Twin Paradox (thorough explanation needed)

[JesseM]

The universe contains objects with mass, so there most definitely is a theoretical center of mass.

Not if the mass is distributed evenly throughout all of space! How do you compute the "center" of an infinite distribution? And even if space is finite, a perfectly uniform distribution as modeled in FLRW models wouldn't have a center, and random deviations from uniformity would mean the center of mass would itself be a matter of random chance with no real physical significance.

 

[GrayGhost]

I'd say it can't be said who aged less in any objective frame-independent way, as you could always take the perspective of an inertial observer who was at rest relative to B during B's travel, but did not accelerate when B did and just continued past X inertially. In this observer's frame, A ages less than B between the time B departs A and the time B arrives at planet X, and from there on they both age at the same rate so A remains younger than B in this frame.

I suppose. I drew up a quick spacetime diagram of my suggested scenario, and I suppose it remains possible that folks can still disagree on the A-vs-B or B-vs-X relative aging.

Here's another one for you ...

Let's say A & B are inertial upon their first flyby, always traveling colinearly, and then B reverses direction at planet X and returns for another inertial A/B flyby. Would you say " it can't be said who aged less in any objective frame-independent way", or not? IOWs, do you think they have to be both colocated "and" at-rest-with-each-other to make the determination in an objective frame-independent way, or not?

GrayGhost

 

[JesseM]

It's say A & B are inertial upon their first flyby, always traveling colinearly, and then B reverses direction at planet X and returns for another inertial A/B flyby. Would you say " it can't be said who aged less in any objective frame-independent way", or not? IOWs, do you think they have to be both colocated "and" at-rest-with-each-other to make the determination in an objective frame-independent way, or not?

No, as long as they are co-located it doesn't matter if they are at rest relative to each other or not, all frames must agree on what happens at a single point in spacetime, like what two clocks read at that point. So here there has to be a frame-independent answer to how much each one ages between the two local flybys (and in this scenario it is B that ages less because of the change in direction between the flybys)

 

[Mike_Fontenot]

I'd say it can't be said who aged less in any objective frame-independent way, as you could always take the perspective of an inertial observer who was at rest relative to B during B's travel, but did not accelerate when B did and just continued past X inertially. In this observer's frame, A ages less than B between the time B departs A and the time B arrives at planet X, and from there on they both age at the same rate so A remains younger than B in this frame.

You are of course correct in your above statement (in so far as it refers to the answer given by B versus the answer given by the perpetually-inertial observer who is stationary with B during B's outbound leg ... call him observer C). I thought I KNEW what GrayGhost's follow-up question would be, but he surprised me by not asking it. Here's what I THOUGHT he would immediately ask: "Once B becomes stationary wrt A, but not co-located with A, do A and B agree about who aged less?".

I'm sure JesseM already knows what MY answer to that question is, and I already know what HIS answer is. But I was curious what GrayGhost's answer would be, and what GrayGhost's reaction would be to the answer that JesseM would give to that question.

Mike Fontenot

 

[JesseM]

I'm sure JesseM already knows what MY answer to that question is, and I already know what HIS answer is. But I was curious what GrayGhost's answer would be, and what GrayGhost's reaction would be to the answer that JesseM would give to that question.

What are you imagining my answer would be? I'd just say "if they use the inertial rest frame in which both are currently at rest, then they agree that B is younger (and also agree that B was aging slower throughout the trip from A to planet X)". There is no need for B to use a non-inertial frame to answer this question, though he could if he wanted (and in this case the answer would depend how that non-inertial frame was constructed, of course).

 

[Mike_Fontenot]

What are you imagining my answer would be? I'd just say [...]

Yep ... no surprises there.

 

[JesseM]

Yep ... no surprises there.

But presumably you don't disagree with "if they use the inertial rest frame in which both are currently at rest, then they agree that B is younger (and also agree that B was aging slower throughout the trip from A to planet X)", do you? Perhaps you would say that although this is technically correct, you believe that B would somehow be "wrong" to use the inertial frame where he's currently at rest, as opposed to using a non-inertial frame which defines simultaneity according to your CADO rules?

 

[Mike_Fontenot]

[...]

I AM surprised that you didn't immediately KNOW what my answer to the question would be. Perhaps you WOULD have, if I had asked the question somewhat more laboriously, like this:

"Once B becomes stationary wrt A, but not co-located with A, do A and B agree about who aged less, provided that EACH one of them, in order to determine his own "point-of-view", uses a reference frame in which he is perpetually at rest at the origin?".

Mike Fontenot

 

[GrayGhost]

I AM surprised that you (JesseM) didn't immediately KNOW what my answer to the question would be. Perhaps you WOULD have, if I had asked the question somewhat more laboriously, like this:

"Once B becomes stationary wrt A, but not co-located with A, do A and B agree about who aged less, provided that EACH one of them, in order to determine his own "point-of-view", uses a reference frame in which he is perpetually at rest at the origin?".

Mike Fontenot

My original question was the same, really. While all observers at rest in the A-frame (including X) agree with B, that B aged less over the interval (ie A/B-colocation to B-back-at-at-rest-with-A-and-X), other observers who move relatively will disagree. Hence, there is no objective frame-independent way (in the stated scenario) that declares B aged less than A. I also agree in that co-location is what matters, not necessarily being at rest with each other while co-located. I did not wish to lead JesseM in his response, and wanted to see how he'd answer.

Here's the thing though ... it all comes down to how the question is posed, IMO. All observers will agree on how much a clock ticked between 2 points (ie events) upon its own worldline. That's the only thing everyone agrees on, and it doesn't matter what frame or convention is used, assuming it's any good of course. So the only time "all observers" can agree on relative aging is when the 2 worldlines under consideration intersect at both events, and the interval between them considered.

Wrt the highlight I made of your response above, I don't see that it matters what frame is used by the analyst ... assuming the question is how A and B compare their relative aging wrt each other over the interval, not what others think about their relative aging wrt each their own POVs. (which we know can differ).

GrayGhost

 

[DTThom]

JesseM quoted me as follows:

"At rest with the universe" has a clear meaning, relativity or not. Relativity can be fully developed in absolute (universal) terms, and in doing so, it is seen just why it is that we cannot determine our true state of motion relative to the universe.

To which JesseM then replied:

Why do you believe there is such a thing as "true" rest relative to the universe? Given that relativity has no need for such a concept and it does just fine at predicting the results of all measurements ..

As to the second part of your question:

Because -- it is seen just *why* it is that we cannot determine our true state of motion relative to the universe. (See the paragraph of mine which generated your question. You had pasted that paragraph of mine immediately above your question.)

And because -- it shows precisely *why* inertial frames make mutually symmetrical measures of each other's properties (e.g., clock rate, length contraction).

And because -- it plainly shows *why* their is a time differential between two reunited clocks, and shows plainly why it is that the clock that changes frames to facilitate the return is the clock which will register the lesser time, and shows why that result is always symmetrical.

And because -- it allows us to diagram Einstein's clock synchronization in absolute terms. We then understand how to add Einstein's clock synchronization onto our clock rate and length contraction formulas (which we can derive in absolute terms by postulating an actual constant speed for light) to obtain the Lorentz transformations (a very useful pseudo reality for simplifying problems in electrodynamics, as is spacetime a very useful geometrical representation of the Lorentz transformations).


As to the first part of your question:

There is no other way to define inertial frame without using a circular definition.

Beyond that, one cannot pick and choose their absolutes (actualities). An actual "at rest" frame, actual clock rates, actual lengths, actual light speed -- all work together to produce the effectively equivalent inertial frames as we know them, meaning our measures or observations.

There is no other explanation for why two reunited clocks show an actual disparity in their readings.

Wheeler's "jump in time" explanation, also referred to by him as the "misperception" explanation is not valid. Remember, an outbound astronaut will simply hand off his clock reading to an inbound astronaut. There can be no "jump in time" or "misperception". Such "jump" or "misperception" is simply the result of employing Einstein's clock synchronization, whereby the inbound astronaut suddenly inherits a new lattice of clocks with a different synchronization than that used by the outbound astronaut. Such synchronization works perfectly for *predicting* results, but in no way addresses the *explanation* for the results.

Remember, Einstein's clock synchronization can be easily diagrammed against an absolute frame of reference. Such a diagram reveals just why it is that Einstein's clock synchronization nullifies the notion of the underlying reality.

The results of which I speak are not limited to the Twins Paradox. Einstein's method (and therefore spacetime), does not explain the "why" of symmetrically mutual assessments across inertial frames. Einstein's postulates of *measure* simply demand that the parties involved necessarily make these symmetrical observations.

It all comes down to the fact that when we concern ourselves with only measures, as in Einstein's treatment, we are free to ignore the inherent delay involved in making the measure, such delay being the dependence on finite light speed to facilitate every aspect of both our measures and the functioning of clocks (and yes the contraction of rigid bodies).

=======================================

..different inertial frames disagree about the relative rates the two clocks were ticking at different phases of the trip..

What various inertial frames agree upon during the trip interval is not what is relevant.

When the trip is over, all inertial frames agree that the two clocks in question ticked a different number of times from each other during the interval. Specifically, they will all necessarily be in agreement as to precisely what that difference is.

As you stated:

All these frames would nevertheless agree that the total elapsed time of the traveling clock was less than the inertial clock, so it had a slower rate on average over the whole trip, even if they disagree about the relative rates during particular phases of the trip.

It can only have a slower rate on average if its rate did vary from the other clock for at least part of the interval. That is my point -- the rate does vary.

Since *all* inertial frames which anyone could concieve of agree that the rate does vary, the rate must *actually* vary.

This *explains* the time differential -- e.g., *actual* clock rate variation explains the time differential.

====================================

Replace the clock ticks with odometers, if you care to.

Odometers tick at different rates (ticks per unit time) as they speed up or slow down, although for a different reason and according to a different equation.

(Odometers ticking off one mile per mile is not meaningful.)

===================================================

JesseM quoted me:

The only way to avoid circular reasoning is to acknowledge a "time" as kept by a clock at rest with the universe.

Then JesseM replied:

No, you can just talk about coordinate time in different inertial frames, without the need to single out one frame as the one that's "at rest with the universe".

I "can" just talk about coordinate time in different inertial frames, if I only want to *predict* observations. My purpose in this thread (titled - "Twin Paradox (thorough *explanation* needed)") is to *explain*.


JesseM quoted me:

Light has a finite and constant speed relative to the universe. It is the speed by which we define all lesser speeds.

Then JesseM replied:

No, light has a constant speed relative to all inertial frames, not "relative to the universe".

So you did not realize that actual light speed, actual clock rate slowing and and actual length contraction work together to produce the consistently measured speed of light in all directions in all inertial frames.

I had stated it in my original post:

Actual length contraction works in combination with actual time-keeping contraction to preserve the symmetry of measures across inertial frames..

..Special relativity can be charted out in actual terms (absolute terms), where light speed is constant in an actual sense. All the results of special relativity, including the consistent measured speed of light, fall naturally into place when charting these actualities against the (experimentally undetectable) rest state of the universe.

Do you have a problem with defining the position of various points on a 2D plane relative to a Cartesian x-y coordinate system, even though ...

No. See my earlier remarks in this post. The Lorentz transformations are great.


===============================================

the absolute universe you imply would necessarily be characterized as a "block time" model. You've got a big can of worms on your hands if you pursue that concept very far.

Some person's confusion regarding the relationships between the flow of time, clock functioning, the evolving structure of the universe with the corollary evolution of its complexity is not going to affect the notion that the universe can be viewed as a whole from the vantage point of a higher dimension.

(By the way, I consider that the complexity of the universe is what makes the effects of relativity as seemingly perfect and predictable as we know them to be. A simplistic universe containing just a few elements would impart inertial properties in a much "chunkier" manner and we would not have the smooth, seemingly perfectly predictable measures as we know them.)


=========================================

..relativity works just fine without assuming a universal rest frame.

I know that "relativity works just fine" for *predicting* measures obtained across inertial frames. See my earlier remarks.

The title of this thread is "Twin Paradox (thorough *explanation* needed).


============================================


Regarding various commentary about "center of mass" etc:

There are many ways to conceive of a rest state of the universe.

As far as conceiving of a particular point at rest with the universe, it will depend on whether one considers the universe to be:

euclidean with its point of origin existing within its own dimensions (i.e., the Big Bang),

positively curved with its point of origin lying outside its own physical dimensions (inflation),

euclidean with its point (or plane) of origin lying outside its own physical dimensions (inflation),

finite (euclidean or non-euclidean),

infinite (euclidean or non-euclidean),

and so on.


In a euclidean non-inflation finite universe, I certainly claim an actual center of mass, strictly undiscernable by anyone existing in the universe. Even in such a simple universe as this, ones view of the universe will always make it appear as though he is in the center of the universe, even if he happens to live near the "edge" of the universe, due to most of the gravitational source being towards the center from himself, with the resultant bending of his line of sight curving back into the universe, e.g. the geodesics of GR.

In an inflation model, it is the membrane of space which serves as the "point" at rest, meaning any point on the membrane of space is an equally valid center of gravity.

I could go on all day. But why should I? The actual difference in clock ticks between two reunited clocks, agreed upon by members of all inertial frames of the universe, tells me there is an "at rest" frame (experimentally undetectable) with respect to the universe.

A simple utilization of the perspective from a higher dimension, with instant perception as opposed to the finite speed of light perception by which inhabitants of the universe are bound, reveals the machinery of relativity, free of all mystery.

Actually, the mystery simply gets relegated to a deeper level, where it belongs. Shouldn't that be the goal -- to relegate the mystery to the deepest possible level?

=======================================

Final note: (whew)

I have benevolently decided to allow you all to speak of traveling along a world line at a particlur "speed" traditionally used to describe travel through space.

Here is why I don't like it:

A spatial component is graphed against clock ticks to produce a world line. That world line on that graph does not have the same length (pencil mark) as the spatial component. Thus as I travel at a particular speed along the world line (pencil mark) I don't progress as far along the spatial coordinate as I would if I traveled along the spatial coordinate.

Also, why should we talk about traveling at a particular speed along both the spatial coordinate and the world line, but not along the clock tick coordinate?

But... I know full well what you mean when you specify a speed along a world line.

 

[JesseM]

As to the first part of your question:

There is no other way to define inertial frame without using a circular definition.

Sure there is, you just define it in terms of a grid of rulers and clocks at rest relative to each other (the clocks "synchronized" with light signals according to the Einstein convention), and each experiencing no G-forces as measured by an accelerometer--the lack of G-forces is what makes a frame "inertial".

You are free to believe there is an absolute frame as a question of metaphysics, and if you assume rulers shrink length-contract in absolute terms when in motion relative to this frame, and clocks have their time dilated in absolute terms, and light has an absolute velocity of c relative to this frame, and the equations of the laws of physics when expressed in the coordinates of this frame are all Lorentz-symmetric, then this leads to predictions which are indistinguishable from the usual version of relativity which doesn't assume any absolute frame (this is known as a Lorentz ether theory). But the very fact that this leads to no new predictions means there would be no experimental way of determining which frame was the absolute one even if such a frame existed, and so in a practical sense it would be irrelevant to how physicists design all their experiments (including how they define 'inertial frames' in practice).

Beyond that, one cannot pick and choose their absolutes (actualities). An actual "at rest" frame, actual clock rates, actual lengths, actual light speed -- all work together to produce the effectively equivalent inertial frames as we know them, meaning our measures or observations.

There is no other explanation for why two reunited clocks show an actual disparity in their readings.

Again, let's talk about the geometric analogy. Do you think we need an absolute truth about which Cartesian coordinate system on a plane has its x-axis pointed in the "correct" direction, and that without this "there is no explanation for why two reunited cars show an actual disparity in their odometer readings"? Do you think there needs to be an "actual" truth about the rate a car's odometer reading is increasing relative to the car's increase in x-coordinate at a particular point on its path, in order to explain how there is an absolute truth about the total increase in odometer reading from starting point to ending point? If not I don't see why you can't accept that there similarly may be no "actual" truth about the rate a clock's reading is increasing relative to the t-coordinate at a particular point on its worldline, even though there is obviously an absolute truth about the total increase in clock reading from starting point to ending point.

Wheeler's "jump in time" explanation, also referred to by him as the "misperception" explanation is not valid.

It's valid relative to a particular non-inertial coordinate system, though of course there is no reason to prefer that coordinate system over any other. Similarly if you use a non-Cartesian spatial coordinate system on a plane, it might be true that during a very short segment of car #2's path where its odometer only increases from 100 miles to 100.0001 miles, car #1 might show an odometer reading of 5 miles at the point on its path that has the same x-coordinate as the point where car #2's odometer reads 100 miles, while car #1 might show an odometer reading of 305 miles at the point on its path that has the same x-coordinate as the point where car #2's odometer reads 100.0001. So, over this increment in x-coordinate, car #2's odometer only increases by 0.0001 miles while car #1's odometer "jumps" by the large increment of 300 miles. But this would just be a consequence of the funky way curves of constant x-coordinate were defined in this non-Cartesian coordinate system, it wouldn't have any deep physical meaning.

It can only have a slower rate on average if its rate did vary from the other clock for at least part of the interval. That is my point -- the rate does vary.

And in the geometric example, all Cartesian coordinate systems agree on the total length of each path so they all say the same thing about how much each car's odometer reading has increased, and so they all agree which had a greater average rate of increase in odometer reading relative to increase in x-coordinate. Do you think this means there has to be some absolute coordinate-independent truth about the "rate of increase in odometer reading relative to increase in x-coordinate" at each point along the path, even though different coordinate systems have their x-axes oriented in different directions?

Replace the clock ticks with odometers, if you care to.

Odometers tick at different rates (ticks per unit time) as they speed up or slow down, although for a different reason and according to a different equation.

No, you're missing the point of the analogy, it's meant to be purely spatial, time is irrelevant. I just brought in the concept of cars driving along the paths with odometers running as a shorthand way of talking about path lengths along paths through space, analogous to proper time along worldlines. If we have a path between points A and B, and I want to know the "path length" from A to any point P along the path up to and including B, then it's easier to just talk about how much a car's odometer reading would increase if it drove from A to P, an amount which depends only on the spatial properties of the path, not on time-dependent aspects of the car's driving like its speed or acceleration. And if we draw a spatial cartesian coordinate system on the 2D plane where the path exists, then we can also talk about the x-coordinate of any given point P (analogous to the t-coordinate of any event on a worldline in spacetime). Likewise we can talk about the slope of the path at P, the rate at which a car's y-coordinate would change relative to its x-coordinate as it traveled through P, which again depends only on the spatial properties of the path and the Cartesian spatial coordinate system we choose, though it's analogous to the concept of velocity in spacetime. And finally we can talk about the rate that "path length" (or odometer reading) is increasing relative to an increase in x-coordinate at any give point P along the path, again a purely spatial notion that doesn't involve time, though it's analogous to the concept of the rate a clock's reading is increasing relative to the t-coordinate in spacetime.

(Odometers ticking off one mile per mile is not meaningful.)

No, but it is meaningful to say for example that if a certain segment of the path has a slope dy/dx of 3/4, that means if you have a car driving along this segment, every time its x-coordinate increases by 4 its y-coordinate increases by 3, so by the Pythagorean theorem its odometer reading (measuring path length) increases by \sqrt{4^2 + 3^2} = \sqrt{25} = 5. So, in this case the rate that odometer reading is increasing relative to x-coordinate is 5/4. But if we chose a different Cartesian coordinate system with its x-axis oriented differently the slope would be different and so would rate of odometer increase relative to x-coordinate, and I bet unlike when we talk about the rate a clock is ticking relative to coordinate time t, in this case you wouldn't insist there has to be any "absolute" truth about the value of odometer increase relative to x-coordinate. That's the beauty of the geometric analogy, it shows you have a double standard with regard to time vs. space.

 

[GrayGhost]

Remember, Einstein's clock synchronization can be easily diagrammed against an absolute frame of reference. Such a diagram reveals just why it is that Einstein's clock synchronization nullifies the notion of the underlying reality.

If light's speed is invariant in all inertial frames, then if there is an aether frame it does not matter from a standpoint of spacetime transformations. Maybe it matters from some other standpoint, I don't know.

If light's speed is invariant in only a master (or aether) frame, then this nullification you speak of should require "an apparent" invariant 2-way speed of light, as opposed to being real, yes?

GrayGhost

 

[JesseM]

This nullification you speak of would seem to require "an apparent" invariant 2-way speed of light, as opposed to being real, yes?

In a Lorentz ether theory light would have a 2-way speed of c in the absolute or "ether" frame (and a 1-way speed of c in this frame as well), but other observers who measure it to have a 2-way speed relative to themselves are just measuring the speed with objectively shrunken rulers and objectively slowed-down clocks, so their measurements are "mistaken" in some sense.

 

[MikeLizzi]

In my copy,

http://books.google.com/books?id=mi...ook_result&ct=result&resnum=1&ved=0CCcQ6AEwAA,

the quote is at the bottom of page 156.

Found it where you indicated. Thanks GeorgeJones. (And thanks JesseM too). Now I have to figure out why that statement is so surprising to me. It seems to imply A.P. French believes in an absolute reference frame and that he believes most other physicists do too. Maybe I'm interpreting it wrong. But that would be a subject for a different thread.

 

[JesseM]

Found it where you indicated. Thanks GeorgeJones. (And thanks JesseM too). Now I have to figure out why that statement is so surprising to me. It seems to imply A.P. French believes in an absolute reference frame and that he believes most other physicists do too. Maybe I'm interpreting it wrong. But that would be a subject for a different thread.

For the record I doubt French's statement their represents a majority view, but he seems to be referring to [URL[/URL] principle[/url], a philosophical idea that Einstein was inspired by in creating general relativity even though he ultimately decided the finished theory didn't really obey it. [url=http://www.platonia.com/papers.html]Julian Barbour[/url] has some ideas on how one might create a theory of gravity similar to GR but more truly "Machian", though, he discusses this on the website above and also in his book [URL='https://www.amazon.com/dp/0195145925/?tag=pfamazon01-20']The End of Time[/url].

 

[Dale]

I have benevolently decided to allow you all to speak of ...

All hail the mighty and benevolent king DTThom!

 

[DTThom]

..the lack of G-forces is what makes a frame "inertial".

I'll just quote myself from an old source:

"To define inertial system without appealing to a physical universal
system is to limit oneself to only kinematics (considerations of motions
of objects absent of force), and to define inertial system in a circular (or
some would say strictly relative) manner.

In a physical sense, to be in what is called an inertial system is to have
an absence of experience (detection) of any force that could be construed
as acceleration (or equivalently, gravity) based."

My machian perspective about that has always been as follows:

The origin of such force must come from a relationship with the totality
of the environment outside of the system in question, thus implying there
is such an environment and that if you changed your state of motion
relative to it, you would experience force. (Any generation of force
inside the system merely creates a new system within the system, with
no change in the overall motion of the system.) And no meaning can be
attached to a net movement of the totality of the external environment,
which is the universe itself.

There is no way around this.

It won't do you any good to imagine that your little system is all alone in
the universe and that there is therefore no external environment, for all
you would accomplish is to define your little system as the universe
itself, to which no meaning of net motion can be attached, and whereby
any motion inside that little system must now be seen as different from
its net external system, i.e., your original little system (the new universe).

(this is known as a Lorentz ether theory).

Of course people are going to think I embrace LET. But I do not believe
in the aether. It's not rational for multiple reasons.

I believe in an evolving structure of the universe and an interconnectedness
between all elements. The communication which establishes the connectedness
can proceed only at light speed.

..a car's odometer reading..

I won't discuss odometers with you. Why do you lean on *any* analogy.
The analogy doesn't fit with process of clock functioning and its reliance
on the immutable speed of light.

I will discuss clock functiong and light speed on their own merits.

In a Lorentz ether theory light would have a
2-way speed of c in the absolute or "ether" frame (and a 1-way speed
of c in this frame as well), but other observers who measure it to have
a 2-way speed relative to themselves are just measuring the speed with
objectively shrunken rulers and objectively slowed-down clocks, so their
measurements are "mistaken" in some sense.

Observers do not measure it to have a 2-way speed relative to themselves.

Their slowed clocks and shrunken rods work together to insure a consistently
measured speed for light in all directions of light travel.

I know there are some aetherists who believe in anisotropic light speed
measures. It's not rational, and neither is aetherism in any case.


=======================

Thankyou for not jumping on this silly thing I wrote:

Also, why should we talk about traveling at a
particular speed along both the spatial coordinate and the world line,
but not along the clock tick coordinate?

Please ignore it.

 

[DTThom]

All hail the mighty and benevolent king DTThom!

shucks..

 

[Dale]

(Odometers ticking off one mile per mile is not meaningful.)

Sure it is. When you speak of the "rate" of a clock you are speaking of the number of seconds the clock marks per second. So the geometric analogy is a number of miles the odometer marks per mile.

If you prefer a more explicitly geometric analogy you can certainly use a measuring tape instead. Consider two tape measures measuring the distance from A to B, one tape measure goes in a straight line, and the other goes via point C which is not colinear. When the tape measure readings are compared at B they show an ACTUAL disparity in their measured distance. Does that necessarily imply that there must have been an ACTUAL difference in their marking "rates"? No, both tape measures could still have accurately measured one cm per cm and yet obtained different distance readings.

The key idea here is whether you attribute the difference in readings to a difference in the measuring device or if you attribute the difference in readings to a difference in the thing being measured. It is easy to see the difference in the thing being measured when discussing paths in space, and it is not much more difficult to see it when discussing paths in spacetime.

 

[bobc2]

Originally Posted by bobc2 :
the absolute universe you imply would necessarily be characterized as a "block time" model. You've got a big can of worms on your hands if you pursue that concept very far.

Some person's confusion regarding the relationships between the flow of time, clock functioning, the evolving structure of the universe with the corollary evolution of its complexity is not going to affect the notion that the universe can be viewed as a whole from the vantage point of a higher dimension.

I've got to hand it to you, DTThom, you're sure unafraid to take on all comers.

How does the universe "evolve" if it is all there at once ("...universe can be viewed as a whole from the vantage point of a higher dimension")? If the universe is 4-D and static (including 4-D structure of observer bodies), how do the observers move along the world lines?

 

[DTThom]

To JesseM and DaleSpam et al.

I don't know whether you ever agree to acknowledge a clock "rate",
even a purely relative one.

People in all inertial frames will agree that there *exists* an
interval *during* which two departed-then-reunited clocks tick a
different number of times.

And they all agree as to what the numerical difference is in
ticks.

=========================

It is during that interval, that a clock at rest with the
universe will tick the maximum number of times, due to the
fact that no vector component of motion has been added to the
clock, which is constrained in its functioning by light speed.
(Photons cannot possibly acquire greater speed when
a vector component of motion has been added to a clock which
contains the photons. Therefore the photons will produce fewer
ticks of the clock as they maintain their constant speed).

Atomic, chemical, mechanical, biological -- doesn't matter.

==========================

Mixing up the concept of clock ticks with the flow of time
(time in the history sense) can certainly create a communication
problem. I believe relativity (and physics in general for now) is
concerned only with clock ticks, not the flow of time.

==========================

[How does the universe "evolve" if it is all there at once ("...universe
can be viewed as a whole from the vantage point of a higher dimension")?

"all there at once" vs. "has always all been there"

Would could you be driving at here.

[If the universe is 4-D and static (including 4-D structure of observer bodies),
how do the observers move along the world lines?

What world lines in the higher dimension. Did I say
there are world lines there? I don't know anything
about the nature of a higher dimension, save my
notion of light having a finite speed in our dimensions,
and the notion that such movement of light can
be charted out in a "frozen" form on a "map" to be
percieved by the higher dimension without the
delay of light speed affecting such perception.

I don't even care if there is no such higher dimension.
It is still an analytical tool I can use to chart out
the effects of relativity as we know them, with an
arbitrary assignment of a line segment to represent
the distance of one light second, and with
speeds less than light speed to be defined in accordance with
the speed of light as established by the distance
of one light second.

==========

I'm headed off to work. Try to manage without me, as
I have no computer available during that interval
by which to help you out. (chuckle)

 

[JesseM]

Of course people are going to think I embrace LET. But I do not believe
in the aether. It's not rational for multiple reasons.

I think the modern understanding of "Lorentz ether theory" does not presuppose any sort of physical ether, just an absolute reference frame with clocks slowing down absolutely when moving relative to this frame, and rulers shrinking absolutely.

I won't discuss odometers with you. Why do you lean on *any* analogy.
The analogy doesn't fit with process of clock functioning and its reliance
on the immutable speed of light.

You seemed willing enough to discuss it before when you said "Replace the clock ticks with odometers, if you care to." I guess now you changed your mind because you realize my point that this analogy shows your double standard with regard to time vs. space, believing absolute statements about "rates" are necessary in one case but not the other. The analogy "fits" exactly in the sense that every single aspect of clocks and inertial frames in spacetime maps neatly to some aspect of odometers and cartesian coordinates in 2D space. So if you won't even explain why you think "the analogy doesn't fit", that just shows the hollowness of your position.

To JesseM and DaleSpam et al.

I don't know whether you ever agree to acknowledge a clock "rate",
even a purely relative one.

Then you haven't been reading very carefully, I have talked multiple times about the rate of proper time/coordinate time defined relative to an inertial frame, and compared it to odometer increase/x-coordinate increase. In post #107 I said:

We must say that the two clocks ticked at different rates, i.e., ticks per unit "time". That "time" can only be some "time" by which to distinguish the "time" recorded by the two clocks.

Yes, it's coordinate time in different inertial frames. But different inertial frames disagree about the relative rates the two clocks were ticking at different phases of the trip--for example one frame may say the traveling clock was ticking slower than the inertial clock for both the inbound and outbound leg of its journey (this would be true in the rest frame of the inertial clock), another frame may say the traveling clock was ticking faster than the inertial clock during the outbound leg but slower than the inertial clock during the inbound leg (this would be true in the inertial frame where the traveling clock was at rest during the outbound leg), and a third may say the traveling clock was ticking slower than the inertial clock during the outbound leg and faster during the inbound leg (this would be true in the inertial frame where the traveling clock was at rest during the inbound leg). All these frames would nevertheless agree that the total elapsed time of the traveling clock was less than the inertial clock, so it had a slower rate on average over the whole trip, even if they disagree about the relative rates during particular phases of the trip.

Again this is analogous to odometers, as you can see if you read my [post=2972720]linked post[/post] on the geometric analogy. Instead of talking about the rate that a clock is ticking relative to coordinate time t in some inertial frame, we can talk about the rate a car's odometer reading is increasing relative to the car's coordinate position x along the x-axis in some Cartesian spatial coordinate system. Different Cartesian coordinate systems with their axes oriented at different angles will disagree about (change in odometer/change in x-coordinate) during different phases of the trip, but they will all be able to calculate the total change in odometer reading as a function of how (change in odometer/change in x-coordinate) varies along the path (and the rate at each point is just a function of the path's slope at that point), and will all agree that the car that traveled in a straight line had a smaller total change in odometer reading than the one that didn't. This is just like how different inertial frames disagree about (change in clock reading/change in t-coordinate) during different phases of the trip, but they can all calculate the total change in clock reading as a function of how (change in clock reading/change in t-coordinate) varies along the path (and the rate at each point is just a function of the clock's speed at that point), and will all agree that the clock that moved inertially had a greater total change in clock reading than the one that didn't.

And I made the same point in my more recent post #131:

And finally we can talk about the rate that "path length" (or odometer reading) is increasing relative to an increase in x-coordinate at any give point P along the path, again a purely spatial notion that doesn't involve time, though it's analogous to the concept of the rate a clock's reading is increasing relative to the t-coordinate in spacetime.

No, but it is meaningful to say for example that if a certain segment of the path has a slope dy/dx of 3/4, that means if you have a car driving along this segment, every time its x-coordinate increases by 4 its y-coordinate increases by 3, so by the Pythagorean theorem its odometer reading (measuring path length) increases by \sqrt{4^2 + 3^2} = \sqrt{25} = 5. So, in this case the rate that odometer reading is increasing relative to x-coordinate is 5/4. But if we chose a different Cartesian coordinate system with its x-axis oriented differently the slope would be different and so would rate of odometer increase relative to x-coordinate, and I bet unlike when we talk about the rate a clock is ticking relative to coordinate time t, in this case you wouldn't insist there has to be any "absolute" truth about the value of odometer increase relative to x-coordinate. That's the beauty of the geometric analogy, it shows you have a double standard with regard to time vs. space.

 

[ghwellsjr]

Why do people make things so difficult for themselves? Did it never occur to them that when two reunited clocks (meaning they are now once again at the same place-moment) show an ACTUAL disparity in their recorded time, that there must necessarily have been an ACTUAL difference in clock rates involved while they were in relative motion with each other?

One should never suggest (as they so often do) that there was some sort of "jump in time" involved with the change of inertial frame (meaning at the turn-around point). The simple act of starting a clock as an inbound astronaut passes an outbound astronaut cannot possibly create a "jump in time". (Remember, the outbound astronaut hands off his clock reading to the inbound astronaut.)

The time contraction formula [t' = t * sqr rt of (1 - v^2)] is not linear. That is why the party who changes frames to bring the two parties back together will register the least amount of time on his clock with the symmetry of the situation preserved.

The actual distances and speeds relative to the universe will vary depending on which party changes frames, but the parties involved cannot possibly detect that. That is in keeping with the postulates and deductions of special relativity.

Time-keeping, distance and speed are interminably bound in one equation. Therefore, actual differences in clock rates implies actual length contraction dependent on actual speed relative to the universe. Actual length contraction works in combination with actual time-keeping contraction to preserve the symmetry of measures across inertial frames.

There is clock functioning at every level, dependent on actual light speed, at even the atomic level. Our observations and measuring paradigms of every nature are constrained by the speed of light, as is our "synchronizing" of clocks.

Special relativity can be charted out in actual terms (absolute terms), where light speed is constant in an actual sense. All the results of special relativity, including the consistent measured speed of light, fall naturally into place when charting these actualities against the (experimentally undetectable) rest state of the universe.

Actual time-keeping and length contraction arise naturally from the fact that all phenomena are dependent on the speed of light, which is itself invariant in actuality, being massless.

Consider that A.P. French writes on page 150 of Special Relativity: "Note, though, that we are appealing to the reality of A's acceleration, and to the observability of the inertial forces associated with it. Would such effects as the twin paradox exist if the framework of fixed stars and distant galaxies were not there? Most physicists would say no. Our ultimate definition of an inertial frame may indeed be that it is a frame having zero acceleration with respect to the matter of the universe at large."

And I feel very sorry for any physicist who doesn't understand that.

Michio Kaku states on page 80 of Einstein's Cosmos that bringing the twins together "determines which twin was "really" moving."

Martin Gardner writes on page 114 of Relativity Simply Explained: "There is one all important difference between the relative motion of the astronaut and the relative motion of the stay-at-home. The stay-at-home does not move relative to the universe."

Both Kaku and Gardner were using the simplest of twins paradox scenarios, in which one party is assumed to be at rest with the cosmos. But that need not be the case. There can be any number of "in between" situations, leading to a lesser time differential. It is also not necessary for the twins to reunite to determine which one was "really moving". The noted asymmetry (noted by both parties) in the time-keeping difference builds incrementally, beginning at the moment of inertial change for one party, when radio or light signals are regularly sent forth and back to check on current clock status.

One should do a search on Einstein's clock synchronization, and its bearing on spacetime diagrams. He or she will find that the notorious "jump in time" is built into that clock synchronization, because it is a one way synchronization, which gets instantly replaced with a different synchronization when a new inertial frame is adopted.

There is all the difference of night and day between predicting and explaining. We can use Einstein's clock synchronization and spacetime to predict a time differential, but we must look at relativity in the universal frame of reference to explain not only that time differential, but also all the mutually symmetrical measures made across inertial frames.

The preceding remarks were copied off my copyrighted web document.

There are a lot of similarities and even some exact phrases between your comments above and the wiki page under the section entitled, "Understanding the time differential as a consequence of actual clock slowing":

http://en.wikipedia.org/wiki/Twin_paradox

Looks very suspicious to me.

Also, since I am having a very difficult time trying to understand your postition, could you provide a link to your copyrighted web document please?

 

[GrayGhost]

Remember, Einstein's clock synchronization can be easily diagrammed against an absolute frame of reference. Such a diagram reveals just why it is that Einstein's clock synchronization nullifies the notion of the underlying reality.

If light's speed is invariant in all inertial frames, then if there is an aether frame it does not matter from a standpoint of spacetime transformations. Maybe it matters from some other standpoint, I don't know.

If light's speed is invariant in only a master (or aether) frame, then this nullification you speak of should require "an apparent" invariant 2-way speed of light, as opposed to being real, yes?

In a Lorentz ether theory light would have a 2-way speed of c in the absolute or "ether" frame (and a 1-way speed of c in this frame as well), but other observers who measure it to have a 2-way speed relative to themselves are just measuring the speed with objectively shrunken rulers and objectively slowed-down clocks, so their measurements are "mistaken" in some sense.

JesseM,

Indeed. That was my point, and why I used the word "apparent". IMO, the Einstein convention doesn't nullify a master frame (assuming it really exists). Because, if a master frame exists, then Einstein's convention would have to be wrong. Therefore, it only "appears" to be the case that "an underlying real master frame would be nullified", because what you measure is "apparent" vs real ... and for the reason you mentioned here.

So, although the LTs are the same in both LET and SR, the meaning of the theories differ. After thinking on it a little more here, I suppose DTThom's statement means only this ... Einstein's convention makes any aether frame superfluous, because no frame (including an aether frame if it exists) is preferred. But then, that's what Einstein states upfront in his OEMB, so.

However, DTThom suggests to assume a master frame "does exist", and then draft Einstein's simultaneity convention on a spacetime diagram. In doing so, the 1-way speed of light within said illustration is NOT c, even though the convention assumes such. The 2-way speed of light is not c either, although it appears to be, due only to measurements that differ from reality in just the precise needed to produce "a seemingly invariant 2-way speed of light". As Minkowski would put it, a mere lucky gift from above.

GrayGhost

 

[DrGreg]

There are a lot of similarities and even some exact phrases between your comments above and the wiki page under the section entitled, "Understanding the time differential as a consequence of actual clock slowing":

http://en.wikipedia.org/wiki/Twin_paradox

Looks very suspicious to me.

Look at the history of who edited that article recently. That entire section was written by a user called "D.T.Thom".

 

[Mentz114]

People in all inertial frames will agree that there *exists* an interval *during* which two departed-then-reunited clocks tick a different number of times.

(what do the *'s mean ? It makes your text look like a crackpot tract)
No they won't.

And they all agree as to what the numerical difference is in ticks.

Ticks are events and every frame ( inertial or not) will agree on the number of ticks.

You use very flowery language to disguise what I suspect is a fundamental misunderstanding of relativity.

 

[Dale]

Of course people are going to think I embrace LET. But I do not believe in the aether. It's not rational for multiple reasons.

It sure seems like you believe in LET to me. All of these quotes seem to be just LET dressed up in new language:

a clock at rest with the universe

there must necessarily have been an ACTUAL difference in clock rates ... The actual distances and speeds relative to the universe will vary ... Therefore, actual differences in clock rates implies actual length contraction dependent on actual speed relative to the universe.

one party is assumed to be at rest with the cosmos, ... "in between" situations -- such as both parties having motion relative to the universe

"At rest with the universe" has a clear meaning, relativity or not. Relativity can be fully developed in absolute (universal) terms ... Light has a finite and constant speed relative to the universe.

"A rose by any other name ...".

Tell me, what exactly do you think is different from the LET aether frame and your cosmos frame? It is certainly not obvious.

 

[GrayGhost]

It sure seems like you believe in LET to me. All of these quotes seem to be just LET dressed up in new language:"A rose by any other name ...".

Tell me, what exactly do you think is different from the LET aether frame and your cosmos frame? It is certainly not obvious.

It would seem that DTThom doesn't want to define an aether. Whereas Einstein and Galileo ascerted all motion per POV, DTThom ascerts all motion wrt a common reference ... one defined by "the universe in collective" ... whatever that means. He's been very vague on this.

GrayGhost

 

[Dale]

DTThom ascerts all motion wrt a common reference

Which is LET.

 

[yogi]

For the record I doubt French's statement their represents a majority view, but he seems to be referring to [URL[/URL] principle[/url], a philosophical idea that Einstein was inspired by in creating general relativity even though he ultimately decided the finished theory didn't really obey it. [url=http://www.platonia.com/papers.html]Julian Barbour[/url] has some ideas on how one might create a theory of gravity similar to GR but more truly "Machian", though, he discusses this on the website above and also in his book [URL='https://www.amazon.com/dp/0195145925/?tag=pfamazon01-20']The End of Time[/url].[/QUOTE]

I would agree - and ad further that it is unwise to bank upon some of the explanations proposed by the so called experts as they differ widely and are in some cases totally contradictory

But I will again assert that acceleration plays no part in the age difference between the twins - although as the problem is presented it is usually present at some phase of the thought experiment

The ambiguities are resolved by the principle of interval invariance - whether it be the orbits of satellites in motion, or the one way trip a pion makes in the lab - the problem can always be reduced to a thought experiment where no acceleration is needed - for example, it is not necessary that the twins be reunited in order to determine that the traveler has accumulated less time. Acceleration is simply a circumstance involved with getting the twin back home - the difference in time is the result of spacetime unity ... when one frame is selected to be at rest - the problem degenerates to a spacetime mensuration - and the twin taken to be at rest will necessarily have accumulated the most time because he has not accumulated a space distance - the traveler must always experience the same spacetime interval - so his interval comprises both a spatial and temporal component, ergo his temporal component must be less