| Topic: |
Science > Physics |
| User: |
"muser" |
| Date: |
09 Jan 2005 04:17:56 PM |
| Object: |
Androcles and draper. |
Why don't you continue your argument, but put it in layman terms. For
instance is time a vector? Androcles do you mean that to say that time
isn't flowing forward and can't be used in any equation, because of
how we perceive it (cause and effect)?
Draper is there any reference frames for ensteins special theory of
relativity you could use to persuade the layman of your convictions?
.
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| User: "RP" |
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| Title: Re: Androcles and draper. |
09 Jan 2005 09:19:55 PM |
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muser wrote:
Why don't you continue your argument, but put it in layman terms. For
instance is time a vector? Androcles do you mean that to say that time
isn't flowing forward and can't be used in any equation, because of
how we perceive it (cause and effect)?
Draper is there any reference frames for ensteins special theory of
relativity you could use to persuade the layman of your convictions?
Androcles doesn't understand yet that *time* as it enters into the
equations of physics, is not equivalent to our perceived *flow of
time*, the latter being a process rather than a dimensional quantity,
one that involves both time and space. According to Maxwell's
equations the arrow of time is a line rather than a ray. I'm not sure
how this plays on BB theory, but surely it can't bode well.
As noted in the Wheeler-Feynman absorber theory, causality runs both
ways equally well. Now keeping in mind that if we only exist in the
moment (in the sense of the awareness of our existence), and keeping
in mind that it is entirely possible that in that moment we scan what
is recorded in memory as a static 4D graphical representation of that
is only interpreted as 3D plus time, then it is entirely possible that
we only *conclude* that we are moving exclusively forward in time.
IOW, we would have precisely the same thoughts in any given
vanishingly small interval whether time were progressing forward or
backward. But since in backward time our memories are undergoing
erasure, then we can only base our conclusions on what is contained in
memory in that moment, that being only those events that occurred
backward in time beginning from that moment, i.e. those memories are
necessarily of the past.
OTOH, unless information is equally erased from spacetime as well,
then one might suspect that the information of the future could very
well be embedded in the past when tracing it through backward time,
just as it is embedded in the future in forward time. How to extract
that information is another matter, and of course if it were possible
to do so, even in theory, it would be logically constrained to
discovery only in instances such that the previous knowledge obtained
was of systems outside of our light cone, and thus unalterable. But
once again I digress. Back to the question: I don't agree with
Androcles that time isn't a vector, but I'll keep my mind open to
other possibilities.
Richard Perry
.
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| User: "Androcles" |
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| Title: Re: Androcles and draper. |
10 Jan 2005 05:21:44 AM |
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"RP" <no_mail_no_spam@yahoo.com> wrote in message
news:34eacpF4adamuU1@individual.net...
muser wrote:
Why don't you continue your argument, but put it in layman terms. For
instance is time a vector? Androcles do you mean that to say that
time
isn't flowing forward and can't be used in any equation, because of
how we perceive it (cause and effect)?
Draper is there any reference frames for ensteins special theory of
relativity you could use to persuade the layman of your convictions?
Androcles doesn't understand yet that *time* as it enters into the
equations of physics, is not equivalent to our perceived *flow of
time*, the latter being a process rather than a dimensional quantity,
one that involves both time and space.
Androcles understands all too well that "our" flow of time is physics
and a dimensional quantity, not just some 't' stuck in an equation to
be treated as if it were a distance. Time is NOT a vector because it
is NOT flowing backwards.
According to Maxwell's equations the arrow of time is a line rather
than a ray. I'm not sure how this plays on BB theory, but surely it
can't bode well.
"It is known that Maxwell's electrodynamics--as usually understood
at the present time--when applied to moving bodies, leads to
asymmetries
which do not appear to be inherent in the phenomena." - Einstein.
As noted in the Wheeler-Feynman absorber theory, causality runs both
ways equally well. Now keeping in mind that if we only exist in the
moment (in the sense of the awareness of our existence), and keeping
in mind that it is entirely possible that in that moment we scan what
is recorded in memory as a static 4D graphical representation of that
is only interpreted as 3D plus time, then it is entirely possible that
we only *conclude* that we are moving exclusively forward in time.
IOW, we would have precisely the same thoughts in any given
vanishingly small interval whether time were progressing forward or
backward. But since in backward time our memories are undergoing
erasure, then we can only base our conclusions on what is contained in
memory in that moment, that being only those events that occurred
backward in time beginning from that moment, i.e. those memories are
necessarily of the past.
OTOH, unless information is equally erased from spacetime as well,
then one might suspect that the information of the future could very
well be embedded in the past when tracing it through backward time,
just as it is embedded in the future in forward time. How to extract
that information is another matter, and of course if it were possible
to do so, even in theory, it would be logically constrained to
discovery only in instances such that the previous knowledge obtained
was of systems outside of our light cone, and thus unalterable. But
once again I digress. Back to the question: I don't agree with
Androcles that time isn't a vector, but I'll keep my mind open to
other possibilities.
Richard Perry
I deal in science and mathematics. Conjectural sci-fi I leave to
Richard Perry.
Androcles.
.
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| User: "RP" |
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| Title: Re: Androcles and draper. |
10 Jan 2005 01:23:06 PM |
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Androcles wrote:
"RP" <no_mail_no_spam@yahoo.com> wrote in message
news:34eacpF4adamuU1@individual.net...
muser wrote:
Why don't you continue your argument, but put it in layman terms. For
instance is time a vector? Androcles do you mean that to say that
time
isn't flowing forward and can't be used in any equation, because of
how we perceive it (cause and effect)?
Draper is there any reference frames for ensteins special theory of
relativity you could use to persuade the layman of your convictions?
Androcles doesn't understand yet that *time* as it enters into the
equations of physics, is not equivalent to our perceived *flow of
time*, the latter being a process rather than a dimensional quantity,
one that involves both time and space.
Androcles understands all too well that "our" flow of time is physics
and a dimensional quantity, not just some 't' stuck in an equation to
be treated as if it were a distance. Time is NOT a vector because it
is NOT flowing backwards.
According to Maxwell's equations the arrow of time is a line rather
than a ray. I'm not sure how this plays on BB theory, but surely it
can't bode well.
"It is known that Maxwell's electrodynamics--as usually understood
at the present time--when applied to moving bodies, leads to
asymmetries
which do not appear to be inherent in the phenomena." - Einstein.
And after his modification the asymmetries disappeared.
As noted in the Wheeler-Feynman absorber theory, causality runs both
ways equally well. Now keeping in mind that if we only exist in the
moment (in the sense of the awareness of our existence), and keeping
in mind that it is entirely possible that in that moment we scan what
is recorded in memory as a static 4D graphical representation of that
is only interpreted as 3D plus time, then it is entirely possible that
we only *conclude* that we are moving exclusively forward in time.
IOW, we would have precisely the same thoughts in any given
vanishingly small interval whether time were progressing forward or
backward. But since in backward time our memories are undergoing
erasure, then we can only base our conclusions on what is contained in
memory in that moment, that being only those events that occurred
backward in time beginning from that moment, i.e. those memories are
necessarily of the past.
OTOH, unless information is equally erased from spacetime as well,
then one might suspect that the information of the future could very
well be embedded in the past when tracing it through backward time,
just as it is embedded in the future in forward time. How to extract
that information is another matter, and of course if it were possible
to do so, even in theory, it would be logically constrained to
discovery only in instances such that the previous knowledge obtained
was of systems outside of our light cone, and thus unalterable. But
once again I digress. Back to the question: I don't agree with
Androcles that time isn't a vector, but I'll keep my mind open to
other possibilities.
Richard Perry
I deal in science and mathematics. Conjectural sci-fi I leave to
Richard Perry.
Androcles.
It isn't conjecture to state that the flow of time that we perceive is
a perception, that being a tautology. And since it is a perception,
then it should be thoroughly examined in light of the science and
mathematics before even attempting to judge the qualities of the
object of that perception.
Time, in the mathematical/physical sense, is a dimensional quantity
representing comparative changes in two systems over two sets of
simultaneous states of the two. One of these systems is taken as a
uniform standard in order to provide us with the *t* to plug into our
equations. The change is synonymous with flow of time, but the change
is itself is a physical process, and as such requires displacements
not only in time but also in space. This change that we *percieve* as
a flow of time is more accurately the *observance* of processes, all
of which incorporate changes in space and time (spacetime) wrt our
standards of measure.
Thus the *flow of time* isn't even a quantity, let alone a vector.
Time OTOH *is* a vector, and it doesn't flow. The expression *flow of
time* is absolutely meaningless if taken literally. Time won't run
down a trough. OTOH water will, and that process can be quantified,
but psychologically that process is incorrectly associated with time
itself, and this is done without regard to the changes in position
that have also occurred during the same process. The flow of water
involves changes in position of particles wrt time, i.e. motion,
and thus microscopically the term flow is equivalent to a complex
drift of particles wrt a frame of reference. Are you still convinced
that time can flow? Does it consist of particles in motion? Does the
term flow even sensibly
apply to time? No.
The *flow of time* falls into the same category as
*free will*, both meaningless word combinations that deluded souls
have forced meaning upon.
Richard Perry
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| User: "RP" |
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| Title: Re: Androcles and draper. |
10 Jan 2005 01:17:17 PM |
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Androcles wrote:
"RP" <no_mail_no_spam@yahoo.com> wrote in message
news:34eacpF4adamuU1@individual.net...
muser wrote:
Why don't you continue your argument, but put it in layman terms. For
instance is time a vector? Androcles do you mean that to say that
time
isn't flowing forward and can't be used in any equation, because of
how we perceive it (cause and effect)?
Draper is there any reference frames for ensteins special theory of
relativity you could use to persuade the layman of your convictions?
Androcles doesn't understand yet that *time* as it enters into the
equations of physics, is not equivalent to our perceived *flow of
time*, the latter being a process rather than a dimensional quantity,
one that involves both time and space.
Androcles understands all too well that "our" flow of time is physics
and a dimensional quantity, not just some 't' stuck in an equation to
be treated as if it were a distance. Time is NOT a vector because it
is NOT flowing backwards.
According to Maxwell's equations the arrow of time is a line rather
than a ray. I'm not sure how this plays on BB theory, but surely it
can't bode well.
"It is known that Maxwell's electrodynamics--as usually understood
at the present time--when applied to moving bodies, leads to
asymmetries
which do not appear to be inherent in the phenomena." - Einstein.
And after his modification the asymmetries disappeared.
As noted in the Wheeler-Feynman absorber theory, causality runs both
ways equally well. Now keeping in mind that if we only exist in the
moment (in the sense of the awareness of our existence), and keeping
in mind that it is entirely possible that in that moment we scan what
is recorded in memory as a static 4D graphical representation of that
is only interpreted as 3D plus time, then it is entirely possible that
we only *conclude* that we are moving exclusively forward in time.
IOW, we would have precisely the same thoughts in any given
vanishingly small interval whether time were progressing forward or
backward. But since in backward time our memories are undergoing
erasure, then we can only base our conclusions on what is contained in
memory in that moment, that being only those events that occurred
backward in time beginning from that moment, i.e. those memories are
necessarily of the past.
OTOH, unless information is equally erased from spacetime as well,
then one might suspect that the information of the future could very
well be embedded in the past when tracing it through backward time,
just as it is embedded in the future in forward time. How to extract
that information is another matter, and of course if it were possible
to do so, even in theory, it would be logically constrained to
discovery only in instances such that the previous knowledge obtained
was of systems outside of our light cone, and thus unalterable. But
once again I digress. Back to the question: I don't agree with
Androcles that time isn't a vector, but I'll keep my mind open to
other possibilities.
Richard Perry
I deal in science and mathematics. Conjectural sci-fi I leave to
Richard Perry.
Androcles.
It isn't conjecture to state that the flow of time that we perceive is
a perception, that being a tautology. And since it is a perception,
then it should be thoroughly examined in light of the science and
mathematics before even attempting to judge the qualities of the
object of that perception.
Time, in the mathematical/physical sense, is a dimensional quantity
representing comparative changes in two systems over two sets of
simultaneous states of each. One of these systems is taken as a
uniform standard in order to provide us with the *t* to plug into our
equations. The change is synonymous with flow of time, but the change
is itself is a physical process, and as such requires displacements
not only in time but also in space. This change that we *percieve* as
a flow of time is more accurately the *observance* of processes, all
of which incorporate changes in space and time (spacetime) wrt our
standards of measure.
Thus the *flow of time* isn't even a quantity, let alone a vector.
Time OTOH *is* a vector, and it doesn't flow. The expression *flow of
time* is absolutely meaningless if taken literally. Time won't run
down a trough. OTOH after will and that flow can be quantified, but
psychologically that process is incorrectly associated with time
itself, and this is done without regard to the changes in position
that have also occurred in the same process. The flow of water can be
quantified, but it isn't a quantity itself, it's a process, one that
involves just changes in position of particles wrt time, i.e. motion,
and thus microscopically the term flow is equivalent to complex
motions of particles. Are you still convinced that time can flow? Does
it consist of particles in motion? Does the term flow even sensibly
apply to time. No. The *flow of time* falls into the same category as
*free will*, both meaningless word combinations that deluded souls
have forced meaning upon.
Richard Perry
.
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| User: "Androcles" |
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| Title: Re: Androcles and draper. |
10 Jan 2005 01:58:18 PM |
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"RP" <no_mail_no_spam@yahoo.com> wrote in message
news:34g2g2F4arejkU1@individual.net...
Androcles wrote:
"RP" <no_mail_no_spam@yahoo.com> wrote in message
news:34eacpF4adamuU1@individual.net...
muser wrote:
Why don't you continue your argument, but put it in layman terms.
For
instance is time a vector? Androcles do you mean that to say that
time
isn't flowing forward and can't be used in any equation, because of
how we perceive it (cause and effect)?
Draper is there any reference frames for ensteins special theory of
relativity you could use to persuade the layman of your
convictions?
Androcles doesn't understand yet that *time* as it enters into the
equations of physics, is not equivalent to our perceived *flow of
time*, the latter being a process rather than a dimensional quantity,
one that involves both time and space.
Androcles understands all too well that "our" flow of time is physics
and a dimensional quantity, not just some 't' stuck in an equation to
be treated as if it were a distance. Time is NOT a vector because it
is NOT flowing backwards.
According to Maxwell's equations the arrow of time is a line rather
than a ray. I'm not sure how this plays on BB theory, but surely it
can't bode well.
"It is known that Maxwell's electrodynamics--as usually understood
at the present time--when applied to moving bodies, leads to
asymmetries
which do not appear to be inherent in the phenomena." - Einstein.
And after his modification the asymmetries disappeared.
He introduced new ones.
As noted in the Wheeler-Feynman absorber theory, causality runs both
ways equally well. Now keeping in mind that if we only exist in the
moment (in the sense of the awareness of our existence), and keeping
in mind that it is entirely possible that in that moment we scan what
is recorded in memory as a static 4D graphical representation of that
is only interpreted as 3D plus time, then it is entirely possible
that we only *conclude* that we are moving exclusively forward in
time. IOW, we would have precisely the same thoughts in any given
vanishingly small interval whether time were progressing forward or
backward. But since in backward time our memories are undergoing
erasure, then we can only base our conclusions on what is contained
in memory in that moment, that being only those events that occurred
backward in time beginning from that moment, i.e. those memories are
necessarily of the past.
OTOH, unless information is equally erased from spacetime as well,
then one might suspect that the information of the future could very
well be embedded in the past when tracing it through backward time,
just as it is embedded in the future in forward time. How to extract
that information is another matter, and of course if it were possible
to do so, even in theory, it would be logically constrained to
discovery only in instances such that the previous knowledge obtained
was of systems outside of our light cone, and thus unalterable. But
once again I digress. Back to the question: I don't agree with
Androcles that time isn't a vector, but I'll keep my mind open to
other possibilities.
Richard Perry
I deal in science and mathematics. Conjectural sci-fi I leave to
Richard Perry.
Androcles.
It isn't conjecture to state that the flow of time that we perceive is
a perception, that being a tautology. And since it is a perception,
then it should be thoroughly examined in light of the science and
mathematics before even attempting to judge the qualities of the
object of that perception.
I agree, use science and mathematics. Time is not a vector, so
dont treat it as such.
Time, in the mathematical/physical sense, is a dimensional quantity
representing comparative changes in two systems over two sets of
simultaneous states of each. One of these systems is taken as a
uniform standard in order to provide us with the *t* to plug into our
equations.
That system being the entire universe.
The change is synonymous with flow of time, but the change is itself
is a physical process, and as such requires displacements not only in
time but also in space. This change that we *percieve* as a flow of
time is more accurately the *observance* of processes, all of which
incorporate changes in space and time (spacetime) wrt our standards of
measure.
Sure, and the orbits of the planets, the rotation of the Earth are the
motions by which we observe the changes.
Thus the *flow of time* isn't even a quantity, let alone a vector.
Time OTOH *is* a vector, and it doesn't flow.
It is only a vector if you can get back to when you were.
The expression *flow of time* is absolutely meaningless if taken
literally. Time won't run down a trough.
Water will, but it won't run up one.
OTOH after will and that flow can be quantified, but psychologically
that process is incorrectly associated with time itself, and this is
done without regard to the changes in position that have also occurred
in the same process. The flow of water can be quantified, but it isn't
a quantity itself, it's a process, one that involves just changes in
position of particles wrt time, i.e. motion, and thus microscopically
the term flow is equivalent to complex motions of particles. Are you
still convinced that time can flow? Does it consist of particles in
motion? Does the term flow even sensibly apply to time. No. The *flow
of time* falls into the same category as *free will*, both meaningless
word combinations that deluded souls have forced meaning upon.
Richard Perry
Free will is the option not to do something.
Androcles.
.
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| User: "PDraper" |
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| Title: Re: Androcles and draper. |
11 Jan 2005 10:03:58 AM |
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On 1/10/05 6:21 AM, in article
cztEd.94837$48.68056@fe1.news.blueyonder.co.uk, "Androcles"
<dummy@dummy.net> wrote:
"RP" <no_mail_no_spam@yahoo.com> wrote in message
news:34eacpF4adamuU1@individual.net...
muser wrote:
Why don't you continue your argument, but put it in layman terms. For
instance is time a vector? Androcles do you mean that to say that
time
isn't flowing forward and can't be used in any equation, because of
how we perceive it (cause and effect)?
Draper is there any reference frames for ensteins special theory of
relativity you could use to persuade the layman of your convictions?
Androcles doesn't understand yet that *time* as it enters into the
equations of physics, is not equivalent to our perceived *flow of
time*, the latter being a process rather than a dimensional quantity,
one that involves both time and space.
Androcles understands all too well that "our" flow of time is physics
and a dimensional quantity, not just some 't' stuck in an equation to
be treated as if it were a distance. Time is NOT a vector because it
is NOT flowing backwards.
According to Maxwell's equations the arrow of time is a line rather
than a ray. I'm not sure how this plays on BB theory, but surely it
can't bode well.
"It is known that Maxwell's electrodynamics--as usually understood
at the present time--when applied to moving bodies, leads to
asymmetries
which do not appear to be inherent in the phenomena." - Einstein.
As noted in the Wheeler-Feynman absorber theory, causality runs both
ways equally well. Now keeping in mind that if we only exist in the
moment (in the sense of the awareness of our existence), and keeping
in mind that it is entirely possible that in that moment we scan what
is recorded in memory as a static 4D graphical representation of that
is only interpreted as 3D plus time, then it is entirely possible that
we only *conclude* that we are moving exclusively forward in time.
IOW, we would have precisely the same thoughts in any given
vanishingly small interval whether time were progressing forward or
backward. But since in backward time our memories are undergoing
erasure, then we can only base our conclusions on what is contained in
memory in that moment, that being only those events that occurred
backward in time beginning from that moment, i.e. those memories are
necessarily of the past.
OTOH, unless information is equally erased from spacetime as well,
then one might suspect that the information of the future could very
well be embedded in the past when tracing it through backward time,
just as it is embedded in the future in forward time. How to extract
that information is another matter, and of course if it were possible
to do so, even in theory, it would be logically constrained to
discovery only in instances such that the previous knowledge obtained
was of systems outside of our light cone, and thus unalterable. But
once again I digress. Back to the question: I don't agree with
Androcles that time isn't a vector, but I'll keep my mind open to
other possibilities.
Richard Perry
I deal in science and mathematics. Conjectural sci-fi I leave to
Richard Perry.
Androcles.
Androcles questioned (actually more strongly than that) whether time can be
included in a 4-D spacetime vector space.
As a positional space, I don't think there's an issue, though I have to
admit I'm extrapolating Androcles's thoughts on this without his blessing.
It's perfectly rational to have a negative time *location* for an event.
That's simply a matter of where you place your origin.
The issue comes when you ask whether you can construct a vector space of
spacetime *displacements*, which physically speaking represent a possible
trajectory of a physical object. Androcles's objection at this point is that
there is no permissible timelike trajectory with a minus sign in the time
component -- at least for positive-energy particles, or (said differently)
non-quantum objects. Physical objects do not move backward in time. Thus,
while positive timelike vectors are perfectly fine, negative timelike
vectors are physically excluded. This, then, raises the issue of whether we
can treat physically accessible spacetime displacements as a vector space,
because there is a class of displacements without an additive inverse.
The same argument can be applied to 4-velocities, of course, and
4-accelerations.
This begs the question whether it's still ok to treat the arrow of time as a
separate constraint imposed on spacetime. If it is, then arriving at
spacetime is a two-step process -- building a well-defined vector space (or
a manifold in GR) -- and then imposing the arrow of time.
I confess I don't really have a good answer for Androcles here, and I'm
still thinking about it. Doesn't mean he's right. But it does mean I don't
have a good explanation for him, either.
PD
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| User: "Androcles" |
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| Title: Re: Androcles and draper. |
11 Jan 2005 11:33:07 AM |
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"PDraper" <pdraper@yahoo.com> wrote in message
news:BE09631E.E41%pdraper@yahoo.com...
Androcles questioned (actually more strongly than that) whether time
can be
included in a 4-D spacetime vector space.
That's right. Time is not a vector and cannot be an element of a vector.
As a positional space, I don't think there's an issue, though I have
to
admit I'm extrapolating Androcles's thoughts on this without his
blessing.
It's perfectly rational to have a negative time *location* for an
event.
That's simply a matter of where you place your origin.
Origins can be returned to.
Force is a vector, two opposing forces can cancel.
Velocity is a vector, I can walk to the stern of ship and remain
opposite
a pier as the ship passes it.
I can refer to the pier and remain at the pier.
I can refer to 'then', but I cannot remain at 'then'.
Time is not a vector.
(x,y, xy) is not a vector, the third term is dependent on the first two.
(-1, 1, 1) + (1, 1, 1) = (0,2,2) and xy = -1. It is not equal to 2.
Similarly,
c = x/t, and ct = x.
(x,y, ct) cannot be a vector. It is effectively (x,y,x).
(299792458, 0, 299792458*1) is not a vector,even if you use
units of 299,792,458 metres and write it as
(1,0,1*1)
By multiplying by 2, you obtain (2,0,2) and ct is dependent on x.
There is no coordinate in "spacetime" corresponding to (2,0,1).
Therefore time cannot be a vector.
The issue comes when you ask whether you can construct a vector space
of
spacetime *displacements*, which physically speaking represent a
possible
trajectory of a physical object. Androcles's objection at this point
is that
there is no permissible timelike trajectory with a minus sign in the
time
component -- at least for positive-energy particles, or (said
differently)
non-quantum objects.
Correct.
Physical objects do not move backward in time. Thus,
while positive timelike vectors are perfectly fine, negative timelike
vectors are physically excluded. This, then, raises the issue of
whether we
can treat physically accessible spacetime displacements as a vector
space,
because there is a class of displacements without an additive inverse.
The same argument can be applied to 4-velocities, of course, and
4-accelerations.
Correct.
This begs the question whether it's still ok to treat the arrow of
time as a
separate constraint imposed on spacetime. If it is, then arriving at
spacetime is a two-step process -- building a well-defined vector
space (or
a manifold in GR) -- and then imposing the arrow of time.
I confess I don't really have a good answer for Androcles here, and
I'm
still thinking about it. Doesn't mean he's right. But it does mean I
don't
have a good explanation for him, either.
PD
Time is invariant. Distance is invariant. Speed is NOT invariant, it is
relative.
Here is what happened.
Sam and Joe have a 32 foot long ladder they are carrying between them.
They are walking along at 3 fps, and McCullough's mosquito leaves
Sam and travels along the ladder to Joe at 5 fps relative to the ground,
2 fps relative to the ladder. It takes 16 seconds to reach Joe. It then
turns back toward Sam, still flying at 5 fps relative to the ground, but
this
time at 8 fps relative to the ladder.
Sam, who has heard of Einstein, wants to know when the mosquito reached
Joe, but because the little bug is beyond the capabilites of his
eyesight,
he asssumes it must have flown at one speed only.
He knows how long the ladder is, and it took 20 seconds for the round
trip, so it should have taken 10 seconds to reach Joe. Then he gets TOO
clever, and works out the whole thing algebraically, using coordinates.
He says the equation for this is
½[tau(0,0,0,t)+tau(0,0,0,t+x'/(c-v)+x'/(c+v))] = tau(x',0,0,t+x'/(c-v))
Where c is the speed of the mosquito in the ground frame, 5 fps, and
v is the speed Sam and Joe are walking at, 3 fps.
We put in the numbers,
½[tau(0,0,0,t)+tau(0,0,0,t+32/8+32/2] = tau(32,0,0,t+32/2), or
½[tau(0,0,0,t)+tau(0,0,0,t+4+16] = tau(32,0,0,t+16),
Now we can lose the x, y and arbitrary t, since it matters not whether
this is carried out at mid morning or late afternoon, the first term is
only zero anyway, so we have
½[tau(0,20)] = tau(32,16)
And that is Joe's calculation.
What Joe has not realized is that his ½ never made any sense at all,
for if it had, he would have still wrongly calculated 10 seconds, not
16.
The rest is history. So is SR (and GR)
For the future, the speed of light (or mosquitoes wearing space suits)
in empty space is source dependent.
The evidence for this is to be found in the stars, but like a stick
appears
bent in water, the apparent intensity of the star changes.
http://www.androc1es.pwp.blueyonder.co.uk/actual_data.htm
In this chart, the earlier emitted slow light has been passed by
the later emitted fast light.
The star itself is not changing in brightness at all.
It is very dim today, actually dimmer than it would normaly appear were
i
not moving away from is, and will not appear to flare up for another
couple of centuries. The last time it did so, sufficiently powerful
telescopes were not available. Flare up it will, though.
Androcles, standing on the shoulder's of giants and seeing further
than any man before, but you have to see with the mind, not just the
eye.
.
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| User: "Gregory L. Hansen" |
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| Title: Re: Androcles and draper. |
11 Jan 2005 10:48:26 AM |
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In article <BE09631E.E41%pdraper@yahoo.com>,
PDraper <pdraper@yahoo.com> wrote:
On 1/10/05 6:21 AM, in article
cztEd.94837$48.68056@fe1.news.blueyonder.co.uk, "Androcles"
<dummy@dummy.net> wrote:
Androcles questioned (actually more strongly than that) whether time can be
included in a 4-D spacetime vector space.
As a positional space, I don't think there's an issue, though I have to
admit I'm extrapolating Androcles's thoughts on this without his blessing.
It's perfectly rational to have a negative time *location* for an event.
That's simply a matter of where you place your origin.
The issue comes when you ask whether you can construct a vector space of
spacetime *displacements*, which physically speaking represent a possible
trajectory of a physical object. Androcles's objection at this point is that
there is no permissible timelike trajectory with a minus sign in the time
component -- at least for positive-energy particles, or (said differently)
non-quantum objects. Physical objects do not move backward in time. Thus,
while positive timelike vectors are perfectly fine, negative timelike
vectors are physically excluded. This, then, raises the issue of whether we
can treat physically accessible spacetime displacements as a vector space,
because there is a class of displacements without an additive inverse.
If time went in reverse, we'd lose all memory of the future as we're
carried along with it. Relative to some impish cosmic observer (to make
the very notion of the universe going backwards in time meaningful) our
time could be bouncing back and forth like a yo-yo with no observable
consequences except maybe to weak force interactions.
But that's just an aside. A physical theory is a model, it's not the
real thing. We can run all sorts of thought experiments involving
massless strings, frictionles pullies, and travel through time, without
worrying about whether it can be done in real life. If we let t go
backwards we suppose we're starting with some initial conditions and then
asking what happened in the past such that those conditions would occur.
They've been doing that with Newtonian mechanics long before Einstein came
on to the scene, speculating that if we only had complete information
about the universe at an instant in time we could in principle determine
everything about its past and future. Rolling time into a
four-dimensional vector rather than working with three-vectors plus time
doesn't suddenly make the concept of running the movie backwards invalid.
And the time parameter used in Newtonian mechanics is no more
intrinsically monotonically increasing than the time component of a
four-vector. Which part of Newton's laws or the Galilean transformations
requires t to increase? I think Androcles is making distinctions between
t and x_0 that don't exist.
--
"I fart for joy and I laugh more than if I had cast my old age, as a
serpent does its skin." -- Aristophanes, Peace, 421 BC
.
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| User: "Androcles" |
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| Title: Re: Androcles and draper. |
13 Jan 2005 09:29:21 AM |
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"Gregory L. Hansen" <glhansen@steel.ucs.indiana.edu> wrote in message
news:cs100q$c1c$1@rainier.uits.indiana.edu...
In article <BE09631E.E41%pdraper@yahoo.com>,
PDraper <pdraper@yahoo.com> wrote:
On 1/10/05 6:21 AM, in article
cztEd.94837$48.68056@fe1.news.blueyonder.co.uk, "Androcles"
<dummy@dummy.net> wrote:
Androcles questioned (actually more strongly than that) whether time
can be
included in a 4-D spacetime vector space.
As a positional space, I don't think there's an issue, though I have
to
admit I'm extrapolating Androcles's thoughts on this without his
blessing.
It's perfectly rational to have a negative time *location* for an
event.
That's simply a matter of where you place your origin.
The issue comes when you ask whether you can construct a vector space
of
spacetime *displacements*, which physically speaking represent a
possible
trajectory of a physical object. Androcles's objection at this point
is that
there is no permissible timelike trajectory with a minus sign in the
time
component -- at least for positive-energy particles, or (said
differently)
non-quantum objects. Physical objects do not move backward in time.
Thus,
while positive timelike vectors are perfectly fine, negative timelike
vectors are physically excluded. This, then, raises the issue of
whether we
can treat physically accessible spacetime displacements as a vector
space,
because there is a class of displacements without an additive inverse.
If time went in reverse, we'd lose all memory of the future as we're
carried along with it. Relative to some impish cosmic observer (to
make
the very notion of the universe going backwards in time meaningful)
our
time could be bouncing back and forth like a yo-yo with no observable
consequences except maybe to weak force interactions.
But that's just an aside. A physical theory is a model, it's not the
real thing. We can run all sorts of thought experiments involving
massless strings, frictionles pullies, and travel through time,
without
worrying about whether it can be done in real life. If we let t go
backwards we suppose we're starting with some initial conditions and
then
asking what happened in the past such that those conditions would
occur.
They've been doing that with Newtonian mechanics long before Einstein
came
on to the scene, speculating that if we only had complete information
about the universe at an instant in time we could in principle
determine
everything about its past and future. Rolling time into a
four-dimensional vector rather than working with three-vectors plus
time
doesn't suddenly make the concept of running the movie backwards
invalid.
You can only the move backwards in forward time.
If the movie is the World Trade Centre collapsing, you can put it back
up again and save the lives of the poor sods falling to their death in
the
movie, but you know you cannot do it in the real world. Planes do not
fly backwards, billiard balls do not jump out of the pockets and form
up in a triangle, fires do not unburn into firewood. If you have a model
that can make time and distance itself variable in favour of a speed
being invariant, then the model is as fictional as running a movie
backwards.
Mathematics is a useful tool in the sciences, we use it to model the
real world. It is nevertheless a language and can be used to model
a fictional world also.
When Einstein said "In agreement with experience we ASSUME
2AB /(t'A - tA) = c, he was creating fiction. I certainly have no such
experience except in the trivial case where A and B are not changing
distance between them. When he says "We then MUST have
(tau0 + tau2) / 2 = tau1", why must we? I see no good reason to accept
that the time to fly to New York, (7 hours) plus the time to return to
London (6 hours) means (6+7)/2 = 7, even if you include the
coordinates of London and New York and compute the time from
aboard the plane. It is NOT in agreement with experience, and to claim
it that it is is merely persuasive rhetoric, as is the "We MUST have".
When psychology enters into the realm of physics, we have a disaster
on our hands.
When Sam and Joe carry a 32 ft ladder between them at 3 fps and the
mosquito flies the length of the ladder at 5 fps as measured in the
frame
of the road, it is flying at 2 fps (c-v) and 8 fps (c+v) in the moving
frame. It takes 16 seconds to cover 80 ft in the road frame at 5 fps
and 16 seconds to cover 32 ft in the ladder frame. On the return,
it takes 4 seconds to travel 20 ft at 5 fps in the road frame and
and 4 seconds at 8 fps in the ladder frame, again 32 ft.
For Sam to complain he cannot see the mosquito when it reaches Joe,
so (16+4)/2 = 16 is totally absurd and a fiction. The speed of the
mosquito really is 8 fps and 2 fps in the moving frame. It makes
no sense to say it is 5 fps because the speed of mosquitoes is
invariant. This is actually a scale model of the real world situation
where we replace the length of the ladder with 1,920,000 kilometers,
the mosquito with the tip of the ray, Sam with a flashlight (left on
the ground) and Joe with a mirror, the ladder traveling at 0.6c.
The speed of the light really is c-v and c+v in the frame of the
ladder. You can tell from the doppler shift Sam would perceive.
That is what Michelson was expecting to measure, and it turns
ou that the flashlight was not left on the ground at all, it moved
with the ladder.
The velocity of light is source dependent. It is c+v and c-v
in the road frame (aether) and Michelson (Sam) was moving
in the ladder frame (MMX) along with the light. So he didn't
get any doppler shift.
It doesn't matter how pretty the math is, it is fiction. People
love fiction, Shakespeare is still popular today. It is still fiction,
not science and not history. Richard III was not a hunchback
even though Shakespeare imagined him to be. The portraits
have been examined by X-ray and found to have been tampered
with. Einstein has tampered with the invariance of distance and
time.
And the time parameter used in Newtonian mechanics is no more
intrinsically monotonically increasing than the time component of a
four-vector. Which part of Newton's laws or the Galilean
transformations
requires t to increase? I think Androcles is making distinctions
between
t and x_0 that don't exist.
--
"I fart for joy and I laugh more than if I had cast my old age, as a
serpent does its skin." -- Aristophanes, Peace, 421 BC
"the velocity of light in our theory plays the part, physically, of an
infinitely great velocity." - Albert Einstein.
"Only two things are infinite, the universe and human stupidity, and I'm
not sure about the former." --Albert Einstein
Androcles
.
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| User: "PD" |
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| Title: Re: Androcles and draper. |
11 Jan 2005 01:00:15 PM |
|
|
Gregory L. Hansen wrote:
In article <BE09631E.E41%pdraper@yahoo.com>,
PDraper <pdraper@yahoo.com> wrote:
On 1/10/05 6:21 AM, in article
cztEd.94837$48.68056@fe1.news.blueyonder.co.uk, "Androcles"
<dummy@dummy.net> wrote:
Androcles questioned (actually more strongly than that) whether time
can be
included in a 4-D spacetime vector space.
As a positional space, I don't think there's an issue, though I have
to
admit I'm extrapolating Androcles's thoughts on this without his
blessing.
It's perfectly rational to have a negative time *location* for an
event.
That's simply a matter of where you place your origin.
The issue comes when you ask whether you can construct a vector
space of
spacetime *displacements*, which physically speaking represent a
possible
trajectory of a physical object. Androcles's objection at this point
is that
there is no permissible timelike trajectory with a minus sign in the
time
component -- at least for positive-energy particles, or (said
differently)
non-quantum objects. Physical objects do not move backward in time.
Thus,
while positive timelike vectors are perfectly fine, negative
timelike
vectors are physically excluded. This, then, raises the issue of
whether we
can treat physically accessible spacetime displacements as a vector
space,
because there is a class of displacements without an additive
inverse.
If time went in reverse, we'd lose all memory of the future as we're
carried along with it. Relative to some impish cosmic observer (to
make
the very notion of the universe going backwards in time meaningful)
our
time could be bouncing back and forth like a yo-yo with no observable
consequences except maybe to weak force interactions.
Yes, yes, of course. That's where causality gets built in.
But that's just an aside. A physical theory is a model, it's not the
real thing.
This is true, but somehow unsatisfying. The problem is that I can't put
my finger on where we carry the caveat of causality along in the
mathematical framework of treating spacetime as a vector space (or a
manifold). A model is only good if there is a really clear eye on the
caveats. I suppose what we have to say is that spacetime is a *causal*
vector space, which means, effectively that there are additive inverses
to all spacetime vectors, but some of them are not causal and have to
be thrown out by hand. The "by hand" part is the thing that bothers me,
because I do not have a clear idea in my head how to rigorously define
a causal vector space mathematically. Perhaps there is no good way.
Perhaps that is the way we have to define it: spacetime is a vector
space with causality imposed by hand. I can live with that.
We can run all sorts of thought experiments involving
massless strings, frictionles pullies, and travel through time,
without
worrying about whether it can be done in real life. If we let t go
backwards we suppose we're starting with some initial conditions and
then
asking what happened in the past such that those conditions would
occur.
They've been doing that with Newtonian mechanics long before Einstein
came
on to the scene, speculating that if we only had complete information
about the universe at an instant in time we could in principle
determine
everything about its past and future. Rolling time into a
four-dimensional vector rather than working with three-vectors plus
time
doesn't suddenly make the concept of running the movie backwards
invalid.
But this is different than turning causality backwards and saying that
the world is invariant under that transformation.
And the time parameter used in Newtonian mechanics is no more
intrinsically monotonically increasing than the time component of a
four-vector. Which part of Newton's laws or the Galilean
transformations
requires t to increase? I think Androcles is making distinctions
between
t and x_0 that don't exist.
Sure. If I have a basic trajectory problem of a guy hitting a baseball
and I ask where horizontally the ball will land, because the trajectory
equations are quadratic, I'll end up with two solutions, one behind the
batter. I can say about that solution, "That isn't the one I want," but
I can also say more strongly, "That solution is unphysical," and reject
it. Having to reject a solution by hand does not make the trajectory
equation invalid and mathematically improper, but it *does* say, "Once
you have the solutions, you have to be sure each one is physically
permissible."
I imagine this was a key decision with the negative energy solutions of
the Dirac equation, as well.
PD
.
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| User: "Gregory L. Hansen" |
|
| Title: Re: Androcles and draper. |
11 Jan 2005 02:31:59 PM |
|
|
In article <1105470015.004044.125800@f14g2000cwb.googlegroups.com>,
PD <pdraper@yahoo.com> wrote:
Gregory L. Hansen wrote:
In article <BE09631E.E41%pdraper@yahoo.com>,
But that's just an aside. A physical theory is a model, it's not the
real thing.
This is true, but somehow unsatisfying. The problem is that I can't put
my finger on where we carry the caveat of causality along in the
mathematical framework of treating spacetime as a vector space (or a
manifold). A model is only good if there is a really clear eye on the
caveats. I suppose what we have to say is that spacetime is a *causal*
vector space, which means, effectively that there are additive inverses
to all spacetime vectors, but some of them are not causal and have to
be thrown out by hand. The "by hand" part is the thing that bothers me,
because I do not have a clear idea in my head how to rigorously define
a causal vector space mathematically. Perhaps there is no good way.
Perhaps that is the way we have to define it: spacetime is a vector
space with causality imposed by hand. I can live with that.
I don't see any problem with this that doesn't arise in Newtonian
mechanics. Simultaneity is absolute for time-like separated events, and
spacelike separated events have no causal connection. Beyond that, one
just says "Duh, causes precede effects" as 19th century philosophers had
been doing all along.
We can run all sorts of thought experiments involving
massless strings, frictionles pullies, and travel through time,
without
worrying about whether it can be done in real life. If we let t go
backwards we suppose we're starting with some initial conditions and
then
asking what happened in the past such that those conditions would
occur.
They've been doing that with Newtonian mechanics long before Einstein
came
on to the scene, speculating that if we only had complete information
about the universe at an instant in time we could in principle
determine
everything about its past and future. Rolling time into a
four-dimensional vector rather than working with three-vectors plus
time
doesn't suddenly make the concept of running the movie backwards
invalid.
But this is different than turning causality backwards and saying that
the world is invariant under that transformation.
What transformation does that? Simultaneity, and cause-effect
relationships, are absolute for time-like separated events and have no
meaning for space-like separated events. No boost < c or rotation will
change that. And parity transformations are not limited to relativity.
And the time parameter used in Newtonian mechanics is no more
intrinsically monotonically increasing than the time component of a
four-vector. Which part of Newton's laws or the Galilean
transformations
requires t to increase? I think Androcles is making distinctions
between
t and x_0 that don't exist.
Sure. If I have a basic trajectory problem of a guy hitting a baseball
and I ask where horizontally the ball will land, because the trajectory
equations are quadratic, I'll end up with two solutions, one behind the
batter. I can say about that solution, "That isn't the one I want," but
I can also say more strongly, "That solution is unphysical," and reject
it. Having to reject a solution by hand does not make the trajectory
equation invalid and mathematically improper, but it *does* say, "Once
you have the solutions, you have to be sure each one is physically
permissible."
If the time that the bat hits the ball is defined as t=0 the problem is
defined for t>0 and y>0. For y=0 we have a boundary condition. And for
t=0 we have another boundary condition-- the bat. It's not physics'
fault if we forget to write down the first term in the equation of
motion.
r(t) = (ball goes from pitcher to batter), t<0
= (ball leaves bat), t>0
I imagine this was a key decision with the negative energy solutions of
the Dirac equation, as well.
PD
--
"A good plan executed right now is far better than a perfect plan
executed next week."
-Gen. George S. Patton
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