Help - Can't find my error.
David Seppala
to me. I created a gedunken experiment that leads to a logical
contradiction. I am hoping that someone more knowledgeable can point
out the error I'm making. The problem is listed on my website at:
http://www.2400ad.com/einstein
Any insights will be appreciated
Thanks,
David Seppala
and...@attglobal.net
Climbed out of the woodwork again, haven't you.
(For newcomers to the hg, Mr. Seppala is notorious for posting stuff
that
says "please find my error" as if he understood relativity
well enough to think that the error is hard to find.)
Now he's just trying to avoid the obvious problems by
hiding what he's saying at a website that most people
won't bother to visit.
Post your "problem" here so that there is a dialogue.
John Anderson
David Seppala
how the diagrams will show up since they are generated using text and spacing
so things might get screwed up. If they do, and you want a display of the
diagrams, go to http://www.2400ad.com/einstein - I know how to better
control the spacing of text there. You can skip the editorilizing I do at
the intro do the problem (but I like the Einstein joke-. Anyway here's the
problem
The gedanken experiment presented here is based on a statement made by
Einstein in Special Relativity regarding the
measurement of time at two spatially separated points A and B:
We have not defined a common "time" for A and B, for the latter cannot be
defined at all unless we
establish by definition that the "time" required by light to travel from
A to B equals the "time" it requires to
travel from B to A.
This statement is a hypothesis and is not true by definition. Problems occur
with Einstein's notions of space and time
when clocks are compared using the one way transmission of light instead of
the transmission from A to B and back to A
again. Einstein states a common time cannot be defined without this round
trip definition. However, we can setup a
simple experiment using the one way transmission of light instead of the
round trip and see if Einstein's theory holds.
The Experiment
Experiment as viewed in the rest frame:
The experimental setup consists of a series of equally spaced detectors, and
two monochromatic light sources of the
same frequency. The detectors are placed on a straight line, spaced at
intervals of one half wavelength of the emitted
light. One light source is placed to the left of the detectors and the other
light source is placed to the right of the
detectors. Two beams of light pass by the detectors. One beam is going from
left to right, and the other is going from
right to left. The phase of the two beams is adjusted so that each of the
peaks of the two waves meet at the detectors.
S ------> d d d d d d <------- S
Experiment as viewed by an observer with velocity -V relative to the rest
frame:
Let the experimental setup move from left to right with a velocity V relative
to an observer. Let the distance between
detectors be L (possibly some function of V). For this observer, wave peaks
from the left light source travel a distance
greater than L as the peak goes from detector to detector (since the detector
is moving to the right). And wave peaks
from the right light source travels a distance less than L as the peak goes
from detector to detector. The following
equations are used to compute this distance.
For the beam traveling from left to right, we have
1. c * t = L + (v * t)
2. t = L / (c - V)
3. distance = (c * L) / (c - V) since the speed of light is constant
according to Einstein.
For the beam traveling from right to left, we have (not necessarily the same
t as in equations 1 to 3 )
4. c * t = L - (v * t)
5. t = L / (c + V)
6. distance = (c * L) / (c + V) again since the speed of light is
constant
Without making hypotheses about how measurements in the rest frame of the
setup transform to measurements in the
moving frame, we can still come to several conclusions. First, let's number
the pulses from the left and right light
sources and number the detectors as follows:
L5 L4 L3 L2 L1 L0 ------->
d5 d4 d3 d2 d1 d0
<------------ RO
R1 R2
where L0 is the first peak from the left light source, R0 is the first peak
from the right light source and d0 through d5 are
the detectors. We start the analysis when LO and RO meet at detector d0:
Event 0 (when R0, L0 meet at d0) as viewed with velocity -V relative to the
setup
L4 L3 L2 L1 L0
d5 d4 d3 d2 d1 d0
R0 R1
We can setup equations for the distance between the L0 and L1, and R0 and R1
when event 0 occurs. The distance
between d1 and d0 is L. In this reference frame, the d's are moving to the
right with velocity V, and R0 is moving to the
left at the speed of light. After event 0 occurs, from equation 6, we see
that R0 travels a distance = cL / (c + V) to strike
detector d1. Also, after event 0 occurs, L1 must travel the same distance as
R0 to hit d1 (since R0 and L1 both have the
same speed, c, according to Einstein). Therefore, when event 0 occurs, L1
must be 2cL / (c + V) to the left of L0 as
measured in this frame. The distance between peaks R0 and R1 is computed in
an analogous fashion giving:
2cL / (c - V)
Using, these equations, and letting V = c/2 we can graphically depict
subsequent events.
Event 0 (when R0, L0 meet at d0) viewed in moving frame (-V relative to the
setup)
L4 L3 L2 L1 L0
d5 d4 d3 d2 d1 d0
R0 R1
Event 1 ( when R0, L1 meet at d1) viewed in moving frame (-V relative to the
setup)
L4 L3 L2 L1 L0
d5 d4 d3 d2 d1 d0
R0 R1
Event 2 ( when R0, L2 meet at d2 ) viewed in moving frame (-V relative to
the setup)
L4 L3 L2 L1 L0
d5 d4 d3 d2 d1 d0
R0 R1
Event 3 ( when R0, L3 meet at d3 ) viewed in moving frame (-V relative to
the setup)
L4 L3 L2 L1 L0
d5 d4 d3 d2 d1 d0
R0 R1
Event 4 ( when R0, L4 meet at d4 ) viewed in moving frame (-V relative to
the setup)
L4 L3 L2 L1 L0
d5 d4 d3 d2 d1 d0
R0 R1
Here are the same events viewed in the rest frame of the setup
Event 0 ( when R0, L0 meet at d0 ) - viewed in rest frame of the setup
L4 L3 L2 L1 L0
d5 d4 d3 d2 d1 d0
R0 R1 R2 R1 R0
Event 1 ( when R0, L1 meet at d1 ) - viewed in rest frame of the setup
L4 L3 L2 L1 L0
d5 d4 d3 d2 d1 d0
R0 R1 R2 R1 R0
Event 2 ( when R0, L2 meet at d2 ) - viewed in rest frame of the setup
L4 L3 L2 L1 L0
d5 d4 d3 d2 d1 d0
R0 R1 R2 R1 R0
Event 3 ( when R0, L3 meet at d3 ) - viewed in rest frame of the setup
L4 L3 L2 L1 L0
d5 d4 d3 d2 d1 d0
R0 R1 R2 R1 R0
Event 4 (when R0, L4 meet at d4 ) - viewed in rest frame of the setup
L4 L3 L2 L1 L0
d5 d4 d3 d2 d1 d0
R0 R1 R2 R3 R4
The Problem:
In the rest frame of the setup, we have the following sequence
Event 0: LO,R0&d0
Event 1: L1,R0&d1
Event 2: L2,R0&d2 - L1,R1&d0
Event 3: L3,R0&d3 - L2,R1&d1
Event 4: L4,R0&d4 - L3,R1&d2 L2,R2&d0
In tthe moving frame, we have the following sequence of events:
Event 0: L0,R0&d0
Event 1: L1,R0&d1
Event 2: L2,R0&d2
Event 3: L3,R0&d3
Event 4: L4,R0&d4 L1,R1&d0
In the rest frame of the setup, peaks L1 and R1 meet at d0 (event 2) before
peaks L3 and R0 meet at d3 (event 3).
However, in the moving frame the order is reversed: peaks L1 and R1 meet at
d0 (event 4) after peaks L3 and R0 meet at
d3 (event 3). Note: according to Einstein's theory, L1,R1&d0 and L2,R0,d2
are simultaneous events as viewed in the rest
frame of the setup, whereas L1,R0&d0 and L4,R0&d4 are simultaneous events in
the moving reference frame.
Let's say detector d0 fails when* L3 and R0 meet at d3. An observer in the
rest frame of the setup says that peaks L1
and R1 were detected at d0 (Event 2), since the detector doesn't fail until
after this event. An observer in the moving
reference frame says they were not detected because the detector had failed
before Event 4 occurs. Both observations
cannot be true.
*Rev 11/6/99 the phrasing was changed from "just after" to "when"
because of comments about imprecise meaning
of "just after".
If you see an error in this analysis, please email me with the explanation
(Unlike Niels Bohr, assume that I have zero
knowledge and limited intelligence). Thanks, Email: David Seppala
Paul B. Andersen
>
> Special relativity leads to situations which appear logically incorrect
> to me. I created a gedunken experiment that leads to a logical
> contradiction. I am hoping that someone more knowledgeable can point
> out the error I'm making. The problem is listed on my website at:
> http://www.2400ad.com/einstein
> Any insights will be appreciated
> Thanks,
> David Seppala
That's an easy one. :-)
I cannot see why the complicted setup was necessary, though.
It could be stated like this:
Given three events E1, E2, and E3 separated by a space like intervals.
The events are detected by detectors d1, d2 and d3 respectively.
The detectors are stationary in frame A.
In frame A, the sequence of events is: E1 - E2 - E3
In frame B, the sequence of events is: E3 - E2 - E1
Now your "problem":
Detector d1 fails when [sic] event E2 occurs.
So in frame A, the event E1 will be detected since the detector fails
after the event E1.
But in frame B, the event E1 will not be detected since the detector
fails before event E1 occur.
Both cannot be true, so where is the error?
I strongly suspect that David Seppala knows the answer and is trolling.
However, I will take his words: "assume that I have zero knowledge
and limited intelligence" litterally. They may be true! :-)
The event D1 "detector d1 fails" is separated from the event E1 by a time like
interval (detector present at both events). Thus the sequence of events
E1 - D1 is the same in all frames. If we assume that D1 is after E1,
the sequence of events must be:
Frame A: E1 - E2+D1 - E3
Frame B: E3 - E2 - E1 - D1
The simple point is of course that the statement:
"Detector d1 fails when event E2 occurs"
can only be true in one of the frames, here assumed to be in frame A.
Paul
and...@attglobal.net
>
> In response I posted this problem in this newsgroup, although I'm not certain
> how the diagrams will show up since they are generated using text and spacing
> so things might get screwed up. If they do, and you want a display of the
> diagrams, go to http://www.2400ad.com/einstein - I know how to better
> control the spacing of text there. You can skip the editorilizing I do at
> the intro do the problem (but I like the Einstein joke-. Anyway here's the
> problem
>
> The gedanken experiment presented here is based on a statement made by
> Einstein in Special Relativity regarding the
> measurement of time at two spatially separated points A and B:
>
> We have not defined a common "time" for A and B, for the latter cannot be
> defined at all unless we
> establish by definition that the "time" required by light to travel from
> A to B equals the "time" it requires to
> travel from B to A.
>
> This statement is a hypothesis and is not true by definition.
It's a hypothesis but that hardly means that it's "not true by
definition"
In logic, the only things that have that property are contradictions.
For example, claiming that something is true AND false.
> Problems occur
> with Einstein's notions of space and time
> when clocks are compared using the one way transmission of light instead of
> the transmission from A to B and back to A
> again. Einstein states a common time cannot be defined without this round
> trip definition. However, we can setup a
> simple experiment using the one way transmission of light instead of the
> round trip and see if Einstein's theory holds.
>
I deleted the experiment because it's fairly long and people
can look it up in your posting or on your website.
> The Problem:
> In the rest frame of the setup, we have the following sequence
> Event 0: LO,R0&d0
> Event 1: L1,R0&d1
> Event 2: L2,R0&d2 - L1,R1&d0
> Event 3: L3,R0&d3 - L2,R1&d1
> Event 4: L4,R0&d4 - L3,R1&d2 L2,R2&d0
>
Right away, the terminology that you're using is not
consistent with relativity. In relativity, an event
is something that occurs at a particular place at a
particular time. When you write
Event 2: L2,R0&d2 - L1,R1&d0
you're implying that L2,R0&d2 and L1,R1&d0 are the same event
but they only happen at the same time in this frame, not
at the same place.
> In tthe moving frame, we have the following sequence of events:
> Event 0: L0,R0&d0
> Event 1: L1,R0&d1
> Event 2: L2,R0&d2
> Event 3: L3,R0&d3
> Event 4: L4,R0&d4 L1,R1&d0
>
I didn't go through how you worked these out since I found
your discussion of the experiment confusing. I worked it
out from scratch my own way. I agree with the sequence
of events that you got for the original frame, but not
with the one you get in the other frame. But that's a minor
point. I will concede that a Lorentz transformation may
reverse the time ordering of spacelike separated events.
For people unfamiliar with the terminology, spacelike
separated events are are sufficiently separated in space
that the light travel time between them is greater
than the difference in the event times. In relativity,
information can't be sent between two such events, so
that their time ordering is irrelevant.
> In the rest frame of the setup, peaks L1 and R1 meet at d0 (event 2) before
> peaks L3 and R0 meet at d3 (event 3).
> However, in the moving frame the order is reversed: peaks L1 and R1 meet at
> d0 (event 4) after peaks L3 and R0 meet at
> d3 (event 3). Note: according to Einstein's theory, L1,R1&d0 and L2,R0,d2
> are simultaneous events as viewed in the rest
> frame of the setup, whereas L1,R0&d0 and L4,R0&d4 are simultaneous events in
> the moving reference frame.
>
> Let's say detector d0 fails when* L3 and R0 meet at d3. An observer in the
> rest frame of the setup says that peaks L1
> and R1 were detected at d0 (Event 2), since the detector doesn't fail until
> after this event. An observer in the moving
> reference frame says they were not detected because the detector had failed
> before Event 4 occurs. Both observations
> cannot be true.
As I said, I don't agree with the ordering that you got for the
events in the second frame. But even assuming that it's correct,
I don't see the event "detector fails" anywhere in the sequence.
You told us that it's simultaneous with L3,R0&d3 in the original
frame, but they don't occur at the same place in the original frame.
They are two distinct events, not one event.
Therefore, when you transform the spacetime coordinates to the
second frame, the events L3,R0&d3 and "detector fails" occur
at different times in the two frames.
In essence, you're assuming that both frames observe the
speed of light to be c. This forces relativity of simultaneity
to apply when you change frames. This can lead to the time ordering
of spacelike separated events between the two frames.
But then you go and assume that L3,R0&d3 and "detector fails" occur
at the same time in both frames. So you're implicitly
using relativity of simultaneity to get a result and then
assuming simultaneity is absolute to interpret the result.
So there's a contradiction here, but you introduced it.
Also, just for the record, the events L1,R1&d0 and "detector fails"
occur at different times at the same place, the location of
detector 0. The displacement between the
events is time like. Lorentz
transformations do not reverse the time ordering of timelike separated
events, only spacelike separated ones.
John Anderson
Stephen
> David Seppala wrote:
> >
>[snip]
> >
> > This statement is a hypothesis and is not true by definition.
>
> It's a hypothesis but that hardly means that it's "not true by
> definition"
> In logic, the only things that have that property are contradictions.
I think he meant "not (true by definition)" rather than "(not true), by
definition".
Doesn't affect the rest of the argument though.
--
"The end of our foundation is knowledge of causes,
and secret motions of things; and the enlarging of the bounds
of human empire, to the effecting of all things possible."
- Francis Bacon, "New Atlantis".
and...@attglobal.net
>
> In article <38262F...@attglobal.net>, and...@attglobal.net wrote:
>
> > David Seppala wrote:
> > >
> > >
> > > This statement is a hypothesis and is not true by definition.
> >
> > It's a hypothesis but that hardly means that it's "not true by
> > definition"
> > In logic, the only things that have that property are contradictions.
>
> definition".
> Doesn't affect the rest of the argument though.
>
I didn't think of that way because how can anything in physics
be true by definition? Mathematical axioms are true by definition
unless they contradict each other,
but physics postulates always have to agree with experiment
even if they contain no logical contradictions.
John Anderson
Gerry Quinn
>>
>> > David Seppala wrote:
>> > >
>> > >
>> > > This statement is a hypothesis and is not true by definition.
>> >
>> > It's a hypothesis but that hardly means that it's "not true by
>> > definition"
>> > In logic, the only things that have that property are contradictions.
>>
>> definition".
>> Doesn't affect the rest of the argument though.
>>
>
>I didn't think of that way because how can anything in physics
>be true by definition? Mathematical axioms are true by definition
>unless they contradict each other,
>but physics postulates always have to agree with experiment
>even if they contain no logical contradictions.
>
>John Anderson
There are examples. "The speed of light is c" for example, is 'true by
definition' in a relativistic context, but would not be true in an ether
model in which gravity was considered to reduce the speed of light.
Experiment would support either view in the context of their respective
theories. For example, it is relatively easy to detect that light is
slowed and refracted as it passes close to the Sun - but in a
relativistic context it is said instead that there is more space near
the Sun, and it is actually travelling in a straight line at c.
- Gerry Quinn
and...@attglobal.net
>
> In article <3827B5...@attglobal.net>, and...@attglobal.net wrote:
> >Stephen wrote:
> >>
> >>
> >> > David Seppala wrote:
> >> > >
> >> > >
> >> > > This statement is a hypothesis and is not true by definition.
> >> >
> >> > It's a hypothesis but that hardly means that it's "not true by
> >> > definition"
> >> > In logic, the only things that have that property are contradictions.
> >>
> >> definition".
> >> Doesn't affect the rest of the argument though.
> >>
> >
> >I didn't think of that way because how can anything in physics
> >be true by definition? Mathematical axioms are true by definition
> >unless they contradict each other,
> >but physics postulates always have to agree with experiment
> >even if they contain no logical contradictions.
> >
> >John Anderson
>
> There are examples. "The speed of light is c" for example, is 'true by
> definition' in a relativistic context, but would not be true in an ether
> model in which gravity was considered to reduce the speed of light.
> Experiment would support either view in the context of their respective
> theories.
If you set things up so something is always measured true,
then it really isn't a postulate anymore because you can't test it.
You have incorporated it into the primitive
terms of the theory.
> For example, it is relatively easy to detect that light is
> slowed and refracted as it passes close to the Sun - but in a
> relativistic context it is said instead that there is more space near
> the Sun, and it is actually travelling in a straight line at c.
>
GR explains this effect, but not in terms of slowing of light
in local inertial lines. The effect really comes about
because local inertial frames near different events are accelerating
wrt each other.
John Anderson