.9995m (L').
With this notation, you designate the original frame of the rod to
be the primed frame, and the frame of the accelerated rod to be
the unprimed frame.
In that case, we have the transformation equations.
[1] dx = g ( dx' - v dt' )
[2] dt = g ( dt' - v dx' /c^2 )
with the equivalent inverse
[3] dx' = g ( dx + v dt )
[4] dt' = g ( dt + v dx /c^2 )
where
[5] g = 1/sqrt(1-v^2/c^2)
> The original second is dilated to
> 1.0000005. Both numbers are measured by the observer and confirmed by
> the relativity formulas L'=L*sqrt(1-vv/cc)
Indeed, provided that the lenght of the rod is measured by taking
the distances x1' and x2' simultaneously (dt'=0) in the primed frame,
we get (since dt' = 0) from equation [1] that
dx = g dx'
which gives
dx' = 1/g dx
which translates to your equation
L' = L sqrt(1-v^2/c^2)
> and T'=T/sqrt(1-vv/cc),
That gives the time between two ticks t1 and t2 on a clock at rest
in the unprimed frame of the moving rod (dx = 0). From equation [4]
you get
dt' = g dt
which translates to your equation
T' = T / sqrt(1-v^2/c^2)
> using a value c of 300000000m/sec. The observer calculates that a light
> beam to cover distance L' in 1.0000005 seconds has a speed of
> 299999700m/sec.
It looks like you haven't understood the meaning of the
variables that you are using. It's a very common mistake.
There is no light beam that covers the distance L' in the
time T'.
Remember that this L' was valid for two events that satisfy
dt' = 0 (simultaneous in the primed frame), whereas the T' was
valid for two events that satisfy dx = 0 (at the same place in the
unprimed frame). These are two *differerent* pairs of events.
If you want to combine these equations, then that can only
be for 2 events that have both
dt' = 0 (in your language T' = 0)
and
dx = 0 (in your language L = 0).
You can easily verify that this also implies
dt = 0 (in your language T = 0)
and
dx' = 0 (in your language L' = 0).
So it seems that you can only combine them if everything is zero:
dx = dx' = dt = dt' = 0
or, in your language:
L = L' = T = T' = 0
>
> The rod accelerates to 600000m/sec. The length is now 999.998m (L") and
> the second has further dilated to 1.000002. The observer calculates
> that a light beam to cover distance L" in 1.000002 seconds has now a
> speed of 299998800m/sec.
>
> The observer concludes that the theory of relativity proves that the
> speed of light is not constant. If at rest c is 300000km/sec, at
> 300km/sec it is 299999km/sec and at 600km/sec it is 299998km/sec being
> subject to both the effects of contraction and dilation.
I would conclude that you really haven't understood what
the equations and the variables you were using actually represent.
Perhaps this helped.
Dirk Vdm
Sue...
In real world electromagnetism you find Lorentz contraction
expressed in Maxwell's time dependent equations as:
<< However, when we calculate the contribution of charges and
currents at position r' to these integrals we do not use the values
at time t, instead we use the values at some earlier time . >>
http://farside.ph.utexas.edu/teaching/em/lectures/node50.html
http://arxiv.org/abs/physics/0204034
Sue...
Peri of Pera
is not observed. SR postulates (accepts, requires) time dilation and it
must be applied just as contraction is. Both effects must be taken into
account at the same time. It is not valid to apply only contraction and
ignore time dilation or vice versa. Of course it is necessary for SR
believers to refuse to do so otherwise they have nothing to stand on.
Peter Riedt
Peri of Pera
confronted by the ugly reality about their illogical superstitions.
Contraction and time dilation must be applied together when calculating
SR related motion.
Peter Riedt
Peri of Pera
affect a rod of 1000m length at rest and then at a speed of 300km/sec?
The emphasis is on 'together' and frame considerations should not be
used to confuse the issue.
Peter Riedt
dlzc1 D:cox T:net@nospam.com N:dlzc D:aol T:com (dlzc)
"Peri of Pera" <rie...@yahoo.co.uk> wrote in message
news:1143429642.4...@j33g2000cwa.googlegroups.com...
> David, SR believers always seek refuge in 'frame jumps'
> etc when confronted by the ugly reality
What reality? That you use formulas derived in two different
frames, and then proceed to act like you've discovered the
greatest thing since slide bread?
> about their illogical superstitions.
Pot. Kettle. Black. You supplied the formulae without even
paying attention to their derivation. That is pure religion, and
"illogical superstition". Even an engineer would not make so
fundamental a mistake.
> Contraction and time dilation must be applied
> together when calculating SR related motion.
OK, then let's do it right... Consider a muon created in the
upper atmosphere. The muon, in its frame, see the Earth's
atmosphere as 10s of meters thick. At the speed it "assumes" it
is going in its frame (based on measurements it would be possible
to make with instruments at that speed), it is entirely plausible
that it will survive to strike the surface of the Earth. There
is length contraction. Now in the frame of the Earth, the
atmosphere is 60 kilometers thick, yet muons are still arriving.
What's more, we can create muons in the lab, and note that the
faster we make them go, the longer they seem to "survive".
One frame (A) sees length contraction in the other frame (B), B
sees time dilation in A. Same coin... two sides.
But using measurements and A and B and coming up with an answer
involves a "frame jump". A newbie mistake, yet you have been
making it for some time (I see 2001 on groups.google). This
being the case, you must simply be posting to argue, so you wil
get to remain unconvinced.
David A. Smith
rot...@gmail.com
>must be applied just as contraction is. Both effects must be
>taken into account at the same time. It is not valid to apply only
>contraction and ignore time dilation or vice versa.
I dont agree. In the problem you pose, time contraction must not be
used.
In the Lorentz Equations (LE) , the formula L' = L/g means:
The lenght measured by the observer of the (moving) rod.
Whereas, the formula T' = T/g (T and T' are intervals here...a variant
of the usual form of the LE's) means:
The time measured by the observer of the (moving) rod's (hypothetical)
clock.
IOW, wrt the observer, the lengt of the ROD is contracted and the time
of the ROD is contracted.
The time of the observer is NOT contracted. This is why "time
contraction" factor is not, must not be used in your problem.
The subtility is in "length of the rod" and "time of the rod".
A speed measurement (refering to the measurement of the speed of light
in your problem) needs the measured length of the (moving) rod and the
measured time of the observer and NOT the measured time of the rod.
This is the prescription of speed measurements. In SR theory, you must
use SR's concept (definitions) of lenghts,time and speeds.
.. ?
---
If you want to be sure, then always doubt.
}:-)
Peri of Pera
previous argument that original cosmic ray particles are not found
within a distance from the earth's surface to allow them to be
converted to muons whose lifetime at that stage does not preclude them
from being found near the earth's surface. However, frame jumping is a
spurious argument. SR requires both length contraction and time
dilation and both of them must be applied together. They cannot be
separated into different frames or into separate calculations. Both
appear in the same frame, whether it is an observed frame or not. SR
cannot have it both ways. There is only one interpretation and it means
SR proves that the speed of light is not constant.
Peter Riedt
Bill Hobba
I know you asked Dirk but I suspect you are confused about something.
Lengths and clocks are not affected by motion - travel along with them and
nothing happens. What is affected is how other observers measure it just
like rotating a rod changes its projection - the length is the same - it is
just its measured projection differs. Tom Roberts likes to explain it this
way. A rod will not fit lengthways through a door. Rotate it - its length
has not changed but now it will fit through the door. The reason it can be
measured by different observers as having different lengths is exactly the
same - someone on the rod will always measure its length the same - however
you can change its it horizontal length and fit it through the door by
rotating it. And that is exactly what SR says happens to length - velocity
is equivalent to hyperbolic rotation.
Thanks
Bill
>
> Peter Riedt
>
rot...@gmail.com
>>time of the ROD is contracted.
>rotchm, my argument is based exactly on your IOW.
Exactly why your agument is wrong. You must not use the rod's time.
The speed measurement invoves the measured lenght of the rod and the
measured time of the observer. That is the prescription/definition of
the 'speed'.
Peri of Pera
rod's time because it will always be the same as the instruments of
measurment on a moving object will not register changes in v. The
observer notes contraction and dilation of and on the rod and it is
these that I use in my calculations.
Peter Riedt
dlzc1 D:cox T:net@nospam.com N:dlzc D:aol T:com (dlzc)
"Peri of Pera" <rie...@yahoo.co.uk> wrote in message
news:1143431711.2...@e56g2000cwe.googlegroups.com...
> David, in respect of the cosmic ray muons, I accept
> provisionally your previous argument that original
> cosmic ray particles are not found within a
> distance from the earth's surface to allow them to
> be converted to muons whose lifetime at that stage
> does not preclude them from being found near the
> earth's surface.
Their *rest* lifetime *does* preclude them from being found near
the surface of the Earth. Their measured velocities (in bulk)
are less than c, and measuring the quantites at altitude to the
quantities at the surface of the Earth, generate
> However, frame jumping is a
> spurious argument.
Frame jumping is not an argument. Frame jumping is your mistake.
One you continually make. It is clear you don't understand,
after 5 years. Perhaps you should try learning something else?
> SR requires both length contraction and time
> dilation and both of them must be applied together.
"Must" is your problem. I set up an example. It was simple. It
involved both length contraction and time dilation. If you
cannot understand still, I suggest you go study something simpler
for you.
> They cannot be
> separated into different frames or into separate
> calculations.
You have access to the same internet. The derivation is clear.
The rules are clear. Lorentz made the results as simple as
possible.
> Both
> appear in the same frame, whether it is an
> observed frame or not.
If it cannot be measured in the frame, it cannot be used in the
frame. In the frame of the muon, the muon's clock runs
correctly, and it dies after so many microseconds. Those silly
Earthlings that think they have such a non-dense, thick
atmosphere are simply deluding themselves.
> SR
> cannot have it both ways. There is only one
> interpretation and it means SR proves that
> the speed of light is not constant.
There is clearly at least two interpretations. The right one,
and one involving frame jumps that does not in any way resemble
Nature. Seriously, Peter, you need to try your hand at something
else. If after 5 years you still don't "get it", I don't think
you can.
The world needs bus drivers too. But then there are bus drivers
that "get it".
David A. Smith
rot...@gmail.com
>these that I use in my calculations.
And that is not the prescription (operational definition) of "speed".
If you want to do SR, use SR's concept of speed and not yours.
The observer notes length contraction of the rod and notes time
contraction of the rod's "clock". But speed measurement only involves
the lenght of the rod (as measured by the observer) and not the time of
the rod as measured by the observer.
Peri of Pera
separated but must be applied together. It has nothing to do with my
definition of speed. There is only one universal definition. To treat
contraction and dilation as different and separate factors in SR
defined motion cannot be justified on any grounds even it it has been
the pactice to do so in the past.
Peter Riedt
Peri of Pera
However, I still would like Dirk to explain contraction and dilation as
factors in a rod at rest and at 300km/sec and the effect on c.
Peter Riedt
Peri of Pera
Peter Riedt
rot...@gmail.com
SR implies length contraction and time dilation...But one must
understand what/how this is to be applied in a problem.
>They cannot be separated but must be applied together.
Wrong.
>It has nothing to do with my definition of speed. There is only one universal definition.
Wrong. There are many definitions for "speed'. If you want to do SR,
you must use its definition of 'speed'.
In SR, 'speed' has an operational definition. It is based on the
operational definitions of lenght and time measurements.
Read my prevoius post to you...
Dirk Van de moortel
"Peri of Pera" <rie...@yahoo.co.uk> wrote in message news:1143430441.1...@u72g2000cwu.googlegroups.com...
I just explained in which context the equations for contraction
and dilation that you used are valid, and under which circumstances
they are valid together or 'together'.
1) To measure the length of a moving rod, you use the difference
of the distances between two events, that are simultaneous for
you on both ends on the moving rod.
This way you get length contraction - see my previous message.
2) To measure the time between two ticks on a moving clock,
you use the difference of the times of two events, that happen
at the same place on a clock attached to the rod.
This way you get time dilation - see my previous message.
Unless v = 0 (trivially implying that L' = L and T' = T), the only
way that two measuring events can satisfy *both* conditions
together (or 'together' if you like), is by having two *identical*
events, i.o.w. only one event, i.o.w. a rod of zero length
(L = L' = 0) and a clock that doesn't really tick (T = T' = 0).
If there is anything about this, that you don't understand, feel
free to ask, but *do* quote the text please.
Dirk Vdm
Hexenmeister
|
| >SR postulates (accepts, requires) time dilation and it
| >must be applied just as contraction is. Both effects must be
| >taken into account at the same time. It is not valid to apply only
| >contraction and ignore time dilation or vice versa.
|
|
| I dont agree. In the problem you pose, time contraction must not be
| used.
|
| In the Lorentz Equations (LE) , the formula L' = L/g means:
| The lenght measured by the observer of the (moving) rod.
|
|
| Whereas, the formula T' = T/g (T and T' are intervals here...a variant
|
| of the usual form of the LE's) means:
| The time measured by the observer of the (moving) rod's (hypothetical)
| clock.
|
|
| IOW, wrt the observer, the lengt of the ROD is contracted and the
| time
| of the ROD is contracted.
Let's suppose you are correct.
Does that then mean that the velocity of the hills and trees and grass
coming toward the car, as seen by the occupant, is the same velocity
as the squirrels in the trees and mice in the fields see of the car
moving toward them?
In other words, does (length contracted) / (time contracted) = length/time?
Androcles.
|
| rotchm, my argument is based exactly on your IOW.
|
| Peter Riedt
AllYou!
<rot...@gmail.com> wrote in message
news:1143389876....@u72g2000cwu.googlegroups.com...
But the observer can observe the clock in the rod's frame and note that
it shows a *time* of 1.0000005 seconds for every second in his own
frame.
Dirk Van de moortel
"AllYou!" <Ida...@conversent.net> wrote in message news:PJednfYULslopbTZ...@conversent.net...
That does not give a reason for dividing the measured length
of the rod by this number. Nothing moves between the two
ends of the rod during the time it takes a clock to tick that is
attached to the rod.
You could just as well divide your height by the time it takes
to sneeze and call it the speed of something.
Dirk Vdm
AllYou!
"Dirk Van de moortel" <dirkvand...@ThankS-NO-SperM.hotmail.com>
wrote in message news:44295211$1...@usenet01.boi.hp.com...
I misunderstood the point of his statement. I agree that dividing the
measured length of the rod by the *time* as shown on the observed clock
is meaningless. Thanks for the correction.