On Sunday, January 19, 2025 at 4:27:42 PM UTC-7 Jesse Mazer wrote:
On Sun, Jan 19, 2025 at 5:07 PM Alan Grayson <agrays...@gmail.com> wrote:
On Sunday, January 19, 2025 at 12:05:06 PM UTC-7 Jesse Mazer wrote:
On Sun, Jan 19, 2025 at 12:21 PM Alan Grayson <agrays...@gmail.com> wrote:
On Saturday, January 18, 2025 at 9:30:47 PM UTC-7 Jesse Mazer wrote:
On Sat, Jan 18, 2025 at 8:25 PM Alan Grayson <agrays...@gmail.com> wrote:
On Saturday, January 18, 2025 at 1:25:08 PM UTC-7 Jesse Mazer wrote:
On Sat, Jan 18, 2025 at 2:55 PM Alan Grayson <agrays...@gmail.com> wrote:
On Saturday, January 18, 2025 at 11:50:11 AM UTC-7 Jesse Mazer wrote:
On Sat, Jan 18, 2025 at 1:19 PM Alan Grayson <agrays...@gmail.com> wrote:
On Saturday, January 18, 2025 at 10:24:01 AM UTC-7 Jesse Mazer wrote:
On Sat, Jan 18, 2025 at 12:09 PM Alan Grayson <agrays...@gmail.com> wrote:
On Saturday, January 18, 2025 at 9:15:17 AM UTC-7 Jesse Mazer wrote:
On Sat, Jan 18, 2025 at 9:36 AM Alan Grayson <agrays...@gmail.com> wrote:
On Saturday, January 18, 2025 at 7:19:41 AM UTC-7 Jesse Mazer wrote:
On Sat, Jan 18, 2025 at 9:09 AM Alan Grayson <agrays...@gmail.com> wrote:
On Thursday, January 16, 2025 at 5:52:52 PM UTC-7 Jesse Mazer wrote:
On Thu, Jan 16, 2025 at 7:33 PM Alan Grayson <agrays...@gmail.com> wrote:
On Thursday, January 16, 2025 at 2:39:55 PM UTC-7 Jesse Mazer wrote:
On Thu, Jan 16, 2025 at 2:43 PM Alan Grayson <agrays...@gmail.com> wrote:
On Thursday, January 16, 2025 at 11:36:48 AM UTC-7 Jesse Mazer wrote:
On Tue, Jan 14, 2025 at 12:02 AM Alan Grayson <agrays...@gmail.com> wrote:
Using the LT, we have the following transformations of Length, Time, and
Mass, that is,
x --->x', t ---> t', m ---> m'
The length contraction equation is not part of the Lorentz transformation
equations, the x --> x' equation in the LT is just about the position
coordinate assigned to a *single* event in each frame. The length
contraction equation can be derived from the LT but only by considering
worldlines of the front and back of an object, and looking at *pairs* of
events (one on each of the two worldlines) which are simultaneous in each
frame--length in a given frame is just defined as the difference in
position coordinate between the front and back of an object at a single
time-coordinate in that frame, so it requires looking at a pair of events
that are simultaneous in that frame. The result is that for any inertial
object, it has its maximum length L in the frame where the object is at
rest (the object's own 'rest frame'), and a shorter length L*sqrt(1 -
v^2/c^2) in a different frame where the object has nonzero velocity v.
The t ---> t' equation is likewise not the same as the time dilation
equation, it's just about the time coordinate assigned to a single event in
each frame, although it has a simpler relation to time dilation since you
can consider an event on the worldline that passes through the origin where
both t and t' are equal to 0, and then the time coordinates t and t'
assigned to some other event E on this worldline tell you the time elapsed
in each frame between the origin and E. And the LT don't include any mass
transformation equation.
Jesse
You're right of course. TY. I see the LT as giving appearances because, say
for length contraction, the reduced length is not measured in the primed
frame, but that is the length measurement from the pov of the unprimed or
stationary frame.
In relativity one does not normally designate any particular frame to be
the "stationary frame", since all concepts of motion and rest are defined
in purely relative way; if one has two objects A and B in relative motion,
one could talk about the frame where A is stationary (A's 'rest frame') or
the frame where B is stationary (B's rest frame), but that's all. I'm not
sure what you mean by "the reduced length is not measured in the primed
frame"--which object's length are you talking about? If A's rest frame is
the unprimed frame and B's rest frame is the primed frame, then the length
of object A in the primed frame is reduced relative to its length in its
own rest frame, i.e. the unprimed frame.
*Let's consider a concrete example of a traveler moving at near light speed
to Andromeda. From the traveler's frame, the distance to Andromeda is
hugely reduced from its length of 2.5 MLY from the pov of a non-traveling
observer. This seems to imply that the reduced length is only measured from
the pov of the traveler, but not from the pov of the non-traveler, because
of which I describe the measurement from the pov of the traveler as
APPARENT. Do you agree that the traveler's measurement is apparent because
the non-traveler measures the distance to Andromeda as unchanged? TY, AG *
I don't know what you mean by "apparent", but there is no asymmetry in the
way Lorentz contraction works in each frame--
*I mean, if one uses the LT, to transform from one frame to another frame,
if the resultant parameters in the latter frame are not actually measured
in the latter frame, I refer to those measurements as "apparent". What I'm
stuggling with is what the LT actually results in. Does it tell us what is
actually measured in the latter frame, or not? AG*
Yes, it always tells you what is actually measured in the frame that you're
transforming into, using that frame's own rulers and clocks. You haven't
made it at all clear why you suspect otherwise.
Jesse
*I suspect otherwise because in the Andromeda problem, using the LT from
the pov of the rest frame, at rest relative to the Earth, we get length
contraction in the transformed frame (modeled as a rod moving toward the
Earth)*
I thought the problem was supposed to involve the assumption of a traveler
going from Earth to Andromeda (who I imagined as riding in a rocket), with
a rod that is at rest relative to Earth and Andromeda and whose length
defines the distance between them in each frame? But here you seem to be
talking about a rod moving relative to the Earth? So now I'm not even clear
about what physical scenario you are imagining--please lay it out clearly
by specifying all the physical objects you are imagining in the problem
(like rocket, rod, Earth, Andromeda), which of them have nonzero velocity
in the Earth's frame, and the rest length for any object you want to do
length calculations for.
Jesse
*If you prefer, we can place the traveler to Andromeda in a spaceship
moving with some velocity wrt the Earth, and now imagine a rod whose length
is the distance from Earth to Andromeda.*
So the rod is at rest relative to Earth and Andromeda, as I originally
understood you to be saying?
* Since motion is relative, we can imagine the spaceship is at rest, and
the rod moving toward Earth (since the spaceship is ..imagined as moving
toward Andromeda).*
By "moving toward the Earth" do you mean moving *relative to the Earth*
(i.e. distance between the Earth and either end of the rod is changing over
time), or do you just mean that in the spaceship's frame, the rod is always
moving in the direction of the Earth, but the Earth is moving at the same
speed in the same direction so the end of the rod always coincides with the
Earth (or remains at a fixed negligible distance from it)? If the latter,
"the rod moving toward Earth" seems like confusing terminology for this,
there would be much less room for confusion if you stuck to the language of
talking about movement "relative to" a given object or observer as I
suggested.
* In the rest frame of the spaceship, the rod is contracted since it
appears to be **moving. We can use the LT to calculate how much its length
contracts due to the velocity of the rod. However, as I pointed out
earlier, this measurement is NOT possible IN the frame of the moving rod**,
since nothing is moving within this frame.*
How much its length contracts in the frame of the spaceship, or in the
frame of the rod (assuming the rod is at rest relative to Earth/Andromeda)?
* This is an example of the LT NOT yielding a measurement in the target
frame (in this case the frame containing the rod), which is an exception to
the claim that the LT always predicts what a target frame will actually
measure.*
I don't know why you think that, but you'll have to clearly specify which
frame you want to transform from, and which frame you want to use the LT to
transform into (the 'target frame'). If you mean starting from the
coordinates of the rod in the spaceship's rest frame, and using the LT to
transform into the rest frame of the rod (so the rod's frame is the target
frame), then if you actually do the algebra of the LT you will get the
correct result that the rod is *longer* in its own rest frame than it was
in the spaceship frame, not shorter. And if on the other hand you start
with the coordinates in the rod's rest frame and use the LT to transform
into the spaceship frame (so the spaceship frame is the target frame), you
will get the correct result that the rod is shorter in the spaceship frame
than in its own rest frame.
Jesse
*Let me try again. The spaceship is moving toward Andromeda from the Earth.
Since motion is relative I can assume the spaceship is at rest, and a rod
representing the distance from Earth to Andromeda is moving toward the
Earth, since it is assumed the spaceship was originally moving in the
opposite direction, toward Andromeda. *
You didn't address my question of whether "moving toward the Earth" means
moving *relative* to the Earth (i.e. rod is moving in Earth's rest frame,
and other frames like the spaceship frame see the distance between the end
of the rod and the Earth as changing over time), or if it just means that
in the rod is moving in the direction of the Earth at the same speed that
the Earth itself is moving in this frame, so the distance between any point
on the rod and the Earth is unchanging. If you mean the latter, this is
confusing terminology, definitely not the sort of thing you would find in
any relativity textbook. Either way, can you *please* stick to defining
movement and rest "relative to" specific objects or observers to prevent
this kind of verbal ambiguity?
*I assume, and you can as well, that the Earth is at rest, and the
spaceship is moving toward Andromeda. Can you assume the Earth is at rest
in this model and not allow us to get into a discussion of what "at rest"
means? AG*
I think this way of speaking just leads to confusion, which is why I'd
prefer that you not designate any particular frame as being "at rest" and
talk exclusively in a relative way about "the rest frame of the Earth" and
"the rest frame of the spaceship". Even if you are stubborn about this and
really want to designate one frame as being "at rest" and one as "moving",
you are not even being consistent in your designation, since in your post
immediately before this you said "Since motion is relative I can assume the
spaceship is at rest". There would be much less room for confusion if you
would just do as I suggest and use "rest" and "moving" in a relative way
('the rest frame of X', 'X is moving relative to Y' etc.), would you be
willing to do this for my sake or do you absolutely refuse? Please answer
this question directly, I've asked before and you've simply not responded.
Also, note that my question above was specifically about the *rod", which
you didn't mention at all in your response above--I was asking about the
meaning of your statement that the rod is "moving toward the Earth", can
you please just answer yes or no if the rod is meant to be at rest relative
to the Earth, and therefore moving at the same velocity as the Earth in the
spaceship rest frame?
*I was thinking the spaceship is relatively at rest,*
"Relatively at rest" is a meaningless phrase unless you specify what
*specific object* it is at rest relative to. Are you so attached to your
own non-standard way of talking that you refuse to just use the
formulations "at rest relative to X" and "moving relative to X" (where X is
some object in the problem) as a small concession towards being understood
by others? I have asked if you are willing to do this a bunch of times,
last time I even asked you "please answer this question directly", but you
continue to just ignore it. I'm not going to continue the discussion with
you if you refuse to do me this simple courtesy, without it I genuinely
can't understand what scenario you're envisioning.
Here you have again ignored the general question I ask about whether you
are willing to phrase all your comments about rest/motion in a way that
makes explicit what frame the statement is relative to (like 'moving
relative to the Earth' which makes clear we are talking about motion in the
Earth's rest frame). Are you willing to do this, yes or no? If you won't
give me an answer, I'm not going to continue this discussion with you.
*The rod is moving relative to the Earth, toward the Earth at some velocity
v.*
OK, so both the rod and the spaceship are moving relative to the Earth? Do
they both have the same velocity in the Earth rest frame (so they are at
rest relative to each other), or different velocities? If different, please
give some sort of numerical example so we can actually do some
calculations--for example if the spaceship is moving at 0.6c in the -x
direction in the Earth rest frame, how fast is the rod moving in this
frame, and in what direction?
Your original problem involved the distance from Earth to Andromeda galaxy,
I thought the rod was just supposed to measure that distance by stretching
from Earth to Andromeda--if not, what's the point of adding it to the
problem? Why not just talk about how the distance from Earth to Andromeda
looks in the spaceship frame vs. the Earth frame, why do we also need to
add the idea of a rod whose length is completely unrelated to the
Earth/Andromeda distance?
* The Earth is at rest and the rod is moving. And I've done those LT's in
the past, and I've reviewed those done by Brent on his plots, so there's no
need to do them again. Also, in all discussions about the Parking Paradox,
we have one frame moving and the other at rest. So I don't see why I can't
have the rocket at rest, and the rod moving. You claim that is wrong,*
No, I have never claimed it's wrong to use a frame where the rocket is at
rest and the rod moving, I just said you're wrong to say that when you
start from this frame and use the LT to transform into the rod's frame, the
rod will be CONTRACTED--in fact, if you actually do the math of the LT in
such an example, you will find that the length of the rod in its own rest
frame is predicted to be EXPANDED relative to its length in the rocket
frame where the rod is moving.
* but it's done repeatedly in the Parking Paradox. But we don't need a
rocket ship. We can just calculate using the LT from the Earth to determine
the length contraction. Do you have a better method? I surmise you haven't
reviewed Brent's short posts on this thread. He concedes that one cannot
MEASURE length contraction and time dilution in the target frame of the LT,
because, as he says, nothing is moving WITHIN that frame. So I am not
misinterpreting his words. AG*
I have been asking him to clarify, we'll see what he says, but I still
think you're misunderstanding. In any case, *I* am definitely saying that
the coordinates of any frame can be understood in terms of measurements on
a ruler/clock system at rest in that frame, and this is a standard notion
in relativity textbooks.
* the rod is moving toward the Earth,*
And I likewise asked several times to specify if you mean the rod is moving
*relative* to the Earth (i.e. the distance between the rod and the Earth is
changing over time), or if you just mean it's moving in the direction of
the Earth but at a fixed distance (i.e. it's at rest relative to the
Earth). My question last time was "can you please just answer yes or no if
the rod is meant to be at rest relative to the Earth, and therefore moving
at the same velocity as the Earth in the spaceship rest frame?" If you
aren't willing to answer simple yes-or-no questions like this, then again
I'm not going to continue the discussion.
* and the LT is used by the spaceship to calculate the contraction of the
rod. *
Contraction of the rod in which object's rest frame?
*I tried to make it clear, very clear, but obviously I failed. Let's try
this; since there's general agreement in the physics community that
traveling very fast to Andromeda causes its distance from Earth to
contract. So you tell me; from which frame would you'd like to measure the
contraction?*
In the spaceship frame, obviously.
*And since, as Brent just remarked, in the contracted frame, nothing that
the LT determined, is measurable in the contracted frame, my claim is
proven;*
"Contracted frame" is another unclear phrase, the distance from Earth to
Andromeda is contracted in the spaceship frame but the spaceship itself is
contracted in the Earth/Andromeda frame. *If* by "contracted frame" you
mean the spaceship frame where the distance from Earth to Andromeda is
contracted relative to the distance between them in their rest frame, then
you need to understand that what is measured in the spaceship frame (using
a system of rulers and clocks at rest in that frame, the clocks
synchronized using the Einstein convention) is exactly what would be
predicted if you started with the coordinates in some other frame and use
the LT to transform into the spaceship frame. If you think Brent is saying
otherwise, I can guarantee you've just misunderstood him.
*The spaceship is moving toward Andromeda at some velocity v wrt the Earth.
The rod is moving with velocity -v toward the Earth,*
While "velocity v wrt the Earth" is the sort of phrase I asked for, I have
already commented in three previous posts about the ambiguity of your
statement that the rod is moving "toward the Earth" and asked you to
clarify, which you still have not done, instead you're just repeating the
same ambiguous phrase. As I said before, "moving toward the Earth" could
either mean "moving relative to the Earth" or it could mean "moving in the
direction of the Earth's position, as seen in the spaceship's frame where
both rod and Earth have the same velocity -v" (in the latter case where
they both have the same velocity in the spaceship frame, this would imply
the rod is at rest in the Earth's own frame). Will you please answer my
question about whether the rod is moving *relative to* (or wrt) the Earth,
yes or no?
In general it's frustrating that when I ask you several pointed questions,
especially ones where I ask for a simple yes-or-no answer, you just try to
restate your overall scenario in a way that you perhaps vaguely think
addresses everything, without actually quoting my questions and giving
individual responses to them. Can you please answer each question
individually? I note that you also completely ignored the final question in
my last post about the symmetry of rest vs. moving between frames (see my
last comment below).
*As previously stated, the LT is done from a frame at rest. This is
consistently done by Brent and in all discussions of the Parking Paradox.
So the symmetry you refer to, refers to how each frame can view the other
from assuming it's at rest. *
My question about symmetry was responding to your previous statement "The
spaceship is in one frame, at relative rest WRT the rod; the rod is in
another frame, in relative motion WRT to the spaceship". Do you agree or
disagree that if the spaceship is at rest WRT to the rod, then
automatically that must mean the rod is at rest WRT the spaceship?
*IOW, from the car frame assuming the car is at rest, we can use the LT to
determine what happens in the garage frame which we assume is moving and
contracted, and vice-versa. AG*
[BTW, an alternative way you could avoid all this verbal ambiguity would be
to give an actual numerical example where you state the position as a
function of time for each object in the scenario. For example, say the
spaceship and Earth/Andromeda have a relative speed of 0.6c so that the
distance from Earth to Andromeda is contracted by a factor of 0.8 in the
spaceship rest frame, meaning if the distance is 2.5 Gly in the
Earth/Andromeda rest frame (Gly = Giga-light-years, so 2.5 Gly = 2.5
million light years), then the distance between them would be 2 Gly in the
ship rest frame. In that case, if we also use units of Giga-years for time
so that c=1, then you could say something like "in the ship's rest frame,
at t=0 the initial conditions are that the ship is at position x = 0, the
Earth is also at x = 0, and Andromeda is at position x = -2, and the ship's
position as a function of time in this frame is x(t) = 0, the Earth's
position as a function of time is x(t) = 0.6*t, and the Andromeda galaxy's
position as a function of time is x(t) = 0.6*t - 2". Then if you also gave
the corresponding equations of motion for the front and back of the rod in
the ship's rest frame (I'm still not clear on whether they'd be identical
to the equations of motion for Earth and Andromeda, so that one end of the
rod always coincides with Earth and the other end always coincides with
Andromeda, or if they'd be different) then there would be no ambiguity
about what the rod is supposed to be at rest relative to and what it is
moving relative to.]
* while the spaceship is now at rest wrt the Earth. I am replacing a moving
spacecraft with a moving rod of known initial length, the distance between
Andromeda the the Earth, moving in the opposite direction. Then I am doing
a LT from the stationary frame of the spacecraft to the moving frame of the
rod, to calculate the rod's contraction from the pov of the frame of the
spacecraft. I hope I have met your criterion for defining these frames of
reference clearly.*
*But all this is unnecessary to prove my point; that in the frame of the
rod, observers CANNOT measure its length contraction (or time dilation).
This FACT is universally known and not in dispute, yet at the same time
many people who claim to understand relativity assert that in the target
frame of the LT, that is, in this case, in the frame of the rod, observers
CAN measure what the LT implies. ThIs is FALSE! *
The LT simply doesn't "imply" there would be any length contraction of the
rod "in the frame of the rod",
*Then what does the LT do? AG*
It transforms coordinates from one frame to another. If you use these
coordinates to define the length of an object in both frames, then
depending on the object's velocity in the starting frame, sometimes a given
object will be shorter in the target frame than it was in the starting
frame, and sometimes it will be longer in the target frame than it was in
the starting frame. Only if the object is at rest in the starting frame can
we be confident without any further details that the object will be shorter
in the target frame where it's moving.
so your premise here is completely wrong (if you had an actual numerical
example with the equations of motion x(t) initially stated in the spaceship
rest frame, as I suggested above, you could plug them into the LT equations
directly and see what they predict about the equations of motion x'(t') in
the rod's frame--I assume you have not actually done such an algebraic
exercise and are just relying on some confused verbal argument to get the
wrong idea that the LT would predict contraction of the rod in the rod's
own frame).
*That's NOT my claim but what those allegedly knowledgeable about SR claim;
that the results of the LT give us what is actually MEASURED in the target
frame. In fact, that's what you claimed in some post on this subject. AG*
Yes, that's what I still claim. The premise of yours that is wrong is that
when we apply the LT we predict the rod is CONTRACTED in its own rest frame.
*You got my position totally wrong! That wasn't my position. It is
contracted in its own frame, and we know that from necessary corrections
for GR and SR effects on GPS clocks. What I claimed is that you can't
MEASURE the contraction in its own frame. You claim it's possible. Brent
says it's not possible, because there is no motion WITHIN that frame.
Further, our discussion about travel to Andromeda is totally unnessary. I
was just trying to develop a model for measuring the length contraction to
Andromeda. We don't need a spacecraft. We just need the Earth at rest, and
a rod moving toward the Earth, wrt the Earth, from which we use the LT. The
moving rod is equivalent to a spaceship traveling to Andromeda, so the rod
moves toward the Earth since, as seen by the traveler it moves in the
opposite direction. Finally, about symmetry; what's used in the Parking
Paradox is how symmetry exists between frames. The source frame, from which
the LT is applied, is always at relative rest wrt the moving frame, which
is always length contracted, and vice-versa. AG*
Whatever the LT implies about lengths/times in a specific inertial frame,
it always corresponds exactly to what would actually be measured using a
system of rulers and clocks which are at rest in that frame (the clocks
synchronized by the Einstein convention), no exceptions.
*Brent was explicit; one cannot MEASURE length contraction or time dilation
in the target frame, because there is no motion WITHIN that frame. AG*
See my last question to him, I think he was only talking about a ruler or
clock at rest in the frame we're talking about, in which case I agree you
won't measure any length contraction or time dilation of an object in its
own rest frame.
Jesse
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