Twin Paradox (thorough explanation needed)

[Dale]

I can easily deduce that the two odometers in your example traveled actual different distances, due to the actual difference showing up in the number of odometer ticks at the same place-moment in New York. I can identically deduce that the two reunited clocks I spoke of ticked an actual different number of times while they were apart.

Exactly. Note that this does not imply that the rate of either clock has changed, simply that they are measuring the length of different paths through spacetime (aka worldlines).

I don't care what distance the clocks traveled. You provided a distance problem. An odometer is bound to read true to the distance of the road.

Similarly, a clock is bound to read true to the spacetime interval of its worldline.

You can do relativity the easy way, or you can make it hard for yourself

I agree completely. I find the geometric approach by far the easiest and most intuitive.

A world line is a spacetime construct, not something physical.

A worldline is simply a path through spacetime. It is every bit as physical as a path through space.

 

[JesseM]

"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.

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, this seems like a kind of religious faith.

One can hold two reunited clocks in ones hand and see that one registered more clicks than the other WHILE they were apart. "While" sounds like a "time" word to me. 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.

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

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". In the odometer example, all Cartesian coordinate systems agree on the average rate of (change in odometer reading/change in x-coordinate) for both cars, and agree that the car with the straight path had a smaller average rate than the one with the non-straight path, but presumably you wouldn't say here that we must somehow conclude that we must single out one Cartesian coordinate system as the one with the "true" x-axis direction, so that its value of (change in odometer reading/change in x-coordinate) at any point on a car's path is the only "true" value.

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

No, light has a constant speed relative to all inertial frames, not "relative to the universe". If two events on the worldline of a light ray have (difference in position/difference in time) = c in the coordinates of one inertial frame, then these same events also have (difference in position/difference in time) = c in the coordinates of any other inertial frame, even though different frames may disagree about the specific values of (difference in position) and (difference in time) for a given pair of events. You can use the Lorentz transformation to verify that this is the case.

Without absolutes (actualities) we are left with only circular definitions (strictly relative definitions).

"Relative" is not the same as "circular". 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 you know you have a choice of different Cartesian coordinate systems with their axes pointing at different angles? And note that you can use any given coordinate system to calculate absolute quantities that are the same from one coordinate system to another, like the straight-line distance between two points--if coordinate system #1 assigns points A and B coordinates (x_A, y_A) and (x_B, y_B), then it will calculate the straight line distance between them as $$\sqrt{(x_B - x_A)^2 + (y_B - y_A)^2}$$ (Pythagorean theorem), while coordinate system #2 might assign the same points A and B coordinates (x'_A, y'_A) and (x'_B, y'_B), and therefore compute the distance as $$\sqrt{(x'_B - x'_A)^2 + (y'_B - y'_A)^2}$$. But despite these different coordinates and calculations they will both end up with the same value for the straight-line distance between A and B, i.e. it will be true that $$\sqrt{(x_B - x_A)^2 + (y_B - y_A)^2} = \sqrt{(x'_B - x'_A)^2 + (y'_B - y'_A)^2}$$. It's exactly the same in relativity, where there are plenty of absolutes that different coordinate systems agree on, like the spacetime interval between two events which is computed with the formula $$\sqrt{(x_B - x_A)^2 - c^2 (t_B - t_A)^2}$$.

 

[bobc2]

bobc2 comment after DaleSpam's: Exactly. Right on the money, DaleSpam. (Could it be that each twin travels his own world line at light speed--but their world lines have different path lengths, just like your two different paths from Miami to New York?)

You can travel through space (a distance dimension) at light speed (a speed dimension).

You cannot travel through spacetime at any speed. No meaning can be attached to such a statement.

I think we understand the context when we refer to "moving along the world line at light speed." It's not fruitful at this point to rehash that point (Herman Weyl: "...an observer crawls along his world line.", etc.). But, in any case, 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.

"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.

No further comment is needed. DaleSpam's and JesseM's last posts sum it up pretty well.

 

[GrayGhost]

You can travel through space (a distance dimension) at light speed (a speed dimension). You cannot travel through spacetime at any speed. No meaning can be attached to such a statement.

Hello DTThorn,

Try this on for size maybe ... You and I are inertial, and of a luminal relative velocity. We each hold ourself stationary passing only thru time, and the other passing thru space over time. Which is it? Are we each moving thru space w/o realizing it, or are neither of us moving? If the later, then relative motion is an illusion of sort. If the former, then why do we not realize we pass thru space while stationary?

My opinion is that the former is true. We each move thru a spacetime continuum, and I'd personally agree with bobc2 that we all travel at c thru the continuum. That our relative motion depends only on "the extent of parallelness" of our velocity vectors thru 4d spacetime, otherwise known as our arrows-of-time. When parallel, then zero relative motion. The Minkowski model revealed this notion.

As to why we do not perceive ourselves passing thru space while inertial, is yet another matter. And an interesting one at that, IMO. We perceive space and time differently, yet we know that the inertial fellow over yonder is indeed passing thru 3-space while he knows himself only to transcend time. It seems clear IMO that "space exists", although we measure it differently. Clearly, there is more to time than what is presently known. At this point, we know there is "a spacetime" that exists, because we measure it and we exist in it. It's not just that space and time are interwoven, but also matter and energy ... so all 4 working in concert in unison, all a part of the same single mechanism. That said, it's time for a party!

GrayGhost

 

[yogi]

"Cause" is a vague word, but in SR the fact that one twin accelerates between meetings while the other does not is a necessary and sufficient condition for the twin that accelerated to be younger when they reunite.

It's irrelevant which frame you take to be "at rest", all frames calculate the same answer for the ages of the twins when they reunite.

Wrong - the frame selected as "at rest" defines the proper distance which must be traveled between the two clocks that measure time in the "at rest" frame. This distance will be longer than the distance measured between the two points by the moving twin. If the A frame is selected as the at rest frame and two clocks are separated by a distance L in the A frame both the traveler in the B frame and the fixed twin in the A frame will agree that clocks in the A frame accumulate more time than the moving twins clock during the one way experiment

Acceleration is not a necessary condition to resolve the twin's time difference - two one way trips with clocks synchronized on the fly (close pass by) at the start and stopped when the traveler passes the second clock on the fly can simply be doubled - no acceleration is involved

If the B frame is taken as at rest - then the experiment is different since the proper length will be laid out in the B frame as the distance between two clocks in that frame and at the end of the one way trip both twins willl agree that it is the twin in the B frame who has aged most .,

A round trip is not necessary - to solve problems such as this it is helpful to reduce the situation to one which can eliminate all acceleration and show there is no ambiguity by substituting two one way trips for a round trip

For a true round trip, GPS satellites verify the time dilation due to SR every time they complete an orbit - the satellite is in an inertial frame during the entire experiment (one orbit)and the Earth - while nonetheless in a constant G field, still provides a valid platform for synchronizing ground clocks

 

[JesseM]

Wrong - the frame selected as "at rest" defines the proper distance which must be traveled between the two clocks that measure time in the "at rest" frame.

You're misusing the phrase "proper distance", proper distance is measured between a pair of events (or along a spacelike worldline), and it's frame-invariant.

This distance will be longer than the distance measured between the two points by the moving twin. If the A frame is selected as the at rest frame and two clocks are separated by a distance L in the A frame both the traveler in the B frame and the fixed twin in the A frame will agree that clocks in the A frame accumulate more time than the moving twins clock during the one way experiment

I wasn't talking about a one-way experiment, I was talking about the twin paradox. However, you are wrong that in the one way experiment both frames will agree that the A twin accumulates more time, you are failing to take into account the relativity of simultaneity here. In the rest frame of twin B, the event of him arriving at the distant destination is simultaneous with an event on A's worldline where A is younger. For example, if B travels at 0.6c to a destination which is 15 light-years away in A's frame, then in A's frame it takes 15/0.6 = 25 years to get there, but B is only 25*0.8 = 20 years older on arrival. But in B's frame, the moment he arrives at the destination with his clock showing an elapsed time of 20 years, this is simultaneous with the event of A's clock showing an elapsed time of 20*0.8=16 years.

Acceleration is not a necessary condition to resolve the twin's time difference - two one way trips with clocks synchronized on the fly (close pass by) at the start and stopped when the traveler passes the second clock on the fly can simply be doubled - no acceleration is involved

In this case you aren't dealing with the elapsed time on anyone clock, but rather the sum of two intervals on different clock worldlines. The total path that you are adding the times along is still a bent one in spacetime, no single clock undergoes acceleration but the fact remains that a "straight" path between two points in spacetime will always show a greater proper time than a non-straight path between the same two points, the only relevance of "acceleration" is that it is the cause of a single object's path through spacetime being non-straight.

Again think of the geometric analogy--if you have two roads between points 1 and 2 on a flat surface, and one is straight while the other is not, a car driving along the straight road will always show a smaller increase in its odometer reading than a car on the non-straight road. You're free to imagine two cars traveling along a non-straight V-shaped road, which "synchronize" their odometers at the moment they pass at the tip of the V, so that neither car actually has to deviate from a straight path, but it will still be true that the total odometer increase along the V-shaped road is greater than the odometer increase along the straight road between points 1 and 2.

If the B frame is taken as at rest - then the experiment is different since the proper length will be laid out in the B frame

Why do you say that? You are free to repeat exactly the same experiment while considering the B frame to be at rest, in my above example the distance between A and the destination (both of which are moving in the B frame) could be 0.8*15=12 light years in the B frame, matching the original statement that the distance would be 15 light years in the A frame. The statements about aging in each frame would also be identical, in the A frame A would have aged 25 years while B had aged 20 years at the moment B passed the destination, while in the B frame A would have aged 16 years while B had aged 20 years at the moment B passed the destination.

For a true round trip, GPS satellites

Not SR but GR, so there's no single inertial frame that can cover the entire trip, and the twin paradox is specifically assuming one twin traveled inertially so that the SR time dilation formula applies.

 

[GrayGhost]

You're misusing the phrase "proper distance", proper distance is measured between a pair of events (or along a spacelike worldline), and it's frame-invariant.

I wasn't talking about a one-way experiment, I was talking about the twin paradox. However, you are wrong that in the one way experiment both frames will agree that the A twin accumulates more time, you are failing to take into account the relativity of simultaneity here.

I'm just curious ... Let's say twin B starts at rest with A and ends at rest on planet X (at rest with the A frame). Would you say B aged less than A, or would you say it cannot be said who aged less w/o being "co-located at rest with each other" twice?

GrayGhost

 

[JesseM]

I'm just curious ... Let's say twin B starts at rest with A and ends at rest on planet X (at rest with the A frame). Would you say B aged less than A, or would you say it cannot be said who aged less w/o being "co-located at rest with each other" twice?

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.

 

[MikeLizzi]

Hi DTThom,
I don’t mean to interrupt your dialog with others but I am trying to find a statement that you quoted from the A.P. French book on Special Relativity.

You posted,
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."

I was shocked when I read that and searched for it in my A.P. French book but couldn’t find it. Page 150 in my book is in Chapter 5 “Relativistic Kinematics” in the section entitled “Looking at Moving Clocks and Other Objects”. Could you identify the section in your book from which that quote was taken?

 

[JesseM]

I was shocked when I read that and searched for it in my A.P. French book but couldn’t find it. Page 150 in my book is in Chapter 5 “Relativistic Kinematics” in the section entitled “Looking at Moving Clocks and Other Objects”. Could you identify the section in your book from which that quote was taken?

according to google books that note is at the bottom of p. 150, maybe you have a different edition?

 

[Gulli]

"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.

If we knew the locations and mass of all objects in the universe we could calculate the center of mass of the universe. Being stationary to that center of mass sort of means being stationary to the universe, but 1) we do not have sufficient data to calculate the center of mass of the universe, 2) most galaxies (most likely including our own) are not stationary to the center of mass of the universe, so it wouldn't apply to any of the usual traveler problems and 3) relativity works just fine without assuming a universal rest frame.

 

[George Jones]

according to google books that note is at the bottom of p. 150, maybe you have a different edition?

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.

 

[JesseM]

If we knew the locations and mass of all objects in the universe we could calculate the center of mass of the universe.

The universe is not imagined to have a center of mass in current cosmological models, the FLRW models assume that on large scales the distribution of matter is fairly homogeneous throughout all of space (regardless of whether space is finite or infinite). These models might be oversimplifications in the context of chaotic inflation though, I'm not sure.

 

[Gulli]

The universe is not imagined to have a center of mass in current cosmological models, the FLRW models assume that on large scales the distribution of matter is fairly homogeneous throughout all of space (regardless of whether space is finite or infinite). These models might be oversimplifications in the context of chaotic inflation though, I'm not sure.

The universe contains objects with mass, so there most definitely is a theoretical center of mass. Though it may be impossible to calculate because some mass may be outside the observable universe (there's no way for us to know), likewise I can imagine the fact that the gravitational force has a finite "speed" (the speed of light) would cause some problems if one were to try to calculate an actual universal center of mass.

 

[Dale]

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

Not necessarily. If you have a uniform density then the center of mass corresponds to the geometric center, but many manifolds do not have a gemoetric center. For example, a simple 2-sphere is a manifold with no center. A 2-sphere only has a center if embedded in a flat 3-D manifold, and even then the center is not part of the 2-sphere.

 

[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 ...

:rofl: 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]

:rofl: 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?