Space traveler and time dilation

[Al68]

The distance should be measured in the proper frame defined by the separation between the Earth and target - there is no motion between these two clocks and there is no time difference between them

That's only true in Earth's frame. In the ship's frame, Earth's clock reads less time than the target clock when the ship reaches the target. In the ship's frame, when the ship reaches the target, the Earth twin is much "younger" than the target observer and the Earth twin is also younger than the ship twin.

You can look at it from the traveling twins frame - but the target is moving toward the traveling twins clock so the traveling twin's measure of distance will not be a proper one because the target is not fixed...

I was referring to choosing a second "target" that was at rest with the ship. So the distance between that second target and the ship would be the proper distance in the ship frame, while length contracted in Earth's frame. Then instead of only having a target at rest with Earth and local to the ship at the end, we would also have a target at rest with the ship and local to Earth at the end. And if the second target reaches Earth at the same time (in ship frame) as the ship reaches the first target, the Earth clock will show less elapsed time than the clock on the second target (synched with ship's clock) when the second target reaches earth.

Again, your way is perfectly valid, but many people have questions that it simply doesn't address. Like why did we arbitrarily choose to define the distance in Earth's frame instead of defining it in the ship's frame? Isn't the ship's inertial frame just as valid, and wouldn't it be just as correct to define the distance traveled in the proper frame of the ship, resulting in less elapsed time for the Earth twin?

 

[Ich]

That is a direct contradiction to teaching that "there's no such things as slowing clocks" and bound to be confusing to students.

Where's the contradiction?
How does it confuse?

Clocks are doing fine, but the elapsed time differs for different paths. That's the explanation, nothing else.

it was carefully explained that clocks with relative motion really do physically run at different rates, but we can not tell which clock is really running slower until both clocks are brought to rest with respect to each other,

then I think we'd have managed to introduce completely unnecessary quantum-like uncertainty paradoxes into relativity. Just read again: "really do physically run at different rates, but we can not tell which clock is really running slower until both clocks are brought to rest with respect to each other".
You're claiming that such statements are good teaching praxis to explain that the sum of two sides of a triangle is different from the length of the remaining side?
That it's necessary for a student to "understand" how a number, clock rate, belonging to an object, can be really physically different from the corresponding number of a second object, but that in order to decide which one really really really was larger you have to bring the objects together afterwards?
Come on.

 

[yogi]

That's only true in Earth's frame. In the ship's frame, Earth's clock reads less time than the target clock when the ship reaches the target. In the ship's frame, when the ship reaches the target, the Earth twin is much "younger" than the target observer and the Earth twin is also younger than the ship twin.I was referring to choosing a second "target" that was at rest with the ship. So the distance between that second target and the ship would be the proper distance in the ship frame, while length contracted in Earth's frame. Then instead of only having a target at rest with Earth and local to the ship at the end, we would also have a target at rest with the ship and local to Earth at the end. And if the second target reaches Earth at the same time (in ship frame) as the ship reaches the first target, the Earth clock will show less elapsed time than the clock on the second target (synched with ship's clock) when the second target reaches earth.

Again, your way is perfectly valid, but many people have questions that it simply doesn't address. Like why did we arbitrarily choose to define the distance in Earth's frame instead of defining it in the ship's frame? Isn't the ship's inertial frame just as valid, and wouldn't it be just as correct to define the distance traveled in the proper frame of the ship, resulting in less elapsed time for the Earth twin?

You have raised some good points AI68 - I am not sure I can clarify anything - but I will try The experiment is analogous to the one way trip of a pion. The traveling twin will reach the target clock and the target clock will be read by the traveling twin, and the traveling twin's clock (hereinafter TTC) will be read by the operator at the target. The traveling twin will observe that his clock has logged less time than the target clock, and since the target clock will be in sync with the stay at home twin's clock, there is no disagreement. The TT will justify the difference by using his time to compute the distance he has traveled in his own frame - it will be less than the proper distance between the target clock and Stay at home twin distance. Now, the TT is going to be still perplexed, because if he has not set up a 4th clock in his own frame - so he will be justified in saying that when two clocks pass each other at relative velocity, each will observe the other clock to be running slow. That is where the paradox starts because there is simply not enough information to resolve the root cause of the diffeence ...until the proper space factor is introduced along with the measurement made at the location of the target clock The twin scenario is a measuration problem, not a physical affect. I know you know all of this, but for those who have not dropped from the thread and are still reading the posts, here are a couple of quotes:

For a pion the journey is one way - Resnick had this to say

"The proper time ...is the time interval measured by a clock attached to a pion that is at one place in the rest frame of the pion. In the lab frame the pions are moving at hi speed and the time interval there is an improper one...Thus depending on which frame we choose to make measurements in, this example illustrates the physical reality of either the time dilation or the length contraction predictions of relativity... The moving pion sees the lab distances contracted and in its proper decay time it can cover lab distances greater than those measured in its own frame."


And at page 77 "There are many shorthand expressions in relativity which can easily be misunderstood by the uninitiated Thus the phrase "moving clocks run slow" means that a clock moving at a constant velocity relative to an inertial frame containing synchronized clocks will be found to run slow when timed by those clocks. We compare one moving clock with two synchronised clocks. Those who assume that the phrase means anything else often encounter difficulties."

Again, I know you are fully knowledgeable in these matters - but the point that seems in need of clarification is that the pion's clock (our traveling twin) will always run slower than the lab clock (the stay at home twin clock) if the result is a physical reality - no matter where you anchor the reference frame the same time difference must follow if you account for the non-proper distance in the relatively moving frame in relation to the fame selected to be stationary

 

[yogi]

I was referring to choosing a second "target" that was at rest with the ship. So the distance between that second target and the ship would be the proper distance in the ship frame, while length contracted in Earth's frame. Then instead of only having a target at rest with Earth and local to the ship at the end, we would also have a target at rest with the ship and local to Earth at the end. And if the second target reaches Earth at the same time (in ship frame) as the ship reaches the first target, the Earth clock will show less elapsed time than the clock on the second target (synched with ship's clock) when the second target reaches earth.

Cont of Post 73 - To further clarify - if you placed two clocks in the frame of the traveling twin and moved the frame containing the stay put twin and target clock relative thereto at constant velocity v, you of course we get the opposite result. The Earth and target clocks would accumulate less time during the experiment than the clocks in the TT frame. Adding a second clock to the TT fame will define a proper distance and sync time in the TT frame, a different result is to be expected than the case where the same experiment is worked from the point of view of the TT fame without the addition of any other measuring help in the TT frame.

 

[JesseM]

Again, I know you are fully knowledgeable in these matters - but the point that seems in need of clarification is that the pion's clock (our traveling twin) will always run slower than the lab clock (the stay at home twin clock) if the result is a physical reality - no matter where you anchor the reference frame the same time difference must follow if you account for the non-proper distance in the relatively moving frame in relation to the fame selected to be stationary

But to measure the time in the lab frame you have to use two different clocks at different locations to make local measurements of the time t₀ when the pion is created and the time t₁ when it decays. And since you're making local measurements, the synchronization convention makes all the difference. If you synchronize the two lab clocks according to the definition of simultaneity in the lab frame, then (t₁ - t₀) is greater than the time as measured by the pion's clock (i.e. the pion's clock is running slow), but if you synchronize them according to the definition of simultaneity in the pion frame, then even though the two clocks are still running at a normal rate in the lab frame, (t₁ - t₀) will be less than the time measured by the pion's clock.

 

[Al68]

Cont of Post 73 - To further clarify - if you placed two clocks in the frame of the traveling twin and moved the frame containing the stay put twin and target clock relative thereto at constant velocity v, you of course we get the opposite result. The Earth and target clocks would accumulate less time during the experiment than the clocks in the TT frame. Adding a second clock to the TT fame will define a proper distance and sync time in the TT frame, a different result is to be expected than the case where the same experiment is worked from the point of view of the TT fame without the addition of any other measuring help in the TT frame.

This is why a one way inertial trip doesn't go very far to explain anything. Adding a second clock at rest with the ship wouldn't change the result we got using the other clocks. All that did was provide a means to better measure the complete results that already existed in reality. Regardless of whether there is a second clock in either frame, the fact remains that at any given time in Earth's frame (including any target being reached), the ship's clock reads less than Earth's clock. And at any given time in the ship's frame (including any target being reached) Earth's clock reads less than the ship's clock.

Sure we can hypothesize "targets" at rest in either frame, and accordingly measure proper distance in whichever frame we choose, but such targets (and proper distances) are irrelevant if nothing happens at them.

But if a target happens to be the location at which the ship changes velocity relative to earth, then it becomes relevant to the situation.

 

[yogi]

But to measure the time in the lab frame you have to use two different clocks at different locations to make local measurements of the time t₀ when the pion is created and the time t₁ when it decays. And since you're making local measurements, the synchronization convention makes all the difference. If you synchronize the two lab clocks according to the definition of simultaneity in the lab frame, then (t₁ - t₀) is greater than the time as measured by the pion's clock (i.e. the pion's clock is running slow), but if you synchronize them according to the definition of simultaneity in the pion frame, then even though the two clocks are still running at a normal rate in the lab frame, (t₁ - t₀) will be less than the time measured by the pion's clock.

Quite right Jesse. I have been trying to avoid the initial sync problem to eliminate acceleration from the reasoning - so I think you could do the thought experiment by having the high speed pion already up to speed when it enters the room carrying within its velocity frame a second clock - the pion frame now becomes the proper frame and the lab is making a one way journey between thye two clocks in the pion frame - in this arrangement the lab clock will appear slower - since these measurments are local in the sense of all being carried out in the space of the lab, then because the reciprocal experiment first discussed considers the lab at rest leads to the apparent result that the pion clock runs slow, its easy to conclude the affect is not real nor objective. I think we talked about this before - anyway, perhaps we can agree that all clocks run at the same rate but log different times depending upon which frame is selected for the proper distance (i.e., the two clock frame).

 

[yogi]

Let me embellish upon post 77 - as far as Special Relativity is concerned, there does not appear to be any reason why clocks should run at differnt rates - so if a clock on a one way trip reads different than another clock to which it was initially synchronized - the differnce must be due to the spatial part of the interval - so if t* measures time in the pion frame and t measures time in the lab frame - then if the lab is taken as the rest frame the pion will have traveled a distance vt in the lab, whereas if the pion frame is considered stationary, the lab will have traveled a distance vt* in the pion frame - so the spatial part of the spacetime interval determines which clock appears to run slow

 

[Mike_Fontenot]

One of the central tenets of special relativity is that there is NO privileged inertial frame. If neither twin ever accelerates, they are each essentially a clock in a (different) inertial frame. There's no way either one of those clocks can be privileged, in any absolute or invariant sense.

Mike Fontenot

 

[yogi]

One of the central tenets of special relativity is that there is NO privileged inertial frame. If neither twin ever accelerates, they are each essentially a clock in a (different) inertial frame. There's no way either one of those clocks can be privileged, in any absolute or invariant sense.

Mike Fontenot

True - in all of the above there is no distinction as to which frame is moving and which is at rest - in SR there will be no true rest frame involved in any event.. at best a true rest frame might be definable in connection with a point where the CBM is isotropic, but this appears to no better than any other arbitrary inertial frame for SR problems. In SR only relative motion is significant, and in Einstein's world, acceleration is also relative - the reationary force felt by masses should be the same irrespective of whether an object is accelerated relative to the universe, or the universe is accelerated relative to the object.