SR on accelerating frame of reference
Curious
Can you apply SR principles from an accelerating frame of reference?
And if not, since the Earth is accelerating away from the far side of
the universe, does this pose any problems?
Dirk Van de moortel
"Curious" <anthonyros...@yahoo.co.uk> wrote in message news:1117305473.3...@g43g2000cwa.googlegroups.com...
The general consensus will soon be be that you are a troll:
http://groups.google.co.uk/group/sci.physics.relativity/msg/7e30c3d20096a5fd
| "Well, thanks for your sincere input, but please know that
| I've had a sufficiency. Sorry for being blunt but I have come
| to believe in saying it like I see it when an answer is required.
| Guess you're going to have to lump me with the cranks!"
The only thing left to find out, is your previous name.
Watch your style :-)
Dirk Vdm
Curious
Dirk Van de moortel wrote:
> "Curious" <anthonyros...@yahoo.co.uk> wrote in message news:1117305473.3...@g43g2000cwa.googlegroups.com...
> > What's the general consensus in this group on the following question:
> > Can you apply SR principles from an accelerating frame of reference?
> > And if not, since the Earth is accelerating away from the far side of
> > the universe, does this pose any problems?
>
> The general consensus will soon be be that you are a troll:
How very kind of you. Thanks for the compliment!
Anthony Rose (this is my first and only life)
FrediFizzx
news:1117305473.3...@g43g2000cwa.googlegroups.com...
I suppose you can apply SR carefully if you wish to avoid the
complexities of GR. I don't think you even have to consider "far side
of the Universe". The general thinking now is that the expansion of our
Universe is accelerating and you don't have to go to the "far side" to
see this. But this could change again.
FrediFizzx
http://www.vacuum-physics.com/QVC/quantum_vacuum_charge.pdf
or postscript
http://www.vacuum-physics.com/QVC/quantum_vacuum_charge.ps
Ben Rudiak-Gould
> What's the general consensus in this group on the following question:
I don't know what the general consensus is, but I'll tell you the right
answer, if that helps...
> Can you apply SR principles from an accelerating frame of reference?
This is the same as asking whether you can do Euclidean geometry in polar
coordinates. The answer is yes you can, and the fact that you can is
independent of the details of the theory. It's simply a mathematical
substitution of variables.
Of course, the laws of physics will "look different" in terms of
accelerating coordinates.
> And if not, since the Earth is accelerating away from the far side of
> the universe, does this pose any problems?
The Earth as a whole is not accelerating, in the sense that an accelerometer
would indicate inertial motion (if you discount the rotational acceleration).
To understand the large-scale expansion of the universe, you need to
understand GR, and in particular you need to understand what this means:
ds^2 = dt^2 - R(t)(dx^2 + dy^2 + dz^2)
When people say that the expansion of the universe is accelerating, they
mean that d^2R/dt^2 > 0. This is a different meaning of the word
"acceleration"; it doesn't have anything to do with objects accelerating in
spacetime.
-- Ben
Bilge
>Can you apply SR principles from an accelerating frame of reference?
>And if not, since the Earth is accelerating away from the far side of
>the universe, does this pose any problems?
No. The universe is described by general relativity. Special
relativity is inly a limiting case when gravitational fields
don't matter.
Curious
Thanks
Curious
FrediFizzx wrote:
[snip]
> I suppose you can apply SR carefully if you wish to avoid the
> complexities of GR. I don't think you even have to consider "far side
> of the Universe". The general thinking now is that the expansion of our
> Universe is accelerating and you don't have to go to the "far side" to
> see this. But this could change again.
>
Thanks
Curious
Ben Rudiak-Gould wrote:
> Curious wrote:
> > What's the general consensus in this group on the following question:
>
> I don't know what the general consensus is, but I'll tell you the right
> answer, if that helps...
Thanks!
>
> > Can you apply SR principles from an accelerating frame of reference?
>
> This is the same as asking whether you can do Euclidean geometry in polar
> coordinates. The answer is yes you can, and the fact that you can is
> independent of the details of the theory. It's simply a mathematical
> substitution of variables.
>
> Of course, the laws of physics will "look different" in terms of
> accelerating coordinates.
>
But for example, in the twin paradox, if we viewed the entire thing
from a frame of reference centered on the travelling twin, with the
Earth 'accelerating' away, then decelerating, then the reverse for the
return journey, we'd still get the same final age difference predicted,
wouldn't we?
> > And if not, since the Earth is accelerating away from the far side of
> > the universe, does this pose any problems?
>
> The Earth as a whole is not accelerating, in the sense that an accelerometer
> would indicate inertial motion (if you discount the rotational acceleration).
>
> To understand the large-scale expansion of the universe, you need to
> understand GR, and in particular you need to understand what this means:
>
> ds^2 = dt^2 - R(t)(dx^2 + dy^2 + dz^2)
>
> When people say that the expansion of the universe is accelerating, they
> mean that d^2R/dt^2 > 0. This is a different meaning of the word
> "acceleration"; it doesn't have anything to do with objects accelerating in
> spacetime.
>
What is R please? Do people mean the distance between two galaxies (for
example) is increasing at an accelerating rate?
Thank you
> -- Ben
xx...@bellsouth.net
xxein: Nice touch. Unfortunately, they cannot feel it. No wonder
there's entropy.
macro...@internetcds.com
shrink. You have to arrive at the shrinking of
space-time at high speed in SR through the
acceleration that gets you there.
How simple is that?
The Ghost In The Machine
<macro...@internetCDS.com>
wrote
on 28 May 2005 22:40:04 -0700
<1117345204.7...@z14g2000cwz.googlegroups.com>:
[1] Speeding up relative to who?
[2] Whose space-time metric?
[3] SR doesn't do accelerations (though one can use methods
similar to Dirk van der Mortel's (aargh; how does one spell
it?) to derive useful results by assuming infintesimal (dt)
"coasts").
[4] Lorentz is quite clear on this: space-time does not shrink,
but *twists*.
x_A = (x_O - (v/c) * c * t_O) / sqrt(1-v^2/c^2)
c * t_A = (c * t_O - (v/c) * x_O) / sqrt(1-v^2/c^2)
This slightly unusual method of rewriting the Lorentz might
show the twist. A simpler method might be setting c = 1
(one could, for instance, measure length in terms of
"giganils" -- 1 nil is the distance light travels in 1 nanosecond --
and time in seconds). This yields
x_A = (x_O - v * t_O) / sqrt(1-v^2)
t_A = (t_O - v * x_O) / sqrt(1-v^2)
If one writes u_0 = i * t_O, then t_0 = -i * u_0 and
one can rewrite the Lorentz
x_A = (x_O - v * (-i) * u_O) / sqrt(1+(-i * v)^2)
u_A = i * (-v * x_O - i * u_O) / sqrt(1+(-i * v)^2)
= (-v * i * x_0 + u_0) / sqrt(1+(-i * v)^2)
= (v * (-i) * x_0 + u_0) / sqrt(1+(-i * v)^2)
If cos a = 1 / sqrt(1 + (-i * v)^2), then
one value of sin a can be expressed
sin a = (-i * v) / sqrt(1 + (-i * v)^2) (the
other value is the negative) and we do indeed
have a rotation, albeit with a strange coordinate
system and an even stranger angle.
However, time in Minkowski is an imaginary anyway.
Not all that simple, but mathematically it works
reasonably well.
--
#191, ewi...@earthlink.net
It's still legal to go .sigless.
macro...@internetcds.com
contracted. Bow do you get to these high speeds?
So acceleration through space is the cause.
Period.
Tom Roberts
> What's the general consensus in this group on the following question:
> Can you apply SR principles from an accelerating frame of reference?
The consensus among knowledgeable people is that SR can indeed be
applied to accelerating coordinates. Note, however, that accelerating
coordinates do not truly correspond to a "frame of reference" (the
difficulty is in the word "frame", because in SR the usual
infinitely-extended frame cannot be constructed unless it is inertial).
[In GR such an infinitely-extended frame can be constructed
only in a flat manifold (i.e. one empty of any energy or
mass) with suitable topology. That is precisely the
condition necessary to use SR (except SR can always be
applied _approximately_ in a local region).]
> And if not, since the Earth is accelerating away from the far side of
> the universe, does this pose any problems?
I have not a clue what you mean by "far side of the universe", or how
you expect to establish "acceleration" relative to it.
To discuss cosmological questions (as this appears to be), one must use
GR, not SR....
Tom Roberts tjro...@lucent.com
The Ghost In The Machine
<macro...@internetCDS.com>
wrote
<1117351874....@g43g2000cwa.googlegroups.com>:
An interesting if curious point. SR can't address this
(mostly because SR doesn't do acceleration) and GR only
deals with the acceleration -- once the body stops
accelerating, it is still moving (SR) but no longer has
effects because of the acceleration (GR).
Spoonfed
Gravity vs. Acceleration: The Principle and Limits of Equivalence
In short, I think YES you can apply principle of SR to an accelerated
frame. And whether or not you can, I am attempting to demonstrate this
until I can show the principle of equivalence through SR or I see a
clear reason that you cannot apply SR to an accelerated frame.
Secondly, I have little idea where your idea that the earth is
accelerating away from the far side of the universe. Finally, the
links to my demos on accelerated frames are as follows:
http://www.spoonfedrelativity.com/files/myGravity7.swf
http://www.spoonfedrelativity.com/files/myGravity-contractionvelocity.swf
Now for the really long part...
If gravity is equivalent to acceleration and an object on the surface
of the earth is experienceing the same effects as an object as an
object on an accelerated surface, then it follows that an object on the
surface of the earth must be accelerating toward the edge of the
universe...
But there are limits to the Principle of Equivalence. Gravity and
acceleration differ in certain ways, or else there would be no need to
have two words for the same phenomenon.
Off hand, I can think of two main differences between gravity and
acceleration, one very obvious and usually ignored, and the other
somewhat more subtle.
The subtle difference between gravity and acceleration is the fact that
gravitational fields are not uniform around masses, so they cause tidal
effects, stretching falling objects vertically, and smashing them
horizontally. This effect is a true effect on the free-falling object,
and is not due to differences in perception. On the other hand, if an
accelerated platform were to come toward a free-falling object, it
would NOT be distorted by tidal effects at all.
The obvious difference between gravity and acceleration is that objects
far away from the gravitational source are barely affected by it at
all. That is, the change in the relative rapidity (v/sqrt(1-(v/c)^2))
between the two objects is proportional to the 1/distance^2 (distance
in the gravitating body's frame.
On the other hand, if you accelerate toward an object, no matter how
far away it is, the change in relative rapidity is equal to your change
in rapidity.
I realize this directly confronts your statement that we are
accelerating toward the edge of the universe. I have heard your idea
before, but never with evidence sufficient to back it up, nor with any
sort of argument which seems to hold together. My idea that we are NOT
only comes from assuming a simple model.
So gravity differs from acceleration in these two very important ways.
But is there any way to reduce the differences, or eliminate them
altogether?
Yes. If you've taken any courses in electromagnetism, you will be
familiar with the idea of point, line, and plane geometries for fields.
In a point geometry, the field is proportional to 1/r^2, for line,
it's 1/r and for plane geometries, the field never dissipates.
If we had a gravitational field that never dissipated, such as would be
the case in an infinite plane gravitational source, then we would
eliminate both effects mentioned above, which make gravity different
from acceleration.
(There would still be one remaining difference: the fact that an
accelerated plane has things falling away from it's back side, while an
infinite plane gravity source would have objects attracted to both
sides.)
By assuming an infinite plane, we eliminate the tidal effects, and the
reduction over distance normally associated with gravity. Then,
hypothetically, we should be able to derive the non-tidal effects of
general relativity directly from the Special Theory (and a few
differential equations, and possibly some interpolation functions.)
I've been working on this problem off and on for a month or two, and
put together two demonstrations.
The <A HREF="http://www.spoonfedrelativity.com/files/myGravity7.swf">
First Demo</A> shows what would happen if the speed of light were
constant, but no length contraction or time dilation took place.
The <A
HREF="http://www.spoonfedrelativity.com/files/myGravity-contractionvelocity.swf">
second demo</A> applies length contraction but not time dilation. It
is inconclusive so far. I employed a terrible programming technique of
successive addition of floating point numbers to determine positions.
This propagates rounding errors horribly. However, finding space-time
position as a function of time has proved difficult.
For math whizzes, my problem is that t'[t]=EllipticE[ArcSin[a*t],2]/a
and I need to get the inverse, t[t'] to render the events properly in
the animation. There's probably no closed form solution, so I'll have
to put together an interpolation function. a is acceleration in
nils/nanosecond^2, where a nil is a light nanosecond.
Dirk Van de moortel
"The Ghost In The Machine" <ew...@sirius.athghost7038suus.net> wrote in message news:up0pm2-...@sirius.athghost7038suus.net...
http://hermes.physics.adelaide.edu.au/~dkoks/Faq/Relativity/SR/acceleration.html
http://groups.google.co.uk/groups?&threadm=bi75vd$qbm$1...@glue.ucr.edu
http://www.geocities.com/slithytove5/AccelClocks.htm
http://users.pandora.be/vdmoortel/dirk/Physics/Acceleration.html
Dirk Vdm
Ben Rudiak-Gould
> But for example, in the twin paradox, if we viewed the entire thing
> from a frame of reference centered on the travelling twin, with the
> Earth 'accelerating' away, then decelerating, then the reverse for the
> return journey, we'd still get the same final age difference predicted,
> wouldn't we?
I'm not sure whether you're suggesting that the prediction would be the same
regardless of reference frame (which is correct), or whether the predictions
for earth and rocket ship would be reversed.
Let me work through a similar problem in Euclidean analytic geometry, since
the mathematics is exactly the same. Please follow along and work it out
yourself -- it's not hard at all. Don't just skip over the equations, or the
whole thing will be useless.
Suppose we have a weird curve on the Euclidean plane, given by
x(q) = q^3 for -2 <= q <= 2
y(q) = q^5
The parameter q is totally arbitrary: all I care about is the curve that's
traced out by the points with coordinates (x(q),y(q)) as I vary q.
How can I figure out the length of this curve? The answer is to divide it
into a bunch of differential pieces, and apply the Pythagorean formula to
each one -- in other words, to compute
integral {curve} ds where ds^2 = dx^2 + dy^2
= integral {-2 to 2} (ds/dq) dq
We can compute ds/dq by differentiating the formulas for x(q) and y(q):
(ds/dq)^2 = (dx/dq)^2 + (dy/dq)^2
= (3 q^2)^2 + (5 q^4)^2
ds/dq = sqrt(9 q^4 + 25 q^8)
so the integral is
integral {-2 to 2} sqrt(9 q^4 + 25 q^8) dq
which I'm not going to bother trying to evaluate.
Now, let's think about other ways we could solve this. First of all, we
could parameterize in terms of x instead of q, since the curve doesn't
"double back on itself": then we have
y = f(x) = x^(5/3)
(ds/dx)^2 = (dx/dx)^2 + (dy/dx)^2
= 1 + (5/3 x^(2/3))^2
length = integral {curve} ds
= integral {-8 to 8} (ds/dx) dx
= integral {-8 to 8} sqrt(1 + (5/3 x^(2/3))^2) dx
This looks like a very different integral, but it had better give us the
same value! If it doesn't, either we've discovered a flaw in calculus, or I
made a mistake somewhere (probably the latter). Let me point out, by the
way, that if you do this for a general f(x), you get
length = integral {xi to xf} sqrt(1 + f'(x)^2) dx
which is the graph-length formula that you probably learned in high school
calculus.
Another thing we can do is work in another coordinate system. For example,
we can work in polar coordinates (r,theta), given by
x = r cos theta
y = r sin theta
But we certainly can't say that ds^2 = dr^2 + dtheta^2. Instead we need to
work out the correct formula by taking the total derivative of the equations
above:
dx = dr cos theta - r sin theta dtheta
dy = dr sin theta + r cos theta dtheta
and substituting:
ds^2 = dx^2 + dy^2
= (dr cos theta - r sin theta dtheta)^2
+ (dr sin theta + r cos theta dtheta)^2
= dr^2 + r^2 dtheta^2
Now we can work out the equation of the curve in terms of r and theta, and
integrate, and hopefully get the same answer, though the math is much uglier
than before (a good reason not to use this coordinate system for this problem).
There's a particularly nice family of coordinate systems in which ds^2 has
the same form as in our original (x,y) coordinate system. They're related to
(x,y) by the following parameterized family of transformations:
x = x' cos theta + y' sin theta + x0
y = y' cos theta - x' sin theta + y0
You should convince yourself that ds^2 = dx'^2 + dy'^2 regardless of the
values of theta, x0, and y0.
Okay, enough of that. Special relativity is exactly the same, except that
one of the coordinates is a time coordinate, the curves have a new
interpretation (worldlines), the length s has a new interpretation (elapsed
proper time), and the formula for ds^2 is slightly strange:
ds^2 = dt^2 - dx^2 (- dy^2 - dz^2)
But all the mathematical machinery that applied before still applies here.
We can give a worldline parameterized by q, such as
x(q) = cosh q
t(q) = sinh q
(that's a uniformly accelerating worldline, by the way), and we can compute
its length in the range -2 <= q <= 2 by computing
length = integral {worldline} ds
= integral {-2 to 2} (ds/dq) dq
= integral {-2 to 2} sqrt((dt/dq)^2 - (dx/dq)^2) dq
= ...
We can also reparameterize the worldline in terms of t. Unlike the Euclidean
case, this /always/ works, because real particles never double back on
themselves in the time direction. If we write x = f(t) = ..., then we have
length = integral {worldline} ds
= integral {ti to tf} (ds/dt) dt
= integral {ti to tf} sqrt(1 - (dx/dt)^2) dt
= integral {ti to tf} sqrt(1 - v(t)^2) dt
which you will recognize as the integral of the time dilation factor. That's
where time dilation comes from -- no conspiracy of nature, just a change of
variables.
We can also switch to a different coordinate system. There's a particularly
nice family of coordinate systems in which ds^2 has the same form as in our
original (x,t) coordinate system. They're related to (x,t) by the Lorentz
transformations, and you should verify this.
>>To understand the large-scale expansion of the universe, you need to
>>understand GR, and in particular you need to understand what this means:
>>
>> ds^2 = dt^2 - R(t)(dx^2 + dy^2 + dz^2)
>>
>>When people say that the expansion of the universe is accelerating, they
>>mean that d^2R/dt^2 > 0. This is a different meaning of the word
>>"acceleration"; it doesn't have anything to do with objects accelerating in
>>spacetime.
>
>What is R please? Do people mean the distance between two galaxies (for
>example) is increasing at an accelerating rate?
>Thank you
I hope you have a slightly better understanding now of what R(t) means in
the formula above. There's still a lot I haven't explained, but I think it
would be better to learn it from a textbook.
-- Ben
Curious
Tom Roberts wrote:
> Curious wrote:
> > What's the general consensus in this group on the following question:
> > Can you apply SR principles from an accelerating frame of reference?
>
> The consensus among knowledgeable people is that SR can indeed be
> applied to accelerating coordinates. Note, however, that accelerating
> coordinates do not truly correspond to a "frame of reference" (the
> difficulty is in the word "frame", because in SR the usual
> infinitely-extended frame cannot be constructed unless it is inertial).
>
> [In GR such an infinitely-extended frame can be constructed
> only in a flat manifold (i.e. one empty of any energy or
> mass) with suitable topology. That is precisely the
> condition necessary to use SR (except SR can always be
> applied _approximately_ in a local region).]
>
Thanks very much
The Ghost In The Machine
<dirkvand...@ThankS-NO-SperM.hotmail.com>
wrote
on Sun, 29 May 2005 18:14:30 GMT
<aEnme.104626$Rp6.6...@phobos.telenet-ops.be>:
Oops. Well, now at least I can see your name to spell it correctly. :-)
I'll admit I've no idea where the OP is going (accelerating?) with this
statement of his.
Einsteinhoax
correctly derived after eliminating the rather stupid mathematical error
made by Dr. Einstein which required him to rely on the fakery of "curved
space" to make his solution work, rgw Universe is seen to be contracting in
ABSOLUTE terms rather than expanding since the time of the alleged "big
bang". For more insformation refer to the rigorously derived "Gravity" at
http://members.isp.com/einste...@isp.com/einsteinhoax/gravity.htm.
rot...@gmail.com
>the length s has a new interpretation (elapsed
>proper time), and the formula for ds^2 is slightly strange:
> ds^2 = dt^2 - dx^2 (- dy^2 - dz^2)
>But all the mathematical machinery that applied before still applies here.
The "length" has a new interpretation...Ok, but mathematically, it is
not a length. The strange ds^2 formula does not define/satisfy a
metric.
So, not "all" mathematical machinery that can be applied to ds^2=dx^2 +
dy^2 can be applied to ds^2=dt^2-dx^2.
Should that be of concern?
Ben Rudiak-Gould
> Btw, nice posts.
Thanks :-)
>The "length" has a new interpretation...Ok, but mathematically, it is
>not a length. The strange ds^2 formula does not define/satisfy a
>metric.
>So, not "all" mathematical machinery that can be applied to ds^2=dx^2 +
>dy^2 can be applied to ds^2=dt^2-dx^2.
>Should that be of concern?
I only meant the mathematical machinery that I'd introduced previously in
that post. But you're right, I should at least have added scare quotes when
I wrote "length". It's certainly a mistake to assume that results that apply
to ordinary (positive definite) metrics will generalize to metrics of
arbitrary signature.
A lot does generalize, though. I'm a bit surprised that no mathematician
seems to have investigated this prior to Minkowski, especially given that
Sylvester's law of inertia dates from around 1850, and that Sylvester
apparently said (according to [1]):
"Aspiring to these wide generalizations, the analysis of quadratic
functions soars to a pitch from whence it may look proudly down on
the feeble and vain attempts of geometry proper to rise to its level
or to emulate it in its flights."
-- Ben
[1] http://www-groups.dcs.st-and.ac.uk/~history/Quotations/Sylvester.html
Spoonfed
I think it is of great concern. Namely distance can exist between
objects, while spacetime interval exists between events. Distance
between objects is determined by the spacetime interval between events
which occur on the objects simultaneously. Simultaneity is determined
by the observer, not by either object's proper time.
Depending on what problem you are solving, s can be a very useful
quantity. When it is real-valued, it can be divided by c to give the
time passed for an observer which measures the two events at the same
location.
When it is imaginary valued, it can be divided by the square root of -1
to give the distance between the two events for an observer who
measures them to occur simultaneously.
=====================
I'm not sure how helpful this will be, but in the animation,
http://www.spoonfedrelativity.com/files/world-lines.gif the point at
the origin represents the reference event. The red curves represent
the set of events which occur with imaginary-valued spacetime interval
(from the reference event) of distance 1, 2, 3, 4 nils (approximately 1
foot) etc.
The purple curves represent the set of events which occur with
real-valued spacetime intervals (from the reference event) of 1, 2, 3,
4 nanoseconds, etc.
The motion in the animation does not represent motion in time, but
changing between reference frames.
The (mostly) vertical line of black dots represent events which happen
in the same place as the reference event in each of these frames.
The (mostly) horizontal line of black dots represents events which are
observed to be simultaneous with the reference event in each of these
frames.
The grid partitions off space and time in one nanosecond and one nil
increments for each of the frames.
====================
If you add the dimension of time to the dimensions of space, you get
spacetime, so the location of a particle is no longer described by a
point, but instead by a line (or a curve if it the particle is
accelerated). How do you calculate the distance between two particles?
...if the lines are parallel and vertical?
...if the lines are parallel and slanted?
...if the lines are not parallel?
If we want to use the spacetime interval tool to find the distance,
first we have to pick the two events. To get a distance, we must pick
two simultaneous events, but simultaneous to whom?
Knowing the spacetime interval is imaginary only tells us that there is
some reference frame where two events occurred simultaneously at
different locations. Only in that frame does the spacetime interval
equal the distance between the two events. But we are not necessarily
IN that reference frame.
We must take proper care when picking the two events that they are
simultaneous in our reference frame, if we want to know how far apart
the two objects are in OUR reference frame. And once we do that, of
course:
ds^2=(c dt^2) - dx^2
= 0 - dx^2
ds = i dx
Which basically says that when an observer measures a distance between
objects at a particular time, he is referring to a very explicitly and
carefully defined pair of events which happen to be simultaneous in his
own reference frame.
A confusion arises because for a pair of events, the spacetime interval
IS independent of reference frame. It is seen to be the TRUE quantity,
while distance and time are seen to be illusions created by our
primitive senses. If a person were rigid in this belief, they might
give up the idea of simultaneity completely. After all, the term which
I usually refer to as desynchronization is referred to by most as "the
relativity of simultaneity" giving the idea that there is not such a
thing as simultaneity.
=============
Perhaps I should continue to leave the following argument alone, at
least until I finish reading Schutz, since unfortunately, it exiles me
from the ranks of respected physicists. One person actually emailed me
and told me that he was not going to read anything I said because I was
a crank.
It seems to me that we agree on so much, yet this one subtle difference
in a definition of simultaneity can make such a huge difference in the
concept of the shape of the universe. I am making the argument now,
because it reminds me to continue working on it, and on the off chance
that something I say might get through to someone who hasn't read it
before.
If a person thought this simultaneity term was meaningless and
flexible, they might allow themselves to redifine it carelessly; for
instance: redefine simultaneous events to mean "a set of events
attached to objects which are at the same proper age" instead of "a set
of events which a single observer can measure to have occured at the
same time" then you could make statements like:
"If you want to get an intuition for it without actually learning GR,
you're better off thinking in Newtonian terms (no speed limit; no time
dilation; the "outer shell" expands at infinite speed)"
"At cosmological scales the universe we inhabit is observed to be
reasonably isotropic and homogeneous, but at smaller scales it
manifestly is neither."
(with apologies to Mr. Rudiak and Mr Roberts)
By mixing the actual definition of simultaneous ("a set of events which
a single observer can measure to have occured at the same time") and
the new mathematical definition (a set of events attached to objects
which are at the same proper age) it becomes apparent how these
misconceptions might arise, because in each section of the universe, as
the stars and planets within it reach 13.7 billion years, they should
all look pretty similar to what things look like from here and now. So
one could say, the universe, at 13.7 billion years PROPER time, is
isotropic and homogeneous, and is infinite in expanse, and thus expands
at infinite speed. This
And thus the universe would look something like this, though no
observer would actually be able to see it:
http://www.spoonfedrelativity.com/files/galileanreal.gif
(warning--sudden fast graphics; epileptic seizure warning...)
But if you use the actual definition of simultaneous for both the
mathematics and the conceptualization, determining distance in terms
of simultaneous events according to the observer's time instead of the
"proper" time (note how loaded the terms are here. Apparently the
observer's time is improper.) the universe would appear somewhat like
this to an actual observer:
http://www.spoonfedrelativity.com/files/rel-big-bang.gif
My big bang theory is not popular, and you may wish to look at other
opinions--I may be unwittingly misrepresenting something other people
have said.
http://groups-beta.google.com/group/sci.physics.relativity/browse_frm/thread/d92bd5950d6ca0be?scoring=d&hl=en
(Space is flat on a cosmological scale but spaceTime is not--space is
expanding.)
http://groups-beta.google.com/group/sci.physics.research/browse_frm/thread/aa200f8f4c1a451d/ecb7aa485c14c063?hl=en#ecb7aa485c14c063
(370 km/second measured against CMBR? Urban Legend--they don't have
anywhere near the accuracy to measure it.)
Pmb
No. One must apply the principles of general relativity. The principle of
which I speak is the one that states that the laws of physics are the same
in all coordinate systems. This is a GR principle called the principle of
covariance.
Pmb
Dirk Van de moortel
"Pmb" <some...@somehow.com> wrote in message news:H9adndHuP-K...@comcast.com...
Ha, another psychopath joining the "Confuse Anthony Rose"
party :-)
http://hermes.physics.adelaide.edu.au/~dkoks/Faq/Relativity/SR/acceleration.html
http://groups.google.co.uk/groups?&threadm=bi75vd$qbm$1...@glue.ucr.edu
http://www.geocities.com/slithytove5/AccelClocks.htm
Dirk Vdm
Mike Fontenot
>
> What's the general consensus in this group on the following question:
> Can you apply SR principles from an accelerating frame of reference?
Yes. For an example of a generalized version of the "twin paradox"
(with 1-g accelerations), see my web page at
http://home.comcast.net/~mlfasf
which is based on the results in my paper:
"Accelerated Observers in Special Relativity",
PHYSICS ESSAYS, Sept 1999, p629.
Mike Fontenot
Spoonfed
Sounds pretty accurate: One clarification on point number 4, you say:
"4. According to an accelerating observer, for a one g acceleration
occurring when the separation is sufficiently great, the object's
maximum (in magnitude) rate of ageing is greater than the accelerating
observer's rate of ageing by a factor approximately equal to their
separation, as measured in the object's frame, in lightyears. If the
observer is accelerating toward the object, the object will be getting
older at that rate. If the observer is accelerating away from the
object, the object will be getting younger at that rate."
You are technically correct in that "the object's maximum (in
magnitude) rate of ageing is greater than the accelerating observer's
rate of ageing by a factor approximately equal to their separation, as
measured in the object's frame," but this seems very carefully worded,
and this is a rare case where you refer to how things are measured in
the distant object's frame instead of the accelerated object's frame.
The separation as measured from the object's frame may be length
contracted in the accelerating observer's frame, and this length
contraction can go anywhere from infinitesimal to 1. If the distance
is length contracted to very very small, accelerating toward the
distant object which is originally moving away, this distance
*uncontracts* causing the object to move away at unlimited "speed" and
age by an unlimited amount.
But, it's technically correct
Curious
Thank you! Very interesting.
What happens if you accelerate, and coast, at right-angles (perhaps in
a distant orbit) at relativistic speeds?
Ben Rudiak-Gould
> http://home.comcast.net/~mlfasf
>
> which is based on the results in my paper:
>
> "Accelerated Observers in Special Relativity",
> PHYSICS ESSAYS, Sept 1999, p629.
I don't understand this fascination with computing a quantity which is so
obviously devoid of physical content. First of all, as you point out, it
wobbles crazily back and forth through time, but there's no actual time
travel associated with this, no reverse aging, no phenomenon of any kind.
Second, the quantity you're computing can't even be defined on a
pseudo-Riemannian manifold, so it doesn't pertain to the real world in any
case, even as an artificial construct.
What you're doing is exactly the same as calculating the intersection of a
curve with a plane normal to another curve at some point, as the point
varies. Sure, if the second curve is a sine wave or something, then the
plane will sweep back and forth over the other curve, whee! But it's silly.
The rules of Euclidean geometry allow you to calculate that if you do this
silly thing, you will get this silly result. But if you think that Euclidean
geometry encourages you to do this silly thing, or says it's a meaningful
thing to do, then you've seriously misunderstood Euclidean geometry.
Nothing that we observe about the universe involves planes of simultaneity.
They're meaningless mathematical artefacts. The whole thing reminds me of
the textbook question Feynman mentions in _Surely You're Joking_ that
involved computing the "total temperature" of several stars by adding their
individual temperatures. You can do it; it's well-defined mathematically.
But it's silly.
-- Ben
Spoonfed
Ben Rudiak-Gould wrote:
> Mike Fontenot wrote:
> > http://home.comcast.net/~mlfasf
> >
> > which is based on the results in my paper:
> >
> > "Accelerated Observers in Special Relativity",
> > PHYSICS ESSAYS, Sept 1999, p629.
>
> I don't understand this fascination with computing a quantity which is so
> obviously devoid of physical content.
These would be completely measurable effects, so I don't see how they
are devoid of physical content. I find it refreshing to see Mr.
Fontenot's straightforward application of Lorentz Transformations.
He recognizes that accelerating toward an object causes you to move to
a reference frame where that object is older, while accelerating away
from an object causes you to move to a reference frame where it is
younger.
This should be special relativity 101, but unfortunately this usually
gets skipped in the rush toward group theory and abstract algebra. Not
only is it skipped but it is completely denied by the most respected
physicists.
> First of all, as you point out, it
> wobbles crazily back and forth through time, but there's no actual time
> travel associated with this, no reverse aging, no phenomenon of any kind.
Right, only if a signal were able to pass between the objects at faster
than the speed of light would there be time travel associated with it.
This is precisely the reason that FTL is often associated with time
travel, and FTL communications are called Tachyons in science
fiction...
> Second, the quantity you're computing can't even be defined on a
> pseudo-Riemannian manifold, so it doesn't pertain to the real world in any
> case, even as an artificial construct.
>
The quantity he is computing is the proper age of a distant object in
the MCRF (Momentarily Comoving Reference Frame) for the observer at a
given observer-instant.
If this quantity truly cannot be defined in any Riemannian manifold, it
indicates a problem with the flexibility of that tool.
> What you're doing is exactly the same as calculating the intersection of a
> curve with a plane normal to another curve at some point, as the point
> varies. Sure, if the second curve is a sine wave or something, then the
> plane will sweep back and forth over the other curve, whee!
=========================
An illustration of changing MCRF is given in this animation.
http://www.spoonfedrelativity.com/files/Minkowski-Yoink.gif
Notice the worldline of every particle coming from the origin is at the
center of the ellipses formed by the intersection of the cone and its
worldregion. This is the first step of creating a transformation which
preserves the speed of light.
For this animation in context:
http://www.spoonfedrelativity.com/worldRegions.html
Yes, perhaps mathematically this is calculating the intersection of a
curve with a plane normal to another curve at some point, and as we
accelerate and decelerate, the plane sweeps back and forth over the
other curve. And yes, it is a rather fun process, often lending to a
visceral sense of vertigo. As you ran through this process, you would
also find effects of stellar aberration causing stars to converge in
front of you, and appear to move at superluminal speeds toward you.
Wheee!
> But it's silly.
I disagree. It's no sillier than solving problems in physics with the
absence of friction. It is at least a first-order approximation of
reality, and probably a very accurate one.
> The rules of Euclidean geometry allow you to calculate that if you do this
> silly thing, you will get this silly result. But if you think that Euclidean
> geometry encourages you to do this silly thing, or says it's a meaningful
> thing to do, then you've seriously misunderstood Euclidean geometry.
>
Euclidian geometry is a tool. It is not telling me to do things. I
leave tools telling their master's what to do to Reimannian Geometry.
> Nothing that we observe about the universe involves planes of simultaneity.
> They're meaningless mathematical artefacts.
Not at all. There is a big difference between being hit first on the
left then the right vs. being hit first on the right then the left.
Two objects moving in different reference frames would experience these
different phenomena, even though we see them both get hit
simultaneously on the left and right side.
> The whole thing reminds me of
> the textbook question Feynman mentions in _Surely You're Joking_ that
> involved computing the "total temperature" of several stars by adding their
> individual temperatures. You can do it; it's well-defined mathematically.
> But it's silly.
>
> -- Ben
You can also find a metric which allows the distribution of stars in
the universe to be spatially isotropic for infinite distance in all
directions. You can do it; it's well-defined mathematically. But it's
silly.
Mike Fontenot
>
> What happens if you accelerate, and coast, at right-angles (perhaps in
> a distant orbit) at relativistic speeds?
When the motion is transverse, the two twins will always agree
about the correspondance between their ages. The traveler
will age more slowly (by the factor gamma, exactly as in the
one-dimensional case), but there will be no disagreement
between the twins about their ages.
(Although most of my paper assumes one-dimensional motion, I
do generalize my CADO equation for three-dimensional motion,
in equation 8b, page 640.)
Mike Fontenot
Mike Fontenot
>
> You are technically correct in that "the object's maximum (in
> magnitude) rate of ageing is greater than the accelerating observer's
> rate of ageing by a factor approximately equal to their separation, as
> measured in the object's frame," but this seems very carefully worded,
> and this is a rare case where you refer to how things are measured in
> the distant object's frame instead of the accelerated object's frame.
The only reason that I use the object's measurement of separation here
is because that's how I get the simplist equations.
>
> The separation as measured from the object's frame may be length
> contracted in the accelerating observer's frame, and this length
> contraction can go anywhere from infinitesimal to 1. If the distance
> is length contracted to very very small, accelerating toward the
> distant object which is originally moving away, this distance
> *uncontracts* causing the object to move away at unlimited "speed" and
> age by an unlimited amount.
>
I wrote a followup paper which addresses the fact that an accelerating
observer's conclusions about his speed relative to the distant object
are different from the object's measurement of speed, and are
even different from the conclusions of the MSIRF at any instant!
This seemed counter-intuitive to me at first, because by definition,
at any instant, the MSIRF is momentarily stationary wrt the traveler.
So one might certainly think that the MSIRF and the traveler must
certainly agree about the traveler's speed relative to the distant
object...but they don't! (In the traditional "twin paradox" problem,
the twins never disagree about their relative speed...any two
inertial observers will always agree about their relative speed).
So in my first paper, I SHOULD have always stated that the velocity
v was "as measured by the distant object". I didn't say that,
because I hadn't yet realized that the (non-inertial) traveler
wouldn't agree with her about their relative speed.
In that second paper, I give the bizarre result that (given
appropriate separation), a traveler who is initially motionless
wrt his sister can point his rocket
away from his sister (i.e., blast the rocket exhaust toward
her), accelerate at 1 g (according to his accelerometer), and
still conclude that their separation is DECREASING...i.e,
he will conclude that he is moving closer to her!
The situation is somewhat analogous to a bug moving to the right
on a plastic sheet that is being heated and is thus shrinking.
If the shrinking is fast enough, the bug will be getting closer
to a fixed point on the sheet to his left, even though he IS
moving to the right wrt the plastic immediately beneath him.
My followup paper is:
"Erratum and Addendum: Accelerated Observers in Special
Relativity", Physics Essays, September 2002, p357.
(I also just discovered that my reference to my original
paper gave an incorrect date: it was December, 1999 (not
September 1999 as I previously said). Sorry for the mistake.)
Mike Fontenot
>
> I don't understand this fascination with computing a quantity which is so
> obviously devoid of physical content.
I believe that anyone who was actually on an extended space voyage
of many years (in the traveler's time), far from earth and at speeds
near c, would certainly wonder what the people they cared about were
currently doing back on earth. Of course, because of the finite
speed of light, if they were many tens of lightyears away from
earth, they can't KNOW what their friends are currently doing. But
they can at least imagine what their friends' existance might be
like, if they at least know how old their friends currently are.
So I believe that anyone on such a voyage would at least want to
know what the current date is, back on earth. And I don't believe
anyone would be satisfied with an answer like "It's meaningless to
ask that question...just forget about that!"
Given that anyone would demand an answer to that question, I maintain
that the ONLY answer that is consistent with special relativity is
the one that I give via my CADO equation.
Mike Fontenot
Dirk Van de moortel
"Mike Fontenot" <mlf...@comcast.net> wrote in message news:42A0C4AF...@comcast.net...
> Ben Rudiak-Gould wrote:
> >
> > I don't understand this fascination with computing a quantity which is so
> > obviously devoid of physical content.
>
> I believe that anyone who was actually on an extended space voyage
> of many years (in the traveler's time), far from earth and at speeds
> near c, would certainly wonder what the people they cared about were
> currently doing back on earth. Of course, because of the finite
> speed of light, if they were many tens of lightyears away from
> earth, they can't KNOW what their friends are currently doing. But
> they can at least imagine what their friends' existance might be
> like, if they at least know how old their friends currently are.
>
> So I believe that anyone on such a voyage would at least want to
> know what the current date is, back on earth. And I don't believe
> anyone would be satisfied with an answer like "It's meaningless to
> ask that question...just forget about that!"
Well, when you are accelerating, your plane of simultaneity is
continuously shifting, so how old they are "now" is a rather
"volatile concept", so to speak. But indeed, I would agree that
the question how much time will have passed on Earth at some
point when they are at rest w.r.t. Earth is a bit relevant, and the
question how much *when they return* even more so - that is
of course, unless during the trip the travellers were toasted by
X-ray shifted radiation ;-)
Dirk Vdm
Spoonfed
Dirk Van de moortel wrote:
>
> Well, when you are accelerating, your plane of simultaneity is
> continuously shifting, so how old they are "now" is a rather
> "volatile concept", so to speak. But indeed, I would agree that
> the question how much time will have passed on Earth at some
> point when they are at rest w.r.t. Earth is a bit relevant, and the
> question how much *when they return* even more so - that is
> of course, unless during the trip the travellers were toasted by
> X-ray shifted radiation ;-)
>
> Dirk Vdm
>
You realize you are choosing to pick one particular inertial reference
frame (the frame at rest w.r.t earth) as being more "valid" than the
inertial frame of the rocketship when it switches off it's engines.
You are granting certain planes of simultaneity special status as being
true.
I think it is appropriate to pick a particular inertial reference
frame, but that should be whatever frame the observer is in. In this
case, the MCRF, momentarily Comoving Reference Frame.
Though the plane of simultaneity is continuously shifting, both v[t],
and v[t'] are continuous functions, so the particular plane of
simultaneity in which the traveler finds himself is well-defined at
each point in time.
And... I hope you're not talking about X-ray shifted CMBR radiation.
;)
Jonathan Doolin
Spoonfed
I fullheartedly concur with this bizarre result.
In fact, the actual distance would decrease, and the apparent distance
would decrease further still.
A yet more bizarre result is that
Meanwhile, out in front of you, the actual distance would decrease, but
the apparent distance would INCREASE. The object would then appear to
approach superluminally.
http://www.spoonfedrelativity.com/files/newYears2.swf
Dirk Van de moortel
"Spoonfed" <jonatha...@spoonfedrelativity.com> wrote in message news:1117839588.7...@g44g2000cwa.googlegroups.com...
>
>
> Dirk Van de moortel wrote:
>
> >
> > Well, when you are accelerating, your plane of simultaneity is
> > continuously shifting, so how old they are "now" is a rather
> > "volatile concept", so to speak. But indeed, I would agree that
> > the question how much time will have passed on Earth at some
> > point when they are at rest w.r.t. Earth is a bit relevant, and the
> > question how much *when they return* even more so - that is
> > of course, unless during the trip the travellers were toasted by
> > X-ray shifted radiation ;-)
> >
> > Dirk Vdm
> >
>
> You realize you are choosing to pick one particular inertial reference
> frame (the frame at rest w.r.t earth) as being more "valid" than the
> inertial frame of the rocketship when it switches off it's engines.
Of course. I pick that frame because it is the only frame
in which it really makes sense to compare the clock with the
Earth clock in order to "compare ages now". The reason is
that doing this needs the notion of simultaneity. This notion
does not exist between different frames, not even between
inertial ones in uniform relative movement.
>
> You are granting certain planes of simultaneity special status as being
> true.
That sounds very weird: planes with a "status as being true".
All I am doing is saying that I personally find the notion of
simultaneity between frames in relative movement meaningless.
>
> I think it is appropriate to pick a particular inertial reference
> frame, but that should be whatever frame the observer is in. In this
> case, the MCRF, momentarily Comoving Reference Frame.
Not even that one. The "now" of that frame is not the "now"
of the Earth frame. As far as I am concerned, saying that a
clock on Earth shows such and such "now", is a bit silly, unless
you are at rest w.r.t. Earth.
When you both agree about the simultaneity of two events,
you can -meaningfully- compare your ages. Otherwise, you
can make "statemenents" about it, but you have to use scare
quotes all over the place.
>
> Though the plane of simultaneity is continuously shifting, both v[t],
> and v[t'] are continuous functions, so the particular plane of
> simultaneity in which the traveler finds himself is well-defined at
> each point in time.
With suitable notation and initial conditions v(t) and v(t') are
given by
v(t') = c tanh( a/c t' )
v(t) = a t / sqrt( 1 + (a/c t)^2 ),
so sure, the planeS (plural!) are well defined, but IMO useless
to compare ages, unless you make the text unreadable with scare
quotes and warnings.
Apart from being a matter of taste, I think this is also a
very important pedagogical issue - as can be seen on this
forum ;-)
Dirk Vdm
Mike Fontenot
> All I am doing is saying that I personally find the notion of
> simultaneity between frames in relative movement meaningless.
I doubt that you would be able to hold to that view if you
ACTUALLY (1) were in the middle of a 10 year (your time)
voyage, (2) were 50 lightyears from earth, (3) were moving
at 0.9c wrt the earth, and (4) were badly missing a loved-one
back on earth.
Mike Fontenot
Dirk Van de moortel
"Mike Fontenot" <mlf...@comcast.net> wrote in message news:42A1E204...@comcast.net...
Hehe, you play my emotions :-)
What you say is true of course but *only* in the exact
middle of the voyage, where, assuming that my proper
acceleration history is symmetrical on both parts of the
voyage, I will indeed find myself to be in the same frame
as my loved-one, so the age comparison really makes
sense - in that special case.
As soon as I start heading home, the numbers immediately
lose their physical relevance again. Only at the Big Hug
Event will they regain significance :-)
Dirk Vdm
Mike Fontenot
> What you say is true of course but *only* in the exact
> middle of the voyage, where, assuming that my proper
> acceleration history is symmetrical on both parts of the
> voyage, I will indeed find myself to be in the same frame
> as my loved-one, so the age comparison really makes
> sense - in that special case.
Actually, I didn't intend any significance to my choice
of the middle of your voyage...I just intended it to
indicate that you had been away from home for a long time,
and were very far away from earth. I wasn't restricting
myself to the standard travelling twin problem, with its
symmetry about the midpoint.
There is another argument for why the CADO ("current age
of a distance object") must be considered to be meaningful.
I think it might be more appropriate for me to post that
in response to Ben Roudiak-Gould's posting, so I'll go do
that now.
Mike Fontenot
Dirk Van de moortel
"Mike Fontenot" <mlf...@comcast.net> wrote in message news:42A1F8EA...@comcast.net...
> Dirk Van de moortel wrote:
>
> > What you say is true of course but *only* in the exact
> > middle of the voyage, where, assuming that my proper
> > acceleration history is symmetrical on both parts of the
> > voyage, I will indeed find myself to be in the same frame
> > as my loved-one, so the age comparison really makes
> > sense - in that special case.
>
> Actually, I didn't intend any significance to my choice
> indicate that you had been away from home for a long time,
> and were very far away from earth. I wasn't restricting
> myself to the standard travelling twin problem, with its
> symmetry about the midpoint.
Yes I know. But your usage of "the middle" came out just
the way I wanted it to get my message across - again :-)
>
> There is another argument for why the CADO ("current age
> of a distance object") must be considered to be meaningful.
> I think it might be more appropriate for me to post that
> in response to Ben Roudiak-Gould's posting, so I'll go do
> that now.
Okay. But please not that Ben is even more skeptic than
I am. I think I'm somewhere in the middle.
Cheers,
Dirk Vdm
Spoonfed
Implicitly or explicitly, the scare quotes are always going to be
present.
My car has a maximum "velocity" of ninety miles per hour. And I mean
velocity in the sense of a relative motion with the road. We are
treating the road as though it is stationary in this case instead of
revolving at 900 miles an hour, orbiting at 19 miles per second around
the sun and at a million miles a day around the milky way, three
hundred thousand miles per second toward Andromeda, etc.
Oh well, I gotta go now. But you should be able to determine what you
mean exactly with other methods than scare quotes.
Dirk Van de moortel
"Mike Fontenot" <mlf...@comcast.net> wrote in message news:42A1F8EA...@comcast.net...
> Dirk Van de moortel wrote:
>
> > What you say is true of course but *only* in the exact
> > middle of the voyage, where, assuming that my proper
> > acceleration history is symmetrical on both parts of the
> > voyage, I will indeed find myself to be in the same frame
> > as my loved-one, so the age comparison really makes
> > sense - in that special case.
>
> Actually, I didn't intend any significance to my choice
> of the middle of your voyage...I just intended it to
> indicate that you had been away from home for a long time,
> and were very far away from earth. I wasn't restricting
> myself to the standard travelling twin problem, with its
> symmetry about the midpoint.
Yes I know. But your usage of "the middle" came out just
the way I wanted it to get my message across - again :-)
>
> There is another argument for why the CADO ("current age
> of a distance object") must be considered to be meaningful.
> I think it might be more appropriate for me to post that
> in response to Ben Roudiak-Gould's posting, so I'll go do
> that now.
Okay. But please note that Ben is even more skeptic than
Mike Fontenot
> I don't understand this fascination with computing a quantity which is so
> obviously devoid of physical content.
There is another argument, other than the philosophical argument
that I gave earlier, for why the CADO ("current age of a distant
object") must be considered meaningful. The short version of
that reason is that it would be impossible for the traveler
to be a practicing experimental physicist, at least for long,
if he believed that the CADO had no meaning.
I go to considerable lengths in my paper to show the following:
If a traveler (moving in an arbitrary manner) receives several
radio messages reporting the age of the distance object (at the
times of message transmission, of course), it is possible for
the traveler to DEDUCE the current age of the distance object,
at the time of reception of the latter messages. The traveler
can do this even if he has no knowledge of special relativity:
he only needs to make use of "first principles" that are
unquestioned by any physicist. If he DOES know about special
relativity, then the deduction is quicker (requires fewer
messages) and more direct, but the answer obtained is the
same in either case. And the answer obtained is the same
answer as is given by my CADO equation.
So, if a traveling experimental physicist insists on believing
that the CADO is a meaningless concept, he will have to disregard
his own measurements...which probably means that he would have
to give up his profession, and get into some other line of work.
Mike Fontenot
Spoonfed
There would be two other emotionally significant seeming Earth times.
At what Earth-time did Earth's messages leave, and what earth-time will
our messages arrive at earth? (if we are the travelers).
These questions about the time *on earth* are independent of frame,
because they specify the frame. They are most easily calculated from
the Earth's frame, since it is a calculation of Earth's time. But the
travelers would not generally be *calculating* the time on earth when
the message was sent. They would simply be receiving it, and perhaps
looking at the timestamp in the message. They would have to perform
calculations to figure out what Earth-time their messages would be
received, but they also might perform calculations to figure out what
time it was on earth "NOW" and the question is whether they would use
Earth's plane of simultaneity or their own.
I don't think we can really predict which one of these would become the
convention. But I am sure that they would recognize it was a
convention.
I think they would be more likely to adopt the convention of looking at
their star maps in their own changing reference frame, rather than
trying to see it in Earth's frame. Unless they were somehow restricted
to paper or other non-electronic media, it seems highly unlikely that
they would rely on static maps made in Earth's frame. Instead, for
navigation, they would use maps that showed the position of stars and
planets in their own current frame.
===================
Now, for a moment, I'd like to see for sure we're on the same page.
If me and my twin (33 years old) both undergo a symmetrical
acceleration, so that the relative velocity is 99% of the speed of
light, gamma is approximately 7. For me, seven years pass, and I am
40.
Now, according to my idea, where my reference frame is valid, my twin
is 7*.99 light years away, and he's only 34.
According to your idea, it only makes sense to refer to his age if I
enter his reference frame. In that case, I put on the brakes, to get
into his reference frame. He is now 49*.99 light years away, and we
are both aged 40.
What I am arguing is that both ideas are perfectly valid, as long as
things are made explicit.
======================
Jonathan Doolin
www.spoonfedrelativity.com
Dirk Van de moortel
"Spoonfed" <jonatha...@spoonfedrelativity.com> wrote in message news:1117984282.5...@g43g2000cwa.googlegroups.com...
>
>
> Dirk Van de moortel wrote:
> > "Mike Fontenot" <mlf...@comcast.net> wrote in message news:42A1E204...@comcast.net...
> > > Dirk Van de moortel wrote:
> > >
> > > > All I am doing is saying that I personally find the notion of
> > > > simultaneity between frames in relative movement meaningless.
> > >
> > > I doubt that you would be able to hold to that view if you
> > > ACTUALLY (1) were in the middle of a 10 year (your time)
> > > voyage, (2) were 50 lightyears from earth, (3) were moving
> > > at 0.9c wrt the earth, and (4) were badly missing a loved-one
> > > back on earth.
> >
> > Hehe, you play my emotions :-)
> >
> > What you say is true of course but *only* in the exact
> > middle of the voyage, where, assuming that my proper
> > acceleration history is symmetrical on both parts of the
> > voyage, I will indeed find myself to be in the same frame
> > as my loved-one, so the age comparison really makes
> > sense - in that special case.
> > As soon as I start heading home, the numbers immediately
> > lose their physical relevance again. Only at the Big Hug
> > Event will they regain significance :-)
> >
> > Dirk Vdm
>
> There would be two other emotionally significant seeming Earth times.
>
>
> At what Earth-time did Earth's messages leave, and what earth-time will
> our messages arrive at earth? (if we are the travelers).
Indeed. You can imagine your loved-one having a
certain age when she has sent a message or when she
will receive one from you.
>
> These questions about the time *on earth* are independent of frame,
> because they specify the frame.
That is exactly why they are *dependent* of frame ;-)
You always wonder what time it is on Earth "now", and this
"now" is in your frame.
> They are most easily calculated from
> the Earth's frame, since it is a calculation of Earth's time.
Actually everything is most easily calculated from the Earth's
frame, since it is inertial. All you have to know is your
entire v(t) history as seen in Earth coordinates.
> But the
> travelers would not generally be *calculating* the time on earth when
> the message was sent. They would simply be receiving it, and perhaps
> looking at the timestamp in the message.
Indeed.
> They would have to perform
> calculations to figure out what Earth-time their messages would be
> received, but they also might perform calculations to figure out what
> time it was on earth "NOW" and the question is whether they would use
> Earth's plane of simultaneity or their own.
I wholehaertedly disagree with that last part. As a traveller, your
idea of
"what time it is "now" on earth"
is useless, for the simple reason that you can manipulate it
by adjusting your thrusters. You can even make your idea of
"what time it is "now" on earth"
to run backward. That makes it, at least for me, useless.
But YMMV.
>
> I don't think we can really predict which one of these would become the
> convention. But I am sure that they would recognize it was a
> convention.
>
> I think they would be more likely to adopt the convention of looking at
> their star maps in their own changing reference frame, rather than
> trying to see it in Earth's frame. Unless they were somehow restricted
> to paper or other non-electronic media, it seems highly unlikely that
> they would rely on static maps made in Earth's frame. Instead, for
> navigation, they would use maps that showed the position of stars and
> planets in their own current frame.
>
> ===================
>
> Now, for a moment, I'd like to see for sure we're on the same page.
>
> If me and my twin (33 years old) both undergo a symmetrical
> acceleration, so that the relative velocity is 99% of the speed of
> light, gamma is approximately 7. For me, seven years pass, and I am
> 40.
>
> Now, according to my idea, where my reference frame is valid, my twin
> is 7*.99 light years away, and he's only 34.
>
> According to your idea, it only makes sense to refer to his age if I
> enter his reference frame. In that case, I put on the brakes, to get
> into his reference frame. He is now 49*.99 light years away, and we
> are both aged 40.
Yes.
>
> What I am arguing is that both ideas are perfectly valid, as long as
> things are made explicit.
I agree, perfectly valid.
But even more perfectly useless ;-)
Dirk Vdm
Spoonfed
Is this the conventional method of referring to both age and distance
to stars in the universe? Does the process of making star-maps involve
discovering its redshift to find its relative velocity, then performing
a Lorentz transformation to its reference frame, pivoting on the event
that earth reaches its current proper age, then stating its distance
from earth in that frame?
Is this my long-sought "question" to the FLRW Metric solution?
http://spoonfedrelativity.com/phpBB/viewtopic.php?t=13
> >
> > What I am arguing is that both ideas are perfectly valid, as long as
> > things are made explicit.
>
> I agree, perfectly valid.
> But even more perfectly useless ;-)
>
> Dirk Vdm
Don't assume that by leaving out all references to simultaneity all
people will naturally adopt this supposedly obvious convention.
If astronomers and cosmologists are mapping the cosmos by rapidity
space* instead of velocity space, they should recognize their own
convention, and the difference between rapidity space and velocity
space. In rapidity space, it makes sense to say that the universe is
(possibly) infinite, expanding at a (possibly) infinite rate, and
uniform throughout. In velocity space, it makes sense to say that the
universe is spherical, with a (possibly) infinitely dense surface,
expanding outward at the speed of light.
*Rapidity is v/sqrt(1-(v/c)^2)
Rapidity space: By finding the direction and rapidity of an object
relative to the earth, and multiplying by the age of the universe, you
find its current distance in rapidity space. This distance is equal to
the distance the object will be from earth in the object's reference
frame at the time when earth's proper time reaches earth's current age.
Jonathan Doolin
There are a couple of questions I'd like to revisit, if any of the other participants are still active.
(1) whether "valid but useless" is a solid criticism of any idea
That is, whether or not you believe that your hyperplane of simultaneity is a useful idea, it is certainly a well-defined mathematical construct. "useless" implies that it has no use. But obviously, if you can use that hyperplane of simultaneity to describe or represent information, then it has been put to use... ergo, it is NOT useless.
and
(2) What represents the "visceral" experience of the traveling twin.
I'd like to imagine two different versions of the visceral experience.
(2a) In one version, one envisions an animated space-time diagram, in which one can see events swinging forward and backward in time.
https://en.wikipedia.org/wiki/Talk:Twin_paradox#Some_more_thought_on_WWoods_diagrams_in_archives_11_and_12_and_13
You can see here that Dirk Van de Moortel is still basically making the argument that representations of animated space-time diagrams are valid but useless.
In my opinion, they are not useless at all, but give clarity to an idea that has been terribly muddled or ignored by traditional texts on relativity.
(2b) In another version of visceral experience, one envisions what an accelerating observer would actually see. In this, you can see that when you accelerate toward something, it's image jumps forward away from you, and when you accelerate away from something, it's image jumps back toward you.
This is confirmed in a free simulation game from MIT, which you could download here:
http://gamelab.mit.edu/games/a-slower-speed-of-light/
Now as to whether these ideas are useless, largely depends on what you are trying to do with them. True ideas are generally useful for something.
For instance, in December 2015, I was able to find a way to independently confirm something I doubted in the MIT demonstration.
I did not believe at first that spheres would maintain their apparent shapes on Lorentz Contraction.
After quite a bit of simulation, I was able to see, to my surprise that perfect spheres maintain their apparent shape during Lorentz Transformation, just as they do in rotation.
https://www.physicsforums.com/threads/terrell-revisited-the-invisibility-of-the-lorentz-contraction.520875/
Alan Folmsbee
? Can you apply SR principles from an accelerating frame of reference?
"No. One must apply the principles of general relativity. The principle of
which I speak is the one that states that the laws of physics are the same
in all coordinate systems. This is a GR principle called the principle of
covariance."
Jonathan Doolin
The truth is, I didn't know what he was talking about 11 years ago, and I'm still not sure.
It seems like it would be a fairly simple task to describe the Rindler Coordinate System by using an accelerating reference frame.
One could, perhaps invoke a principle of covariance instead, and get the same answer.
But to claim that the laws of physics are the same, for instance, within a Rindler system, and a Minkowski reference frame...?
Well, if you drop something in a Rindler coordinate system, it falls. If you drop something in a non-accelerating inertial frame, it floats or moves with whatever initial velocity you gave it.
I suppose one could argue that the physics are the same; only the coordinate system is different... But I think that unless you make very clear exactly what you mean by "same" it's a very misleading sort of statement.
Understanding is accomplished by making a distinction between two similar ideas; not by conflating them.
Tom Roberts
> On Thursday, August 11, 2016 at 2:19:09 PM UTC-5, Alan Folmsbee wrote:
>> The original question was answered by PmB,
>>
>> ? Can you apply SR principles from an accelerating frame of reference?
>>
>> "No. One must apply the principles of general relativity. The principle of
>> which I speak is the one that states that the laws of physics are the same
>> in all coordinate systems. This is a GR principle called the principle of
>> covariance."
spacetime manifold is flat. To do this, one usually starts from an inertial
frame and performs a change of variables to the accelerated coordinates. The
tools of GR can assist in doing this, but at base bare algebra will suffice.
> It seems like it would be a fairly simple task to describe the Rindler
> Coordinate System by using an accelerating reference frame.
> One could, perhaps invoke a principle of covariance instead, and get the same
> answer.
and projecting it onto the accelerating coordinates.
> But to claim that the laws of physics are the same, for instance, within a
> Rindler system, and a Minkowski reference frame...?
field equation of GR is the same when projected onto any coordinates, including
both of these.
Because coordinates are an arbitrary human construct, and nature clearly does
not use them, any valid laws of physics must be completely independent of
coordinates. So, for instance, the Einstein field equation can be written in
terms of the tensors (which have no dependence on coordinates):
G + 𝚲 g = k T
But also one can project the tensors onto an arbitrary coordinate system and
obtain the equation in terms of tensor components (now 16 equations):
G_ij + 𝚲 g_ij = k T_ij
> Well, if you drop something in a Rindler coordinate system, it falls. If you
> drop something in a non-accelerating inertial frame, it floats or moves with
> whatever initial velocity you gave it.
(accelerates); the same rock relative to an inertial frame does not. The rock
does not "change", nor does it motion (however defined), only the DESCRIPTION
changes because the coordinates used to generate it changed.
> I suppose one could argue that the physics are the same; only the coordinate
> system is different...
humans to DESCRIBE it. Change coordinates, and the description also changes,
even though the underlying system/object/physics does not.
> But I think that unless you make very clear exactly
> what you mean by "same" it's a very misleading sort of statement.
"physics" is no different. Just like "=" in math.
> Understanding is accomplished by making a distinction between two similar
> ideas; not by conflating them.
must be kept distinct.
Tom Roberts
Jonathan Doolin
First of all, I want to distinguish between "description dependent" coordinates and "observer dependent" coordinates. I try to make the distinction between those two ideas here:
http://www.spoonfedrelativity.com/pages/Types-of-Transformations.php
I was trying to shift the focus to observer dependent changes in locations of events, because I feel that is my area of expertise.
But of course, you can ignore what I'm saying, if I cannot demonstrate some working knowledge of description dependent relativity. So I'm willing to work at it, time permitting.
On the subject of description-dependent relativity, I'm not sure whether we disagree at all. However, when you say "tensors have no dependence on coordinates" it is difficult to find an interpretation of that statement I can agree with.
See here, that the Del operator, (usually denoted \nabla) has a very different form in different coordinate systems.
https://en.wikipedia.org/wiki/Del_in_cylindrical_and_spherical_coordinates
I have not done much work on understanding tensors for a couple of years, but my analysis and confusion from December 2014 is on public display on a playlist here:
https://www.youtube.com/watch?v=foRPKAKZWx8&list=PLC-qVSnsyc7-6MXt0ZakH4s4EDOINGiOl&index=1
Here I will copy and paste my questions from there:
=====================================
I notice a lot of the posts here are questions and/or complaints about the notation used in the video. I am convinced that there may be some way to improve on Einstein Notation, so for a start, I have been trying to translate the Einstein Notation into matrix multiplication notation. I'll just be audacious here and post a link to the playlist of videos I've made while struggling through this stuff.
https://www.youtube.com/watch?v=5hK_PCXNLH4&list=PLC-qVSnsyc7-6MXt0ZakH4s4EDOINGiOl
Merry Christmas!
Is there an equation 6, or did I miss it?
Reply
I think what equation 6 needs to be is something along the lines of $dV_y^m\overset{?}{=}dV_x^n\frac{\partial x^m}{\partial y^r}$. Though I'm not sure that's right You have a transformation of a differential path element at 47:30. My concern is that what I've written above is sort of a reversal on the equation at 47:30, e.g. replacing dy^n with V_x^n, and dx^m with V_y^m..
You don't discuss the transformation of a vector field, except for the path element, itself... Am I stumbling upon the rationale for distinguishing between contravariant and covariant? Is the difference between "upstairs" indices and "downstairs" indices the same as the difference between differential path elements and differentials of vector fields?
Edit: No, I guess not. At 33:36, you show a transformation of the vector field that suggest it goes exactly the same as the differential path element. I'll keep working at it.
I've come to the conclusion that the equation at 33:36 (Equation 3) should have both a covariant and contravariant form, just like equation 4 does. Later on in the video, 59:26, he's doing a partial derivative of the covariant form of Equation 3.
========================================
My biggest concern about Einstein Notation was that it tends to render errors in commutativity very hard to detect.
mlwo...@wp.pl
> Because coordinates are an arbitrary human construct, and nature clearly does
> not use them, any valid laws of physics must be completely independent of
> coordinates.
of numbers, equations and whole mathematics. And they shouldn't
use other, non-mathematical words, too.
Right, poor idiot?
mlwo...@wp.pl
these wise things you're talking about models
sometimes.
Jonathan Doolin
Your self-dialog reminds me of some lyrics from a song "Little Talks" by "of Monsters and Men"
Female singer confesses: "Sometimes I don't know if I am wrong or right"
Male voice (ironically reassuring): "Your mind is playing tricks on you my dear."
Then, rather than arguing, "No. I am either wrong, or I am right, there seems to be a rather sudden forced consensus:"
Consensus: "Though the truth may vary, this ship will carry our bodies safe to shore."
mlwo...@wp.pl
> On Tuesday, August 16, 2016 at 8:06:05 AM UTC-5, mlwo...@wp.pl wrote:
> > W dniu wtorek, 16 sierpnia 2016 15:01:42 UTC+2 użytkownik mlwo...@wp.pl napisał:
> > > W dniu niedziela, 14 sierpnia 2016 21:47:31 UTC+2 użytkownik tjrob137 napisał:
> > >
> > > > Because coordinates are an arbitrary human construct, and nature clearly does
> > > > not use them, any valid laws of physics must be completely independent of
> > > > coordinates.
> > >
> > > Samely, valid laws of physics must be completely independent
> > > of numbers, equations and whole mathematics. And they shouldn't
> > > use other, non-mathematical words, too.
> > > Right, poor idiot?
> >
> > BTW - I always knew you really don't believe
> > these wise things you're talking about models
> > sometimes.
>
> Thanks mlwo. Took me several readings to realize you are trolling yourself.
>
> Your self-dialog reminds me of some lyrics from a song "Little Talks" by "of Monsters and Men"
rethoric. As expected from fanatic idiot.
Jonathan Doolin
mlwo...@wp.pl
Jonathan Doolin
mlwo...@wp.pl
Jonathan Doolin
I'm no strawman, either. If you nail me, you nail me. But for now, I still live.
Maciej Woźniak
Użytkownik "Jonathan Doolin" napisał w wiadomości grup
dyskusyjnych:8ede7e9d-84a2-47dc...@googlegroups.com...
still live.
Don't know Jesus, so I can't tell whether he was a fanatic.
I can tell it about you, however.
JanPB
suffers from some autism-like cognitive problem. It's a standard symptom.
You have to spell everything out and talk to him like you would to Mr. Spock.
(It's a fun and endearing character in movies but in real life it's something
else :-) )
His approach to science is an example of this, his entire conceptual framework
is swamped and overloaded by literal meanings. A typical example of this is his
claim that according to physics trees move when you walk.
--
Jan
mlwo...@wp.pl
suffers from some extreme stupidity cognitive problem. It's a standard
literal content of his mumble is insignificant, what matters is that
he is a GURU, so he must be listened, bowed before and obeyed.
Jonathan Doolin
> > > > > > > > > Samely, valid laws of physics must be completely independent
> > > > > > > > > of numbers, equations and whole mathematics. And they
> > > > > > > > > shouldn't
> > > > > > > > > use other, non-mathematical words, too.
> > > > > > > > > Right, poor idiot?
> > > > > > > >
> > > > > > > > BTW - I always knew you really don't believe
> > > > > > > > these wise things you're talking about models
> > > > > > > > sometimes.
> > > > > > >
> > > > > > > Thanks mlwo. Took me several readings to realize you are
> > > > > > > trolling yourself.
> > > > > > >
> > > > > > > Your self-dialog reminds me of some lyrics from a song "Little
> > > > > > > Talks" by "of Monsters and Men"
> > > > > >
> > > > > > Having no arguments, you can only use "ad personam"
> > > > > > rethoric. As expected from fanatic idiot.
> > > > >
> > > > > You've nailed me.
> > > >
> > > > I have. You're no challenge.
> > >
> > > Neither was Jesus.
> >
> > If he weren't they wouldn't kill him, poor idiot.
>
>
> |I'm no strawman, either. If you nail me, you nail me. But for now, I
> still live.
>
> You still live, but I've nailed you, as you wrote yourself.
> Don't know Jesus, so I can't tell whether he was a fanatic.
> I can tell it about you, however.
A fanatic is a person filled with excessive and single-minded zeal.
Perhaps you would like to make an attempt to nail me down further by describing what my zeal is for?
Then we can determine whether you have nailed me, or a strawman.
Jonathan Doolin
> is swamped and overloaded by literal meanings.
>A typical example of this is his
> claim that according to physics trees move when you walk.
>
> --
> Jan
Julio Di Egidio
> But for example, in the twin paradox, if we viewed the entire thing
> from a frame of reference centered on the travelling twin, with the
> Earth 'accelerating' away, then decelerating, then the reverse for the
> return journey, we'd still get the same final age difference predicted,
> wouldn't we?
Yes, because the clock difference is acquired in correspondence (and only in correspondence) with an actual acceleration, and it is the travelling twin that is subject to (and indeed perceives) the acceleration, not the twin that stays home: so the final result is the same regardless of the frame one takes to be the "rest" frame.
IOW, as long as the twins just travel past each other but neither accelerates in any way, the perceived clock difference will be instead symmetrical and no actual clock difference will be acquired. It's the turn around that causes the clock difference.
(I know the above is essentially correct, but please feel free to nitpick.)
Julio
mlwo...@wp.pl
I don't like Tom's logic: "nature doesn't use x, so laws of physics
have to be x-independent".
What is your answer? "Troll! Fool!" You probably didn't even read,
what I wrote. Did You?
mlwo...@wp.pl
and saying "I'm immobile and these buildings are moving
around"?
Literally - relativity is false. Since the very beginning.
And as it's obviously impossible that so many so wise
gurus were all wrong, it's the literal meaning that must be
wrong.
Simple?
paparios
> I don't like Tom's logic: "nature doesn't use x, so laws of physics
> have to be x-independent".
> What is your answer? "Troll! Fool!" You probably didn't even read,
> what I wrote. Did You?
paparios
>
> Yes, it is. But, do you know ANYONE walking the street
> and saying "I'm immobile and these buildings are moving
> around"?
Jonathan Doolin
"nature doesn't use x, so laws of physics have to be x-independent."
It should not be a question of whether nature does use x. It is a question of whether it is capable of using x.
But I don't think I've "nailed" Tom Roberts. I have only "nailed" a possible interpretation of a set of words, which might possibly represent Tom Robert's ideas, or it might be a strawman interpretation of Tom Robert's ideas.
Odd Bodkin
> On Friday, August 19, 2016 at 10:40:40 AM UTC-3, mlwo...@wp.pl wrote:
>
>> >
>> > Yes, it is. But, do you know ANYONE walking the street
>> > and saying "I'm immobile and these buildings are moving
>> > around"?
> You are the only one here saying that nonsense. But if you sit in a coach
> at a train station and the train besides you starts to move, then most people
> feel that they are doing the move and not the other train. If you are standing
> on the street, can you point the true direction of you movement?
Indeed the point is that ANY statement by ANYONE about whether something
is moving or not in any absolute sense is garbage.
No one sensible will say while walking that "I'm immobile, but the
buildings are moving." But on the other hand, no one sensible will say
"The buildings are immobile, and I am moving," either. BOTH statements
are wrong, and it doesn't take long to dismantle either one.
Common sense may tell you that the buildings must be immobile because
they are fixed to the ground. But then you can ask such a person, "And
is the ground immobile?" If they say yes, then ask them what causes the
change from day to night? Only a fool would say that the sun moves
around the immobile earth, and it's the sun's movement that causes that
change. Any CHILD knows that it is the ground's movement because of the
rotation of the earth that causes that change. So then going back, ask
again, "So are the buildings, which are fixed to the ground, immobile or
not?" Then see what common sense tells you.
--
Odd Bodkin --- maker of fine toys, tools, tables
Jonathan Doolin
> W dniu piątek, 19 sierpnia 2016 15:05:53 UTC+2 użytkownik Jonathan Doolin napisał:
> > On Thursday, August 18, 2016 at 5:22:04 PM UTC-5, JanPB wrote:
> >
> > > is swamped and overloaded by literal meanings.
> >
> > What is wrong with literal meaning?
> >
> >
> > >A typical example of this is his
> > > claim that according to physics trees move when you walk.
> > >
> > > --
> > > Jan
> >
> > Isn't the essence of Galilean Relativity precisely this point?
>
> Yes, it is. But, do you know ANYONE walking the street
> and saying "I'm immobile and these buildings are moving
> around"?
"So what is the reference frame of the traveling twin? There are five requirements that any such frame must have. (1) It must be such that the traveler is perpetually located at its spatial origin."
https://sites.google.com/site/cadoequation/cado-reference-frame#The%20Non-Invertibility%20of%20the%20CADO%20Frame
Tom Roberts
> the clock difference is acquired in correspondence (and only in
> correspondence) with an actual acceleration, and it is the travelling twin
> that is subject to (and indeed perceives) the acceleration, not the twin that
> stays home: so the final result is the same regardless of the frame one
> takes to be the "rest" frame.
observing), but your reasoning is faulty.
Acceleration does NOT affect the ticking of a clock, as long as it is mild
enough to not break the clock. Two gedankens that demonstrate this:
1) the "triplet paradox" in which three inertial triplets A,B,C move
so B departs from A, B meets C far from A, and C comes back to A.
The sum of the elapsed proper time between meetings for B+C is
smaller than that of A. There is no acceleration anywhere in this
scenario.
2) Put clocks on the edges of circular tables that rotate around centers
at rest in an inertial frame, such that the clocks pass each other
periodically (the tables are tangent to each other with a rational
ratio of their rotation periods). By selecting the radius of each
table, it is possible to have a situation in which clock A moves
faster relative to that frame than B, but has a smaller acceleration.
A will experience less proper time between meetings than B.
Bottom line: it is the path through spacetime that matters, not any
acceleration. Of course acceleration may be required to make paths meet multiple
times, but the calculation is an integral over the path, performed in an
inertial frame: \integral sqrt(1-v^2/c^2) dt. This obviously does not depend on
acceleration.
> IOW, as long as the twins just travel past each other but neither accelerates
> in any way, the perceived clock difference will be instead symmetrical and no
> actual clock difference will be acquired. It's the turn around that causes
> the clock difference.
twin between meetings.
Tom Roberts
Jonathan Doolin
, but the calculation is an integral over the path, performed in an
> inertial frame: \integral sqrt(1-v^2/c^2) dt. This obviously does not depend on acceleration.
>
>
I see confirmation of your path integral, Tom
https://en.wikipedia.org/wiki/Proper_time
But where can I find a definition of velocity that frees it from its dependency on acceleration?
Julio Di Egidio
> On 8/19/16 8/19/16 - 8:09 AM, Julio Di Egidio wrote:
> Acceleration does NOT affect the ticking of a clock, as long as it
> is mild enough to not break the clock.
> Of course acceleration may be required to make paths meet multiple
times,
> > IOW, as long as the twins just travel past each other but neither accelerates
> > in any way, the perceived clock difference will be instead symmetrical and no
> > actual clock difference will be acquired. It's the turn around that causes
> > the clock difference.
>
> Closer, but it's not really the turnaround, it's really the entire path of each
> twin between meetings.
Julio
Julio Di Egidio
an acquired clock difference even if the travelling twin just changes speed,
but I still haven't worked out all cases and details...
Julio
Tom Roberts
> there is no acquired clock difference
> unless there is a *change of path* (i.e. a deviation for the rectilinear
> path) at some point.
In GR, for small objects an "inertial path" is a geodesic. Two test particles in
orbit around a massive object are both in inertial motion, and yet you can
arrange their orbits so they have repeated meetings with different elapsed
proper times between them.
Yes, in SR there must be some non-inertial motion in order for two objects to
meet more than once. In GR this is not required.
Concentrating on "changes in path" is unwarranted. The ONLY general way to
compute the elapsed proper time along a path is to integrate the metric along
the path. In particular, this works for all continuous paths (and non-continuous
paths are unphysical).
Tom Roberts
Julio Di Egidio
EOD.
Julio
Maciej Woźniak
Użytkownik "paparios" napisał w wiadomości grup
dyskusyjnych:dbbd8eaa-1995-4c6b...@googlegroups.com...
On Friday, August 19, 2016 at 10:22:09 AM UTC-3, mlwo...@wp.pl wrote:
> I don't like Tom's logic: "nature doesn't use x, so laws of physics
> have to be x-independent".
> What is your answer? "Troll! Fool!" You probably didn't even read,
> what I wrote. Did You?
|For sure, Nature does not use coordinates (x,y,z,t). If you believe that is
incorrect, then show where in Nature are those x, y, z and t located.
Coordinates are old human invention.
words, definitions and many more. Surely idiots like you or Tom don't have
to use it. Sittting on a tree and eating bananas is a right place for you.
Maciej Woźniak
Użytkownik "paparios" napisał w wiadomości grup
On Friday, August 19, 2016 at 10:40:40 AM UTC-3, mlwo...@wp.pl wrote:
>
> Yes, it is. But, do you know ANYONE walking the street
> and saying "I'm immobile and these buildings are moving
> around"?
|You are the only one here saying that nonsense. But if you sit in a coach
at a train station and the train besides you starts to move, then most
people feel that they are doing the move and not the other train.
Anyway, nobody walking the street is saying "I'm immobile
and these buildings are moving around". Maybe with
the exception of Gary, poor idiot.
Naive Galileo's guesses about observers and their
point of views were - naive guesses.
Maciej Woźniak
Użytkownik "Jonathan Doolin" napisał w wiadomości grup
dyskusyjnych:b71e5d6a-78ce-4fcc...@googlegroups.com...
On Friday, August 19, 2016 at 8:40:40 AM UTC-5, mlwo...@wp.pl wrote:
> W dniu piątek, 19 sierpnia 2016 15:05:53 UTC+2 użytkownik Jonathan Doolin
> napisał:
> > On Thursday, August 18, 2016 at 5:22:04 PM UTC-5, JanPB wrote:
> >
> > > is swamped and overloaded by literal meanings.
> >
> > What is wrong with literal meaning?
> >
> >
> > >A typical example of this is his
> > > claim that according to physics trees move when you walk.
> > >
> > > --
> > > Jan
> >
> > Isn't the essence of Galilean Relativity precisely this point?
>
> Yes, it is. But, do you know ANYONE walking the street
> and saying "I'm immobile and these buildings are moving
> around"?
|Mike Fontenot has said this:
|"So what is the reference frame of the traveling twin? There are five
requirements that any such frame must have. (1) It must be such that the
traveler is perpetually located at its spatial origin."
paparios
Maciej Woźniak
Użytkownik "paparios" napisał w wiadomości grup
Vectors are surely one of them.
Jonathan Doolin
If acceleration is defined by Newton's Second Law.
a=\Sigma F / m
And force is determined by the Universal Law of Gravity:
F = G m1 m2 / r^2
And inertial is defined as "not accelerating"
Then Tom is clearly wrong.
But Tom has Non Newtonian, GR definitions of these words. Where "inertial" means "geodesic".
Jonathan Doolin
I have presented an animated spacetime diagram on Wikipedia where the observations of a traveling twin are held immobile, while all of the events in spacetime move around.
https://commons.wikimedia.org/wiki/File:Lorentz_Transformations_of_Twin_Paradox_Minkowski_Diagram.gif
And I said, two days ago, "nature does provide us each with the perceptions of the universe around us, and indeed constructs an "ironically inertial" reference frame from the point-of-view of an accelerating observer."
http://www.spoonfedrelativity.com/pages/CADO-v-PLADO.php
mlwo...@wp.pl
obvious yes or no question. No spacetime
diagrams needed.
> And I said, two days ago, "nature does provide us each with the perceptions of the universe around us, and indeed constructs an "ironically inertial" reference frame from the point-of-view of an accelerating observer."
then it's NOT provided by nature.
And, unless you know someone walking the
wrote about point-of-views is a simple
fabricated bullshit.
Jonathan Doolin
No results found for
"I'm immobile and these buildings are moving around".
>
>
> > And I said, two days ago, "nature does provide us each with the perceptions of the universe around us, and indeed constructs an "ironically inertial" reference frame from the point-of-view of an accelerating observer."
>
>
> If a chimpanzsee from a jungle can't do it
> then it's NOT provided by nature.
> And, unless you know someone walking the
> street and saying "I'm immobile and these
> buildings are moving around" - whatever you
> wrote about point-of-views is a simple
> fabricated bullshit.
Since google has not offered anyone who has said this, I will now.
"I'm immobile, and these buildings are moving around."
Certainly, it is such a horrible statement of the idea that it would be easy to misinterpret if you sought misunderstanding, and easy to mock if you sought foolishness. But in the sense that "I have no other perspective than my own; I am immobile within my own viewpoint." It is absolutely true.
JanPB
it means you are adding an extra meaning (or a definition) to the words
"immobile" and "moving around" beyond those which the model uses.
The model with this symmetry property works (meaning, its quantification agree
with experimental results to an error margin deemed acceptable).
As far as the extra meanings and definitions go, you are on your own. Or
at least you have to say what you mean precisely. You keep using words
with precise meanings in physics in new, undefined ways, hence the confusion.
--
Jan
mlwo...@wp.pl
REAL observer with "point of view" you're
describing?
> > If a chimpanzsee from a jungle can't do it
> > then it's NOT provided by nature.
> > And, unless you know someone walking the
> > street and saying "I'm immobile and these
> > buildings are moving around" - whatever you
> > wrote about point-of-views is a simple
> > fabricated bullshit.
>
> The chimpanzee cannot, except via simulation, adopt another point-of-view, other than its own. In that sense, it is immobile within the point-of-view offered to it by nature.
> Since google has not offered anyone who has said this, I will now.
>
> "I'm immobile, and these buildings are moving around."
>
> Certainly, it is such a horrible statement of the idea that it would be easy to misinterpret if you sought misunderstanding, and easy to mock if you sought foolishness. But in the sense that "I have no other perspective than my own; I am immobile within my own viewpoint." It is absolutely true.
A classical fanatic lie for the
"absolutely right" insane ideology.
Of course, I won't prove you anything.